Pvtx Properties of Saline Aqueous Fluids at High PT Conditions From

Research Collection

Doctoral Thesis

PVTx properties of saline aqueous fluids at high P-T conditions from acoustic velocity measurements using Brillouin scattering spectroscopy

Author(s): Mantegazzi, Davide

Publication Date: 2012

Permanent Link: https://doi.org/10.3929/ethz-a-007582357

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DISS. ETH NO. 20358

PVTx properties of saline aqueous uids at high P-T conditions from acoustic velocity measurements using Brillouin scattering spectroscopy

A dissertation submitted to

ETH ZURICH

for the degree of

Doctor of Sciences

presen ted by

Davide Mantegazzi

Diplom in Naturwissenschaften ETH ETH Zürich

born on January 8, 1983

citizen of Riva San Vitale (TI)

accepted on the recommendation of

examiner Prof. Dr. C. Sanchez-Valle ETH Zurich co-examiner PD Dr. T. Driesner ETH Zurich co-examiner Prof. Dr. R.J. Bodnar Virginia Tech. (VA) co-examiner Prof. Dr. L.W. Diamond UNI Bern

2012

Abstract

Saline aqueous fluids play a fundamental role in several geological processes. Despite the great importance of these fluids for the heat and mass transport i for their contribution to geodynamical cycles, their thermodynamic data are limited to low pressure conditions, typically below 0.5 GPa (ca. 15 km depth). The lack of PVTx properties for saline aqueous fluids at higher pressure considerably limits the quantitative modelling of fluid-rock interactions at pressure and t crust and the upper mantle.

The goal of this study was to determine experimentally the equation of state and thermodynamic properties of several model saline aqueous fluids at elevated pressure and temperature conditions. The densities of the fluids are determined from acoustic velocity measurements performed in an externally heated membrane-type diamond anvil cell (mDAC) using Brillouin scattering spectroscopy. The maximal pressure and temperature conditions investigated in this study, i.e. 800 °C and 4.5 GPa, are representative for cold subduction zone settings at shallow to intermediate depths. The compositions of the saline water-rich fluids investigated, namely chlorined, sulphate-, carbonate and bicarbonate-bearing binary aqueous solutions, are reasonable analogs for aqueous fluids involved in geological processes, including metasomatism and melt production at subduction zones, hydrothermal alteration of the seafloor and ore deposits formation. The choice of solute concentrations, which range between 0m and 3m (mol/kg H 2O), was made in order to represent realistic concentrations of natural geological fluids, and were also influenced by the availability of literature data on the investigated compositions.

The acoustic velocities V P(P,T,x) measured using Brillouin spectroscopy were inverted to calculate the density (P,T,x) of the solution of interest following basic thermodynamic relationships. Successively, the experimentally derived density data were fitted with an equations of state (EoS) which were then used to derive all other thermodynamic properties of geological interest ( i.e. , coefficient of thermal expansion, isobaric heat capacity, adiabatic bulk modulus and compressibility, isothermal bulk modulus and compressibility, partial molar properties and water fugacity). In case of multi-concentration systems the molality- dependence of the PVTx data were provided. The effects of salt-addition on the thermodynamic properties of the pure solvent ( i.e. water) were discussed, and the main

iii changes were ascribed to the structure breaking/making behaviour of the dissolved electrolyte species.

We have provided the first equation of state and constraints on the thermodynamic properties of H2O-NaCl fluids up to 800 °C and 4.5 GPa. The results were used to evaluate the effect of dissolved NaCl species on the location of dehydration reaction boundaries in subducting oceanic slabs. We find that the transition from greenschist to blueschist metamorphic facies shifts toward shallower depths when the activity of water decreases due to the presence of NaCl species dissolved in the fluid.

The partial molar volumes and compressibility in the carbonate-bicarbonate aqueous systems obtained from the acoustic velocity measurements were used to determine the effect

nd - 2- + of pressure on the 2 dissociation reaction of carbonic acid (HCO 3 = CO 3 + H ) up to 300 °C and 3 GPa. The volume of reaction Vr is negative in the investigated P-T range, indicating 2- - that carbonate ions (CO 3 ) are favoured over the bicarbonate ions (HCO 3 ) at high pressure and temperature conditions, in agreement with experimental and theoretical studies. This 2- implies that CO 3 ions may be the dominant dissolved carbon species in subduction zone fluids.

We have shown that the experimental set-up and the numerical data treatment proposed in this study is a powerful tool to determine the thermodynamic properties of saline water-rich solutions up to pressure and temperature conditions relevant for the lower crust and the upper mantle. This technique can be applied to all other binary water-salt and molecular systems, and the continuous development of the DAC technique may extend the pressure and temperature range investigated to deeper Earth conditions.

iv Riassunto

I fluidi acquosi salini svolgono un ruolo chiave in numerosi processi geologici. Nonostante la loro grande importanza come vettori di trasporto per calore ed elementi disciolti e la loro influenza sui cicli geodinamici della Terra, la conoscenza delle loro proprietà termodinamiche è limitata a condizioni di bassa pressione, tipicamente sotto i 0.5 GPa, che corrispondono ad una profondità di circa 15 km. La mancanza di dati termodinamici per le soluzioni acquose saline a più alte pressioni, limita in modo considerevole la modellizzazione quantitativa delle interazioni tra fluidi e rocce a condizioni di pressione e temperature rilevanti per gli strati della crosta terrestre inferiore e del mantello terrestre superiore.

Questo manoscritto presenta per la prima volta le proprietà termodinamiche di numerosi fluidi acquosi salini di riferimento ad alte pressioni e temperature, determinate da misurazioni di velocità acustica compiute in una cella ad incudine di diamante con membrana (membrane- type diamond anvil cell, abbreviata mDAC) usando la spettroscopia Brillouin. La temperatura e la pressione sperimentale massimale, 800 °C e 4.5 GPa, corrispondono a condizioni di bassa e media profondità in una zona di subduzione a basso gradiente geotermico.

Le composizioni dei fluidi acquosi salini studiati in questa tesi di dottorato, - 2- corrispondenti a sistemi binari contenenti acqua e ioni cloruro (Cl ), acqua e solfati (SO 4 ), 2- - acqua e carbonati (CO 3 ) e infine acqua e bicarbonati (HCO 3 ), modellizzano alcuni dei più importanti fluidi geologici, che ricoprono un ruolo fondamentale in processi come il metasomatismo e la generazione di magma calc- idrotermale del fondo oceanico e la formazione di giacimenti minerari. Le concentrazioni molali dei fluidi investigati, che variano da 0 m a 3 m (moli sale / kg H 2O) , sono realistiche per alcuni fluidi geologici naturali, e la loro scelta è stata dettata anche dalla disponibilità di dati nella letteratura scientifica già pubblicata precedentemente.

Le velocità acustiche V P(P,T,x) misurate con la spettroscopia Brillouin sono state invertite secondo principi termodinamici base per calcolare la densità (P,T,x) dei fluidi acquosi salini. Successivamente, i valori di densità calcolati dai dati sperimentali sulle velocità acustice sono stati modellizzati con equazioni di stato (EoS) di tipo polinomiale. Da queste EoS sono state derivate tutte le altre importanti proprietà termodinamiche. Specificatamente, queste propietà sono: coefficiente di espansione termale, calore specifico isobarico, bulk modulus e compressibilità adiabatici, bulk modulus e compressibilità isotermici, volume molare parziale, fugacit e velocità acustica. Nei sistemi acqua- v sale, dove gli esperimenti sono stati condotti in più concentrazioni molali, la dipendenza dei dati termodinamici dalla molalità è stata inclusa nelle EoS. I cambiamenti subiti dalle proprietà termodinamiche del solvente (acqua) in seguito n soluzione sono stati descritti e ricondotti distruttivo o costruttivo degli ioni sulla struttura molecolare del solvente.

Il presente studio presenta per la prima volta le proprietà termodinamiche del sistema binario H 2O-NaCl fino a 800 °C e 4.5 GPa. Gli esperimenti sono stati condotti in più dalla molalità è stata determinata. Questi valori di fugacità sono stati successivamente usati per modellizzare una tipica reazione di disidratazione che avviene nelle rocce basiche della crosta oceanica durante la loro subduzione, alle condizioni di transizione dalla facies a scisti verdi alla facies a scisti blu. I risultati di questo lavoro mostrano che la reazione di disidratazione avviene a temperature e pressioni diverse a dipendenza della concentrazione salina del fluido rilasciato durante il metamorfismo progrado. Infatti, si sposta a profondità minori.

Le misure sperimentali effettuate nei sistemi contenenti ioni disciolti di carbonato e bicarbonato hanno permesso di determinare la dipendenza dalla pressione della seconda - 2- costante di equilibrio dell 3 = CO 3 + H+) fino a condizioni di 200 °C e 3 GPa. I risultati di questi esperimenti suggeriscono che a 2- condizioni di alte pressioni gli ioni di carbonato CO 3 sono favoriti rispetto agli ioni di - bicarbonato HCO 3 , in accordo con altri studi sperimentali. Questo fatto implica che nei fluidi acquosi presenti nelle zone di subduzione gli ioni di carbonato potrebbero essere la fase disciolta dominante che immagazzina il carbonio, con implicazioni per il ciclo geodinamico di

In questa tesi di dottorato abbiamo dimostrato, che l erimentale e la procedura numerica usati per acquisire ed elaborare i dati, permettono di determinare le proprietà termodinamiche dei fluidi acquosi salini fino ad alte pressioni e temperature. Questo metodo può essere applicato a qualsiasi altro sistema binario composto da acqua e sale. Il continuo sviluppo tecnico delle celle ad incudine di diamante potrà permettere di raggiungere pressioni e temperature sperimentali maggiori, caratteristiche delle regioni più profonde della Terra.

vi Contents

Abstract iii

Riassunto v

Contents vii

1 Introduction 1

1.1 Origin and composition of the geological fluids 1

1.2 Thermodynamic properties of saline aqueous fluids: state of the art 11

1.3 Aim of the project 14

1.4 Experimental approach 14

1.5 Chapter overview 15

2 Experimental Method 29

2.1 Sample description and preparation 29

2.2 Diamond Anvil Cell techniques 30

2.2.1 The diamond anvil cell 30

2.2.2 Pressure generation 34

2.2.3 High temperature conditions 35

2.2.4 The metallic gasket 37

2.2.5 Pressure calibration 38

2.3 Brillouin scattering spectroscopy 48

2.3.1 Principles 48

2.3.2 The Fabry-Pérot Interferometer 50

2.3.3 Brillouin scattering spectroscopy 54

2.3.4 The Brillouin system at ETH Zurich 58

vii 3 The numerical data treatment: from the experimental acoustic velocities

VP to an equation of state 75

3.1 Inversion of the density from the measured acoustic velocities V P(P,T,x) 75

3.2 The equation of state (EoS) 77

3.3 Test to the inversion procedure 78

3.4 Assessment of errors 82

3.5 Derivation of the PVTx properties of saline aqueous fluids 85

4 Thermodynamic properties of aqueous sodium sulfate solutions to 773 K and

3 GPa derived from acoustic velocity measurements in the diamond anvil cell 89

4.1 Introduction 89

4.2 Experimental Methods 92

4.2.1 Diamond anvil cell techniques 92

4.2.2 Brillouin scattering spectroscopy 94

4.3 Results and Discussion 96

4.3.1 Acoustic velocities in Na 2SO 4 aqueous solution 96

4.3.2 Data inversion and equation of state 101

4.3.3 Thermodynamic properties of aqueous sulfate solutions 106

4.3.4 Effect of sulfate ions on the structure and compressibility of water 112

4.4 Conclusions 113

5 Equation of state of NaCl aqueous fluids to 1073 K and 0.5 to 4.5 GPa 123

5.1 Introduction 124

5.2 Experimental Methods 125

5.2.1 Diamond anvil cell techniques 125

5.2.2 Brillouin scattering spectroscopy 127

viii 5.3 Results 128

5.3.1 Acoustic velocities in NaCl aqueous solutions 128

5.3.2 Equation of state (EoS) for aqueous NaCl solutions 134

5.3.3 Extension of the EoS to 1073 K 142

5.3.4 Partial molar volume and fugacity of water in salt solutions 144

5.4 Discussion 148

5.4.1 Comparison with other EoS in the H 2O-NaCl binary system 148

5.4.2 Thermodynamic properties of H 2O-NaCl fluids to 1073 K and 4.5 GPa 149

5.5 Effect of fluid composition on dehydration reactions in subducted

oceanic crust 153

5.6 Conclusions 158

6 PVTx properties of a 1 m SrCl 2 solution and the effect of metal cations

on the compressibility of Cl-bearing aqueous solutions 177

6.1 Introduction 177

6.2 Experimental Method 179

6.3 Results 181

6.3.1 Acoustic velocities in H2O-SrCl 2 solutions 181

6.3.2 Equation of state for 1 m H2O-SrCl 2 solution to 200 °C and 2.3 GPa 184

6.4 Discussion 188

6.5 Conclusions 195

7 Thermodynamic properties of carbon-bearing aqueous solutions and the

2nd dissociation constant of carbonic acid at high pressure and temperature 201

7.1 Introduction 201

7.2 Experimental Method 203

ix 7.2.1 Sample preparation 203

7.2.2 Diamond anvil cell technique 204

7.2.3 Brillouin scattering spectroscopy 205

7.3 Results 207

7.3.1 Acoustic velocities in H2O-Na 2CO 3 and H2O-NaHCO 3 solutions 207

7.3.2 Inversion of the acoustic velocity data 214

7.3.3 Polynomial equation of state (EoS) for carbon-bearing aqueous fluids 218

7.3.4 The effect of pressure on the 2 nd ionization constant of carbonic acid 230

7.4 Discussion 240

7.4.1 Thermodynamic properties of carbonate-bicarbonate bearing

aqueous solutions 240

7.4.2 Implications for the carbonate-bicarbonate equilibrium in high

pressure fluids 243

7.5 Conclusions 244

8 Conclusions and outlook 251

8.1 Conclusions 251

8.2 Outlook 253

A Appendix i

B Appendix vii

Acknowledgments xxxvii

Curriculum Vitae xxxix

x Chapter 1

Introduction

Saline aqueous fluids play a fundamental role in many geological processes in the s crust and mantle (Peacock, 1990; Yardley, 2009). Typical examples are magma production in the mantle wedge above subduction zones (Ulmer, 2001), where the mantle solidus temperature is decreased by the influx of aqueous fluids released through metamorphic devolatilization reactions in the subducting oceanic lithosphere (Schmidt and Poli, 1998), hydrothermal alteration of the seafloor (Jarrard, 2003; Bonifacie et al., 2008) and metasomatic reactions (Jamtveit and Austrheim, 2010; Putnis and Austrheim, 2010). Moreover, aqueous fluids are responsible for mass and energy transfers at depth (Bodnar and Costain, 1991), and therefore, they are related to ore deposit formation processes (Heinrich, 2005; Heinrich, 2007) and to element mobilization at subduction zones (Manning, 2004; Antignano and Manning, 2008). Despite the great importance of saline aqueous fluids in several geological processes, the knowledge of their thermodynamic properties is restricted to low pressure conditions, typically below 0.5 GPa. This fact drastically limits the quantitative modeling of fluid mediated geological processes at pressure and temperature conditions relevant for the deep E , this work aims at the experimental determination of the PVTx properties of different model saline aqueous fluids up to pressure and temperature conditions relevant for shallow to intermediate subduction zone settings.

1.1 Origin and composition of the geological fluids

The saline aqueous fluids have different origins and compositions depending on the geological setting. Two main examples are illustrated in the next paragraphs: aqueous fluids at subduction zones and ore-forming fluids.

1 a) Hydrothermal alteration of the seafloor and subduction zone fluids

The hydrothermal alteration of the oceanic lithosphere at mid oceanic ridges (Fig.

1.1) results in the uptake of volatiles (e.g., H2O, CO 2, alkalies, chlorine) successively released at subduction zones (Schmidt and Poli, 1998; Alt and Teagle, 1999; Scambelluri and Philippot, 2001; Jarrard, 2003). In fact, during the hydrothermal alteration of the peridotitic oceanic rocks the mantle mineral assemblage is replaced by hydrous phases such as serpentines, brucite, phyllosilicates and amphiboles (Scambelluri et al., 1997); this process is sometimes accompanied by the formation of brecciated serpentines along tectonic fractures, cemented by a calcitic matrix, also called ophicarbonates (Bonatti et al., 1974; Poli and Schmidt, 2002). On the other side, the hydrothermal metamorphism of the basaltic and gabbroic rocks of the oceanic crust produces hydrous phases mainly represented by amphiboles and chlorites (Ito et al., 1983; Philippot et al., 1998). Moreover, during the off-axis passive fluid circulations, an additional alteration process is the carbonate precipitation in voids and cracks (Poli and Schmidt, 2002). Although sediments represent only a small fraction of the oceanic crust they contribute to the global volatiles budget, for instance, with CO 2 in siliceous limestone (Kerrick and Connolly,

2001a) and H 2O and alkalies in metapelites and metagreywacks (Schmidt and Poli, 1998).

Successively, during the subduction of the altered oceanic lithosphere (Fig. 1.2), water-rich fluids are continuously released through metamorphic devolatilization and dehydration-melting reactions at almost any depth to ca. 150-200 km (Schmidt and Poli, 1998). These prograde metamorphic reactions may result in the formation of dry eclogites and peridotites, or in case of a cold subduction regime, the volatiles (i.e., water) may be stored in dense hydrous magnesium silicates (DHMS), like phase A, and recycled into deeper mantle (Schmidt and Poli, 1998; Scambelluri and Philippot, 2001; Rupke et al., 2004). The carbonate minerals that are sequestered in rocks and veins in the upper oceanic crust during hydrothermal alteration processes (Alt and Teagle, 1999), are believed to survive subduction-related dehydration and silicate melting reactions in the upper mantle (Biellmann et al., 1993; Molina and Poli, 2000; Kerrick and

Connolly, 2001b), resulting in a recycling of carbon to deeper mantle. However, experimental studies (Newton and Manning, 2002; Caciagli and Manning, 2003; Sanchez-Valle et al., 2003) and thermodynamic calculations (Kerrick and Connolly, 2001b; Dolejs and Manning, 2010) show that the devolatilization of carbonate minerals is enhanced by the presence of aqueous fluids released at depth. Devolatilization mineral reactions accompanying the subduction of the altered oceanic lithosphere are likely to generate overpressure in the hosting rock and lower the effective compressive stress, inducing earthquakes via hydrofracture (Jarrard, 2003). The devolatilization of the oceanic crust and the underlying serpentinized oceanic mantle may therefore, be responsible for the intermediate depth and deep earthquakes observed in the double seismic Benioff zone in the subducting oceanic plate (Meade and Jeanloz, 1991; Peacock and Wang, 1999; Peacock, 2001). Deep focus earthquakes (to 700 km depth) may also be induced by dehydration reaction in metastable hydrous mineral phases (Peacock, 2001), or alternatively, by transformational faulting expressed as sudden failures localized in thin shear zones, where metastable phases (olivine and clinoenstatite) transform to denser and finer-grained minerals (ringwoodite and ilmenite, respectively) (Kirby et al., 1996).

Devolatilization reactions at subduction zones

In detail, the source lithology of the saline aqueous fluids released at subduction zones changes with depth (Rupke et al., 2004). At burial depth (< 10 km) pore water with a salinity similar to seawater is mainly released through compaction of sediments and alterated oceanic crust, with additional water coming from the smectite/illite transformation in both sediments and extrusive basalts (Jarrard, 2003). Successively, a large amount (up to 75%) of the water structurally bound in sediments and metasediments (e.g. in clay minerals, opal and chlorite) is dehydrated at shallow to intermediate depth (Schmidt and Poli, 1998; Rupke et al., 2004). From ca. 100 km depth the residual water is mostly stored in lawsonite and phengite, which can be stable up to > 200 km depth. The

CO 2 bound in carbonate minerals may be stored in subducting siliceous limestones (Kerrick and Connolly, 2001b), carbonated pelites (Grassi and Schmidt, 2011) and

3 ophicarbonates (Kerrick and Connolly, 1998). In absence of the infiltration of water-rich fluids the CO 2 is retained in marine sediments and ophicarbonates up to deep mantle conditions (Kerrick and Connolly, 1998; Kerrick and Connolly, 2001b). For instance, carbonated pelites are believed to melt between 8 and 13 GPa or when the subducting slabs stop or deflect at the 660 km discontinuity, leaving more time for thermal relaxation (Grassi and Schmidt, 2011).

A blueschist rock of basaltic origin can contain up to 6 wt% H 2O stored in hydrous phases (Schmidt and Poli, 1998). The oceanic crust dewaters almost completely (to 92%) between 50 and 200 km depth, where the main hydrous phases (i.e. chlorite, amphibole, zoisite, chloritoid) become unstable (Schmidt and Poli, 1998; Rupke et al., 2004). Again, lawsonite controls the water recycling up to 8-9 GPa in cold subduction; additionally, in K-bearing systems phengite becomes an important water carrier between 3 and 10 GPa (Schmidt and Poli, 1998; Rupke et al., 2004). Deep fluid production is dominated by the dehydration of serpentine, which occurs between 120 and 200 km depth (Schmidt and Poli, 1998; Rupke et al., 2004). The dewatering of serpentine (13 wt % H 2O) does not take place at shallower depths, because the temperature in the peridotitic oceanic lithosphere is lower than in the overlying oceanic crust, and lower than the serpentine thermal stability maximum ( e.g. 720 °C at 2 GPa) (Schmidt and Poli, 1998). The other hydrous phases in the ultramafic system ( i.e . brucite, amphibole and talc) have much narrower stability fields and dehydrate at shallow depth (Schmidt and Poli, 1998). Chlorite can incorporate up to 13 wt% H 2O but dewaters at pressure below 5 GPa (Schmidt and Poli, 1998). If the temperature at 180 km depth (ca. 6 GPa) is lower than 600°C, serpentine reacts to phase A with a water conserving reaction (Schmidt and Poli, 1998; Rupke et al., 2004), and therefore, recycling water into deeper mantle. The age, and therefore the thermal structure, of the subducting oceanic slab have a large influence on the dehydration magnitude. Young and hot slabs experience up to 95% dehydration, while old and cold oceanic lithospheres only 70% (Rupke et al., 2004).

Composition of subduction zone fluids

The chemical composition of subduction zone fluids is controlled by their reactivity with the surrounding minerals and their ability to dissolve alkaline and alkaline-earth halides, silicates, carbonates and sulfates under the pressure and temperature conditions of the mantle. It is well accepted, that the migration of these aqueous fluids along the slab or into the overlying mantle wedge metasomatizes the slab and mantle wedge, subsequently leading to the generation of magmas that produce calc-alkaline arc magmatism, when temperatures of 1300-1350 °C are reached (Peacock, 1990; Schmidt and Poli, 1998; Ulmer, 2001; Stern, 2002; Manning, 2004). The picritic basaltic magmas generated act then as second mass transfer agent, as they migrate toward the surface carrying slab- and mantle-derived components (Manning, 2004). As a direct sampling of subduction zone fluids is possible only at very shallow depths in locations such as the Costa Rica (Silver et al., 2000) and the Izu-Bonin/Mariana (Fryer et al., 1999; Savov et al., 2007) convergent margins, information about the chemical composition of the fluid phases present in deep subduction environments are provided by fluid inclusions preserved in high and ultrahigh pressure rocks (Roedder, 1984; Philippot et al., 1995; Scambelluri and Philippot, 2001), by the study of high pressure veins in blueschists (Gao and Klemd, 2001) and eclogites (Heinrich, 1986; Philippot and Selverstone, 1991; Becker et al., 1999), and by high pressure experiments (Schneider and Eggler, 1986; Brenan et al., 1995; Ayers et al., 1997; Scambelluri et al., 2001). For instance, the fluid inclusions (F.I.) in the high pressure veins analyzed by Gao and Klemd (2001) provide information about the composition of the aqueous fluids released at the blueschist-eclogite facies transition depth (ca. 50 km). These fluids were channelized in fractures created by hydraulic overpressure generated by the dehydration reactions in the host rock (Gao and Klemd, 2001). During the precipitation in the veins, the high pressure minerals ( i.e. , omphacite) entrapped saline H 2O-rich fluid inclusions. The analysis of these F.I. evidence similar compositions for the fluids entrapped in minerals in the host rock and in the high pressure veins, demonstrating the syn- metamorphic origin of these fluids (Gao and Klemd, 2001). The aqueous fluids have

5 salinity up to 7 wt% NaCl equivalent (Gao and Klemd, 2001), suggesting little water-rock interaction, which would have produced higher salinities (Philippot et al., 1995; Scambelluri and Philippot, 2001). According to the studies cited above, subduction zone fluids at shallow to intermediate depths have low salinities and are H2O-rich, with a total dissolved solids (TDS) value only two to three times larger than seawater (Manning, 2004). During high pressure recrystallization and vein forming in the presence of the released aqueous fluids chlorine and alkalies are strongly partitioned into the fluid phase, while H 2O is incorporated in new hydrous phases (Scambelluri et al., 1997; Markl and Bucher, 1998). This process results in the entrapment of high salinity brines (up to 84 wt% NaCl equivalent) in F.I. in high pressure minerals (Philippot et al., 1995; Philippot et al., 1998; Scambelluri et al., 1998).

- The solute fraction in subduction zone fluids is dominated by alkalies, Cl , SiO 2 and

Al 2O3, and sulfur species are also present (Jarrard, 2003; Manning, 2004; Newton and Manning, 2010). These findings are corroborated by several experimental works (Manning, 1994; Newton and Manning, 2000; Newton and Manning, 2005; Manning,

2006; Shmulovich et al., 2006), which evidence that the solubility of SiO 2 , Al 2O3 and anhydrite (CaSO 4) in H 2O NaCl solutions increases with pressure and temperature. Together with the chemical-physical properties ( e.g., dielectric constant) of the solvent water (Dolejs and Manning, 2010), the mineral solubility, and therefore, the fluid - - 2- composition, is controlled by the presence of ligands (e.g., Cl , HS , SO 4 ) and/or the formation of alkali-Si-Al-polymers (Manning, 2004; Manning, 2006). For instance, Al has low solubility in pure water, and should therefore behave as immobile element during fluid-rock interactions (Manning, 2007). However, the combined effects of temperature, pressure, dissolved Si and NaCl increase the solubility of Al-bearing phases, like corundum and alumosilicates, through the formation of Na-Al-Si-O clusters and polymers (Manning, 2007). The solubility of rutile (Ti-bearing) is also enhanced by the formation at high pressure and temperature of complexes with dissolved Na, Al and Si (Antignano and Manning, 2008). On the other side, the amount of dissolved quartz at high pressure decreases by increasing NaCl and/or CO 2 concentration in water (Newton and Manning,

2000; Newton and Manning, 2010); this effect is probably induced by the lowered water activity, because quartz dissolves forming water-SiO 2 complexes (H 4SiO 4 and H 6Si 2O7) (Newton and Manning, 2000). Differently from quartz, the minerals calcite, anhydrite and apatite become more soluble with the addition of NaCl to water (Newton and Manning, 2002; Newton and Manning, 2010). The chemical composition of subduction zone fluids is therefore continuously evolving, from low salinity H 2O-rich fluids at relative shallow depth, to fluids which become increasingly enriched in Si, Al and other elements at higher pressure and temperature conditions. Although carbonates are thermally stable at modern subduction zone conditions (Biellmann et al., 1993; Molina and Poli, 2000; Dasgupta et al., 2004; Grassi and

Schmidt, 2011), decarbonation reactions are promoted by the infiltration of H 2O-rich fluids at depth (Kerrick and Connolly, 2001a; Newton and Manning, 2002; Caciagli and Manning, 2003; Sanchez-Valle et al., 2003; Dolejs and Manning, 2010). The finding of

CO 2 (Roedder, 1984; Philippot et al., 1995) and carbonate daughter-minerals (Wang et al., 1996; Korsakov and Hermann, 2006) in fluid and melt inclusions in high pressure minerals confirms that C-bearing phases are mobile at such deep Earth conditions.

All these observations point out that subduction zone fluids at shallow to intermediate depths are mainly composed of H 2O, CO 2 and NaCl, with other dissolved solutes dominated by SiO 2, Al 2O3 and sulfur-species, which become more important at higher pressure and temperature conditions.

According to trace elements concentration analysis, these fluids show enrichment in LILE, Pb, Th and U relative to rare earth elements (REE) (Scambelluri et al., 2001; Hermann et al., 2006). In fact, trace elements in arc magmas (Tatsumi et al., 1986; Kelemen et al., 1990; Hawkesworth et al., 1993; Brenan et al., 1994) show a depletion enrichment signature typical for hydrous melting of a source metasomatized by slab- derived components (Becker et al., 1999; Scambelluri and Philippot, 2001; Manning, 2004; Hermann et al., 2006).

7 b) Ore forming fluids

Although composition and concentration of ore forming hydrothermal fluids may vary widely (Skinner, 1997), they consist mainly of H 2O, CO 2 and NaCl (Roedder and Bodnar, 1997; Kesler, 2005). Other dissolved elements include K, Ca, Mg, Fe, Br, Sr, S + - (as sulfate or sulfide), NH 4 and HCO 3 (Roedder, 1984; Skinner, 1997; Heinrich, 2005; Kesler, 2005). The study of fluid inclusions is the main source of knowledge of the composition of ore forming fluids (Roedder, 1984; Roedder and Bodnar, 1997; Skinner, 1997), but contrary to subduction zone fluids, direct sampling of hydrothermal fluids can be conducted at modern active geothermal systems (Seward and Barnes, 1997; Vondamm et al., 1997; Brown and Simmons, 2003). The origin of the hydrothermal water (surface water, groundwater, metamorphic or magmatic water) can be attested through isotopic studies (e.g., H/D and 16 O/ 18 O ratios), whereas the source of the solutes mainly depends on the geological environment and on fluid/rock interactions (Skinner, 1997; Heinrich, 2005). Ore metals are transported in hydrothermal fluids as complex ions, with Cl -, HS - 2- and SO 4 being among the most important ligands in these fluids (Seward and Barnes, 1997; Wood and Samson, 2006). c) Summary

Summarizing the information concerning subduction zone fluids and ore forming fluids, natural geological fluids are generally water rich and contain dissolved components. The most important are salts , non-polar gas components

(CO 2 and CH 4) and different sulfur and nitrogen species (Liebscher and Heinrich, 2007).

Therefore, fluids in the ternary system H 2O-NaCl-CO 2 approximate many natural geological fluids (Bodnar and Costain, 1991; Kesler, 2005), with other elements like S playing also an important role.

Figure 1.1. The hydrothermal alteration of the seafloor at Mid Oceanic Ridges (MOR) results in the uptake of volatiles (e.g., H 2O, CO 2, alkalies) in the oceanic lithosphere (Jarrard, 2003). Typically, the oceanic lithosphere is composed by a sediment layer on the top, an oceanic mafic crust (from top to the bottom: seafloor basalts, sheeted dikes, gabbros and cumulates) and a peridotitic oceanic mantle. Depending on the mineralogical composition, different volatile- bearing phases are generated during the hydrothermal alteration of the oceanic lithosphere. For instance, serpentines in ultramafic rocks, and amphiboles and chlorite in the mafic oceanic crust.

In the sediment layer, water is structurally bound in clays and in opal, whereas CO 2 in carbonates. Pore water, with the same salinity of seawater (Jarrard, 2003), is also present in the upper layers of the oceanic lithosphere.

Figure 1.2. Fluid involving geological processes related to a subduction zone setting. During the subduction of the hydrothermal altered oceanic lithosphere, saline aqueous fluids are released through metamorphic devolatilization reactions (Schmidt and Poli, 1998). These fluids may trigger the partial melting in the mantle wedge overlying the subducting oceanic plate (Ulmer, 2001), to initiate arc magmatism. The emplacement of batholithic bodies may represent a new fluid source, when the country rocks undergo contact metamorphism, or the residual aqueous-rich magmatic fluids migrate away from the crystallizing batholiths. Saline aqueous fluids are fundamental for the transport of heat and chemical species, and they are therefore, related to ore deposit formation processes (Heinrich, 2007). Indicative pressure-depth references for a subducting slab geotherm of 7 °C/km: greenschist-blueschist facies transition at ca. 0.8 GPa and 400-500 °C, blueschist-eclogite facies transition at 1.5-2.0 GPa and 500-600 °C.

1.2 Thermodynamic properties of saline aqueous fluids: state of the knowledge

The use of numerical modeling in geological sciences has become of great importance to test hypotheses and get information about geological processes that take place in environments inaccessible to direct studies. For instance, the modeling of phase equilibria in the subducted oceanic lithosphere provide insights into metamorphic devolatilization reactions at depth and the transport and recycling of volatiles into the (Kerrick and Connolly, 1998; Kerrick and Connolly, 2001b; Kerrick and Connolly, 2001a). Additionally, numerical modeling in Earth sciences can be useful to understand more catastrophic processes, like seismic and volcanic activities related to slab subduction and metamorphism (Hacker et al., 2003b), with clear implications for the daily life on the Earth. However, in order to model fluid-involving geological processes and extend our knowledge about fluid-rock interactions at deep Earth conditions, the thermodynamic data of the phases involved are a fundamental prerequisite. While these data are available for the most important rock-forming minerals (Hacker et al., 2003a; Stixrude and Lithgow-Bertelloni, 2005), the information about aqueous fluids other than pure water remain scarce at elevated pressure and temperature conditions. In fact, although the several equations of state (EoS) for pure water (Holland and Powell, 1991; Brodholt and Wood, 1993; Wiryana et al., 1998; Wagner and Pruss, 2002; Abramson and Brown, 2004; Asahara et al., 2010) provide PVTx data up to pressure and temperature conditions relevant for the deep Earth interior (Fig. 1.3), this is not the case for different fluid compositions. For instance, published thermodynamic data in the binary system H 2O NaCl are available up to 1000 °C, but the pressure range is restricted to 0.5 GPa (Driesner, 2007). For other geological relevant fluid compositions the P-T space covered by their PVTx data is dramatically smaller: H 2O Na 2SO 4 solutions ( e.g., proxy for sulfate-bearing solutions), 0.04 GPa and 300 °C (Millero et al., 1982; Phutela and Pitzer,

1986; Azizov and Akhundov, 2000; Apelblat et al., 2009); H 2O Na 2CO 3 solutions ( e.g., proxy for carbonate-bearing solutions), 0.052 GPa and 350 °C (Hershey et al., 1983;

Apelblat et al., 2009); and H2O NaHCO 3 solutions (e.g., proxy for carbonate-bearing

11 solutions), 0.028 GPa and 350 °C (Perron and Desnoyers, 1975; Sharygin and Wood, 1998). It is evident, that the lack of thermodynamic data for fluid compositions other than pure water at pressure and temperature conditions relevant for the lower crust and the upper mantle considerably limits the quantitative modeling of subduction-related geological processes (Manning, 2004), as well as the correct interpretation of fluid inclusion data (Scambelluri and Philippot, 2001).

Figure 1.3. Diagram summarizing the available thermodynamic data for H2O-NaCl aqueous solutions. Data for pure water are from: Holland and Powell, 1991; Brodholt and Wood, 1993; Wiryana et al., 1998; Wagner and Pruss, 2002; Abramson and Brown, 2004; Asahara et al., 2010 and Sanchez-Valle et al. (Appendix B). The data in the yellow field represent H2O-NaCl aqueous solutions and are from: Pitzer et al., 1984; Tanger and Pitzer, 1989; Archer, 1992; Anderko and Pitzer, 1993; Shen, 1994; Driesner, 2007; Mao and Duan, 2008.

1.3 Aim of the project

The aim of this PhD thesis was to determine experimentally the thermodynamic (PVTx) properties of various saline-rich aqueous fluids over a broad range of pressure and temperature conditions relevant for subduction zone settings. The results of this project provide the first self consistent database for the PVTx data of the most relevant geological fluids at pressures and temperatures of the lower crust and the upper mantle. The investigated fluid compositions are representative for the chemistry of geological fluids produced in various tectonic settings (see section 1.1) and include:

H2O-Na Cl system

H2O-Sr Cl 2 system

H2O-Na 2SO 4 system

H2O-Na 2CO 3 system

H2O-Na HCO 3 system

The solution molalities investigated in this study ranged between 0 m and 3 m (i.e., mole salt / kg H 2O), and are believed to be reasonable analogs for the dilute saline aqueous fluids present, for example, in subduction zone environments at shallow to intermediate depths (see section 1.1). The choice of the fluid concentrations investigated was also influenced by the availability of literature data for the compositions of interest. In some of the binary water-salt systems studied, experimental measurements were performed in several concentrations in order to provide the molality dependence of the PVTx data derived.

1.4 Experimental approach

In this study, the PVTx thermodynamic properties of aqueous fluids at high pressure and temperature conditions were determined from acoustic velocity measurements in an externally heated membrane-type diamond anvil cell (mDAC) using

Brillouin scattering spectroscopy. Brillouin scattering spectroscopy is an accurate technique to measure the velocity of acoustic waves propagating in a sample. From the measured speed of sound data important chemical and physical parameters of the sample investigated are derived (Sinogeikin and Bass, 2000; Abramson and Brown, 2004; Sanchez-Valle et al., 2010). The use of an externally heated mDAC allows performing Brillouin measurements at pressure and temperature conditions up to 500 °C and 4.5 GPa at least. Acoustic velocities measured along different isotherms from 20 °C to 500 °C are used to determine the density of the aqueous solutions by applying fundamental thermodynamic relations. In a second part, the experimentally derived density values are fitted with equations of state (EoS) in order to provide the PVTx data of the most representative geological fluids that will facilitate their application to geochemical calculations up to pressure and temperature conditions of the lower crust and upper mantle. From the EoS proposed all thermodynamic parameters of geological interest can be derived, including density, specific volume, acoustic velocity, coefficient of thermal expansion, isobaric heat capacity, isothermal bulk modulus and compressibility, adiabatic bulk modulus and compressibility, partial molar volume and water fugacity. The experimental methods and the derivation of the EoS from the acoustic measurements are described in detail in Chapter 2 and 3.

1.5 Chapters overview

This PhD thesis is organized as follows: Chapter 2: Experimental Method. In this chapter the experimental methods developed in this thesis to measure the acoustic velocity on aqueous electrolytes at high pressure and temperature conditions are extensively illustrated. This includes details of the sample preparation, the description of the membrane-type diamond anvil cell (mDAC) used to generate high pressure and temperature conditions, and details of the pressure calibration. Finally, the theoretical basics of Brillouin spectroscopy are

15 presented together with a description of the Brillouin system installed in our laboratory, including calibrations and possible error sources. Chapter 3: The numerical data treatment: from the experimental acoustic velocities VP to an equation of state.

In this chapter, the numerical procedure applied to invert the acoustic velocity VP measured to obtain the density of the aqueous solutions investigated is explained, including tests performed with literature data and the considerations about the uncertainties in the values derived. Chapter 4: Thermodynamic properties of aqueous sodium sulfate solutions to 773 K and 3 GPa derived from acoustic velocity measurements in the diamond anvil cell.

In this chapter the volumetric properties of a 1 m aqueous Na 2SO 4 solution are determined up to 500 °C and 3 GPa. The PVTx values obtained are then compared with literature data for sulfate-bearing aqueous solutions with different concentrations and with pure water. Along the 20 °C isotherms evidences for the liquid-liquid transition in the solvent (sparse to dense water transition) are observed between 0.2-0.4 GPa. The effect of the dissolved sulfate ions on the molecular structure of the water is discussed.

Chapter 5: Equation of state of NaCl aqueous fluids to 1073 K from 0.5to 4.5 GPa.

The thermodynamic data of H2O NaCl mixtures, with molality between 0 m and 3m, are determined up to 400 °C and 4.5 GPa with the approach presented in Chapter 2. The data are subsequently extrapolated to 800 °C, and a possible application to the petrology of a subducting oceanic slab is illustrated.

Chapter 6: PVTx properties of a 1m aqueous SrCl 2 solution and the effect of metal cations on the compressibility of Cl-bearing aqueous solutions. Following the lead of Chapter 4 and 5 the thermodynamic data of a 1m aqueous

SrCl 2 solution are determined up to 200 °C and 2.3 GPa. The volumetric data obtained are compared with the values of H2O NaCl aqueous solutions, and the

16 differences observed are explained in term of different effects of the dissolved metal cations on the molecular structure of the solvent. Chapter 7: Thermodynamic properties of carbon-bearing aqueous solutions and the 2 nd dissociation constant of carbonic acid at high pressure and temperature conditions. The PVTx data of the following carbonate- and bicarbonate-bearing aqueous solutions were investigated: 1 m aqueous Na 2CO 3 up to 400 °C and 3.7 GPa; 0.1 m and 0.5 m aqueous Na 2CO 3 up to 300 °C and 3 GPa; 0.1 m and 0.5 m aqueous

NaHCO 3 up to 300 °C and 3 GPa. The experimentally derived density data for the 0.1 m and 0.5 m carbonate- and bicarbonate-bearing aqueous solutions are fitted together with values of pure water, in order to provide a predictive model for the volumetric properties of H 2O-Na 2CO 3 and H 2O-NaHCO 3 solutions from 0 m to 0.5 m up to 300 °C and 3 GPa. Using the proposed EoS, the pressure and temperature dependence of the equilibrium constant of the 2 nd deionization reaction of carbonic acid is provided up to 200 °C and 3 GPa. Chapter 8: Conclusions and outlook. In this last chapter the main conclusions are summarized suggesting future research fields.

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Ulmer P. (2001) Partial melting in the mantle wedge - the role of H 2O in the genesis of mantle-derived 'arc-related' magmas. Physics of the Earth and Planetary Interiors 127 (1-4), 215-232. VonDamm K. L., Buttermore L. G., Oosting S. E., Bray A. M., Fornari D. J., Lilley M. D., and Shanks W. C. (1997) Direct observation of the evolution of a seafloor 'black smoker' from vapor to brine. Earth and Planetary Science Letters 149 (1-4), 101-111. Wagner W. and Pruss A. (2002) The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 31 (2), 387-535. Wang A., Pasteris J. D., Meyer H. O. A., and DeleDuboi M. L. (1996) Magnesite-bearing inclusion assemblage in natural diamond. Earth and Planetary Science Letters 141 (1-4), 293-306. Wiryana S., Slutsky L. J., and Brown J. M. (1998) The equation of state of water to 200 °C and 3.5 GPa: model potentials and the experimental pressure scale. Earth and Planetary Science Letters 163 (1-4), 123-130.

Wood S. A. and Samson I. M. (2006) The aqueous geochemistry of gallium, germanium, indium and scandium. Ore Geol. Rev. 28 (1), 57-102. Yardley B. W. D. (2009) The role of water in the evolution of the continental crust. J. Geol. Soc. 166 , 585-600.

Chapter 2

Experimental Methods

This chapter describes in detail the experimental method used in this work. In the first section the samples investigated are presented, while in the second section the attention is focused on the membrane-type diamond anvil cell (mDAC) used to achieve high pressure and temperature conditions during the Brillouin scattering spectroscopy measurements. This analytical technique is then illustrated in the third part of the chapter.

2.1 Samples description and preparation

The samples used in this study were saline aqueous solutions prepared by mixing an accurately weighed amount of high purity salt with high degree deionized Milli-Q water (© EMD Millipore Corporation). Table 2.1 summarizes the different solutions analyzed and their concentrations. For each composition, an adequate quantity of each solution that allows the repetition of several experiments was prepared. The mixtures were stored in small containers and refrigerated at 5 °C until used.

Table 2.1. Aqueous solutions investigated in this work.

Composition Reagent powder Molality m Wt.% salt (mol / kg H 2O) ® H2O - NaCl NaCl (99.999 %, Sigma Aldrich ) 1 and 3 5.5 and14.9 ® H2O - SrCl 2 SrCl 2 ) 1 13.7 ® H2O - Na 2SO 4 Na 2SO 4 (99.99+ %, Sigma Aldrich ) 1 12.4 ® H2O - Na 2CO 3 Na 2CO 3 (99.995%, Sigma Aldrich ) 1, 0.5 and 0.1 9.6, 5.0 and 1.1 ® H2O - NaHCO 3 NaHCO 3 (99.7-100.3%, Sigma Aldrich ) 0.5 and 0.1 4.2 and 0.8

29 2.2. Diamond Anvil Cell techniques

2.2.1. The diamond anvil cell

The diamond anvil cell (DAC) is a powerful tool for generating high pressure and high temperature conditions during experiments and in-situ measurements. Two gem quality diamonds serve as anvils, whereas the sample is loaded in a drilled metallic gasket located between the two diamonds (Fig. 2.1 and 2.2). Diamonds have two main qualities that make them ideal for this high pressure analytical technique: 1) the strength and 2) the transparency to a wide range of the electromagnetic spectrum. In order to reach P-T conditions relevant for geological processes (e.g., hydrothermal alteration of the seafloor or subduction zone setting) different heating techniques have been developed that allow high temperatures during high pressure experimental measurements in a diamond anvil cell. The most popular are the resistive heating and the laser heating (Bassett, 2009). The laser heating technique permits temperatures up to 6000-7000 K (Heinz et al., 1991; Bassett, 2009) and is based on the principle of absorption of infrared laser light by the sample after the light has passed through the diamond anvils with minor intensity loss (Ming and Bassett, 1974; Bassett, 2001; Zha and Bassett, 2003). Although this heating method prevents anvils oxidation/graphitization and possible damages of the DAC assembly caused by high temperatures (Dubrovinskaia and Dubrovinsky, 2003), the very localized heating zone results in very steep temperature gradients and possible thermal stress inside the sample (Dubrovinskaia and Dubrovinsky, 2003; Zha and Bassett, 2003). Moreover, the temperature measurement is complex, because it is based on the pressure and temperature dependence of the infrared absorption of the sample (Dubrovinskaia and Dubrovinsky, 2003; Zha and Bassett, 2003). Different types of resistive heaters have been developed parallel to the laser heating technique. For instance, heaters surrounding the whole body of the cell (Schiferl, 1987; Mao et al., 1991; Fei and Mao, 1994; Dubrovinskaia and Dubrovinsky, 2003), only the diamond seats (Bassett et al., 1993) or both diamonds and gasket assemblage (Fei and Mao, 1994). Additionally, internal resistive heaters may be located directly inside the sample chamber (Boehler et al., 1986; Zha and Bassett, 2003; Miletich et al., 2009) or they are represented by the gasket itself (Moore et al., 1970). The major advantages of the resistive

30 heating technique are the stable and homogeneous temperature field in the sample chamber and the simple temperature monitoring with thermocouples (Dubrovinskaia and Dubrovinsky, 2003; Miletich et al., 2009). On the other side, the disadvantages are the diamond graphitization at T > 1200 °C, the softening of the metallic gaskets and the deformation of some DAC assemblages (Dubrovinskaia and Dubrovinsky, 2003; Zha and Bassett, 2003). All high temperature experiments presented in this manuscript were performed with a double resistance heater configuration, in fact, as it is explained in section 2.3, an external heater surrounding the body of the cell is coupled with an internal heater located around the anvils. Over the last 50 years the diamond anvil cell has been combined with a broad variety of analytical methods ( e.g ., X-rays diffraction and absorbtion, Raman and Brillouin spectroscopy) that have provided a wealth of information about the behavior of materials at high pressure and temperature conditions, see Bassett (2009) for a review.

Figure 2.1. Sketch showing the diamond anvil cell. The sample chamber is drilled in a pre-indented metallic gasket and is located between the two diamonds. The sample is loaded in the experimental chamber together with an optical pressure sensor (red dot).

Figure 2.2. View of the experimental chamber as seen through the top diamond (Fig. 2.1). The sample chamber was drilled in a stainless steel gasket and loaded with a 0.5 m Na 2CO 3 aqueous fluid at 20 °C. The presence of a small air bubble indicates that the sample is at room pressure. By increasing pressure the air bubble disappears. A ruby sphere is loaded in the experimental chamber to serve as pressure sensor during the experiments.

All experiments presented in this manuscript were conducted in a membrane-type diamond anvil cell (mDAC) with large optical opening (98 deg) and mounted with two low fluorescence Ia-type diamonds of 500 m culet diameter (Chervin et al., 1995). Figures 2.3 and 2.4 display the different components of the mDAC design used in this study. The cell body is machined in maraging steel treated to full hardness (Letoullec et al., 1988; Chervin et al., 1995). Prior to the experiments, the two diamonds are aligned relative to conical apertures in the mDAC, and then fixed with high temperature cement (Resbond 940 HT ® Cotronics corporation or EPO-TEK 353ND ® EPOTEK). In a second step, the diamonds are adjusted relative to each other (horizontal position and parallelism of the culets). Finally, the internal heater is glued around the diamonds and the K-type thermocouple fixed close to the compression chamber.

Figure 2.3. Top and bottom components of the membrane-type diamond anvil cell used in this work, also referred as piston and body of the cell. The conical aperture is of 98 deg. The connectors for the heater power supply and for the thermocouple reading are visible.

Figure 2.4. View of the inner part of the piston and the body of the mDAC used in this work. The dark dashed line in the bottom component highlights the position of the K-type thermocouple glued on the lower diamond. The ceramic blanket serves to isolate the internal heater from the body of the cell.

33 2.2.2 Pressure generation

The experimental approach of this work is to perform isothermal measurements with changing pressure. Therefore, a diamond anvil cell that allows a pressure regulation even at high temperatures is needed. Differently from the screw-type cells, like the hydrothermal diamond anvil cell (HDAC) (Bassett et al., 1993), the mDAC have a remote pressure control that allows pressure changes to be made without touching or moving the body of the cell (Chervin et al., 1995). In fact, an external pressure controller connected to the mDAC with a metallic tube is used to fill or empty the metallic membrane located above the upper diamond (Fig. 2.5, 2.6a and 2.6b). For this purpose the chemically inert Ar gas is used. The metallic membrane is welded in the cover which is used to close the mDAC screwing it on the body of the cell (Fig. 2.4). When the metallic membrane is filled with Ar gas the upper diamond is translated against the lower diamond, generating pressure in the sample chamber positioned between the two anvils.

Figure 2.5. The remote pressure controller is connected through a metallic tube to the membrane that is welded in the cover part of the mDAC.

Figure 2.6. a) Sketch representing the metallic membrane located above the upper diamond. When the membrane expands the upper diamond translates against the lower diamond increasing the pressure in the sample chamber. b) Membrane-type diamond anvil cell designed by Chervin et al. (1995): (1) cap with membrane chamber (1m) and gas inlet (1i) of the ram, (2) piston, (3) lower body, (4) WC diamond seats, (5) anvils.

2.2.3 High temperature conditions

In order to reach high temperature conditions during the isothermal experimental measurements an internal Pt resistive heater (Fig. 2.4 and 2.7) and an external ring-shaped resistive heater (Fig. 2.8) surrounding the whole cell (Dubrovinskaia and Dubrovinsky, 2003) were used simultaneously, allowing temperatures in the sample chamber up to 500 °C. The body of the internal heater is made of pyrophyllite, a phyllosilicate appreciated for its high thermal stability and that can be easily machined. As shown in Figure 2.7, the Pt wire is wrapped to form coils passing through small holes drilled in the body of the heater. The temperature in the sample chamber was monitored to ±2 °C with a K-type (Chromel-Alumel) thermocouple attached to one of the diamonds close to the sample chamber (Fig. 2.3, 2.6 and 2.7). The thermocouple was calibrated relative to the melting point of S (115 °C) and NaNO 3 (308 °C). An additional thermocouple is included in the external

35 heater and was calibrated against the internal thermocouple before the experiments according to Chervin et al. (2005).

Figure 2.7. Details of the internal heater and the K-type thermocouple used in the high temperature experiments. The heater is not covered yet with the ceramic cement to highlight the coils made by the Pt-wire. A thermocouple is attached very close to the lower diamond culet to monitor the temperature in the compression chamber.

Figure 2.8. Picture showing the mDAC mounted on the 3-circle goniometer of the Brillouin system. The cell is surrounded by a cylindrically shaped external heater. The connections of the internal K- type thermocouple are also labeled.

2.2.4 The metallic gasket

The sample chamber (Fig. 2.2) is drilled using a Motorized Electric Discharge Machine (EDM) MH20M (© BETSA France) in pre-indented stainless steel or rhenium gaskets of about 80- experimental of about 1:3. The pre-indentation procedure is necessary to decrease the gasket thickness and to increase its stiffness. Stainless steel gaskets are used in experiments up to 200 °C whereas at higher temperature, rhenium gaskets are employed because of its lower chemical reactivity in the investigated temperature range (up to 500 °C). After the loading of the pressure sensors (see section 2.5) and a drop of the fluid in the experimental chamber, the cell is immediately closed and pressurized to avoid fluid evaporation and/or solute precipitation that would modify the composition of the solution. The reliability of the loading procedure is confirmed by the reproducibility of the isothermal

37 experimental runs repeated with new loadings of the same solution, by the consistence of the measurements performed at room conditions inside and outside the mDAC (i.e., in a silica glass cuvette) and by the agreement with the literature (see section 2.3.4 and Fig. 2.21 for more details).

2.2.5 Pressure calibration

As discussed in Chapter 1, the goal of this work is to experimentally derive the thermodynamic properties of the different saline aqueous solutions investigated up to high pressure and temperature conditions and present new equation of states for these solutions. For this reason, accurate and precise pressure and temperature monitoring during the isothermal experimental measurements is of fundamental importance. While the temperature in the sample chamber is monitored with several K-type thermocouples (section 2.3), the pressure is determined with pressure sensors loaded in the sample chamber. The choice of a pressure marker relative to another depends on the experimental conditions. In fact, some pressure sensors are not adequate for pressure calibrations at high temperature, because of a decreased precision in the pressure monitoring, and because of their chemical reactivity in saline aqueous fluids at high P-T conditions that would change the composition of the solution investigated. The several pressure calibrants used in this work are described, compared and discussed in the following paragraphs.

a) The pressure sensors

The optical and Raman pressure markers are loaded in the experimental chamber together with the sample analyzed (Fig. 2.2). Table 2.2 summarizes the different pressure markers used in this work together with the temperature range in which they were used and appropriate references for the pressure calibration applied.

38 Table 2.2. Pressure sensors used in this work.

Pressure sensor Analytical Temperature Selected references Method Mao et al. (1978) 20°C, 100°C, Ragan et al. (1992) ruby spheres Fluorescence 200°C, 300°C Chervin et al. (2003) Datchi et al. (2007b) 20°C, 100°C, Schmidt and Ziemann quartz chips Raman 200°C, 300°C (2000) 200°C, 300°C, Datchi et al. (2007a) cubic boron nitride (cBN) chips Raman 400°C, 500°C 1-symmetric stretching mode of unassociated 400°C, 500°C Schmidt (2009) 2- Raman SO 4 ions (sulfate-bearing solutions)

Pressure determination with optical and Raman sensors is based on the calibrated pressure-dependent wavelength shift of either fluorescence ( e.g., ruby) or Raman ( e.g., 2- quartz, cBN, SO 4 ) signals relative to an initial wavelength at known pressure and temperature conditions. As the temperature-effect on the position of the signal used for pressure calibration has to be taken into account an accurate temperature monitoring is essential. The different pressure calibrations used in this work are briefly presented here:

3+ Ruby ( Cr : Al 2O3) spheres: the position of the R1 and R2 (Eggert et al., 1989) fluorescence lines is pressure and temperature dependent (Fig. 2.9). For this reason ruby can be used as pressure marker (e.g. , Piermarini et al., 1975; Mao et al., 1978; Datchi et al., 2007b) or as temperature sensor when combined with other pressure calibrants (Datchi et al., 1997; Datchi et al., 2007b) . The ruby spheres used in this work (Fig. 2.2) and a Cr concentration of about 3600 ppm (Chervin et al., 2003). The pressure is calculated from the calibrated shift of the R1 fluorescence line according to the equation (Mao et al., 1978)

B A P(GPa ) 1 1 (1) B 0

39 0 0, A = 1904, B = 7.715 (assuming hydrostatic conditions) and A/B = 308.8. Temperature has a large influence on the position of the R1 fluorescence line and therefore, the -effect prior pressure calculation using the following equation (Datchi et al., 2007b)

.0 00664 )4( T 76.6 52( ) 10 6 T 2 33.2 16( ) 10 8 T 3 (2)

T 0 (at 296 K and 1bar) = 694.28 nm.

-1 Quartz chips: the pressure-induced shift of the 464 cm A1 Raman mode of quartz (Fig. 2.10), corresponding to the bending vibrations of Si-O-Si angles (Etchepar et al., 1974), is used to calibrate pressure according to the slope (Schmidt and Ziemann, 2000):

-1 ( 464 / P) T = 9 cm /GPa.

The temperature contribution on the measured shift of the 464 cm -1 mode is described by (Schmidt and Ziemann, 2000):

(cm 1) .2 50136 10 11 T 4 .1 46454 10 8 T 3 T 464 ,P 1.0 MPa (3) 1.801 10 5 T 2 0.01216 T 0.29

This calibration is valid up to 560 °C (Schmidt and Ziemann, 2000). The chips of synthetic quartz used in this wor

40 Figure 2.9. Typical ruby fluorescence spectra collected at different temperatures in the mDAC. The ruby spheres are loaded in the experimental chamber together with the investigated sample. From room temperature to 300 °C the R1 and R2 fluorescence bands broaden and partially overlap whereas the relative intensity decreases and the background increases.

Figure 2.10. Raman spectra of a quartz chip loaded in the mDAC with a 1 m Na 2SO 4 aqueous solution at 200 °C and 1.4 GPa (blue solid line), and of a cBN chip loaded in a mDAC together with a 1 m Na 2SO 4 aqueous solution at 400 °C and 1.85 GPa (red solid line). The Raman signals corresponding to the A1 (464) bending vibration mode of quartz, the

TO mode of cBN and 1 symmetric stretching mode of the unassociated sulfate ions are clearly visible and distinguishable.

41 Cubic boron nitride (cBN) chips: the cubic modification of the BN (cBN) has a diamond-like structure, and it is well known for its hardness, chemical inertness, mechanical and thermal stability (Datchi and Canny, 2004). Boron nitride exists only as synthetic product (Wentorf, 1957). The calibrated (Kawamoto et al., 2004; Goncharov et al., 2005; Datchi et al., 2007a) pressure-dependent shift of the 1054 cm - 1 Raman transverse optical mode (TO) can be used for pressure determination as alternative to ruby spheres and quartz chips (Fig. 2.10). The pressure in the sample chamber is calculated according to the equation (Datchi et al., 2007a):

.2 876 B (T) TO (P,T) 0 (4) P(GPa ) TO 1 B'0 0 (T)

where B 0 0 is its first pressure-derivative and

0(T) is the variation with temperature of the wavelength shift at ambient pressure:

B'0 62.3

6 2 B0 T 396 )5(5. .0 0288 14( ) T 300 84.6 77( ) 10 T 300 (5)

TO 5 2 0 T 1058 )5(4. .0 0091 23( ) T 54.1 22( ) 10 T (6)

where TO (P,T) is the measured frequency shift. This pressure scale is valid in the P- T range 0-100 GPa and 300-1000 K (Datchi et al., 2007a). Prior the loading in the mDAC, Raman spectra of cBN chips were collected at room P-T conditions outside the diamond anvil cell, and only the chips showing the higher signal-to-noise ratio were selected as pressure marker. The size of these chips varied between 40 and 8

2- 2- 1-symmetric stretching mode of unassociated SO 4 ions: when loaded with a SO 4 -bearing aqueous solution the pressure in the sample chamber can be calculated from

42 the pressure-induced shift of the Raman-active 1-symmetric stretching mode (Fig. 2- 2.10) of the unassociated sulfate ions (SO 4 ) according to the isothermal slopes (Schmidt, 2009) reported in Table 2.3.

-1 2- Table 2.3. Isothermal slopes (cm /GPa) for the 1-mode of unassociated sulfate ions (SO 4 ). From Schmidt (2009).

2- -1 Temperature 1-SO 4 / P (cm /GPa) 20°C and P<0.2GPa 6.51 20°C and P>0.2GPa 4.25 100°C 7.45 200°C 6.79 300°C 6.71 400°C 6.33 500°C 6.27

b) Comparison between different pressure markers and discussion

The mutual agreement between the different pressure markers (i.e. , ruby, quartz, cBN, Sulfate-ions) was checked by loading the mDAC with several pressure sensors at the same time. As reported in Table 2.4 and in Figure 2.11, good agreement is found within the pressure determined from the different pressure standards, indicating that pressure can be determined with equivalent precision using any of the selected pressure standards. The choice of a pressure sensor for a specific type of experiments is thus dictated by two factors:

i) the chemical stability of the pressure marker at the experimental P-T conditions;

ii) the effect of the temperature on the Raman or fluorescence signal used for pressure calibration.

43 Ruby and quartz always display a very high signal-to-noise ratio (Fig. 2.9 and 2.10) at low temperature but at high temperature these two sensors become inadequate for pressure calculation. At temperatures above 280 °C, the broadening and overlapping of the R1 and R2 fluorescence lines, the higher background and the reduction of the signal-to-noise ratio (Fig. 2.9) decrease the precision on pressure determination using ruby spheres (Datchi et al., 1997; Datchi et al., 2007b). Additionally, R1 wavelength has a large temperature dependence, which increases with increasing temperature, and therefore, errors in the temperature determination will automatically influence the pressure calculation (Datchi et al., 2007b). An additional important point that has to be considered is the possible sample contamination caused by the enhanced chemical reactivity of this pressure marker at high pressure and temperature conditions. In fact, in experiments with H2O-NaCl solutions the solubility of

Al 2O3 at high P-T conditions is higher than in pure water (Manning, 2006). For all these reasons, ruby spheres as used for pressure monitoring during experiments at temperature up to 300 °C; whereas measurements at 300° C are repeated with a second pressure sensor (e.g., quartz and cBN) as a control.

Compared to the other pressure sensors, the large pressure induced wavelength shift (9 cm -1/GPa) of the 464 cm -1 Raman band makes quartz the ideal sensor for monitoring very small pressure changes. For this reason, quartz is the best pressure marker to determine the pressure during measurements in the low pressure and temperature range, where the fluids investigated have the higher compressibility, and therefore, very small pressure increases are necessary to characterize the aqueous solutions properly. Differently from the fluorescence standards, the frequency of the 464 cm -1 Raman mode can still be accurately determined under high temperature conditions because it does not merge with other intense bands, like in the case of the R1 and R2 fluorescence signals of the ruby spheres (Hess and Schiferl, 1990).

On the other hand, the solubility of SiO 2 in saline aqueous fluids increases with temperature at low pressure (Manning, 1994; Newton and Manning, 2000; Shmulovich et al., 2006), and this - at low solution density has been experimentally observed (Newton and Manning, 2000; Shmulovich et al., 2006). This implies an increase of quartz solubility as the salt concentration and the temperature increase, up to a maximum value of 70 wt% NaCl at 700°C and low pressure < 2 kbar (Newton and Manning, 2000). Therefore, to avoid any

44 possible sample contamination due to quartz dissolution, other pressure standards (e.g. cBN 2+ and SO 4 ions) are employed in experiments at very high temperature (T 400°C).

Among the different pressure markers, cBN is the most chemically inert and the width of its Raman transverse optical TO phonon mode is almost insensitive to temperature, making this compound very suitable pressure sensor at temperatures above 200 °C. Nevertheless, the sensitivity to pressure variations of the TO Raman band and the signal-to- noise ratio are lower than those of the ruby fluorescence or the quartz Raman mode; consequently, pressure determination may have a larger associated uncertainty (Datchi et al., 2007a). In any case, a good agreement with other pressure standards was always observed (Fig. 2.11); therefore, the use of cBN does not decrease the precision in the pressure determination.

In experiments conducted in 1m Na 2SO 4 aqueous solutions up to 500 °C (Chapter 3), pressure in the sample chamber was monitored without secondary pressure sensors ( i.e ., ruby, cBN or quartz) to avoid any possible sample contamination due to the dissolution of the pressure sensors. In this case, pressure was calibrated using the 1-symmetric stretching 2- mode of unassociated SO 4 ions. This pressure calibration technique was firstly tested at lower temperature conditions with a secondary pressure sensor (see Fig. 2.10, Fig. 2.11 and Tab. 2.4)

45 Table 2.4. Comparison between the different pressure markers used in this work. These data are reported in Figure 2.11.

Pressure calculation [GPa] 2- Pressure calculation [GPa] Ruby Quartz cBN SO 4 group 2- Ruby Quartz cBN SO 4 group 20°C 300°C 0.11 0.12 2.40 2.43 0.27 0.29 1.32 1.31 0.35 0.37 0.38 2.34 2.39 2.36 0.46 0.44 2.45 2.47 2.43 100°C 3.03 3.02 0.26 0.24 1.88 1.88 1.93 0.49 0.44 2.79 2.75 2.74 1.12 1.14 2.74 2.77 1.71 1.73 0.46 0.48 400°C 0.49 0.50 1.3 1.32 0.69 0.68 1.85 1.88 0.69 0.71 1.76 1.72 0.51 0.53 0.54 1.85 1.84 0.63 0.66 0.62 0.69 0.68 0.63 200°C 0.98 1.03 1.06 1.08 1.32 1.31 1.16 1.16 1.18 1.17 1.19 1.27 1.28 1.29 1.40 1.42 1.62 1.64 1.61 1.06 1.08 1.11 1.86 1.80 1.78

46 ork. Systematic trends in the pressure differences differences pressure the in trends Systematic ork.

Comparison between the different pressure markers used in this w in used markers differentpressure the between Comparison Figure 2.11. Figure depending on temperature or pressure are not visible. notare orpressure temperature on depending

47 2.3 Brillouin scattering spectroscopy

2.3.1. Principles

Brillouin scattering spectroscopy is based on the interaction between electromagnetic waves (light photons) and thermally induced density variations (lattice vibrations) called acoustic phonons. The French physicist Léon Brillouin was the first to predict the inelastic scattering of photons by acoustic phonons in transparent and homogeneous bodies (Brillouin, 1914). The propagation of the acoustic phonons in a material causes fluctuations in the refractive index, and consequently of the dielectric constant, from which the light is scattered (Fig. 2.12) undergoing Doppler effect. This light scattering is therefore inelastic, with the photons losing (Stokes process) or gaining (anti-Stokes process) energy with respect to the incident light.

Figure 2.12. Schematic representation of the Brillouin scattering process. The acoustic phonons are fluctuations in the refractive index of the material investigated and they can be viewed as a diffraction grating (re scattering angle, f 0 k are the frequencies of the incident light, scattered light and acoustic phonons, respectively. c 0 and V k 0 K are the velocity and the wavelength of the incident photons and the acoustic phonons, respectively, and d is the space between two diffracting planes

48 More precisely, the incident photons experience a double Doppler effect, with the acoustic phonons acting firstly as a moving receiver, and secondly as a moving sender. The frequency of the inelastic scattered photon can be expressed as:

2 2 ' Vk sin 2/ Vk sin 2/ 2 Vk sin 2/ Vk sin 2/ f f0 1 1 1 (7) c c c c2

where the different symbols are explained in Figure 2.12 and c is the photon velocity in a medium with refractive index n.

As V k << c, then:

' 2 Vk sin 2/ 2 n Vk sin 2/ f f0 1 f0 1 (8) c c0

where, c 0 is the velocity of light in vacuum (c = c 0/n). It follows that the frequency shift

' 2 n f 0 Vk sin 2/ 2 n Vk sin 2/ f f f 0 (9) c0 0 . with c 0 0 f0.

V 0 2 d sin 2 k sin (10) n 2 fk 2

Vk with d k . fk

Solving for f k we obtain:

2 n Vk sin 2/ fk (11) 0

49 From equations (9) and (11) is clear that the frequency shift undergone by the photons is equivalent to the frequency of the acoustic phonons: f fk . The frequency shift experienced by the photons is called Brillouin shift. Because the Brillouin shift is relatively small, in the order of 0.1-6 cm -1 from the reference Rayleigh signal ( e.g. , Raman scattering is between 10 and 1000 cm -1), a high resolution six-pass tandem Fabry-Pérot interferometer (Sandercock, 1982) is needed for analyzing the scattered light.

2.3.2 The Fabry-Pérot Interferometer

The Fabry-Pérot interferometer (FPI) is composed on two parallel partially transmitting plane mirrors separated by a distance d (Fig. 2.13). The maximal light transmission through the mirrors is achieved when (Sandercock, 2001):

n d m (12) 2

wavelength of the transmitted light and m is an integer. From this relationship it is evident that the wavelength of the transmitted light can be controlled by varying the distance d between the two transmitting mirrors. A tandem Fabry-Pérot interferometer the first one (Fig. 2.13). In each pair the left mirror has a fixed position, while the right mirror is mounted on a translation stage. Moving the translation stage the distances d 1 and d 2 are changed simultaneously and all the frequencies (wavelengths) of the scattered light can be analyzed. The use of a tandem FPI, instead of a single FPI, is necessary for two main reasons (Sandercock, 1982):

a) to better discriminate the wavelength of the transmitted light; b) to increase the contrast.

Figure 2.13. Sketch of a tandem Fabry-Pérot Interferometer. On each FPI the right mirror is mounted on the translation stage. Modified after Sandercock (2001). See text for more details. a) Wavelength discrimination

The transmission function of a FPI is defined as (Sandercock, 2001):

1 I I (13) t 0 1 F sin 2 2/

where I t and I 0 are the intensity of the transmitted and the incident light,

4 R F (14) 1 R 2 where R is the mirror reflectivity.

51 The transmission function is periodic, with maximal values at

2 m , with m . (15)

If only one pair of transmitting mirrors is used, the periodicity of the transmission function is clearly visible in the spectra collected (Fig. 2.14). In fact, Stokes and anti- Stokes peaks of different orders ((n-1) . . . . may overlap in the same region of the spectra. This fact precludes the correct determination of the phonon wavelength (Sandercock, 2001).

In a tandem Fabry-Pérot Interferometer the distance d 2 between the second pair of mirrors is

d2 d1 cos (16)

with d 1 equal to the distance between the first pair of transmitting mirrors (Fig. 2.13 satisfy equation . (12) for the distances d 1 and d 2 simultaneously. This implies that the lower (e.g. , (n-1) ) and high (e.g. , (n+1) . ) order wavelengths are transmitted by FPI 2 with a different mirror distance compared to FPI 1. As Figure 2.14 shows, the use of a tandem Fabry-Pérot Interferometer inhibits the low and high order wavelengths, because the total transmission intensity is the product of both FPI, allowing a more correct determination of the phonon wavelength (Sandercock, 2001). b) The contrast

The contrast is defined as the ratio between the maximum transmission intensity and the minimum transmission intensity, and quantifies the capability of a FPI to measure signals that have a smaller intensity relative to the Rayleigh scattered light (Sandercock, 2001). As the Brilluoin signals have a lower intensity relative to Rayleigh peak a ratio (contrast) of 1:10 10 is necessary to analyze the scattered light (Sandercock, 1982). The use of a tandem setup increases considerably the contrast of a FPI because the scattered

52 light is forced to pass 6 times (3 times FPI 1 + 3 times FPI 2) through the transmitting mirrors (Fig. 2.13).

Figure 2.14. Simplified representation of Brillouin spectra. The green and the red filled peaks are anti-Stokes and Stokes signals, respectively. The higher and broader peaks are Rayleigh (elastic) signals. With only one pair of mirrors ( e.g. , only FPI 1 or FPI 2) it is not possible to assign the correct wavenumber to the Brillouin scattered peaks because of the periodicity of the transmission function: Stokes and anti-Stokes signals from different orders may overlap in the same region of the spectra, and in some case it may be not possible to determine the origin of the signal (Stokes or anti-Stokes scattering). The use of a tandem Fabry-Pérot Interferometer ( i.e. , FPI 1 + 2) solves this problem. Modified after Sandercock (2001).

53 2.3.3 Brillouin scattering spectroscopy

Brillouin scattering spectroscopy is used to measure the velocity of acoustic phonons propagating in a sample according to the Brillouin equation (rearranged from Eq. 9):

0 i Vi (17) 2 n s sin / 2

where V i 0 is the laser wavelength, i is the Brillouin shift, n s ering angle. The index i refers to one of the three modes (V P, V SV , V SH ) of acoustic waves propagating in a body (i.e., body waves). V P is called longitudinal (or compressional) velocity, while V SV and V SH are vertically and horizontally polarized shear velocities, respectively. In a solid sample all the three modes may be observed, whereas in fluids V S (i.e., VSV and V SH ) are absent, because the shear modulus is equal to zero ( VS /

The samples analyzed by Brilluoin scattering spectroscopy can be fluids or solids (single crystals or polycrystalline material). From equation (17) it is clear that the knowledge of the refractive index of the sample analyzed as a function of pressure and temperature is a prerequisite to calculate the acoustic velocities at different P-T conditions. Unfortunately, the refractive indexes of aqueous solutions are not well characterized at high pressure and temperature conditions. For instance, measured and extrapolated data for pure liquid water do not exceed 200 °C in temperature (Schiebener et al., 1990; Grimsditch et al., 1996; Li et al., 2005). In order to avoid this problem all Brillouin measurements of this work were performed using a symmetric (platelet) scattering geometry.

Figure 2.15. Representation of the symmetric (platelet) scattering geometry. Solid lines indicate the direction of the incident and scattered beam in the sample (blue lines) and outside the sample are the angles between the incident and the scattered beams and sample face * are the internal and the external scattering angles. n a and n s refer to the refractive index of the two different media. a) Platelet (symmetric) geometry

In platelet, or symmetric, scattering geometry all the refracting surfaces of a sample are parallel (Fig. 2.15), and the sample analyzed must be transparent. The use of a platelet geometry eliminates the uncertainties in the acoustic velocity calculations due to uncertainty in the refractive index (Sinogeikin and Bass, 2000). . 2.15 for more details):

na sin ns sin (18)

and with the refractive index of the air n a ~ 1, equation (18) becomes:

55 sin( ) sin( ) (19) ns

The intern

180 (180 2 ) 2 (20)

On the same way, the external scattering angle is:

* 180 (180 2 ) 2 (21)

and consequently:

* (22) 2

The Brilluoin equation can now be rewritten (Whitfield et al., 1976):

0 fi 0 fi 0 fi 0 fi Vi (23) 2 ns sin / 2 2 ns sin sin * 2 ns 2 sin ns 2

* is now the external scattering angle (Fig. 2.15). As it is demonstrated in the calculations above the use of a platelet scattering geometry eliminates the refractive index of the sample n s from equation (17) (Whitfield et al., 1976).

Equation (23) is valid also for Brillouin measurements performed in a diamond anvil cell as long as all the refractive surfaces of the two diamonds are parallel. If the analyzed sample is a solid (e.g., single crystal) its refractive surfaces need to be parallel (Fig. 2.16). Zha et al. (1996) and Sinogeikin and Bass (2000) performed a 2-D analysis of several individual cases of deviation from a perfect parallel geometry. Sinogeikin and

56 Bass (2000) concluded that although a deviation from symmetric platelet geometry caused by a not perfect parallelism of refractive surfaces is always present to some degree, all the different effects will partially cancel or counteract each other. Therefore the cumulative error in velocity measurements will not exceed 0.5% (Sinogeikin and Bass, 2000).

Figure 2.16. Diamond anvil cell loaded with a solid sample (yellow rectangle). If all the refractive surfaces of the diamonds and the sample are parallel, equation (23) can be used to calculate the velocity of acoustic waves propagating in the sample.

dimensions of the DAC have been distorted to highlight the light path. Abbreviations - D: diamond; G: metallic gasket; SC: sample chamber.

b) Vignetting

A more significant error in velocity determination can be caused by vignetting effects that are introduced when part of the incident and/or scattered light cone is blocked by the diamond supports and/or the gasket (Oliver et al., 1992; Sinogeikin and Bass, 2000). Vignetting usually decreases the Brillouin shift, leading to systematically lower acoustic velocities. Sinogeikin and Bass (2000) found that vignetting may lower by 4% the speed of sound measured.

57 To solve this problem, a mDAC with a large conical aperture is used (98 deg) and the sample chambers drilled in the metallic gaskets have a thickness to diameter ratio of 1:3 or even smaller, to avoid any blocking of the light by the gasket.

2.3.4 The Brillouin system at ETH Zürich a) Description

All experimental measurements of this work have been performed at the ETH Zürich. Figure 2.17, modified from Sanchez-Valle et al. (2010), illustrates the experimental setup used for these experiments. Briefly, the Brillouin system utilizes a ® solid state Nd:YVO 4 laser (Verdi Coherent , 0 = 532.15 nm) as light source and a six pass tandem Fabry-Pérot Interferometer (Sandercock, 1982) equipped with a photomultiplier tube to analyze the scattered light. The system is designed to work in between the different scattering geometries is based on the sample environment: goniometer head (Fig. 2.19) or spectroscopic cell (i.e., DAC). A motorized Eulerian cradle combined with motorized horizontal rotation stage and high-resolution XYZ translational stages (Fig. 2.18) is used to control the orientation of the sample respect to the laser beam. A metallic mask with a narrow vertical slit is mounted before the collecting lens, in order to acquire only the scattered light coming from the sample, and not, for example, the light scattered from the laboratory walls. Brillouin spectra are acquired using the software Ghost version 6.06 ( JRS and Brillouin res. group Perugia , Italy). A Raman collection system installed in the same optical bench allows the collection of Raman or fluorescence signals from the pressure sensors loaded in the DAC. The scattered light is redirected to the Raman system with a flip mirror placed behind the collecting lens (Fig. 2.17). The light passes through a holographic supernotch filter to attenuate the laser light and then is focused into an optical fiber coupled to a SpectraPro 500i spectrometer equipped with a thermoelectrically cooled charge-coupled device detector and gratings of 1200 and 1800 grooves/mm. Raman and fluorescence spectra

58 were fitted to Voigt functions using the software Peakfit version 4.12 (© Seasolve Incorporation).

59 BS: BS: er; FC: fiber coupling; coupling; fiber FC: er;

h is modified after Sanchez-Valle et al. (2010). Abbreviations Abbreviations al. et (2010). after modified is Sanchez-Valle h ; SF: spatial filter; PMT: photomultiplier tube. photomultiplier PMT: filter; spatial ; SF: : diaphragm; M: mirror; L: lens; CL: collecting lens; N: notch filt notch N: lens; collecting CL: L: lens; mirror; M: diaphragm; : Brillouin scattering system used for the measurements. The sketc The measurements. thefor used system scattering Brillouin Figure 2.17. Figure MC: microscope with camera; Po: linear polarizer; P: prism P: polarizer; linear Po: camera; with microscope MC: D expander; beam rotator; BE: polarizer PR: splitter; beam 60 Figure 2.18. Motorized Eulerian cradle combined with a horizontal stage and translational stages.

b) System calibration

Brillouin spectroscopy is extremely sensitive to the scattering geometry, and a geometric error in the external scattering angle will automatically produce an error in the measured acoustic velocities, with the relation: n the speed of sound (Sinogeikin and Bass, 2000). According to Sinogeikin and Bass (2000), when the scattering geometry is well controlled, the uncertainty in measured velocities is typically less than 0.5-1%. The use of a DAC introduces additional refracting surfaces, and therefore additional sources of error. If all the possible errors are identified and corrected the uncertainty in the velocity measurements introduced by the DAC is less than 0.5% (Sinogeikin and Bass, 2000). In the sections below we report the results of calibration runs conducted using a MgO single-crystal and well-characterized aqueous solutions at room conditions to test the accuracy and reproducibility of the Brillouin system before the high P-T experiments were conducted.

61 i) MgO single crystal

The extensive experimental work on MgO elasticity (Spetzler, 1970; Yoneda, 1990; Chen et al., 1998; Sinogeikin and Bass, 1999; Sinogeikin and Bass, 2000) makes of this compound an excellent standard for measurements of elastic properties of materials (Sinogeikin and Bass, 2000), and consequently, the ideal candidate for testing the accuracy of the Brillouin scattering setup used in this work.

Figure 2.19. MgO single- crystal mounted on a goniometer head. The crystal dimensions are 2 x 1 x 0.5 mm. The goniometer head has additional axes that can be used to adjust the position of the crystal relative to the beam.

The acoustic velocities were measured at room conditions in the (100) crystallographic plane of a MgO single-crystal, with lateral dimensions 2 mm x 1 mm and a thickness of 0.5 mm. The refractive surfaces are perfectly parallel and polished. The MgO single crystal is mounted on a goniometer head (Fig. 2.19) and then positioned on the Eulerian cradle. The speed of sound measurements have been performed in all three (50°, 80° and 90°) scattering geometries over an angular range of 180° (chi angle), with 15° interval

62 (Fig. 2.20). The reproducibility in repeated measurements was found to be better than 0.5% of the measured velocities (Sanchez-Valle et al., 2010).

Figure 2.20. Acoustic velocities of MgO as a function of the crystallographic direction collected sample by 180° relative to its vertical axis in order to check for the parallelism of the two refractive surfaces. The solid lines are velocities calculated from the best-fit C ij elastic model. Errors are as big as the symbol size.

In the cubic crystal system the elastic moduli tensor C ijk has the form:

C11 C12 C12 0 0 0

C12 C11 C12 0 0 0

C12 C12 C11 0 0 0 Cijkl (24) 0 0 0 C44 0 0

0 0 0 0 C44 0

0 0 0 0 0 C44

with only three independent stiffness constants (C 11 , C 12 and C 44 ).

63 The measured acoustic velocities (V P and V S) are used to solve Christoff equations for the MgO crystal and determine the three independent elastic constants (Musgrave, 1970):

2 det Cijkl n jn l V ik 0 (25)

where C ijkl is the single-crystal elastic moduli tensor, n j and n l the direction cosines

of the phonon, the density, ik the Kronecker delta and V the acoustic velocities

measured. Table 2.5 summarizes the elastic constants (C 11 , C 12 and C 44 ) obtained solving

equation (25), as well as the aggregate elastic properties (bulk modulus KS, shear

modulus G, V P and V s) calculated from the components of the elastic tensor C ijkl using Voigt-Reuss-Hill average (VRH) method (Watt et al., 1976). Experimental results are reported in the three different scattering geometries together with reference values from Sinogeikin and Bass (2000) and Spetzler (1970).

Table 2.5. Elastic properties of the MgO single crystal determined with the Brillouin system at the ETH Zurich in comparison with literature data.

Scattering angle (this work) Literature data 50° 80° 90° Sinogeikin and Bass (2000) Spetzler (1970) C11 (GPa) 295.9 (3.0) 297.9 (3.0) 298.00 (3.0) 297.9 (1.5) 297.4 C12 (GPa) 93.9 (1.0) 95.8 (1.0) 94.8 (1.0) 95.8 (1.0) 95.57 C44 GPa) 154.3 (1.0) 154.4 (1.0) 156.6 (1.0) 154.4 (2.0) 156.2 KS,VRH (GPa) 161.2 (1.0) 163.2 (1.0) 162.5 (1.0) 163.2 (1.0) 162.8 GVRH (GPa) 130.2 (1.0) 130.3 (1.0) 131.7 (1.0) 130.2 (1.0) VP(km/s) 9.67 (0.1) 9.70 (0.1) 9.72 (0.1) 9.70 (0.1) VS(km/s) 6.03 (0.06) 6.03 (0.06) 6.06 (0.06) 6.03 (0.06)

The calculated single-crystal and Voigt-Reuss-Hill aggregate elastic properties of MgO from acoustic measurements in the three different scattering geometries in our Brillouin system are identical within the uncertainties and in perfect agreement with the results of the Brillouin measurements of Sinogekin and Bass (2000) and ultrasonic data from Spetzler (1970). This demonstrates the absence of geometrical and other systematic errors in the Brillouin setup installed at ETH Zürich.

64 ii) Saline aqueous solutions at room conditions

As already mentioned, the use of a DAC during the Brillouin measurements may introduce additional error sources. For this reason, Brillouin spectra of each investigated aqueous solution have been collected at room conditions in silica glass cuvettes (90 deg scattering geometry), which have lateral dimension of 20 mm x 25 mm and a thickness of 1 mm, and in the mDAC (50 deg scattering geometry) carefully closed without pressurization (Fig. 2.2). The data collected are then compared with literature values (Fig. 2.21). All the saline aqueous fluids analyzed in this study show an excellent agreement between data collected in the mDAC and in the silica glass cuvette, within 0.5% of the acoustic velocity. This fact shows that the use of a mDAC does not increase the uncertainty in the acoustic velocity measurements by more than 0.5% of the acoustic velocity. The Brillouin data perfectly match the literature data shown for comparison in Figure 2.21. This agreement between different experimental techniques (e.g. ultrasonic measurements in a larger volume) highlights again the accuracy of the Brillouin scattering setup used in this work, the absence of geometrical errors in the scattering geometries, and that the loading procedure is correct and does not introduce additional and systematic errors, e.g. , changes in the solution concentration due to water evaporation or solute precipitation.

Figure 2.21. Acoustic velocity measurements performed at room conditions in the different saline-rich aqueous solutions analyzed in this work. Experiments are conducted in the mDAC (black dots) and in a silica glass cuvette (yellow squares). The error bars showed represent 0.5% error in the speed of sound values. Literature data (Del Grosso and Mader, 1972; Millero et al., 1977; Hershey et al., 1983; Millero et al., 1987; Abramson et al., 2001; Apelblat et al., 2009, Sanchez-Valle et al, 2012) for the solutions of interest are also plotted for comparison.

66 iii) Pure water

Additionally to the saline aqueous solutions, acoustic velocity measurements at room conditions have been performed in pure water loaded in the mDAC (Sanchez-Valle et al., 2012) and in the silica glass cuvettes (50°, 80° and 90° scattering geometries). Table 2.6 reports the Brillouin measurements in pure water together with selected literature values.

Table 2.6. Acoustic velocity measured in pure water at room conditions (20 °C and 1 atm). Literature data are also reported for comparison.

VP Error (m/s) (m/s) Glass cuvette 50° scattering geometry (this work) 1490 15 80° scattering geometry (this work) 1474 15 90° scattering geometry (this work) 1479 15 mDAC 50° scattering geometry (Sanchez -Valle et al., 201 2) 1485 15 Ultrasonic Del Grosso and Mader (1972) 1482

The measurements conducted in the glass cuvette and in the mDAC (Sanchez-Valle et al., 2012) are performed with the same Brillouin setup, and are identical within the maximum expected experimental error (less than 1% of the acoustic velocity). These values perfectly agree with the ultrasonic measurements of Del Grosso and Mader (1972). These results show again the absence of geometrical errors in the three scattering geometries of this Brillouin scattering system and that the use of a mDAC does not introduce additional uncertainties in the speed of sound measured. c) Remarks

In conclusion, the accurate system calibration experimentally demonstrates that the Brillouin scattering spectroscopy setup at the ETH Zürich allows the measurement of acoustic velocities with an error smaller than 0.5-1% of the acoustic velocity, and that the use of a mDAC does not increase the total uncertainty above 1% of the acoustic velocity. Additionally, the loading procedure of saline aqueous fluids does not introduce

67 systematic errors caused by concentration changes due to fluid evaporation and/or solute precipitation. At high temperature conditions additional errors may derive from pressure calculation using optical pressure sensors, mainly caused by the uncertainties in the temperature monitoring (precision of the thermocouple), the decreased quality of the spectra collected (e.g., Fig. 2.9), and the increased temperature induced shift of the optical signals used for pressure determination ( e.g. , ruby and quartz). Taking into account these possible error sources and all the calibrations done (for thermocouples and Brillouin setup) the maximal total expected experimental uncertainty is between 1% and 2%.

68 2.4 References

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74 Chapter 3

The numerical data treatment: from the experimental acoustic velocities VP to an equation of state

In this chapter, the method used to obtain the density of the aqueous solutions from the acoustic velocities measured up to high pressure and temperature in the diamond anvil cell using Brillouin spectroscopy is described. The inversion procedure is explained in detail, as well as the equation of state (EoS) formalism chosen for the fit of the density data. The numerical inversion procedure was implemented in Matlab® (see source code in Appendix A) and tested using available acoustic velocity data for water from a previous Impulsive stimulated scattering (ISS) in the diamond anvil cell (Abramson and Brown, 2004).

3.1 Inversion of the density from the measured acoustic velocities

VP(P,T,x)

The acoustic velocities VP P,( T, )x in the fluid are related to the density P,( T, )x through the thermodynamic relationships: T 2 1 P (1a) P 2 C T VP P

1 P (1b) T P

C 2 P T v T 2 P 2 P (1c) P T T P T P

3 where VP is the measured acoustic velocity (m/s), is the density (kg/m ), P the -1 -1 -1 coefficient of thermal expansion (K ), CP the specific heat capacity (Jkg K ) and v the specific volume (m 3/kg).

75 Following the lead of previous studies (Wiryana et al., 1998; Abramson and Brown, 2004; Asahara et al., 2010), the density of the saline aqueous solutions investigated in this work (Chapter 2, Table 2.1) are inverted from the measured sound velocities VP by the recursive integration of the equations (1a), (1b) and (1c). The procedure starts with the integration of equation (1a) at an arbitrary initial pressure, where density and heat capacity CP values are known, and where acoustic velocity measurements have been acquired at least at some of the temperatures investigated. This first iteration step is

2 performed assuming that the isothermal-adiabatic correction term (T P / CP ) is negligible. The resulting density values are used to calculate a first approximation of P and CP with equations (1b) and (1c), respectively. The P and CP values calculated are further used in a new integration of equation (1a) without neglecting the isothermal- adiabatic correction term. This process is reiterated until convergence. The integration procedure was implemented in Matlab® and first tested using acoustic velocity data for

H2O reported in previous Brilloun scattering studies by Wiryana et al. (1998) and (Abramson and Brown, 2004) and with the acoustic velocities calculated with the IAPWS-95 equation of state (Wagner and Pruss, 2002). The Matlab® code written to perform the integration is reported in the Appendix I. The critical step in the integration is the choice of the reference pressure that it is dictated by the availability of density and C P data for the aqueous solution and by the pressure-temperature space covered by the experimental VP data. Typically, the integration starts at 0.4 GPa but available data for sulfate or carbonate aqueous solutions are restricted to pressures below 0.05 GPa (Hershey et al., 1983; Sharygin and Wood, 1998; Azizov and Akhundov, 2000; Apelblat et al., 2009). The strategy adopted to determine the initial values of and CP at the reference pressure for the different aqueous solutions investigated in this study was described in detail in the corresponding chapters.

With the intention of integration the experimentally measured speed of sound data

VP are fitted and interpolated to produce a dense acoustic velocity matrix in the pressure-temperature space using the following expression:

76 ln V c c T c ln P c T ln P c ln P 2 c T ln P 2 (2) P 1 2 3 4 5 6 where T is the temperature in Kelvin, and P is the pressure in GPa. The coefficients c of i equation (2) are obtained by the least squares fit of the pressure dependence of VP along each isotherm. The dimension of the VP matrix are determined by the experimental conditions (e.g ., from 20 to 400°C and from 0.4 to 4 GPa) and the acoustic velocities were interpolated, for instance, every 20°C and 0.2 GPa. The acoustic velocity matrix is then implemented in the Matlab® code, in order to solve equation (1a) (see Appendix A).

3.2 The equation of state (EoS)

The equations of state of aqueous fluids for geologic, geochemical and petrologic applications were recently reviewed in Gottschalk (2007). Although most of the presented EoS have a theoretical physical-chemical background, the quality and the success of the EoS is difficult to evaluate and may vary with the specific requirements of applications (Gottschalk, 2007). As the development of an equation of state with a strong theoretical physical-chemical fundament was not the aim of this work, the density values determined from the acoustic velocity measurements through the recursive integration of equations (1a) (1c) were fitted using an equation of state (EoS), which has the general form:

T,P a(T) b(P) c(T,P) (3)

with:

a(T) a1 a2 T

2 3 b(P) b1 P b2 P b3 P b4 P

c(T,P) c1 T ln( P) c2 T P

77 where, T is the temperature in Kelvin, P is the pressure in Pascal. The coefficients ai ,bi and ci are obtained by the least squares fit of the experimentally derived densities (Eq. 1a-1c), and therefore, the EoS proposed is derived from the fit of the experimental results. Depending on the investigated fluid composition the components a(T), b(P) and c(T, P) may have a different form. The main advantage of a fit using our EoS lies in its simplicity. In fact, with a single EoS the experimentally derived density data (P,T ) can be simultaneously fit at all the temperatures and pressure investigated. For multiple concentration systems additional parameters can be easily add (see Chapters 5 and 7) in order to represent the concentration-dependence of the density data. Prior the fit with our EoS, attempts with modified Tait equations (Dymond and Malhotra, 1988) and modified Redlich-Kwong EoS (like in Brodholt and Wood, 1993) were done. The main difficulty was to appropriately express the EoS parameters in order to account for temperature, pressure and concentration dependence of the volumetric data at the same time, without losing the physical-chemical meaning of the EoS and without adding too many empirical parameters and/or virial terms. In fact, the modified Tait equations (Dymond and Malhotra, 1988) and modified Redlich-Kwong EoS (Brodholt and Wood, 1993) were working well for single isotherms and concentrations, but all the attempts to extend the validity ranges to other temperatures and/or concentrations failed. It has thus been decided to use simpler EoS. The polynomial fit of density data derived from Brillouin spectroscopy measurements were already performed with success by Abramson and Brown (2004).

3.3 Test to the inversion procedure

In order to test the iterative and fitting procedure explained above, density values of pure water were calculated from the acoustic velocity measurements of Abramson and Brown (2004) performed using Brillouin scattering spectroscopy in a diamond anvil cell up to 400 °C and 5.5 GPa. A dense VP matrix from 100 to 400°C and from 1 to 6 GPa, with VP values calculated every 20°C and 0.2 GPa, is obtained following the procedure

78 illustrated in Abramson and Brown (2004) and implemented in the Matlab code. The recursive iteration of equations (1a)-(1c) starts at 1 GPa, where initial values of density and isobaric heat capacity C P are taken from the IAPWS-95 EoS of pure water (Wagner and Pruss, 2002). Table 3.1 reports the density values obtained from equations (1a) (1c) in comparison with the values calculated by (Abramson and Brown, 2004). The agreement is excellent with a maximum deviation of 0.36% of the density at 300 °C and pressures above 4.6 GPa. This value is very similar to the absolute uncertainty of 0.3% for the density at high pressure given by Abramson and Brown (2004) for their EoS.

Table 3.1 Comparison between the density values calculated in this work from the experimentally measured V P data of (Abramson and Brown, 2004) through the recursive iteration of equations (1a)-(1c) and the density data obtained by Abramson and Brown (2004) here after referred to as AB.

Density (kg/m 3) 100°C 200°C 300°C 400°C P (GPa) this work AB this work AB this work AB this work AB 1 1200.6 1201.0 1152.6 1152.6 1104.2 1104.2 1056.5 1056.4 1.2 1230.1 1229.8 1183.2 1183.0 1136.4 1137.2 1092.0 1092.4 1.4 1256.7 1255.7 1210.5 1210.4 1165.2 1166.6 1123.4 1124.1 1.6 1280.8 1279.5 1235.3 1235.4 1191.3 1193.2 1151.6 1152.7 1.8 1303.0 1301.3 1258.1 1258.4 1215.3 1217.6 1177.4 1178.6 2 1323.5 1321.6 1279.2 1279.7 1237.4 1240.2 1201.2 1202.6 2.2 1342.7 1340.7 1298.9 1299.7 1258.2 1261.2 1223.3 1224.8 2.4 1317.3 1318.5 1277.6 1281.0 1244.0 1245.6 2.6 1334.8 1336.3 1296.0 1299.6 1263.6 1265.1 2.8 1351.3 1353.2 1313.5 1317.3 1282.1 1283.6 3 1367.1 1369.3 1330.1 1334.2 1299.7 1301.2 3.2 1382.1 1384.7 1346.0 1350.2 1316.5 1318.0 3.4 1396.6 1399.4 1361.3 1365.7 1332.6 1334.0 3.6 1410.4 1413.7 1375.9 1380.5 1348.0 1349.4 3.8 1423.8 1427.4 1390.0 1394.7 1362.9 1364.2 4 1403.7 1408.5 1377.2 1378.5 4.2 1416.9 1421.8 1391.0 1392.3 4.4 1429.7 1434.7 1404.5 1405.7 4.6 1442.1 1447.3 1417.5 1418.6 4.8 1454.2 1459.4 1430.1 1431.2 5 1465.9 1471.3 1442.4 1443.4 5.2 1477.4 1482.8 1454.4 1455.3 5.4 1488.6 1494.0 1466.1 1466.8 5.6 1499.5 1505.0 1477.5 1478.1 5.8 1510.2 1515.7 1488.6 1489.2 6 1520.7 1526.2 1499.5 1499.9

79 The experimentally derived density data are then fitted with an EoS with the form:

T,P a(T) b(P) c(T,P) (3b)

and,

a(T) a1 a2 T

b(P) b1 P b2 P

c(T,P) c1 T ln( P)

where, the symbols has the same meaning as in Eq. (3). The coefficients ai ,bi and ci obtained by the least squares fit of the experimentally derived densities of Table 3.1 are reported in Table 3.2. This EoS reproduces the density values of Abramson and Brown (2004) with a r 2 value of 0.999998 and a maximum misfit of 0.34% at 200 °C and 3.8 GPa. The maximal uncertainty of this fitting procedure is also in good agreement with the absolute uncertainty of 0.3% proposed by (Abramson and Brown, 2004) for their EOS at high pressure.

Table 3.2. Numerical coefficients of equation (3b)

Parameters 1.2009 .10 3 a1 -3.5851 a2 6.0516 .10 -3 b1 -2.6415 .10 -9 b2 1.4894 .10 -1 c1

Equation (3b) is then used to derive the acoustic velocity VP of pure water from 100 to 400 °C and 1 to 6 GPa. The values are reported in Table 3.3 and plotted in Figure 3.1 together with the experimentally measured speed of sound data (Abramson and Brown, 2004). The speeds of sound data calculated from equation (3b) reproduce the

80 Brillouin measurements of Abramson and Brown (2004) within a maximal deviation of 2% of the acoustic velocity, and a general agreement better than 1.5%. The differences are within the overall experimental and analytical uncertainties.

The data treatment procedure described above, and tested with literature data (Abramson and Brown, 2004), is able to reproduce the density values with a maximal associated uncertainty of 0.3-0.4% at high pressure and temperature conditions. These values match the uncertainty given in the literature source (Abramson and Brown, 2004).

Table 3.3. Acoustic velocity Vp (m/s) of pure water calculated from equation (3b).

P (GPa) 100 °C 200 °C 300 °C 400 °C 1 2761 2682 2618 2572 1.2 2935 2857 2794 2748 1.4 3088 3011 2947 2901 1.6 3224 3148 3084 3037 1.8 3348 3271 3207 3160 2 3461 3384 3319 3271 2.2 3565 3488 3423 3374 2.4 3585 3519 3468 2.6 3675 3608 3557 2.8 3760 3692 3640 3 3840 3772 3718 3.2 3916 3847 3792 3.4 3988 3918 3862 3.6 4057 3986 3929 3.8 4123 4052 3993 4 4114 4055 4.2 4174 4113 4.4 4232 4170 4.6 4288 4225 4.8 4342 4278 5 4394 4329 5.2 4445 4379 5.4 4494 4427 5.6 4542 4474 5.8 4588 4519 6 4634 4564

Figure 3.1. Speed of sound data measured in pure water. The different symbols and colors represent the experimental values acquired with Brillouin scattering spectroscopy by Abramson and Brown (2004). The dashed lines are the acoustic velocities calculated from equation (3b) and reported in Table 3.3. The symbol size is about 2% of the acoustic velocity value at high pressure.

3.4 Assessment of errors

As discussed in the presentation of the Brillouin scattering technique (Chapter 2), the accuracy of velocity determinations at high pressure and temperature conditions in the mDAC is better than 1%, which translates into a precision of 0.3% for the inverted densities (Sinogeikin and Bass, 2000). On the other hand, a systematic 1% error in the experimental pressure calculation generates 0.1% change in density at high pressure (Abramson and Brown, 2004). The numerical fit of the experimentally measured acoustic velocities with equation (2) or with the procedure used by Abramson and Brown (2004)

82 carries a maximal associate uncertainty of about 1.5%, considering possible errors deriving by the pressure calculation at high temperature. An uncertainty in the acoustic velocity interpolations of 1.5% would consequently results in about 0.4% differences in density. An additional source of uncertainty on the inverted densities is the choice of data for the density and isobaric heat capacity values at the initial pressure, where the iteration of equations (1a)-(1c) starts. As it will be explained in the chapters presenting the results for saline aqueous fluids (Chapters 4 to 7), the estimation of the thermodynamic parameters and C P at the initial conditions often relies on significant extrapolations and approximations, and therefore, the contribution of this approach to the final density has to be discussed in more detail. According to Abramson and Brown (2004) for the data on pure water, a shift in the initial density of 0.1% (e.g., uncertainty of the IAPWS-95 EoS, Wagner and Pruss, 2002) changes the calculated densities by the same amount, while a shift of 10% in the initial

CP values will generate a shift in the densities of about 0.2%. Therefore, summarizing the possible error sources listed above, the numerical data treatment for the inversion of the density values of pure water from the acoustic velocities measured in a DAC with Brillouin scattering spectroscopy (Abramson and Brown, 2004) have a total uncertainty between 0.3%-0.5%, as a result from the 1.5% maximal deviation in VP and the 0.1% error in the initial values taken from the IAPWS-95 EoS (Wagner and Pruss, 2002). The fit of the calculated density data with our EoS (Eq. 3b) reproduces the density values of Abramson and Brown (2004) within a maximal misfit of 0.34% of the density, which is again in excellent agreement with the expected largest deviation of 0.3-0.5%. Additionally, acoustic velocity values calculated from our EoS (Eq. 3b) proposed reproduce within a maximal difference of 1.5-2% the experimentally measured VP values (Fig. 3.1). Considering the error propagation (see below), the VP values confirm again the agreement between the experimental approach and the numerical data treatment proposed in this work (see below). As it was pointed out in the introduction, PVTx data for saline aqueous fluids other than H 2O-NaCl mixtures (Driesner, 2007) are not available at pressures of 0.4 0.5 GPa,

83 which represents the lowest pressure limit for the EoS of the saline aqueous fluids investigated in this work. The strategies adopted to obtain initial density and heat capacity values for the different H 2O-salt mixtures studied here are explained in the respective chapters. In any case, in order to demonstrate that the density data calculated from the EoS have the same maximal associated uncertainty of 0.3-0.5% as for pure water, where the initial values of density are well constrained, acoustic velocity data are derived from the EoS proposed and compared with the experimentally measured VP . When the differences in the acoustic velocities is less than 1.5-2%, like for pure water (Fig. 3.1), the uncertainty in density is believed to be between 0.3% and 0.5%.

In summary, the Brillouin scattering measurements in the mDAC, the fit and interpolation of the obtained acoustic velocities VP and the iteration procedure (equations 1a-1c) generate density values with an associated maximal deviation between 0.3 and 0.5% at high pressure and temperature conditions (500 °C and 4 GPa), where the pressure calibration has the largest uncertainty. The fit of the experimentally derived density data with our EoS (Eq. 3) does not increase this maximal uncertainty, and the derived VP data have a maximal misfit of about 1.5-2% of the value.

The numerical data treatment proposed in this work was tested with VP data from Brillouin scattering measurements in a DAC loaded with pure water (Abramson and Brown, 2004) because Brillouin scattering studies on saline aqueous fluids at high pressure and temperature conditions are not available yet. Other tests performed with acoustic velocity data of water taken from different data sources (Wiryana et al., 1998; Wagner and Pruss, 2002) confirm the results described above. Additionally, the PVTdata of pure water proposed by Sanchez-Valle et al. (Appendix B) obtained from Brillouin scattering measurements in a mDAC up to 400 °C and 7 GPa are derived with the same procedure explained here (see Appendix B). The density values of Sanchez-Valle et al. (2012) agree within a maximum deviation of 0.19% with the data of Abramson and Brown (2004) at high pressure and temperature. This fact shows again the reproducibility of the density data obtained with the data treatment explained above.

84 3.5 Derivation of the PVTx properties of saline aqueous fluids

The knowledge of the density over a wide range of pressure and temperature conditions (Eq. 3) allows the calculation of all other thermodynamic properties. Equation (3) is used to derive the PVTx properties of the saline aqueous fluids investigated in this work using the following relationships: -1 Coefficient of thermal expansion P (K ) 1 P (4) T P

. -1. -1 Isobaric heat capacity CP (J kg K )

2 CP v T 2 (5) P T T P where v is the specific volume (m 3/kg). -1 Adiabatic compressibility S (Pa ) and adiabatic bulk modulus K S (Pa)

1 (6) K 1 (7) s 2 S VP s -1 Isothermal compressibility T (Pa ) and adiabatic bulk modulus KT (Pa)

2 1 T (8) K 1 (9) T 2 C T VP P T Calculations of thermodynamic properties, such as thermal expansion coefficients and heat capacity, have a larger associated uncertainty, because they are related to temperature derivatives of the density (Eq. 4 and 5). Therefore, a small difference within different EoS expressed in terms of density will result in a larger uncertainty in P and

CP values (Wagner and Pruss, 2002; Abramson and Brown, 2004). For the compressibility (adiabatic S or isothermal T ) the uncertainties may be even larger, because they include derived V,P P and CP values. According to classical error propagation calculations (Caporaloni et al., 1987), and assuming a maximum misfit for and derived VP data of 0.5% and 2%, respectively,

P and CP values have maximal associated uncertainties of 1-1.5%. For adiabatic

85 properties (compressibility and bulk modulus) the uncertainty is around 4.5-5% of the value, while for isothermal properties (compressibility and bulk modulus) the maximal possible misfit increases to 8% of the value. For derived VP data the calculated uncertainty is about 1.5-2%.

3.6 References

Abramson E. H. and Brown J. M. (2004) Equation of state of water based on speeds of sound measured in the diamond-anvil cell. Geochimica Et Cosmochimica Acta 68 (8), 1827-1835. Apelblat A., Manzurola E., and Orekhova Z. (2009) Thermodynamic Properties of Aqueous Electrolyte Solutions. Volumetric and Compressibility Studies in 0.1 mol .kg -1, 0.5 mol .kg -1, and 1.0 mol .kg -1 Sodium Carbonate and Sodium Sulfate Solutions at Temperatures from 278.15 K to 323.15 K. J. Chem. Eng. Data 54 (9), 2550-2561. Asahara Y., Murakami M., Ohishi Y., Hirao N., and Hirose K. (2010) Sound velocity measurement in liquid water up to 25 GPa and 900 K: Implications for densities of water at lower mantle conditions. Earth Planet. Sci. Lett. 289 (3-4), 479-485.

Azizov N. D. and Akhundov T. S. (2000) The bulk properties of the Na 2SO 4-H2O system in a wide range of the parameters of state. High Temp. 38 (2), 203-209. Brodholt J. and Wood B. (1993) Simulations of the Structure and Thermodynamic Properties of Water at High-Pressures and Temperatures. J. Geophys. Res.-Solid Earth 98 (B1), 519-536. Caporaloni M., Caporaloni S., and Ambrosini R. (1987) La misura e la valutazione della sua incertezza nella fisica sperimentale . Zanichelli.

Driesner T. (2007) The system H 2O-NaCl. Part II: Correlations for molar volume, enthalpy, and isobaric heat capacity from 0 to 1000 °C, 1 to 5000 bar, and 0 to 1 X-NaCl. Geochimica Et Cosmochimica Acta 71 (20), 4902-4919. Dymond J. H. and Malhotra R. (1988) The Tait Equation - 100 Years On. Int. J. Thermophys. 9(6), 941-951.

86 Gottschalk M. (2007) Equations of state for complex fluids. In Fluid-Fluid Interactions , Vol. 65, pp. 49-97. MINERALOGICAL SOC AMER. Hershey J. P., Sotolongo S., and Millero F. J. (1983) Densities and Compressibilities of Aqueous Sodium-Carbonate and Bicarbonate from 0 °C to 45 °C. J. Solut. Chem. 12 (4), 233-254. Sharygin A. V. and Wood R. H. (1998) Densities of aqueous solutions of sodium carbonate and sodium bicarbonate at temperatures from (298 to 623) K and pressures to 28 MPa. Journal of Chemical Thermodynamics 30 (12), 1555-1570. Sinogeikin S. V. and Bass J. D. (2000) Single-crystal elasticity of pyrope and MgO to 20 GPa by Brillouin scattering in the diamond cell. Physics of the Earth and Planetary Interiors 120 (1-2), 43-62. Wagner W. and Pruss A. (2002) The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 31 (2), 387-535. Wiryana S., Slutsky L. J., and Brown J. M. (1998) The equation of state of water to 200 °C and 3.5 GPa: model potentials and the experimental pressure scale. Earth Planet. Sci. Lett. 163 (1-4), 123-130.

88 Chapter 4

Thermodynamic properties of aqueous sodium sulfate solutions to 773 K and 3 GPa derived from acoustic velocity measurements in the diamond anvil cell

Davide Mantegazzi *, Carmen Sanchez-Valle *, Eric Reusser and Thomas Driesner Institute for Geochemistry and Petrology, ETH Zurich, Clausiusstrasse 25, 8092 Zurich *corresponding authors: [email protected]; [email protected]

Accepted for publication in J. Chem. Phys.

Abstract

The thermodynamic properties of a 1 molal (1m) Na 2SO 4 solution have been determined to 773 K and 3 GPa from acoustic velocity measurements in externally heated diamond anvil cell using Brillouin spectroscopy. The measured acoustic velocities were inverted to obtain the density of the aqueous electrolyte solution with an accuracy of 0.3- 0.5%, and an equation of state (EoS) valid in the 293 - 773 K and 0.4 - 3 GPa range is proposed. The new EoS reproduces the experimental acoustic velocity data with a maximal deviation of 1.5% and allows deriving all thermodynamic properties of the aqueous solution, including isobaric heat capacity ( CP ), thermal expansion ( P ) and compressibility ( ) with an accuracy better than 3-8%. The addition of dissolved sulfate species decreases the compressibility of water, consistent with the structure-maker 2- character of SO 4 ions in solution that enhance the hydrogen-bond network of the solvent.

4.1. Introduction

The thermodynamic properties of aqueous electrolyte solutions at elevated pressure and temperature conditions are of fundamental importance for a number of natural and

89 industrial processes (Newman et al., 1980; Abdulagatov et al., 2007). interior, aqueous fluids containing large amounts of dissolved electrolytic species (e.g ., NaCl, carbonates and sulfates) mediate processes that take place at great depth, including magma production, element transport in subduction zones, metamorphic mineral reactions and ore deposit formation (Peacock, 1990; Belonoshko and Saxena, 1991; Manning, 2004; Bodnar, 2005; Frezzotti et al., 2011). Therefore, accurate determination of the volumetric properties of these fluids over a broad range of pressure-temperature conditions is necessary for a better understanding of these deep processes. Water has received the most attention in terms of development of equations of state (EoS) to extreme conditions, using both experimental and theoretical approaches (Brodholt and Wood, 1993; Wagner and Pruss, 2002; Abramson and Brown, 2004). However, equations of state for aqueous electrolytes are much scarcer and often only valid in a limited range of pressure (< 0.5 GPa) that does not allow reliable extrapolation to the pressure and temperature conditions of interest in natural processes. Experimental data on the volumetric and calorimetric properties of aqueous electrolyte solutions were determined using a variety of techniques, including vibrating-tube densimeter (Chen et al., 1977; Losurdo et al., 1982; Simonson et al., 1994; Obsil et al., 1997; Apelblat et al., 2009), constant volume piezometer (Azizov and Akhundov, 2000), dilatometer (Rogers et al., 1982; Phutela and Pitzer, 1986), ultrasonic velocimeter (Millero et al., 1987; Apelblat et al., 2009) and flow calorimeter (Rogers and Pitzer, 1981; Pabalan and Pitzer, 1988), but are restricted to pressures below 0.1 GPa. Additional data provided from the study of synthetic fluid inclusions (FI) (Knight and Bodnar, 1989; Bodnar, 1994; Brodholt and Wood, 1994; Schmidt and Bodnar, 2000) does not extend the experimental thermodynamic data of aqueous electrolyte solutions to pressures above 0.5 GPa. As a result, available EoS for saline aqueous fluids, which are usually obtained from the fit of low pressure experimental data (Pitzer and Li, 1983; Pabalan and Pitzer, 1988; Archer, 1992; Anderko and Pitzer, 1993), molecular dynamic (MD) simulations (Madura et al., 1988; Belonoshko and Saxena, 1991; Brodholt and Wood, 1993; Duan et al., 1996; Brodholt, 1998 ) or a combination of both (Anderko and Pitzer, 1992), are valid only at pressure below 0.5 GPa. MD simulations have been extensively used to provide constraints on the PVTx properties of fluids at conditions where experimental data are

90 unavailable or where empirical extrapolations have large associated uncertainties (Kalinichev, 1991). A reliable extrapolation of fluid properties and the validation of theoretical studies thus requires additional experimental constraints on the density of saline solutions at high pressure and temperature conditions.

Brillouin light scattering spectroscopy coupled with a diamond anvil cell (DAC) represents a powerful experimental approach to determine the acoustic velocities of aqueous fluids to high pressure and temperature conditions where other techniques are limited. Measured acoustic velocities in fluids can be readily transformed into PVTx properties that can be used to determine the EoS from which all thermodynamic properties can be derived. This approach has been successfully used to obtain the PVT properties of simple molecular fluid systems to pressures in excess of 25 GPa at 873 K, including water (Wiryana et al., 1998; Abramson and Brown, 2004; Li et al., 2005; Decremps et al., 2006; Asahara et al., 2010; Sanchez-Valle et al., in prep.), fluid oxygen

(Abramson et al., 1999), argon (Jia et al., 2008), CH 4 (Li et al., 2010), H 2 (Matsuishi et al., 2003) and CO 2 (Giordano et al., 2006), and most recently, H2O-CO 2 mixtures with 5 mol% CO 2 (Qin et al., 2010). Investigations in aqueous electrolyte systems at high P-T have so far remained limited to density determinations in 0.148 molal and a 0.5 molal aqueous Na 2SO 4 solution up to 473 K and 3.4 GPa by Abramson et al. (2001) using Impulsive stimulated scattering (ISS). In this paper, we perform Brillouin scattering measurements in externally heated diamond anvil cells to determine the equation of state and thermodynamic properties of a 1 molal (1 m) aqueous Na 2SO 4 solution up to 773 K and 3 GPa. The choice of this electrolyte system is motivated by their relevance in deep geological aqueous fluids (Roedder, 1984; Philippot and Selverstone, 1991; Nadeau et al., 1993; Audetat et al., 2004; Frezzotti et al., 2011) and the availability of preliminary data on the system (Abramson et al., 2001) that provide the foundation to discuss the effect of pressure-temperature and concentration on the thermodynamic properties of water. The results are then used to derive a qualitative interpretation of the structural effect behavior of sulfate ions on the hydrogen bond network of the solvent.

91 4.2. Experimental methods

4.2.1. Diamond anvil cell techniques All measurements were conducted in a membrane-type diamond anvil cell (mDAC) with large optical opening and mounted with low fluorescence type Ia diamonds of 500 m culet diameter (Chervin et al., 1995). A ring-shaped resistive heater surrounding the body of the cell and an internal Pt resistive heater placed around the lower diamond were used simultaneously to generate high temperature conditions up to 773 K. The temperature was monitored to ±2 K with a K-type thermocouple attached to one of the diamonds close to the sample chamber. An additional thermocouple is included in the external heater and was calibrated against the internal thermocouple before the experiments (Chervin et al., 2005). Aqueous solutions containing 0.5 and 1 mol/kg H2O

(m) of Na 2SO 4 were prepared from reagent grade Na 2SO 4 powder (99.99 %, Sigma Aldrich ®) and de-ionized Milli-Q water, sealed in tight containers and refrigerated until used. The aqueous electrolyte solutions were loaded into pre-indented stainless steel or rhenium gaskets of about 80-100 m thickness and drilled with 250 or 300 m wide holes in the center of the indentation, together with a chip of the materials used as pressure sensors. After loading, the cell was immediately closed and pressurized to avoid fluid evaporation and/or solute precipitation that would modify the sulfate concentration. Four different pressure sensors, ruby, quartz, cubic boron nitride (cBN) and the 2- vibrational properties of the SO 4 ions in the aqueous solution, were used in the experiments depending on the investigated temperatures (Table 4.1 and 4.2). A set of measurements up to 573 K were conducted using the calibrated shift of the R1 fluorescence line (Mao et al., 1978) after temperature correction (Ragan et al., 1992; Datchi et al., 2007). At higher temperatures, the use of ruby as a pressure sensor becomes problematic due to 1) the broadening and overlapping of the R1 and R2 fluorescence lines above 553 K, and 2) the temperature-induced shift of the R1 fluorescence line, that decreases the accuracy in the pressure determination (Datchi et al., 1997; Sanchez-Valle et al., 2002; Datchi et al., 2007). In a second set of experiments conducted from 293 to

673 K, pressure was obtained from the Raman shift of the A1 mode of quartz using the pressure scale of Schmidt and Ziemann (2000). The larger pressure-induced frequency

92 -1 shift [( / P) T = 9 cm /GPa] compared to the R1 fluorescence line of ruby makes this pressure sensor appropriate to monitor small pressure changes and provides greater precision in pressure at high temperature because the vibrational band remains well- resolved in the temperature range of interest (Dean et al., 1982; Schmidt and Ziemann, 2000). To exclude any possible sample contamination caused by the dissolution of the quartz chips at high temperature (Newton and Manning, 2000; Shmulovich et al., 2006), additional experiments at 473 K, 573 K and 673 K were performed using chips of cubic boron nitride (cBN) as pressure sensors because of its higher chemical stability at high pressure-temperature conditions (Table 4.1). Pressure was calculated from the frequency shift of the Raman-active transverse optical TO mode using the calibration of (Datchi et al., 2007). Acoustic velocity measurements at 773 K were performed without secondary pressure sensors ( i.e ., ruby, cBN or quartz) to avoid sample contamination. Pressure was thus calculated from the pressure-induced frequency shift of the Raman-active symmetric 2- stretching mode of the unassociated sulfate ions (SO4 ) in the fluid (Schmidt, 2009). Experiments were repeated at 293 and 673 K using only the Raman signal of the solution for pressure calculation and excellent agreement was found with the acoustic data collected using ruby, cBN and quartz as pressure sensor (Table 4.1 and Table 4.2). All Raman and fluorescence spectra were fitted to Voigt functions using the software Peakfit version 4.12 ( ©Seasolve Incorporation).

The estimated uncertainty in pressure monitoring with ruby spheres is better than 0.01-0.02 GPa at T < 473 K but decreases to 0.04 GPa above this temperature, whereas the quartz standard provides a reproducibility of 0.01 GPa over the investigated temperature range. The sensitivity to pressure variations of the TO Raman band is smaller than that of the ruby or of the quartz sensors and therefore, the calculated pressures have a larger associated uncertainty of 0.03 GPa at the conditions of the experiments (Datchi et al., 2007) (Table 4.2). In general, pressure determination with ruby and quartz sensors agrees within 0.02 GPa, while the agreement between ruby (or quartz) and cBN or the Raman signal of the solution is better than 0.05-0.06 GPa as shown by control experiments performed with multiple pressure sensors loaded in the experimental

93 chamber. Above 573 K, the pressures calculated with the cBN and from the Raman stretching mode of sulfate ions agree within a maximal deviation of 0.05 GPa.

4.2.2. Brillouin scattering spectroscopy

Brillouin scattering measurements were conducted at ETH Zurich using a Nd:YVO 4

0 = 532.1 nm) as light source and a six-pass tandem Fabry-Perot interferometer of Sandercock type (Sandercock, 1982) equipped with a photomultiplier (PMT) detector to analyze the scattered light. The system is coupled to a Raman system installed on the same optical bench that enables collection of Raman and fluorescence spectra from the pressure sensors without changing the positioning of the mDAC. Additional details of the experimental setup are provided in Sanchez-Valle et al. (2010). All measurements were conducted in symmetric scattering geometry that allows direct determination of the compressional acoustic velocities in the fluid ( VP ) using the relationship (Whitfield et al., 1976):

V 0 P (1) P * 2 sin ( ) 2 * where 0 is the laser wavelength, P the Brillouin shift and the external scattering angle (i.e ., angle between the incident and scattered beam outside the sample). All measurements in the mDAC were conducted using a 50 deg scattering angle, whereas reference spectra for the 1m and a 0.5 m aqueous Na 2SO 4 solutions were acquired at room conditions in 90 deg geometry in glass cuvettes with lateral dimensions of 20 mm x 25 mm and thickness of 1 mm. Brillouin measurements are very sensitive to the scattering geometry and an error in the external scattering angle * will result in systematic errors in the calculated acoustic velocities (Eq. (1)). The scattering geometry was thus calibrated prior to the experiments using a MgO single-crystal standard, for which velocities were measured over 180 deg in the (100) plane in both 50 and 90 deg scattering geometries. The acoustic velocities and elastic properties of MgO determined using the present setup were in excellent agreement with those reported in previous ultrasonic and Brillouin studies (Spetzler, 1970; Yoneda, 1990; Sinogeikin and Bass, 1999; Sinogeikin and Bass, 2000), indicating the absence of geometrical errors in the measurements. In order to avoid

94 vignetting effects that can be introduced by the mDAC, we used a diamond cell with large conical aperture (98 deg) and the gasket holes had a thickness to diameter ratio of about 1:3 (Sinogeikin and Bass, 2000). Additionally, all measurements were conducted using a metallic mask with a narrow vertical slit in front of the collecting lens to collect only the light scattered within the selected scattering angle. The precision in the reported acoustic velocities is better than 0.5 % at room conditions and 0.8-1.0 % at high pressure and temperature (Sanchez-Valle et al., in prep.), whereas the overall accuracy is estimated better than 1.5%

Acoustic velocity measurements were conducted in the 1 molal aqueous Na 2SO 4 solutions along isothermal runs at 293 K, 373 K, 473 K, 573 K, 673 K and 773 K both in compression and decompression experiments. Measurements on the 0.5 molal aqueous

Na 2SO 4 solution were performed at 293 K up to 1.32 GPa to assess the quality of our high pressure measurements by comparison with available literature data (Abramson et al., 2001). More than two spectra were collected at each temperature-pressure point, in different positions of the compression chamber, to verify the homogeneity of the fluid. Typical collection times per spectrum are between 5 to 10 minutes with the output power of the laser kept below 50-80 mW. The pressure and temperature conditions of the Brillouin measurements are summarized in Table 4.1.

Table 4.1. Experimental conditions and pressure sensors used in the experiments.

T P range Pressure sensors (K) (GPa) 293 0 1.37 ruby, quartz, sulfate 1 molal aqueousNa 2SO 4 solution 373 0.48 2.02 ruby, quartz 473 1.03 3.01 ruby, quartz, cBN 573 1.08 3.02 ruby, quartz, cB N 673 0.97 2.00 quartz, cBN, sulfate 773 0.37 1.3 sulfate

0.5 molal aqueousNa 2SO 4 solution 293 0 1.32 ruby

95 Figure. 4.1. Typical Brillouin spectra for a 1m

Na 2SO 4 solution collected in the mDAC at various pressure and temperature conditions.

The compressional VP and the backscattered

signal nV P, where n is the refractive index of the fluid, are labeled. The coefficient n is. The Rayleigh elastic scattering peaks have been removed for clarity.

4.3. Results and Discussion

4.3.1. Acoustic velocities in Na 2SO 4 aqueous solutions

Figure 4.1 displays representative Brillouin spectra collected from the 1 m Na 2SO 4 solution at various pressures and temperatures inside the mDAC. All collected spectra were of excellent quality with high signal-to-noise ratio. They display the compressional wave velocities VP as well as the backscattering velocity nV P, where n is the refractive index of the aqueous solution. The nV P signal arises from light partially reflected from the output diamond anvil and that serves as a secondary excitation light. Figure 4.1 shows the pressure- and temperature-induced shift of the acoustic velocities.

The acoustic velocities VP collected in the samples at room conditions inside and outside the mDAC are reported in Figure 4.2 together with literature data for Na 2SO 4 aqueous solutions at various concentrations. The acoustic velocities measured in the 0.5 and 1 molal aqueous Na 2SO 4 solutions inside the mDAC at room conditions and in the silica glass cuvette are identical within mutual experimental errors (0.6%) and have an average value of 1565 ± 5 m/s and 1635 ± 9 m/s, respectively. The agreement in the results shows that the use of the mDAC does not introduce geometrical or systematic

96 errors, and that fluid evaporation and solute precipitation during the loading procedures is negligible. In addition, measured velocities are in excellent agreement with the data of Millero et al. (1987) and Apelblat et al. (2009), both obtained in large volume samples using ultrasonic methods, and with data reported for the 0.5 m Na 2SO 4 solution at room conditions in a DAC by Abramson et al. (2001) using Impulsive Stimulated Scattering

(ISS). Acoustic velocities in the 1m Na 2SO 4 solution are 70 m/s faster than in the 0.5 m

Na 2SO 4 solution. The acoustic velocities of water at room conditions determined by Brillouin spectroscopy using a similar experimental setup (Sanchez-Valle et al., in prep.) and by ultrasonic methods (Del Grosso and Mader, 1972) are also reported as reference in

Figure 4.2. The VP measured in the 1m Na 2SO 4 solution at room conditions are 152 m/s faster than in pure water.

Figure 4.2. Acoustic velocities in

Na 2SO 4 aqueous solutions at room

conditions as a function of Na 2SO 4 concentration. The error bars correspond to 0.5% of the value. The solid line is a fit to ultrasonic data from Millero et al. (1987).

The acoustic velocity data for the sodium sulfate solutions up to 3 GPa and 500 °C are tabulated in Table 4.2 and displayed in Figure 4.3. The acoustic velocities measured in the 0.5 m H2O-Na 2SO 4 solution up to 1.2 GPa at 293 K compares favorably with data from Abramson et al. (2001) (Fig. 4.3a) and are intermediate between those for the 1m

Na 2SO 4 solution and H 2O (Wagner and Pruss, 2002; Sanchez-Valle et al., in prep.) in agreement with the trend observed at room conditions. Data collected in the 1m Na 2SO 4 solution as a function of pressure along isotherms from 293 to 773 K are reported in

97 Figure 4.3b. Excellent agreement is found between velocities obtained in compression and decompression experiments and in repeated measurements using different pressure sensors in the range of overlapping (Fig. 4.3b). The latest observation confirms the absence of sample contamination due to the dissolution of the pressure sensors (e.g., quartz) and that the employed pressure sensors provide the level of accuracy necessary for this study.

Figure 4.3. a) Acoustic velocities measured along the 293 K isotherm in aqueous Na 2SO 4 solutions and water as a function of the pressure. The black dashed line shows acoustic velocities calculated from the IAPWS-95 EoS (Wagner and Pruss, 2002) for water, and from the EOS proposed in this work (Eq. 4) for the 1m Na 2SO 4 solution. b) Acoustic velocities measured in 1 m

Na 2SO 4 solution as a function of pressure along isotherms from 293 to 773 K. Experimental errors (0.5 1%) are about the symbol size. Along each isotherm the different symbols correspond to measurements conducted using different pressure sensors (i.e., ruby, quartz, cBN and the sulfate stretching mode). The black dashed lines are acoustic velocities calculated from the EoS proposed in this work (Eq. (4)).

Overall, the acoustic velocities increase monotonously with pressure along the different isotherms as observed for similar measurements conducted in H 2O (Abramson and Brown, 2004; Decremps et al., 2006; Sanchez-Valle et al.). The only exception is

98 observed along the 293 K isotherm (Fig. 4.3a), where the measured acoustic velocities show a subtle deviation in the pressure response in the 0.2-0.4 GPa interval (Fig. 4.3b). A detailed study of the pressure dependence of the velocities was performed at 293 K up to

0.8 GPa using a quartz chips as pressure sensor to characterize the V P discontinuity. The higher sensitivity to pressure of this sensor allows for very small pressure increments (Schmidt and Ziemann, 2000), providing a very dense dataset that show clear evidence for large scattering in the data in the 0.2-0.4 GPa range and for changes in the slope of the pressure dependence of the acoustic velocities (Fig. 4.4). These anomalies may be related to the liquid-liquid transition in the solvent from low density (LDW) to high density water (HDW) identified by previous Brillouin (Li et al., 2005) and Raman (Kawamoto et al., 2004) studies and molecular dynamic simulations (Saitta and Datchi, 2003) in water, and also reported in similar water-salt systems (Cavaille et al., 1996; Mirwald, 2005; Schmidt, 2009). This phase transformation involves the reorganization of the hydrogen bonding network of water and the collapse of the second coordination shell onto the first one due to broken H bonds, as shown by neutron diffractions studies (Soper and Ricci, 2000). This implies a compaction of the second hydration shell and a reduction of the compressibility compared to LDW 35 , consistent with the increase in the acoustic velocities observed here (Fig. 4.4).

Figure 4.4. Acoustic velocity data for the

1m Na 2SO 4 solution along the 293 K isotherm up to 0.8 GPa. The black solid and dashed lines highlight the different slopes defined by the data point before and after the transition interval from low density (LDW) and high density water (HDW).

99 Table 4.2 Acoustic velocities measured in 1m Na 2SO 4 solution solution to 773 K and 3 GPa. The estimated experimental uncertainties in V P range from 1-1.5%. Errors in pressure range from 0.01 GPa to 0.05 GPa, depending on the pressure sensor and temperature.

293 K 373 K 473 K 573 K 673 K 773 K P sensor P VP P VP P VP P VP P VP P VP (GPa) (m/s) (GPa) (m/s) (GPa) (m/s) (GPa) (m/s) (GPa) (m/s) (GPa) (m/s) Ruby 0.00 1644 1 0.61 2437 1.30 2830 1.09 2564 0.00 1625 0.63 2457 1.52 3000 1.19 2646 0.38 2174 0.67 2470 1.75 3120 1.38 2812 0.43 2259 0.72 2530 2.08 3313 1.63 2995 0.50 2341 0.79 2586 2.18 3322 1.79 3097 0.55 2388 0.84 2640 2.36 3411 2.18 3296 0.59 2429 0.88 2694 2.86 3627 2.04 3207 0.61 2458 0.90 2718 3.01 3683 1.85 3118 0.66 2475 0.99 2782 2.69 3536 0.70 2504 1.06 2804 2.51 3464 0.74 2550 1.26 2936 0.85 2668 1.39 3025 0.99 2751 1.75 3215 1.10 2819 1.86 3244 1.21 2890 2.02 3335 1.34 2959 1.71 3149 1.37 3000 1.55 3097 1.28 2943 1.20 2887 1.02 2777 0.93 2700 0.80 2604 0.59 2427 0.47 2314 0.39 2206 0.33 2092 0.14 1870 Quartz 0.05 1703 0.48 2279 1.17 2760 1.81 3112 1.30 2663 0.09 1749 0.50 2304 1.28 2847 2.39 3384 1.47 2776 0.13 1831 0.55 2348 1.42 2941 2.45 3426 1.78 2963 0.17 1885 0.68 2476 1.64 3082 0.19 1894 0.71 2505 0.22 1945 0.23 1957 0.29 2023 0.32 2076 0.44 2273 0.47 2305 0.39 2195 0.28 2008 0.01 1657 cBN 1.03 2619 2.74 3528 1.76 2932 1.08 2647 3.02 3609 1.87 3022 1.32 2811 1.88 3167 2.00 3088 1.80 3148 1.55 2910 Sulfate 0.01 1657 0.97 2424 0.37 1651 0.10 1758 0.41 1615 0.37 2174 1.30 2610 Notes: Characters in italics are acoustic velocities measured on decompression experiments. 1Velocity measured in a glass cuvette using 90 deg scattering geometry at room conditions.

100 4.3.2. Data inversion and equation of state

The acoustic velocities VP are related to density through the thermodynamic relationships: T 2 1 P (2a) P 2 C T VP P

1 P (2b) T P

C 2 P T v T 2 P (2c) P 2 P T T T P P

3 where VP is the measured acoustic velocity , is the density in kg/m , P the -1 . -1. -1 coefficient of thermal expansion in K , CP the specific heat capacity in J kg K and v 3 the specific volume in m /kg. The density of the 1 m Na 2SO 4 solution was calculated from the measured sound velocities by the recursive integration of the Eqs. (2a), (2b) and (2c) following previous studies (Wiryana et al., 1998; Abramson and Brown, 2004; Giordano et al., 2006; Sanchez-Valle et al., in prep.). Briefly, the procedure starts with the integration of Eq. (2a) at an arbitrary reference pressure with known density assuming

2 that the isothermal-adiabatic correction term (T P / CP ) is negligible. The resulting density is used to calculate a first approximation for P and CP (Eq. 2b and 2c) that are further used in the next integration of Eq. (2a). The process is then reiterated until convergence. Prior to the integration, the experimental acoustic velocities determined in this study were interpolated to produce a mesh of acoustic velocity values in the pressure- temperature space using the analytical expression:

2 2 ln VP c1 c2 T c3 ln P c4 T ln P c5 ln P c6 T ln P (3) where T is in Kelvin and P in GPa. The most representative fit of the experimental data is obtained by fitting the 293 K isotherm separately from the data collected along the higher

101 temperature isotherms. Using this approach, the acoustic velocities along the 293 K isotherms are fitted with a R2 whereas the higher temperature data have a R2 > between 373 K and 673

K 773 K . The best-fit ci coefficients for Eq. (3) are reported in Table 4.3.

Table 4.3 Coefficients of Eq. (3) obtained from least-square fitting of the experimental acoustic velocity data.

Coefficients 293 K isotherm 373 773 K isotherms

c1 7.9071431 8.0843069 -5 -4 c2 5.0338449x10 -4.3419544 x 10 -1 -1 c3 2.0562135 x 10 1.5289137 x 10 -4 -4 c4 1.5773615 x 10 2.9919927 x 10 . -1 -3 c5 1.0691773 x 10 -8.9858877 x 10 . -4 -5 c6 -3.0924702 x 10 3.0679284 x 10

Initial values of and CP at 0.4 GPa The integration of the Eqs. (2a)-(2c) starts at a reference pressure at which the and CP are known. We chose 0.4 GPa as reference pressure to avoid the V P discontinuity at 293 K and because it represents the lowest common pressure for which experimental velocity data is available along the different isotherms (Table 4.1). The choice of initial values of density and heat capacity is a critical step in the inversion procedure, but often the available thermodynamic data for the aqueous electrolyte solutions of interest is restricted to pressures well below the reference pressure. In the case of the 1m Na 2SO 4 solution investigated here, the available thermodynamic data are limited to 573 K and 0.04 GPa (Losurdo et al., 1982; Obsil et al., 1997; Azizov and Akhundov, 2000; Apelblat et al., 2009). Therefore, the strategy adopted to determine the initial values for the density and CP at 0.4 GPa and various temperatures from 293 to 773 K consists in finding an

NaCl aqueous solution that has a density similar to the 1m Na 2SO 4 solution

102 in the low pressure region and for which the thermodynamic properties are accurately known up to 0.5 GPa and 1273 K (Driesner, 2007).

In NaCl aqueous solution, the experimental density data of Azizov and Akhundov (2000), was interpolated to obtain the density of 1m

Na 2SO 4 solution up to 573 K and 0.04 GPa and the values compared with the density of the NaCl aqueous solution (Driesner, 2007). At low pressure, a H2O NaCl solution containing 15 wt.% NaCl, corresponding to a molality of 3.02 m, reproduces well

(difference <1%) the density data of a 1 m Na 2SO 4 solution (Azizov and Akhundov, 2000) along the available isotherms at 373, 473 and 573 K. The ratio (1m Na 2SO 4) / (15 wt%

NaCl) was then calculated and fitted with a logarithmic function and extrapolated to 0.4 GPa, in order to determine the correlation between the densities of NaCl- and sulfate- bearing solutions (see Fig. S1a in the Appendix). Along the three isotherms, this ratio approaches a value between 1.001 and 1.007, indicating that a significant deviation between the densities of a 1m Na 2SO 4 solution and a 3.02 m NaCl solution at high pressure should not be expected. The density ratio calculated at 0.4 GPa was then used to obtain an initial guess for the density of 1m Na 2SO 4 solution at this pressure condition. The integration procedure (Eqs. 2a-2c) was repeated varying the density ratio, in order to identify the optimal initial density values for the 1m Na 2SO 4 solution. The best approximation for the density of the solution of interest is found when the acoustic velocities derived from the densities obtained through integration of Eqs. (2a)-(2c) match the experimentally measured speeds of sound data (Eq. 3) within the maximal experimental uncertainty (<1.5%). With ratios of 1.00 and 1.005 for the 293 K and the 373 K isotherm, respectively, and 1.012 for the 473, 573, 673 and 773 K isotherms, the 2 coefficient of correlation R for the sound velocities of the 1m Na 2SO 4 solution has the largest value close to 1, indicating the best possible fit (Fig. S1b in the Appendix).

The initial values of CP at 0.4 GPa were taken from Driesner (2007) assuming a

3.02 m m Na 2SO 4 solution along each isotherm. Note that an error of 8% in the initial values of CP would cause a difference smaller than 0.2% in the calculated density, as shown by inversions performed with variable input values of C p and by previous studies (Abramson and Brown, 2004). Table 4.4 summarizes the initial values of the density and heat capacity at 0.4 GPa and various

103 temperatures up to 773 K used in the integration of the acoustic data, and obtained with the procedure explained above.

Table 4.4 Initial values of density and heat capacity C P at the reference pressure of 0.4 GPa depending on temperature. The density values are determined with the iterative procedure explained in the text.

T Density (kg/m 3) -1 -1 CP (kJkg K ) (K) 293 1221.0 2996.3 373 11 85 .8 3029.9 473 1137.6 3035.0 573 1075.1 3022.9 673 1011.9 3038.3 773 946.9 3063.2

Equation of state (EoS) of 1m Na 2SO 4 solution The PVT relationships determined from the acoustic velocity measurements were fitted to an empirical equation of state (EoS) of the form:

T, P a(T) b(P) c(T, P) (4) with

a(T) a1 a2 T

2 3 b(P) b1 P b2 P b3 P b4 P

c(T,P) c1 T log( P) c2 T P where T is the temperature in Kelvin, P is the pressure in Pascal. The coefficients ai ,bi and ci obtained by least-squares fitting of the inverted densities are listed in Table 4.5.

104

Table 4.5 Regression parameters for Eq. (4).

Parameters 3 a1 1.3800x10 0 a2 -5.1510x10 -3 b1 -2.0652x10 -7 b2 1.4872x10 -17 b3 -1.8677x10 -27 b4 1.8583x10 -11 c1 -5.3200x10 -1 c2 2.3256x10

This new EoS was found to reproduce the densities with a R2 > 0.999 smaller than 0.78%, corresponding to an average precision better than 0.2% of the density and a maximum deviation of 0.9 % at 773 K and 0.4 GPa (Fig. 4.5a). Because of the lack of PVT data for 1m Na 2SO 4 solution s at the investigated conditions, the validity of our EoS for sulfate solutions was assessed by comparing the acoustic velocities calculated from Eq.(4) (Table 4.6) with the experimental acoustic velocities (Fig. 4.3b). Our EoS is found to reproduce the experimental acoustic velocity data in the investigated P-T range with a maximal deviation of 1.5%, which falls within the overall experimental uncertainties. This observation confirms that the proposed EoS can be used to determine the density of 1m Na 2SO 4 solution from 293 to 773 K and 0.4 - 3 GPa with a maximal associated uncertainty of 0.3-0.5% (Abramson and Brown, 2004; Sanchez-Valle et al., in prep.).

The volumetric properties (i.e., density and specific volume) of 1m Na 2SO 4 solution up to 3 GPa and 773 K derived from the proposed EoS are reported in Table 4.6. Figure

4.5b compares the densities of aqueous Na 2SO 4 solutions with variable concentrations and water along isotherms at 473 and 673 K from 1 to 3 GPa. Data for water recently reported by Sanchez-Valle et al. (in prep.) to 7 GPa and 673 K using the same

105 experimental and data analysis applied here was used for the comparison. Figure 4.5b shows that the density of the aqueous solutions increases systematically upon addition of

Na 2SO 4 at each temperature. At 673 K, the density contrast increase to 12.5% and 13.5%, respectively in the same pressure interval, suggesting differences in the compressibility of the aqueous solutions and water. At 2 GPa and 473 K, the 1m Na 2SO 4 solution is 7.8% and 5% denser than the 0.148 m and the 0.5 m (Abramson et al., 2001), respectively.

Figure 4.5. a) Density of the 1m Na 2SO 4 solution to 773 K and 3 GPa. The solid lines are fits to the data using the equation of state proposed in this work (Eq. 4). b) Comparison between the densities of the 1 m Na 2SO 4 solution (solid lines), water (Sanchez-Valle et al., in prep.) (dashed lines) and 0.148 m and 0.5 m Na 2SO 4 solutions (Abramson et al., 2001) (dashed-dotted lines) at various temperatures.

4.3.3. Thermodynamic properties of aqueous sulfate solutions

The equation of state for 1m Na 2SO 4 solution (Eq. (4)) was used to determine the pressure and temperature dependence of thermodynamic properties such as the thermal

1 C 2 expansion , isobaric heat capacity P T v , as well as P 2 T P P T T P

106 T 2 isothermal and adiabatic compressibilities 1 P and 1 , and T 2 C s 2 VP P VP 1 corresponding bulk modulus, KT ,S . All thermodynamic properties derived for the T ,S

1m Na 2SO 4 solution up to 773 K and 3 GPa are listed in Table 4.6. According to error propagation calculations, estimated maximal uncertainties on the coefficient of thermal expansion P and the isobaric heat capacity CP are about 1-1.5%, whereas larger uncertainties of 3.5-4% and 7-8% are estimated for the adiabatic and isothermal bulk modulus (K S and K T) and compressibility ( S and T) , respectively.

In Figure 4.6, the P, C P, K T and T of the 1m Na 2SO 4 solution along isotherms at

473, 673 and 773 K are compared with those of H2O (Sanchez-Valle et al., in prep.) and a

0.5 m Na 2SO 4 solution calculated from the density data reported by (Abramson et al., 2001). Overall, the evolution with pressure and temperature of the thermodynamic properties of 1m Na 2SO 4 solution display a similar trend to that observed for water

(Sanchez-Valle et al., in prep.). Along each isotherm, P decrease with increasing pressure and the concentration of dissolved sulfates: at 1 GPa and 473 K, the coefficient of thermal expansion of 1m Na 2SO 4 solution is smaller than that of the 0.5 molal solution and water (Sanchez-Valle et al., in prep.) by 24% and 29%, and differences increase respectively to 36% and 38% at 2.8 GPa. Temperature, however, has the opposite effect on the thermal expansion coefficient of the 1m Na 2SO 4 solution, increasing by 6.7% from 473 to 673 K at 1 GPa, similarly to what is observed for water (Sanchez-Valle et al., in prep.) (Fig. 4.6a). Although the C P of the solutions also decreases with increasing sulfate concentration, the effect of pressure is much more moderate than that observed for the thermal expansion coefficient and in line with the behavior reported for water (Sanchez-

Valle et al., in prep.). For comparison, the CP of water is 38% larger than the 1m Na 2SO 4 solution at 473 K and 2 GPa, and differences are maintained when temperature increases isobarically to 673 K (Fig. 4.6b). The isothermal compressibility T also decreases upon compression and with the addition of dissolved Na 2SO 4 (Fig. 4.6c). We note that while the differences in the isothermal compressibilities are less than 2% at 473 K and thus remain indistinguishable within errors, the T of the 1m Na 2SO 4 solution decreases faster than that of H2O. This behavior is also reflected by the higher rate of increase of the bulk

107 modulus K T of the sulfate aqueous solution with pressure [ ( KT/ P) T] at 673 K, consistent with the observed increase of the density contrast between the aqueous solution and H 2O (Fig. 4.5b).

Figure 4.6. a) Coefficient of thermal expansion P , b) Isobaric heat capacity CP , c) isothemal compressibility and d) isothermal bulk modulus of aqueous Na 2SO 4 solutions (This work,

Abramson et al., 2001) and H 2O (Sanchez-Valle et al., in prep.) at selected temperatures.

108

Table 4.6 Acoustic velocities and PVT properties of the 1 molal aqueous Na 2SO 4 solution aqueous solution up to 773 K and 3 GPa a.

Temperature 293 K

3 3 -1 . -1. -1 -1 -1 VP (m/s) ) VSP (m /kg) P (K ) CP (J kg K ) S (GPa ) KS (GPa) T (GPa ) KT (GPa) P (GPa) x10 -3 x10 -4 x10 -1 x10 1 x10 -1 x10 1 0.4 2156 1229.5 0.81 4.60 2996.3 1.75 0.57 1.92 0.52 0.6 2432 1271.0 0.79 3.80 2976.1 1.33 0.75 1.44 0.69 0.8 2632 1304.7 0.77 3.27 2962.8 1.11 0.90 1.19 0.84 1 2793 1333.8 0.75 2.89 2953.2 0.96 1.04 1.02 0.98 1.2 2932 1359.8 0.74 2.60 2945.9 0.86 1.17 0.90 1.11 1.4 3057 1383.4 0.72 2.37 2940.1 0.77 1.29 0.81 1.23 Temperature 373 K

3 3 -1 . -1. -1 -1 -1 VP (m/s) ) VSP (m /kg) P (K ) CP (J kg K ) S (GPa ) KS (GPa) T (GPa ) KT (GPa) P (GPa) x10 -3 x10 -4 x10 -1 x10 1 x10 -1 x10 1 0.4 2167 1184.2 0.84 4.78 3029.9 1.80 0.56 2.04 0.49 0.6 2411 1232.4 0.81 3.91 3001.1 1.40 0.72 1.55 0.64 0.8 2599 1270.6 0.79 3.35 2982.6 1.17 0.86 1.28 0.78 1 2758 1303.0 0.77 2.95 2969.3 1.01 0.99 1.09 0.91 1.2 2898 1331.5 0.75 2.65 2959.4 0.89 1.12 0.96 1.04 1.4 3025 1357.1 0.74 2.42 2951.5 0.81 1.24 0.86 1.16 1.6 3143 1380.4 0.72 2.23 2945.1 0.73 1.36 0.78 1.28 1.8 3251 1402.0 0.71 2.07 2939.7 0.67 1.48 0.71 1.40 2 3352 1422.0 0.70 1.95 2935.1 0.63 1.60 0.66 1.52 2.2 3443 1440.7 0.69 1.84 2931.1 0.59 1.71 0.62 1.62 2.4 3525 1458.5 0.69 1.75 2927.6 0.55 1.81 0.58 1.73

109

Temperature 473 K

3 3 -1 . -1. -1 -1 -1 VP (m/s) ) VSP (m /kg) P (K ) CP (J kg K ) S (GPa ) KS (GPa) T (GPa ) KT (GPa) P (GPa) x10 -3 x10 -4 x10 -1 x10 1 x10 -1 x10 1 0.4 1941 1127.6 0.89 5.02 3035.0 2.35 0.43 2.70 0.37 0.6 2212 1184.2 0.84 4.07 2992.7 1.73 0.58 1.95 0.51 0.8 2420 1228.0 0.81 3.47 2966.2 1.39 0.72 1.55 0.65 1 2594 1264.5 0.79 3.04 2947.6 1.18 0.85 1.29 0.77 1.2 2748 1296.2 0.77 2.72 2933.8 1.02 0.98 1.11 0.90 1.4 2887 1324.3 0.76 2.48 2922.9 0.91 1.10 0.98 1.02 1.6 3016 1349.7 0.74 2.28 2914.2 0.81 1.23 0.88 1.14 1.8 3136 1372.9 0.73 2.12 2906.9 0.74 1.35 0.79 1.26 2 3247 1394.3 0.72 1.99 2900.7 0.68 1.47 0.73 1.38 2.2 3350 1414.2 0.71 1.88 2895.4 0.63 1.59 0.67 1.49 2.4 3443 1432.9 0.70 1.78 2890.7 0.59 1.70 0.62 1.60 2.6 3527 1450.6 0.69 1.71 2886.5 0.55 1.80 0.59 1.70 2.8 3599 1467.4 0.68 1.64 2882.6 0.53 1.90 0.56 1.80 3 3658 1483.6 0.67 1.59 2879.2 0.50 1.99 0.53 1.88 Temperature 573 K

3 3 -1 . -1. -1 -1 -1 VP (m/s) ) VSP (m /kg) P (K ) CP (J kg K ) S (GPa ) KS (GPa) T (GPa ) KT (GPa) P (GPa) x10 -3 x10 -4 x10 -1 x10 1 x10 -1 x10 1 0.4 1831 1071.0 0.93 5.29 3022.9 2.78 0.36 3.28 0.30 0.6 2102 1135.9 0.88 4.25 2963.1 1.99 0.50 2.30 0.43 0.8 2314 1185.4 0.84 3.59 2926.7 1.58 0.63 1.79 0.56 1 2493 1226.1 0.82 3.14 2901.7 1.31 0.76 1.47 0.68 1.2 2653 1260.9 0.79 2.80 2883.3 1.13 0.89 1.25 0.80 1.4 2798 1291.5 0.77 2.54 2869.0 0.99 1.01 1.09 0.92 1.6 2933 1318.9 0.76 2.33 2857.6 0.88 1.13 0.96 1.04 1.8 3059 1343.8 0.74 2.16 2848.2 0.80 1.26 0.87 1.16 2 3178 1366.6 0.73 2.03 2840.2 0.72 1.38 0.79 1.27 2.2 3288 1387.7 0.72 1.91 2833.3 0.67 1.50 0.72 1.39 2.4 3390 1407.3 0.71 1.82 2827.2 0.62 1.62 0.67 1.50 2.6 3481 1425.8 0.70 1.74 2821.9 0.58 1.73 0.62 1.61 2.8 3562 1443.3 0.69 1.67 2817.0 0.55 1.83 0.59 1.71 3 3631 1460.0 0.68 1.61 2812.6 0.52 1.92 0.56 1.80

110

Temperature 673 K

3 3 -1 . -1. -1 -1 -1 VP (m/s) ) VSP (m /kg) P (K ) CP (J kg K ) S (GPa ) KS (GPa) T (GPa ) KT (GPa) P (GPa) x10 -3 x10 -4 x10 -1 x10 1 x10 -1 x10 1 0.4 1744 1014.4 0.99 5.58 3038.3 3.24 0.31 3.92 0.26 0.6 2012 1087.7 0.92 4.44 2955.6 2.27 0.44 2.68 0.37 0.8 2225 1142.8 0.88 3.73 2907.0 1.77 0.57 2.05 0.49 1 2407 1187.6 0.84 3.24 2874.2 1.45 0.69 1.66 0.60 1.2 2570 1225.6 0.82 2.88 2850.4 1.24 0.81 1.40 0.72 1.4 2719 1258.7 0.79 2.61 2832.1 1.07 0.93 1.20 0.83 1.6 2859 1288.2 0.78 2.39 2817.6 0.95 1.05 1.06 0.95 1.8 2991 1314.7 0.76 2.21 2805.7 0.85 1.18 0.94 1.06 2 3115 1338.9 0.75 2.07 2795.7 0.77 1.30 0.85 1.18 2.2 3232 1361.1 0.73 1.95 2787.1 0.70 1.42 0.77 1.30 2.4 3341 1381.7 0.72 1.85 2779.6 0.65 1.54 0.71 1.41 2.6 3440 1401.0 0.71 1.77 2772.9 0.60 1.66 0.66 1.52 2.8 3529 1419.2 0.70 1.70 2766.9 0.57 1.77 0.62 1.63 3 3606 1436.4 0.70 1.64 2761.4 0.54 1.87 0.58 1.72 Temperature 773 K

3 3 -1 . -1. -1 -1 -1 VP (m/s) ) VSP (m /kg) P (K ) CP (J kg K ) S (GPa ) KS (GPa) T (GPa ) KT (GPa) P (GPa) x10 -3 x10 -4 x10 -1 x10 1 x10 -1 x10 1 0.4 1676 957.8 1.04 5.91 3063.2 3.72 0.27 4.64 0.22 0.6 1940 1039.4 0.96 4.64 2950.4 2.56 0.39 3.10 0.32 0.8 2152 1100.2 0.91 3.87 2886.3 1.96 0.51 2.33 0.43 1 2334 1149.1 0.87 3.35 2844.2 1.60 0.63 1.86 0.54 1.2 2499 1190.3 0.84 2.97 2814.0 1.35 0.74 1.55 0.65 1.4 2651 1226.0 0.82 2.67 2791.1 1.16 0.86 1.32 0.76 1.6 2795 1257.5 0.80 2.45 2773.1 1.02 0.98 1.15 0.87 1.8 2931 1285.7 0.78 2.26 2758.4 0.91 1.10 1.02 0.98 2 3060 1311.2 0.76 2.11 2746.1 0.81 1.23 0.91 1.10 2.2 3182 1334.6 0.75 1.99 2735.5 0.74 1.35 0.82 1.21 2.4 3297 1356.2 0.74 1.89 2726.4 0.68 1.47 0.75 1.33 2.6 3403 1376.2 0.73 1.80 2718.3 0.63 1.59 0.69 1.44 2.8 3500 1395.1 0.72 1.73 2711.0 0.59 1.71 0.65 1.55 3 3585 1412.9 0.71 1.67 2704.4 0.55 1.82 0.61 1.65

a Uncertainties correspond to 0.3-0.5% in density and specific volume V sp , 1.5% in the calculated acoustic

velocity V P, 1-1.5 % for thermal expansion P and isobaric heat capacity C P, 3.5-4% for adiabatic

compressibility S and bulk modulus K S, 7.5-8% for isothermal compressibility T and bulk modulus K T.

111 4.3.4. Effect of sulfate ions on the structure and compressibility of water The lower compressibility of the sulfate-bearing aqueous solution compared to water observed at high temperature in this study can qualitatively be explained by the changes in the structure of the solvent induced by the dissolved electrolytes. The addition of dissolved electrolytes to water induces changes in the hydrogen-bonding among H2O molecules (Desnoyer et al., 1965; Marcus, 2011) due to ion-solvent interactions in the fluid. The extend of these changes is related to the concentration and the character of dissolved species (Marcus, 2009). Ions dissolved in water can be classified into structure- makers and structure-breakers based on their effect on the hydrogen bonded structure of water outside their vicinity (Marcus, 2009). A more comprehensive picture has been derived by comparing results from thermodynamic, spectroscopic, and computer simulation studies (Marcus, 2010) , and the structure-making or structure-breaking character has been assigned based on the effect on relative viscosity of the solution, the entropy of hydration values ( Sstruc ), and the geometrical factor GHB , which represents the effect of the solute on the geometry of the hydrogen bonded network of water beyond the hydration shells. Accordingly, - NaCl or KBr, causes a significant reorganization of the water molecules in the bulk water and depress the viscosity due to the partial rupture of the H-bonding network (Terpstra et al., 1990; Cavaille et al., 1996). S e.g ., LiF, MgCO 3), on the other hand, enhance the hydrogen bonding in the solvent through their electrical field 2- leading to an increase of the viscosity (Marcus, 2010). Dissolved SO 4 species are considered borderline ions as they enhancing the relative viscosity of the(Marcus, 2010) solvent and preserving the geometry of the hydrogen bonded network of water outside the hydration shells ( GHB = 0), while they -1 -1 have entropy of hydration values ( Sstruc = 8 J K mol ) representative for very weak structure-breaker species. The observed decrease in the compressibility of water upon addition of dissolved sulfate ions (Fig. 4.6c) is thus consistent with the structure maker behavior of sulfate ions in the investigated solutions, in agreement with recent ab initio molecular dynamic calculations and large angle X-ray scattering studies (Walrafen, 1971; Bergstrom et al., 1991; Vchirawongkwin et al., 2007). The addition of dissolved sulfate 2- ions to water thus results in the formation of H-bonds between the oxygen of the SO 4

112 groups and the hydrogen of the water molecules in the first hydration shell (Bergstrom et al., 1991; Cannon et al., 1994; Wang et al., 2006) that lead to the strengthening the hydrogen bond network of the solvent (Walrafen, 1971; Bergstrom et al., 1991; Vchirawongkwin et al., 2007), hence reducing the compressibility of water.

4.4. Conclusions

Acoustic velocity measurements were performed in 1m Na 2SO 4 solution to 773 K and 3 GPa in resistively heated diamond anvil cell using Brillouin scattering spectroscopy. The acoustic velocities were used to determine an empirical PVT equation of state that provides the density of the aqueous solution with an uncertainty of 0.3-0.5% in the 293 - 773 K and 0.4 - 3 GPa range. Using the EoS, we evaluate the pressure- temperature dependence of the thermodynamic properties of 1m Na 2SO 4 solution, including the thermal expansion, isobaric heat capacity as well as the isothermal and adiabatic compressibilities and bulk modulus. The derived thermodynamic dataset extends the available data by almost two orders of magnitude in pressure (Losurdo et al., 1982; Obsil et al., 1997; Azizov and Akhundov, 2000; Apelblat et al., 2009) and can be applied to model fluid processes in a number of geological settings. The decrease in the 2- compressibility of water upon addition of dissolved SO 4 ions thus suggests that they behave as structure maker species in the investigated solutions, leading to the enhancement of the hydrogen bond network of the solvent (Walrafen, 1971; Bergstrom et al., 1991; Vchirawongkwin et al., 2007; Marcus, 2009).

Acknowledgement. We would like to thank two anonymous reviewers and the associate editor Dr. E.W. Castner for efficient editorial handling. This research was supported by the ETHIIRA program of ETH Zürich (grant ETH-30 08-2).

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121 Appendix

Supporting figures

Figure S1. a) Extrapolated ratios between the density of a 1 molal aqueous Na 2SO 4 solution obtained from Azizov and Akhundov (2000) and the density of a H 2O NaCl solution with

15 wt% NaCl (Driesner, 2007) at 373, 473 and 673 K. At 0.4 GPa the ratios approach a value around 1.005 for the three isotherms. b) Coefficient of determination R 2 for the acoustic velocities of the 1 molal aqueous Na 2SO 4 solution as a function of the ratio Na 2SO 4 / NaCl (15 wt%

NaCl) at every temperature investigated in this work. The black symbols represent R 2 calculated from the tests with different initial ratios. The highest R 2 value, corresponding to the best fit, is obtained with a ratio of 1 at 293 K, 1.005 at 373 K and 1.012 at 473, 573, 673 and 773 K, respectively.

122 Chapter 5

Equation of state of NaCl aqueous fluids to 1073 K and from 0.5 to 4.5 GPa

Davide Mantegazzi 1* , Carmen Sanchez-Valle 1* and Thomas Driesner 1

1Institute for Geochemistry and Petrology, ETH Zurich, Clausiusstrasse 25, 8092 Zurich *Corresponding authors: [email protected]; [email protected] Tel. number: +41 44 632 43 19 Fax: +41 44 632 16 36

Prepared for submission to Geochim. Cosmochim. Acta

Abstract

H2O-NaCl fluids are a proxy for saline aqueous solutions in many geological environments, including subduction zones. However, experimental data for their thermodynamic properties are basically inexistent at pressure above 0.5 GPa. We report acoustic velocity measurements on 1 molal and 3 molal NaCl solutions (1 m and 3 m NaCl) using Brillouin scattering spectroscopy in an externally heated diamond anvil cell (mDAC) to determine the first equation of state of NaCl-bearing aqueous fluids up to upper mantle pressure conditions. The densities of NaCl aqueous fluids have been combined with previous data on H 2O to generate an equation of state that can be used to determine the thermodynamic properties of fluids in 0-3m NaCl concentration range and up to 1073 K and 4.5 GPa. The PVTx predictions are in good agreement with available low pressure data (< 0.5 GPa). The equation of state presented here was used to evaluate the effect of fluid composition on the location of reaction boundaries in dehydrating subducting oceanic crust. We observe that the transition from greenschist to blueschist 123

facies along a typical slow subduction geotherm will shift toward shallower depths when the activity of water decreases due to the presence of NaCl species dissolved in the fluid.

5.1. Introduction

Saline aqueous fluids are of fundamental importance in many geological processes (Peacock, 1990; Bodnar, 2005; Yardley, 2009). These processes include magma production in the mantle wedge above subduction zones (Ulmer, 2001), hydrothermal alteration of the seafloor (Jarrard, 2003; Bonifacie et al., 2008) and metasomatic reactions (Jamtveit and Austrheim, 2010; Putnis and Austrheim, 2010). Sodium chloride is the primary solute in aqueous fluids in various geological environments (Roedder, 1984; Jarrard, 2003), and fluids in the H2O-NaCl binary are thus taken as a model system for more complex water-salt system in geological processes (Labotka, 1991; Anderko and Pitzer, 1993; Liebscher and Heinrich, 2007). At subduction zone settings, the metamorphic saline aqueous fluids released from the subducting oceanic lithosphere at shallow to intermediated depths (Schmidt and Poli, 1998; Rupke et al., 2004) typically display salinities in the 10-20 wt% NaCl eq range (Gao and Klemd, 2001; Scambelluri and Philippot, 2001; Liebscher and Heinrich, 2007). These water-rich fluids interact with the overlying mantle wedge, decreasing its solidus temperature and triggering the production of calc-alkaline magmas (Ulmer, 2001; Manning, 2004) at the origin of arc volcanism. Additionally, metamorphic devolatilization processes are believed to be related to seismic activity along subducting slabs (Peacock, 1990; Schmidt and Poli, 1998; Hacker et al., 2003b). Therefore, the accurate characterization of fluid- involving geological events occurring at depth is necessary to better understand and predict catastrophic events, such as volcanic and seismic activity at convergent tectonic margins. Quantitative modeling of fluid-rock interactions at high pressure and temperature conditions requires the knowledge of the thermodynamic properties of the phases involved. While these data are available for most rock-forming minerals (Hacker et al., 2003a; Stixrude and Lithgow-Bertelloni, 2005), this is not the case for aqueous fluids other than pure water. Specifically, high experimental data for the pressure-volume-

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temperature-composition (PVTx) relations, from which the other thermodynamic properties of fluids can be derived, are lacking. Experimentally and theoretically based equations of state (EoS) for pure water are available to extreme P-T conditions (Brodholt and Wood, 1993; Wagner and Pruss, 2002; Abramson and Brown, 2004; Sanchez-Valle et al., in prep.), whereas in the binary system H2O NaCl the experimental PVTx data, obtained, for instance, from vibrating tube densimeter measurements (e.g., Majer et al., 1991; Simonson et al., 1994), acoustic velocities data (e.g., Millero et al., 1987) and synthetic fluid inclusions (FI) studies (e.g., Bodnar et al., 1985; Knight and Bodnar, 1989) are restricted to pressures below 0.5 GPa limiting the validity range of available equations of state (Pitzer et al., 1984; Bischoff and Rosenbauer, 1985; Chou, 1987; Tanger and Pitzer, 1989; Archer, 1992; Anderko and Pitzer, 1993; Driesner, 2007; Mao and Duan, 2008). Published molecular dynamic (MD) simulations (Brodholt, 1998) also only cover the pressure range to 0.5 GPa. The lack of PVTx data for saline aqueous fluids at high pressure conditions limits the quantitative modeling of fluid mediated geological processes occurring at depth in subduction zone environments. In this work, acoustic velocities measured with Brillouin scattering spectroscopy in a membrane-type diamond anvil cell (mDAC) were inverted to calculate the density of a 1 molal and 3 molal NaCl solutions (1 m and 3 m NaCl) in the 0.5-4.5 GPa and 293-673 K pressure-temperature range. The derived density data of NaCl aqueous fluids were combined with densities of pure water (Wagner and Pruss, 2002; Sanchez-Valle et al., in prep.) to generate the first EoS valid in the 0 3m NaCl compositional range, which was then used to derive all thermodynamic properties of NaCl aqueous fluids up to 4.5 GPa and 1073 K.

5.2. Experimental Method

5.2.1 Diamond anvil cell techniques All measurements were conducted in a membrane-type diamond anvil cell (mDAC) with large optical opening and mounted with two low fluorescence type Ia diamonds of 500 m culet diameter (Chervin et al., 1995). A ring-shaped resistive heater surrounding the body of the cell and an internal Pt resistive heater placed around the lower diamond

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were used simultaneously to reach temperatures up to 673 K. The temperature was monitored to ±2 K with a K-type thermocouple attached to one of the diamonds close to the sample chamber. An additional thermocouple was included in the external heater and was calibrated against the internal thermocouple before the experiments (Chervin et al., 2005). The NaCl aqueous solutions were prepared from high purity (99.99 + %, Sigma Aldrich ®) NaCl powder and Milli Q water, sealed in tight containers and refrigerated until used. Two different NaCl concentrations were investigated in this work: a 1 molal (1 m) and a 3 molal (3 m) aqueous NaCl solution, corresponding to 5.5 and 14.9 wt% NaCl, respectively. The aqueous solutions were loaded in a 250 to 300 m hole drilled in a pre-indented stainless steel or rhenium gasket of about 80-100 m thickness, together with a chip of the material used as pressure calibration. After loading, the cell was immediately closed and pressurized to avoid fluid evaporation and/or solute precipitation that would modify the concentration of the solution. The reliability of the loading procedure was confirmed by the reproducibility of the acoustic data collected in repeated loadings, and by the agreement with the data collected outside the mDAC at room conditions and with literature data (Millero et al., 1987). The choice of the pressure sensor ( i.e., ruby spheres or cubic boron nitride chips) was determined by the temperature range investigated. In detail, measurements up to 473 K were mainly conducted using ruby spheres (Chervin et al., 2003), and the pressure was determined using the calibrated shift of the R1 fluorescence line (Mao et al., 1978) after temperature correction (Ragan et al., 1992; Datchi et al., 2007b). At temperature above 550 K, the broadening and overlapping of the R1 and R2 fluorescence lines and the temperature effect on the frequency of the R1 line decrease the precision on pressure determination (Datchi et al., 1997; Sanchez-Valle et al., 2002; Datchi et al., 2007b). Therefore, experiments at 573 K and 673 K were performed using chips of cubic boron nitride (cBN) as pressure marker and the pressure was calculated from the frequency shift of the 1054 cm -1 Raman transverse optical mode (TO) (Datchi et al., 2007a). Cubic BN was used for the high temperature experiments due to its low chemical reactivity with the fluid in the investigated range and the small broadening of the TO band linewidth with temperature that allows for the necessary level of precision on the pressure determination

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(Datchi et al., 2007b). Raman and fluorescence spectra were fitted to Voigt or Pearson functions using the software Peakfit version 4.12 (© Seasolve Incorporation). The precision in the pressure monitoring was better than 0.02 GPa using ruby spheres at temperatures up to 473 K, while the estimated accuracy decreases to 0.04 GPa at 573 and 673 K. Using the cBN pressure standard, the reproducibility of the pressure measured was better than 0.03 GPa at any investigated temperature. Redundant experiments were repeated at 293 K and 573 K using either the ruby spheres or the cBN chips as a pressure marker and differences in calculated pressures did not exceed 0.05 GPa (Mantegazzi et al., submitted).

5.2.2 Brillouin scattering spectroscopy

Brillouin scattering measurements were conducted at ETH Zurich using a Nd:YVO 4

0 = 532.1 nm) as a light source and a six-pass tandem Fabry-Perot interferometer of Sandercock type (Sandercock, 1982), equipped with a photomultiplayer (PMT) detector to analyze the scattered light. The Brillouin system is coupled to a Raman system installed on the same optical bench that enables collection of Raman and fluorescence spectra from the pressure standards (ruby and c-BN) without changing the position of the mDAC. Additional details of the experimental setup are provided in Sanchez-Valle et al. (2010). All measurements were conducted in symmetric scattering geometry that allows direct determination of the compressional acoustic velocities VP in the fluid using the following relationship (Whitfield et al., 1976):

V 0 P (1) P * 2 sin( ) 2

* where 0 is the laser wavelength, P is the Brillouin shift and is the external scattering angle ( i.e ., angle between the incident and scattered beam outside the sample). The measurements in the mDAC were always conducted using a 50 deg scattering angle, whereas reference spectra for the 1m and 3 m aqueous NaCl solutions were acquired at room conditions in 90 deg scattering geometry in a silica glass cuvette. Prior to the measurements, the systems was calibrated using a single-crystal MgO standard measured in both 90 and 50 deg scattering geometries to reduce geometrical and other systematic

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errors in the acoustic velocity determination. Acoustic velocity measurements were conducted in isothermal runs at 293, 373, 473, 573 and 673 K both in compression and decompression experiments. Each temperature-pressure point represents an average of at least two measurements conducted in different positions of the sample chamber to verify the homogeneity of the fluid. When rubies were used as pressure markers, the R1 fluorescence line of rubies was excited focusing the laser beam (15 m diameter) on the sample, and not directly on ruby, to avoid overheating that could result in erroneous pressure determinations. Typical collection times per Brillouin spectrum were between 5 to 10 minutes. The reproducibility of the acoustic velocity measurements is better than 1%, while the accuracy is estimated to be better than 0.5-1% at room conditions and 1% at high pressure and temperature. Additional details about the experiments are reported in Mantegazzi et al. (submitted) and Sanchez-Valle et al. (in prep.)

5.3. Results

5.3.1 Acoustic velocities in NaCl aqueous solutions Fig. 5.1 displays representative Brillouin spectra of the 1m aqueous NaCl solution collected at different pressure and temperature conditions. Each spectrum has an excellent signal-to-noise ratio and shows the compressional acoustic velocity VP and the back scattered compressional acoustic velocity nV P , where n refers to the refractive index of the NaCl aqueous solution. The nV P signal arises from light partially reflected from the output diamond anvil and that serves as a secondary excitation light.

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Figure 5.1. Representative Brillouin spectra collected in the diamond anvil cell in a 1 m aqueous NaCl solution (5.5 wt% NaCl) at different temperature and pressure conditions. The compressional acoustic velocity and the backscattered compressional acoustic velocity are

labeled as V P and nV P, respectively. Typical collection times per spectrum are 5 to 10 minutes. The Rayleigh peak has been removed for clarity.

The acoustic velocities VP of the 1 m and 3 m aqueous NaCl solutions collected at room conditions in the silica glass cuvette and in the mDAC are shown in Fig. 5.2, together with literature data for aqueous NaCl solutions at various concentrations (Millero et al., 1987). The values measured in the silica glass cuvette and in the mDAC without pressurization are identical within mutual uncertainties and have an average value of 1548 ± 8 m/s and 1669 ± 10 m/s for the 1 m and the 3 m aqueous NaCl solutions, respectively. The agreement in the results shows that the use of the mDAC does not introduce geometrical or systematic errors, and that fluid evaporation and solute precipitation during the loading procedures is negligible. Additionally, the measurements performed in this work at room conditions are in good agreement with the data of Millero et al. (1987) obtained in large volume sample using ultrasonic measurements. The acoustic velocities in water at room conditions are on average 64 m/s and 185 m/s slower than in the 1 m and the 3 m aqueous NaCl solution, respectively (Millero et al., 1987;

Sanchez-Valle et al., in prep.). The acoustic velocities VP collected in the aqueous NaCl solutions as a function of the pressure along the five isotherms from 293 K to 673 K are reported in Figs. 5.3a-b and listed in Table 5.1. The acoustic velocities increase smoothly with pressure along the isotherms, and excellent agreement is always found between

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velocities measured in compression and decompression experiments. Additionally, measurements repeated using different pressure sensors are always in good agreement in the range of overlapping.

Figure 5.2. Acoustic velocity measured at room conditions in NaCl aqueous solutions as a function of molality. The black dots and grey squares are velocities measured in this study inside the mDAC (50 deg scattering geometry) and in a silica glass cuvette (90 deg scattering geometry), respectively. The error bars correspond to an error of 0.5%. The black solid line are acoustic velocities from Millero et al. (1987). The black triangle and the empty diamond are acoustic velocities in water taken from Del Grosso and Mader (1972) and Sanchez-Valle et al. (in prep.)

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Figure 5.3. Acoustic velocities measured in a) 1m and b) 3m NaCl solutions as a function of pressure along several isotherms between 293 K and 673 K Full and empty symbols represent data measured in compression and decompression, respectively. Black and grey symbols represent data obtained using ruby and cBN as pressure sensors, respectively. The black dashed lines are acoustic velocities calculated from the EoS determined in this work (Eq. 4). The errors in velocities are smaller than the symbol size (<1.5%).

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Table 5.1. Speed of sound data VP measured in a) 1m NaCl aqueous solution b) 3m NaCl aqueous solution. Values in italic are measurements performed during decompression experiments. Numbers in bold characters represent experiments performed using cBN as pressure sensor. * denotes data acquired in a silica glass cuvette at room conditions.

a) 1 m NaCl solution 293 K 373 K 473 K 573 K 673 K

P VP P VP P VP P VP P VP (GPa) (m/s) (GPa) (m/s) (GPa) (m/s) (GPa) (m/s) (GPa) (m/s) 0.00* 1541* 0.43 2077 0.73 2282 0.82 2218 1.45 2718 0.00 1549 0.46 2098 0.96 2497 0.89 2294 1.48 2756 0.00 1556 0.49 2109 1.25 2753 0.92 2313 1.51 2769 0.09 1674 0.66 2304 1.26 2757 0.92 2306 1.51 2764 0.11 1747 0.71 2347 1.34 2803 1.01 2436 1.60 2827 0.15 1822 0.84 2491 1.36 2819 1.16 2539 1.97 3043 0.16 1835 0.87 2516 1.38 2843 1.19 2558 2.21 3210 0.17 1880 0.91 2549 1.41 2886 1.42 2748 2.55 3375 0.20 1905 1.03 2655 1.47 2895 1.57 2832 2.58 3381 0.32 2089 1.17 2749 1.52 2919 1.75 2983 2.64 3391 0.34 2099 1.22 2774 1.88 3170 1.75 3003 2.76 3444 0.55 2356 1.29 2829 1.90 3148 1.83 3050 2.80 3479 0.61 2375 1.46 2933 2.12 3240 1.96 3133 3.35 3659 0.63 2436 1.56 2988 2.16 3312 1.96 3098 4.10 3911 0.64 2444 1.59 2996 2.35 3378 2.02 3113 0.67 2451 1.77 3105 2.35 3364 2.06 3141 0.78 2539 1.87 3185 2.45 3450 2.13 3209 0.84 2599 2.05 3255 2.58 3499 2.15 3273 0.86 2640 2.37 3347 0.97 2692 2.45 3405 1.03 2740 2.51 3426 2.68 3529 2.72 3549 3.13 3696 3.88 3953 4.01 3972 4.44 4074

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b) 3 m NaCl solution 293 K 373 K 473 K 573 K 673 K

P VP P VP P VP P VP P VP (GPa) (m/s) (GPa) (m/s) (GPa) (m/s) (GPa) (m/s) (GPa) (m/s) 0.00* 1668* 0.49 2199 0.67 2202 1.78 2934 2.25 3124 0.00 1669 0.56 2264 0.72 2259 1.95 3026 2.73 3337 0.00 1671 0.61 2340 0.86 2373 1.98 3064 2.73 3334 0.04 1744 0.72 2422 1.03 2559 1.99 3086 2.79 3382 0.06 1780 0.75 2466 1.10 2603 2.00 3116 3.06 3478 0.09 1829 0.76 2486 1.11 2607 2.11 3125 3.86 3740 0.13 1899 0.78 2484 1.48 2854 2.27 3217 0.18 1983 0.85 2510 1.65 2960 2.29 3223 0.22 2034 0.87 2576 1.71 2941 2.43 3257 0.51 2373 0.97 2644 1.80 3009 2.52 3363 0.70 2545 1.00 2650 2.13 3181 2.55 3301 0.75 2597 1.20 2797 2.19 3272 2.65 3369 0.82 2611 1.31 2873 2.35 3315 2.89 3488 0.90 2730 1.59 3010 2.43 3312 2.99 3544 0.92 2711 1.60 3045 2.56 3428 3.16 3627 1.05 2805 1.84 3174 2.57 3436 3.23 3638 1.06 2800 1.87 3146 2.74 3495 3.25 3654 1.09 2824 1.91 3190 2.86 3539 3.31 3686 1.10 2863 1.97 3210 2.89 3547 3.39 3675 1.14 2876 2.10 3311 3.12 3636 3.72 3776 1.19 2873 2.14 3314 4.72 4071 1.27 2947 2.29 3395 1.42 3011 2.67 3550 1.44 3033 1.65 3134 1.73 3161

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5.3.2. Equation of state (EoS) for aqueous NaCl solutions

The density and the acoustic velocity VP are related through the thermodynamic relationships:

T 2 1 P (2a) P 2 C T VP P

1 P (2b) T P

C 2 P T v T 2 P 2 P P T T P T P (2c)

where VP is the measured acoustic velocity, is the density, P the coefficient of thermal expansion, CP the specific heat capacity and v the specific volume. The density of the 1 m and 3 m aqueous NaCl solutions was inverted from the measured sound velocities VP by recursive integration of Eqs. (2a-c) (Wiryana et al., 1998; Abramson and Brown, 2004; Asahara et al., 2010; Sanchez-Valle et al., in prep.; Mantegazzi et al., submitted). Briefly, the procedure starts with the integration of Eq. (2a) at an arbitrary initial pressure, at which the density and heat capacity CP are known. This first iteration

2 step is performed assuming that the isothermal-adiabatic correction term ( T P / CP ) is negligible. The resulting density is used to calculate a first approximation of P and CP (Eqs. 2b and 2c) that are further used in the second iteration of Eq. (2a) without neglecting the isothermal-adiabatic correction term. This process was reiterated until convergence. Additional details about the inversion procedure are reported in Mantegazzi et al. (submitted).

The experimental acoustic data were interpolated to generate a dense VP matrix in the pressure-temperature space using an analytic expression of the form

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2 2 ln VP c1 c2 T c3 ln P c4 T ln P c5 ln P c6 T ln P (3) where T is the temperature in Kelvin and P is the pressure in GPa. The most representative fit of the experimental data for both solutions is obtained by fitting the 293 K isotherm separately from the data collected at higher temperature. Using this approach, 2 all the acoustic velocity values are modeled with a r > 0.9999. The best-fit ci coefficients for Eq. (3) are reported in Table 5.2.

Table 5.2. Parameters c i for Eq. (3) obtained through least squares fit of the experimentally measured speed of sound data.

Concentration Isotherm: 293 K 373 673 K c1 8.0293089 8.0267824

c x10 -4 -4.3276371 -4.1436263 1m 2 -1 0.6332016 1.1785137 c3x10 -4 c4x10 6.2893331 4.9617178 -1 H2O NaCl c5x10 0.31033798 1.1191385 solutions -4 c6x10 -0.3652444 -2.4907213

c1 8.0691861 8.0939084 -4 c2x10 -4.9271804 -5.6099981 3m -1 c3x10 1.1635878 0.7032335 -4 c4x10 4.3147844 5.5013028 -2 c5x10 8.0935949 9.3968340 -4 -1.7201571 -2.0374168 c6x10

The inversion of the acoustic velocity data started at 0.5 GPa using initial values of density and isobaric heat capacity for the two NaCl aqueous solutions calculated using the SOWAT program (Driesner, 2007) and tabulated in Table 5.3. The densities obtained from the recursive integration of Eqs. (2a) - (2c) are plotted in Figs. 5.4 and 5.5 and reported in Table 5.4. The numerical fit of the experimentally measured acoustic velocities VP with Eq. (3) have a maximal associated error of 1.5%, which corresponds to a precision of 0.4% in the density data calculated. Additional sources of uncertainty are the initial values of density and isobaric heat capacity at 0.5 GPa used in the inversion. The values taken from Driesner (2007) have estimated maximal uncertainties of 0.5% in

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density and 1-2% for C P, which results in about 0.5% errors in the calculated density data (Mantegazzi et al., submitted). Therefore, taking into account the 1.5% error in the fitted and interpolated V P data, and the uncertainty of the initial values of density and isobaric heat capacity, the density is inverted from Eqs. (2a)-(2c) have a total associated uncertainty of 0.3-0.5%.

Table 5.3. Values of density and isobaric heat capacity at 0.5 GPa from Driesner (2007).

Molality (mol/kg) P = 0.5 GPa 293 K 373 K 473 K 573 K 673 K Density (kg/m 3) 1182.0 1142.3 1088.2 1031.2 971.8 1m . -1. -1 CP (J kg K ) 3265.8 3449.5 3452.5 3423.9 3430.7 Density (kg/m 3) 1239.0 1198.6 1145.1 1089.3 1031.6 . -1. -1 3m CP (J kg K ) 2943.4 2952.2 2952.2 2928.4 2929.2 *Calculated using the SOWAT code (http://www.geopetro.ethz.ch/people/td/sowat)

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Table 5.4. Density of 1m (a) and 3m (b) NaCl aqueous solutions determined from the acoustic velocity data. All densities are reported in (kg/m 3)

a) 1 m NaCl P (GPa) 293 K 373 K 473 K 573 K 673 K 0.5 1182.0 1142.3 1088.2 1031.2 971.8 0.7 1220.3 1185.7 1139.2 1091.0 1041.9 0.9 1253.2 1221.8 1179.8 1136.5 1093.3 1.1 1282.5 1252.9 1213.9 1173.8 1134.6 1.3 1280.6 1243.6 1205.7 1169.4 1.5 1305.6 1270.1 1233.8 1199.8 1.7 1328.4 1294.1 1259.1 1227.0 1.9 1349.5 1316.1 1282.1 1251.7 2.1 1369.1 1336.5 1303.3 1274.5 2.3 1387.5 1355.6 1323.1 1295.7 2.5 1404.7 1373.5 1341.6 1315.5 2.7 1390.4 1359.1 1334.3 2.9 1406.4 1375.7 1352.1 3.1 1421.7 1391.4 1369.1 3.3 1436.3 1406.5 1385.4 3.5 1450.2 1420.9 1401.0 3.7 1463.6 1434.8 1416.1 3.9 1476.5 1448.2 1430.6 4.1 1489.0 1461.1 1444.7 4.3 1473.6 1458.3 4.5 1485.8 1471.6 b) 3 m NaCl P (GPa) 293 K 373 K 473 K 573 K 673 K 0.5 1239.0 1198.6 1145.1 1089.3 1031.6 0.7 1275.4 1240.0 1195.2 1149.5 1103.9 0.9 1306.8 1274.8 1235.4 1195.7 1156.9 1.1 1334.8 1305.2 1269.4 1233.8 1199.4 1.3 1360.1 1332.4 1299.2 1266.4 1235.3 1.5 1383.3 1357.1 1325.9 1295.3 1266.6 1.7 1404.8 1379.8 1350.2 1321.3 1294.5 1.9 1400.9 1372.5 1345.1 1319.8 2.1 1420.7 1393.3 1367.1 1343.1 2.3 1439.3 1412.7 1387.6 1364.7 2.5 1456.8 1431.1 1406.8 1384.9 2.7 1473.5 1448.4 1425.0 1403.9 2.9 1464.9 1442.3 1421.9 3.1 1480.6 1458.7 1439.1 3.3 1495.6 1474.4 1455.5 3.5 1510.1 1489.5 1471.2 3.7 1524.0 1504.0 1486.3 3.9 1537.4 1518.1 1500.9 4.1 1550.3 1531.6 1514.9 4.3 1562.8 1544.7 1528.6 4.5 1575.0 1557.4 1541.8

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The densities of the 1 m and 3 m aqueous NaCl solutions were combined with density data for water taken from IAPWS-95 (Wagner and Pruss, 2002) and Sanchez- Valle et al. (in prep.) to determine an empirical equation of state of the form:

T, P, X a(T) b(P) c(X ) d(T, P) e(T, P, X ) (4) H2O H2O H2O

with:

2 a(T) a1 a2 T a3 T

b(P) b1 P b2 P

c(X ) c X c X 2 H2O 1 H2O 2 H2O

d(T,P) d1 T P d2 T log( P) e(T, P, X ) e T X log( P) e T X log( P)2 e T 1( X )2 P H2O 1 H2O 2 H2O 3 H2O e T 1( X )2 / log( P) e T 1( X )2 / P 4 H2O 5 H2O

X where T is the temperature in Kelvin, P is the pressure in Pascal and H2O is the mole fraction of water. The coefficients ai , bi , ci , di and ei (Eq. (4)) determined from a least-square fitting of the experimentally derived density data (r 2 > 0.9999), are listed in Table 5.5.

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Table 5.5. Coefficients for Eq. (4).

Coefficients 12037.65593 ai a1 -8.95238 a2 1.46209x10 -5 a3 5.65321x10 -3 bi b1 5.85867x10 -9 b2 -21303.20538 ci c1 10469.39284 c2 -1.09237x10 -12 di d1 0.62224 d2 4.27249x10 -2 ei e1 1.24044x10 -2 e2 -2.38016x10 -9 e3 -951.29641 e4 1.78313x10 12 e5

The comparison between the experimentally derived densities and the values calculated from Eq. (4) for the 3 different compositions are reported in Figs. 5.4a-c). At pressures above 0.5 GPa the density fit is better than 0.4% and 0.2% for the 1 m and the 3m NaCl solutions, respectively. Only at the lowest pressure (0.5 GPa) and for temperatures above 473 K the misfit is around 0.8%. The density data of pure water (Sanchez-Valle et al., in prep.) are also fitted with accuracy better than 0.5% at pressures above 0.5 GPa (Fig. 5.4c). At this starting pressure, the maximum misfit is 0.7% for the

473 K and the 573 K isotherms. The acoustic velocity VP is derived from Eq. (4) and plotted in Figs. 5.3a and 5.3b. The maximum deviation between experimentally measured and predicted (Eq. (4)) acoustic velocities is about 2%, for all three compositions. According to error propagation calculations (Abramson and Brown, 2004; Sanchez-Valle et al., in prep.; Mantegazzi et al., submitted), an accuracy of 2% in the acoustic velocity values derived from the EoS proposed in this work attests a maximal associated error of 0.5 % in the densities calculated with Eq. (4).

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Figure 5.4. Density of a) 1m, b) 3m and c) 0m aqueous NaCl solutions as a function of pressure along isotherms from 293 to 1073 K. The symbols are densities determined from the integration of the experimental acoustic velocity data (Eqs. (2a)-(2c)) measured in NaCl aqueous solutions (this study) and in water (Sanchez-Valle et al., in prep.). Solid lines are densities calculated from the EoS proposed in this work (Eq. (4)) and the black dashed lines are densities extrapolated to 1073 K. Errors in density are smaller than the symbol size (0.3- 0.5%). The insets display the low pressure data (P < 1.2 GPa) compared with literature data from experimental and theoretical studies. The empty circles, empty squares, empty diamonds and triangles are the data of Mao and Duan (2008), Anderko and Pitzer (1993), Wagner and Pruss (2002), and Driesner (2007), respectively.

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A three-dimensional isothermal density surface calculated from Eq. (4) at 673 K is displayed in Fig. 5.5, and compared with the experimentally derived density data. The EoS (Eq. 4) can be used to determine the density for any concentration between 0 wt% NaCl ( X = 1) and 14.9 wt% NaCl ( X = 0.949). We estimate that a modest H2O H2O extrapolation to concentrations of ca. 22 wt.% NaCl may be permissible (Fig. 5.5). At 0.5 GPa and a water mole fraction of 0.925 (ca. 21 wt.% NaCl) the density values extrapolated from our EoS are compared with the density data calculated with the comprehensive EoS proposed by Anderko and Pitzer (1993). At 673, 873 and 1073 K the densities obtained from the two EoS agree with a misfit of about 1.2%, 1.5% and 1.7%, respectively. Eq. (4) was further used to derive the thermodynamic properties of NaCl aqueous solutions, including thermal expansion, heat capacities and compressibility up to 673 K and 4.5 GPa using well-known thermodynamic relations. The procedure and results are reported in the appendix.

Figure 5.5. Three dimensional plot of the density of fluids in the H 2O NaCl binary system at 673 K from 0.5 to 4.5 GPa as a function of the molar fraction of water. The grey surface is obtained from Eq. (4) for the concentration range investigated in this work (molar fraction of water X H2O between 0.949 and 1). The white surface represents the extrapolation of Eq. (4) up to a molar fractions X H2O = 0.92, corresponding to a 4.83 m aqueous NaCl solution. The black dots are the density data derived from Eqs. (2a)-(2c). The values for water are taken from Sanchez- Valle et al. (in prep.).

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5.3.3 Extension of the EoS to 1073 K Fluid processes in subduction zones typically take place at temperatures in excess of

673 K and therefore, the application of the EoS of fluids in the H2O NaCl binary to model natural processes would require the extension of the data to temperatures beyond those covered by the present experiments. To extend the EoS to 1073 K, several isochores were calculated for each composition up to 673 K using the EoS (Eq. 4). Since isochors are known to be well-behaved over large pressure intervals, we tested the extrapolation behavior of the EoS (Eq. 4) by fitting the isochors to 673 K with quadratic polynomials and comparing the extrapolations of both the polynomials and the EoS to 1073 K (Fig. 5.6a-c). Differences in the extrapolated densities are found to be smaller than 0.3% below 873 K and smaller than 0.7% up to 1073 K. Isochores for water calculate using the EoS (Eq. 4) also agree with values calculated from the IAPWS-95 EoS (Wagner and Pruss, 2002) within 0.5% up to 873 K, which is within the overall accuracy of the EoS, and with a maximal misfit of 1% at 1073K. We conclude that the proposed EoS (Eq. 4) can confidentially be used to calculate the density of NaCl-H2O aqueous solutions up to 1073 K and 4.5 GPa. Fig. 5.7 displays the 95% confidence interval of the fit of the experimentally derived density data with Eq. 4 along some selected isochors for the 1 m aqueous NaCl solution as a function of the temperature. In the extrapolated region (T > 673 K) the confidence interval bands lie within less than 0.85% difference from the isochore values. Successively, all other thermodynamic data were also calculated to 1073 K and reported in Table 5.A1. The acoustic velocity values for the 0 m NaCl solution reported in Table 5.A1 show that at 973 K the V p is about 1.5% larger than at 873 K, while at 1073 K the values are up to 3.7% larger than at 973 K. This observation suggests that in case of the low NaCl concentrations (below 1 m) larger associated uncertainties at T > 873 K in the derived V P (up to ca. 4% at 1073 K), and related properties like adiabatic compressibility and bulk modulus, should be taken into account.

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Figure 5.6. Isochores for the NaCl aqueous solutions investigated in this work: a) 1m, b) 3m and c) 0m aqueous NaCl solutions to 1073 K and 4.5 GPa. The black solid lines are isochors up to 673 K calculated from the EoS proposed in this work (Eq. 4). The black dashed lines are density isochores extrapolated beyond 673 K using the EoS proposed (Eq.4). The black dotted lines are the values obtained from the fit of the densities with 2 nd order polynomial functions at temperatures below 673 K and then extrapolated to higher temperatures. In c) the squares are the densities of pure water calculated with the IAPWS-95 EoS (Wagner and Pruss, 2002).

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Figure 5.7. Selected isochores for the 1 m NaCl solution. The solidlines represent the isochores calculated to 1073 K with the EoS proposed in this work (Eq. 4), while the dashed lines define the confidence intervals (95%) calculated for the different isochores. The grey shadowed area shows the extrapolation of the EoS beyond the temperature range covered by the experiments (T > 673 K).

5.3.5. Partial molar volume and fugacity of water in salt solutions

The partial molar volume and fugacity of the fluid as a function of salt X concentration, expressed as water molar fraction H2O , is a fundamental thermodynamic property in the quantitative evaluation of mineral reactions involving fluid phases. The EoS proposed in this work for salt solutions (Eq. 4) was used to evaluate the partial molar volume and fugacity for fluids in the 0 3m NaCl range up to 1073 K and 4.5 GPa. The fugacity of a pure component ( e.g ., water) is related to its molar volume by the relationship:

P 0 0 0 Vi dP R T ln( fi ) R T ln( fi,P ) (5) 0 P0

0 where, R is the gas constant, T the temperature, Vi is the molar volume of the pure

0 0 component, f is the fugacity of the pure component at P, and f i,P is the fugacity of the i 0 pure component at the reference state pressure P 0. In a mixture (e.g., H 2O-NaCl) the fugacity fi a component is defined by (Aranovich and Newton, 1999):

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P 0 R T ln( fi ) VidP 2 R T ln( X i ) R T ln( fi,P ) (6) P 0 0

where, Vi is the partial molar volume of the component in the mixture, X i is the

0 molar fraction of the component in the mixture and fi,P is the fugacity of the pure 0 component at the reference state pressure P 0. This equation assumes ideal behavior of the

0 components at P 0. Fugacity of pure water at 0.5 GPa ( fi,P ) was calculated from the 0 Compensated Redlich-Kwong (CORK) EoS of Holland and Powell (1991), which provides fugacity of H 2O up to 5 GPa and 1773 K. Water fugacities as a function of the water molar fraction X were calculated from the partial molar volume (Eq. 4) H2O Vi according to the relationship (Anderson, 2005):

V V V m V 1( X ) m (7) i H2O n m H2O X i P,T ,n H2O P,T

where, Vm is the molar volume of the mixture calculated as:

M H O NaCl (X H O ) V (T, P) 2 2 (8) m (T, P, X ) H2O

M (X ) where H2O NaCl H2O is the molar mass of the solution as a function of (T, P, X ) concentration, and H2O is the density calculated using our EoS (Eq. 4). The partial molar volumes of water calculated as a function of the pressure and the temperature in the three concentrations investigated are reported in Table 5.6. Fig. 5.8a shows the partial molar volume of water at 673 K and 1073 K in the three different solutions investigated in this work. The water partial molar volume decreases upon increasing salt concentration, most likely due to the disruption and collapse of the hydrogen-bonded structure of water caused by the NaCl species (Walrafen, 1962; Li et al., 2004). The molar volume of water (0 m) along several isotherms is compared to values calculated from the IAPWS-95 EoS (Wagner and Pruss, 2002) and from the EoS

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proposed by Sanchez-Valle et al. (in prep.) in Fig. 5.8b. The difference between the values calculated in this work and the IAPWS-95 EoS is generally less than 0.4%, with a maximum deviation of 0.7% at 0.5 GPa and 473 K and 573 K. At temperatures higher than 673 K the misfit increases to a maximal value of 0.4%, 0.9% and 1.7% at 873 K, 973 K and 1073 K, respectively. Water fugacities calculated from Eq. (6) using the partial molar volume of water and P 0 equal to 0.5 GPa, are tabulated in Table 5.7.

Table 5.6. Partial molar volume of water (x10 -6 m3/mol) in the different NaCl aqueous solutions investigated in this work.

0m XH20 = 1 P (GPa) 293 K 373 K 473 K 573 K 673 K 773 K 873 K 973 K 1073 K 0.5 15.59 16.27 17.19 18.23 19.39 20.70 22.20 23.92 25.92 0.7 15.06 15.63 16.41 17.25 18.19 19.23 20.38 21.68 23.14 0.9 14.66 15.16 15.83 16.56 17.36 18.23 19.18 20.24 21.41 1.1 14.79 15.38 16.03 16.72 17.48 18.30 19.19 20.18 1.3 14.47 15.01 15.59 16.21 16.88 17.61 18.39 19.24 1.5 14.20 14.70 15.23 15.79 16.39 17.04 17.74 18.49 1.7 13.96 14.42 14.91 15.43 15.98 16.57 17.20 17.87 1.9 13.75 14.17 14.63 15.11 15.62 16.16 16.73 17.34 2.1 13.55 13.95 14.38 14.83 15.30 15.80 16.33 16.89 2.3 13.37 13.75 14.15 14.57 15.02 15.48 15.97 16.49 2.5 13.21 13.57 13.95 14.34 14.76 15.19 15.65 16.14 2.7 13.40 13.76 14.13 14.52 14.93 15.36 15.82 2.9 13.24 13.58 13.94 14.31 14.70 15.10 15.53 3.1 13.10 13.42 13.76 14.11 14.48 14.86 15.26 3.3 12.96 13.27 13.59 13.93 14.28 14.64 15.02 3.5 12.83 13.13 13.43 13.76 14.09 14.43 14.79 3.7 12.71 12.99 13.29 13.59 13.91 14.24 14.59 3.9 12.59 12.86 13.15 13.44 13.75 14.06 14.39 4.1 12.48 12.74 13.02 13.30 13.59 13.89 14.21 4.3 12.63 12.89 13.16 13.44 13.73 14.03 4.5 12.52 12.77 13.03 13.31 13.58 13.87

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X = 1m H20 0.982 P (GPa) 293 K 373 K 473 K 573 K 673 K 773 K 873 K 973 K 1073 K 0.5 15.59 16.25 17.15 18.15 19.26 20.51 21.92 23.53 25.38 0.7 15.06 15.62 16.36 17.18 18.07 19.06 20.14 21.36 22.71 0.9 14.66 15.14 15.79 16.49 17.25 18.07 18.97 19.95 21.03 1.1 14.33 14.77 15.34 15.96 16.62 17.33 18.10 18.94 19.84 1.3 14.45 14.97 15.52 16.12 16.75 17.42 18.15 18.94 1.5 14.18 14.66 15.16 15.70 16.26 16.87 17.52 18.21 1.7 13.94 14.38 14.84 15.33 15.85 16.40 16.99 17.61 1.9 13.73 14.14 14.57 15.02 15.50 16.00 16.53 17.10 2.1 13.53 13.92 14.32 14.74 15.18 15.65 16.14 16.65 2.3 13.36 13.72 14.09 14.49 14.90 15.33 15.79 16.26 2.5 13.19 13.53 13.89 14.26 14.65 15.05 15.48 15.92 2.7 13.37 13.70 14.05 14.42 14.80 15.19 15.61 2.9 13.21 13.53 13.86 14.20 14.56 14.94 15.32 3.1 13.06 13.37 13.68 14.01 14.35 14.70 15.06 3.3 12.92 13.21 13.51 13.83 14.15 14.48 14.83 3.5 12.79 13.07 13.36 13.66 13.96 14.28 14.60 3.7 12.67 12.94 13.21 13.50 13.79 14.09 14.40 3.9 12.55 12.81 13.07 13.35 13.62 13.91 14.21 4.1 12.44 12.69 12.94 13.20 13.47 13.75 14.03 4.3 12.57 12.82 13.07 13.33 13.59 13.86 4.5 12.46 12.70 12.94 13.19 13.44 13.70

X = 3m H20 0.949 P (GPa) 293 K 373 K 473 K 573 K 673 K 773 K 873 K 973 K 1073 K 0.5 15.62 16.15 16.87 17.64 18.48 19.40 20.40 21.51 22.74 0.7 15.07 15.50 16.08 16.69 17.35 18.06 18.82 19.65 20.54 0.9 14.65 15.02 15.51 16.03 16.58 17.16 17.78 18.44 19.14 1.1 14.32 14.64 15.07 15.51 15.98 16.48 17.00 17.55 18.13 1.3 14.04 14.33 14.70 15.10 15.51 15.94 16.39 16.86 17.36 1.5 13.79 14.05 14.39 14.75 15.11 15.49 15.89 16.30 16.73 1.7 13.57 13.81 14.12 14.44 14.77 15.11 15.47 15.83 16.21 1.9 13.60 13.88 14.17 14.47 14.78 15.10 15.43 15.77 2.1 13.41 13.67 13.93 14.21 14.49 14.78 15.07 15.38 2.3 13.23 13.47 13.71 13.97 14.22 14.49 14.76 15.04 2.5 13.06 13.29 13.52 13.75 13.99 14.23 14.48 14.73 2.7 12.91 13.12 13.33 13.55 13.77 13.99 14.22 14.45 2.9 12.97 13.16 13.36 13.57 13.77 13.98 14.20 3.1 12.82 13.00 13.19 13.38 13.57 13.77 13.97 3.3 12.68 12.86 13.03 13.21 13.39 13.57 13.75 3.5 12.55 12.72 12.88 13.05 13.21 13.38 13.55 3.7 12.43 12.58 12.74 12.89 13.05 13.21 13.37 3.9 12.32 12.46 12.60 12.75 12.90 13.04 13.19 4.1 12.20 12.34 12.48 12.61 12.75 12.89 13.03 4.3 12.10 12.23 12.36 12.48 12.61 12.74 12.87 4.5 12.00 12.12 12.24 12.36 12.48 12.60 12.72

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Figure 5.8. a) Partial molar volume of water at 673 K (solid lines) and 1073 K (dashed lines) in the three concentrations investigated in this work calculated with Eq. (7). b) Partial molar volume of water for the 0 m aqueous NaCl solution along several isotherms up to 1073 K. The solid and dashed lines are the values calculated with Eq. (7), while the open squares and the cross symbols are values calculated from the IAPWS-95 EoS (Wagner and Pruss, 2002) and taken from Sanchez-Valle et al. (in prep.), respectively. At this concentration the partial molar volume of water is equivalent to its molar volume.

5.4. Discussion

5.4.1. Comparison with other EoS in the H2O-NaCl binary system The lack of experimental or theoretical equations of state for NaCl aqueous fluids at the pressure conditions of this study limits the comparison of the present results.

Available data for the thermodynamic properties of H 2O-NaCl solutions are restricted to pressures below 0.5 GPa, which set the lower pressure limit for the validity of the EoS proposed here. The insets in Figs. 5.4a-c) show details of the density data predicted in the low pressure range (0.5 1.2 GPa) by the present EoS and available literature data at pressures below 0.5 GPa. This includes the EoS of Driesner (2007), the theoretical EoS of Mao and Duan (2008), the IAPWS-95 EoS for pure water (Wagner and Pruss, 2002), and

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for the 3 m aqueous NaCl solution at high temperature the theoretical EoS of Anderko and Pitzer (1993). The most significant feature of these figures is that the low pressure EoS (Driesner, 2007; Mao and Duan, 2008) and the present EoS agree well in the overlapping conditions, with differences in density smaller that 0.4% at 0.5 GPa to 673 K. At 873 K and 1073 K the misfit with the data of Driesner (2007) at 0.5 GPa increases to 2.7% and 4.2%, respectively. The comparison with the EoS of Anderko and Pitzer (1993) at 0.5 GPa and 673 K (Fig. 5.4b) shows a difference smaller than 0.3%, whereas at 873 K and 1073 K, the misfit increases to about 5% and 7%, respectively. As reported in Section 5.3.2, at higher NaCl concentrations (ca. 21 wt.% NaCl) the comparison between our EoS and the EoS of Anderko and Pitzer (1993) shows a misfit smaller than 2% up to 1073 K at 0.5 GPa. The excellent agreement between the density data of pure water calculate from our EoS and the IAPWS-95 values is showed in the small inset in Fig. 5.4c. The overall agreement is better than 0.5% up to 973 K, and only at 1073 K the differences increases to about 1.5%. These observations suggest that a combination of the low pressure data and the extension of the EoS up to 4.5 GPa proposed here allows to predict continuously the properties of NaCl aqueous fluids from room pressure up to 4.5 GPa. The accuracy of the predicted density data is better than 0.3-0.5% at temperatures up to 673 K, and about 2%-4% in the extrapolated region. The EoS proposed in this work provides a predictive model for the properties of aqueous NaCl fluids up to 1073 K and 4.5 GPa.

5.4.2. Thermodynamic properties of H 2O-NaCl fluids to 1073 K and 4.5 GPa

The thermodynamic properties of H 2O-NaCl fluids calculated from the EoS generated in this wok and its extension up to 1073 K are listed in Table 5.A1 (Appendix). At 673 K and 0.5 GPa, pure water is 5.4% and 12% less dense than 1 m and 3 m NaCl solutions, respectively. At 4.5 GPa these differences decrease to 4.3% and 9.3%. The 3 m NaCl solution is 6.2% denser then the 1 m NaCl solution at 0.5 GPa and 4.7% denser at 4.5 GPa. We note that the changes in density contrast with pressure are larger than the estimated accuracy in the pressure determination and that they are observed along each isotherm investigated and tentatively be explained at the molecular scale. At room conditions, water structure have a three dimensional hydrogen-bonded network

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with tetrahedral arrangement of the nearest neighbors and is characterized by a relative open structure (e.g.,Soper and Ricci, 2000; Saitta and Datchi, 2003; Strassle et al., 2006). An increase in pressure leads to a reduction of the strength (Saitta and Datchi, 2003; Strassle et al., 2006), or to the disruption (Soper and Ricci, 2000) of the intermolecular bonds. The addition of ions to water induces similar structural changes, because the water structure collapses around the ions to solvate them (Leberman and Soper, 1995; Cavaille et al., 1996). An increase in pressure will have, therefore, a larger effect on the open molecular structure of pure water than of an electrolyte solution that already exhibits a more compacted structure. This effect will result in a larger density increment as a function of the pressure, and consequently, in a decreasing density contrast between pure water and H 2O-NaCl solutions. Between two H 2O-NaCl fluids, the concentration of NaCl will determine the magnitude of this change, depending of the degree of disruption on the water structure. We note however that the interpretation of the effect of salt in the density of high pressure water would require structural information on the structure of high pressure salt solutions that is not often available at the pressures of interest. The isobaric heat capacity and thermal expansion as a function of pressure at 473, 673 and 1073 K are plotted in Figs. 5.9a)-f). Literature data for pure water at 473 K (Wiryana et al., 1998; Wagner and Pruss, 2002; Sanchez-Valle et al., in prep.), are also shown for comparison. At 1.1 GPa the pure water has a C P 7.1% and 20.3% larger than the 1 m and the 3 m NaCl aqueous solution, respectively. At 4.1 GPa the difference decreases to 5.3% and 18.1%. From 1.1 GPa to 4.1 GPa the difference between 1 m and 3m NaCl solutions diminishes from 14.2% to 13.5%. On the other hand, the thermal expansion of water at 1.1 GPa is 13% and 21% higher values than the 1 m and the 3 m NaCl solutions, respectively. At 4.1 GPa these differences increase to 27% and 45%, respectively. The 3 m NaCl solution has at 1.1 GPa 9.3% and at 4 GPa 25% lower thermal expansion values than the 1 m NaCl solution. At 3.1 GPa values of (Wiryana et al., 1998) and (Wagner and Pruss, 2002) are 12% and 7% higher than coefficient of thermal expansion for pure water calculated in this work. At 673 K and 1073 K the same trend of decreasing coefficient of thermal expansion with increasing NaCl concentration is observed, although, the values for pure water calculated from Eq. (4) at 3.1 GPa are 4% and 27 % larger than the thermal expansion

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calculated from the IAPWS-95 (Wagner and Pruss, 2002), respectively. The isobaric heat capacity of pure water at 1073 K derived from our EoS shows an unexpected trend becoming smaller than the C P values of the 1 m and the 3 m NaCl solutions by 18% and 11% at 4.5 GPa, respectively.

151

152

Figure 5.9 a)-f) (previous page). Coefficient of thermal expansion and isobaric heat capacity C P at 473 K, 673 K and 1073 K as a function of pressure calculated for the 0 m, 1 m and 3 m NaCl solutions using the EoS proposed in this work (Eq. 4). Values for pure water taken from Wiryana et al. (1998) (dashed dotted dark grey line), IAPWS-95 (Wagner and Pruss, 2002) (light grey dashed line) and Sanchez-Valle et al. (in prep.) (black dashed line) are also shown for comparison.

5.5. Effect of fluid composition on dehydration reactions in subducted oceanic crust

The EoS for NaCl aqueous fluids presented here can be used to evaluate the effect of fluid composition on the location of reaction boundaries in a dehydrating subducting oceanic crust. We chose the reaction albite + chlorite + quartz = glaucophane + paragonite + water that marks the transition from greenschists facies to blueschists facies metamorphism (Bucher and Frey, 1994) during the subduction of mafic ( i.e ., basalt and gabbro) rocks (Fig. 5.10a), and is one of the several mineral reactions responsible for the continuous dehydration of the subducting oceanic lithosphere (Schmidt and Poli, 1998).

The mineral reaction is written as (Bucher and Frey, 1994):

. . 13 NaAlSi 3O8 + 3 Mg 5Al 2Si 3O10 (OH) 8 + SiO 2 = albite chlorite quartz

. . . = 5 Na 2Mg 3Al 2Si 8O22 (OH) 2 + 3 NaAl 3Si 3O10 (OH) 2 + 4 H2O (9) glaucophane paragonite water

At equilibrium: T T C P G ( H ) C dT T S T P dT VdP R T ln( K) 0 r f P0,T0 P P0,T0 T0 T0 T P0 (10)

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where, is the Gibbs free energy of the reaction, ( H ), S , and Gr f P0,T0 P0,T0 CP

V are, the formation enthalpy at the reference state P 0, T 0, the entropy at the reference state P 0, T 0, heat capacity and the volume, respectively, and the delta ( ) notation refers to the difference between the products and the reactants. K is the equilibrium constant of the reaction. For the dehydration reaction (Eq. 9) Eq. (10) becomes:

T T C P G ( H ) C dT T S T P dT VdP 4 R T ln( f ) 0 r f P0,T0 P P0,T0 H2O T0 T0 T P0 (11) applying the relationship:

f H2O aH O (12) 2 f 0 H2O where a is the activity of water. H2O

X The equilibrium temperature as a function of the water molar fraction H2O was calculated at several pressures (Eq. 11) using the water fugacity reported in Table 5.7. The thermodynamic data for the minerals in Eq. (9) were taken from the Thermocalc database (Holland and Powell, 1998). Fig. 5.10b compares the equilibrium pressure and temperature conditions calculated using our EoS for water with the results provided by Thermocalc (Holland and Powell, 1998). The agreement is excellent, with a difference in pressure smaller than 1%. Fig. 5.10b displays the reaction boundaries determined for water activities decreased by the presence of NaCl species dissolved in the fluid.

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Figure 5.10. a) Pressure-Temperature diagram illustrating the different metamorphic facies (modified after Bucher and Frey, 1994). The dashed square highlights the P-T conditions of b). b) Equilibrium P-T conditions of mineral reaction (9) calculated as a function of the water molar fraction for X = 1, X = 0.982 and X = 0.949, corresponding, respectively, to pure H2O H2O H2O

H2O, 1 m NaCl and 3 m NaCl solution. The black dashed line are the equilibrium conditions modeled with Thermocalc (Holland and Powell, 1998). A typical slow subduction geotherm is shown (from Bucher and Frey, 1994).

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-1 Table 5.7. Water fugacity reported as RTlnf H2O (kJ mol ).

0m XH20 = 1 P (GPa) 293 K 373 K 473 K 573 K 673 K 773 K 873 K 973 K 1073 K 0.5 10.94 15.02 22.95 31.77 40.04 49.18 58.02 66.61 74.99 0.7 14.00 18.21 26.31 35.31 43.79 53.16 62.26 71.15 79.87 0.9 16.97 21.28 29.53 38.69 47.34 56.90 66.21 75.33 84.32 1.1 24.28 32.65 41.95 50.75 60.47 69.96 79.27 88.47 1.3 27.20 35.69 45.11 54.04 63.91 73.55 83.03 92.41 1.5 30.07 38.66 48.19 57.24 67.23 77.01 86.64 96.18 1.7 32.88 41.57 51.20 60.36 70.47 80.37 90.13 99.81 1.9 35.65 44.43 54.16 63.41 73.63 83.64 93.52 103.33 2.1 38.38 47.24 57.06 66.41 76.72 86.84 96.83 106.75 2.3 41.08 50.01 59.91 69.35 79.75 89.96 100.06 110.09 2.5 43.74 52.74 62.72 72.24 82.73 93.03 103.22 113.35 2.7 55.44 65.49 75.08 85.66 96.04 106.32 116.55 2.9 58.10 68.22 77.89 88.54 99.01 109.37 119.68 3.1 60.74 70.93 80.66 91.38 101.93 112.37 122.76 3.3 63.34 73.59 83.40 94.18 104.80 115.32 125.79 3.5 65.92 76.23 86.10 96.95 107.64 118.22 128.77 3.7 68.47 78.85 88.77 99.69 110.44 121.09 131.71 3.9 71.01 81.43 91.42 102.39 113.20 123.92 134.60 4.1 73.51 83.99 94.03 105.07 115.94 126.72 137.46 4.3 86.53 96.62 107.71 118.64 129.48 140.29 4.5 89.04 99.19 110.33 121.32 132.21 143.08

X = 1m H20 0.982 P (GPa) 293 K 373 K 473 K 573 K 673 K 773 K 873 K 973 K 1073 K 0.5 10.85 14.91 22.81 31.60 39.84 48.95 57.76 66.32 74.67 0.7 13.91 18.09 26.15 35.12 43.56 52.89 61.95 70.79 79.45 0.9 16.89 21.16 29.37 38.49 47.09 56.60 65.85 74.91 83.82 1.1 19.78 24.15 32.48 41.73 50.47 60.14 69.56 78.79 87.90 1.3 27.08 35.51 44.88 53.75 63.54 73.11 82.50 91.77 1.5 29.94 38.47 47.94 56.93 66.84 76.54 86.07 95.48 1.7 32.75 41.37 50.94 60.03 70.05 79.86 89.51 99.06 1.9 35.52 44.23 53.88 63.06 73.19 83.10 92.87 102.53 2.1 38.24 47.03 56.77 66.04 75.26 86.27 96.13 105.91 2.3 40.93 49.79 59.61 68.96 79.26 89.36 99.32 109.20 2.5 43.59 52.52 62.41 71.84 82.22 92.40 102.45 112.42 2.7 55.21 65.17 74.67 85.13 95.39 105.52 115.57 2.9 57.87 67.89 77.46 87.99 98.38 108.53 118.66 3.1 60.49 70.58 80.21 90.81 101.21 111.49 121.70 3.3 63.09 73.24 82.93 93.59 104.06 114.41 124.69 3.5 65.66 75.87 85.62 96.34 106.87 117.29 127.63 3.7 68.21 78.47 88.28 99.06 109.65 120.12 130.53 3.9 70.73 81.05 90.91 101.74 112.39 122.92 133.39 4.1 73.21 83.60 93.51 104.39 115.10 125.69 136.22 4.3 86.12 96.08 107.02 117.78 128.42 139.04 4.5 88.63 98.64 109.62 120.43 131.13 141.76

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X = 3m H20 0.949 P (GPa) 293 K 373 K 473 K 573 K 673 K 773 K 873 K 973 K 1073 K 0.5 10.68 14.69 22.54 31.27 39.45 48.51 57.26 65.76 74.06 0.7 13.75 17.86 25.83 34.70 43.03 52.24 61.17 69.86 78.37 0.9 16.72 20.91 28.98 37.97 46.42 55.76 64.82 73.67 82.32 1.1 19.62 23.87 32.04 41.12 49.67 59.12 68.30 77.26 86.05 1.3 22.45 26.77 35.02 44.18 52.82 62.36 71.64 80.70 89.59 1.5 25.23 29.61 37.93 47.16 55.88 65.50 74.86 84.02 93.00 1.7 27.97 32.39 40.78 50.08 58.87 68.56 78.00 87.23 96.30 1.9 35.13 43.58 52.94 61.79 71.55 81.05 90.35 99.49 2.1 37.83 46.33 55.75 64.66 74.48 84.04 93.40 102.61 2.3 40.50 49.04 58.52 67.48 77.35 86.97 96.38 105.65 2.5 43.13 51.72 61.24 70.25 80.17 89.84 99.31 108.62 2.7 45.72 54.36 63.92 72.98 82.94 92.66 102.18 111.54 2.9 56.97 66.57 75.67 85.68 95.43 105.00 114.41 3.1 59.55 69.19 78.32 88.37 98.17 107.77 117.22 3.3 62.10 71.77 80.95 91.03 100.87 110.51 119.99 3.5 64.62 74.33 83.54 93.66 103.52 113.20 122.72 3.7 67.12 76.86 86.10 96.25 106.15 115.86 125.42 3.9 69.59 79.37 88.63 98.81 108.75 118.48 127.01 4.1 72.05 81.85 91.14 101.35 111.31 121.08 130.69 4.3 74.48 84.30 93.62 103.86 113.85 123.64 133.28 4.5 76.89 86.74 96.08 106.34 116.36 126.18 135.84

Figure. 5.11. Comparison between equilibrium conditions for the mineral reaction (Eq. 9) for a

NaCl concentration of 3 m (X H2O = 0.949) calculated assuming ideal mixing of water and NaCl (black dashed line) and non-ideal (real) mixing (black solid line).

157

Fig. 5.11 shows the equilibrium line of the mineral reaction (9) calculated assuming ideal mixing of sodium chloride and water (i.e. , a H2O = X H2O ) in comparison with the equilibrium conditions obtained from our EoS (Eqs. 6 and 12) for a NaCl concentration of 3 m. Our results show that at high pressure and temperature conditions NaCl and water . do not mix ideally (i.e. , a H2O = XH2O ), in agreement with the results of high pressure and temperature piston cylinder experiments on the H 2O activity in concentrated NaCl and KCl solutions measured by the brucite-periclase equilibrium (Aranovich and Newton, 1996; Aranovich and Newton, 1997). The experimental data of Aranovich and Newton

(1996) suggest that at low pressure conditions the undissociated NaCl and H 2O do mix ideally, while at pressures higher than 1 GPa the activity of water in NaCl solutions decreases exponentially. This effect most probably derives from pressure-induced dissociation of NaCl to Na + and Cl - (Aranovich and Newton, 1996), as the dissolved Na + and Cl - ions affect the intermolecular structure of water (Leberman and Soper, 1995; Cavaille et al., 1996) decreasing its activity. We observe that the reaction boundaries of the mineral reaction (9) shift towards higher temperature and lower pressures as the molar fraction of water in the fluid decreases (Fig. 5.10b). This observation implies that the transition to blueschist facies metamorphism will take place at shallower depths when the activity of water decreases along a typical slow subduction geotherm. Considering that NaCl are the most important solute species in subduction zone fluids at shallow depth and that salt concentration in the system will decrease as subduction progresses, we may expect an increase in the activity of water and an increase of the depth of the dehydration reactions. In a more general picture, the variation of water activity propagates the depth of dehydration reactions in the P-T space, supporting the idea that dehydration is a continuous process in the geodynamic cycle of a subducting oceanic lithosphere (Schmidt and Poli, 1998).

5.6. Conclusions

With the aim to reducing the gap between the available thermodynamic data of chloride-rich aqueous fluids and deep lithospheric conditions, Brillouin measurements were performed in 1m and 3 m aqueous NaCl solutions in mDAC. The acoustic velocities

158

are measured along five isotherms at 293, 373, 473, 573 and 673 K up to 4.5 GPa, with a precision and an estimated accuracy better than 1%. The density data calculated of these two NaCl aqueous solutions together with densities of pure water taken from Wagner and Pruss (2002) and Sanchez-Valle et al. (in prep.) were fitted with Eq. (4), with a misfit smaller than 0.8% at the starting pressure (0.5 GPa) and a general agreement better than 0.5% at higher pressures. The density values calculated with Eq. (4) are then extrapolated in temperature to 1073 K, and it has been shown that this EoS could be extrapolated in concentration up to a maximal molality equivalent to 4.83 m, corresponding to 22 wt% NaCl. The EoS proposed in this work covers a broad range of temperatures, pressures and compositions, representative for a cold subduction zone environment at shallow to intermediate depth: 293 to 1073 K, 0.5 GPa to 4.5 GPa, 0 m to 3 m. This EoS can be used to derive all other thermodynamic parameters ( e.g. , coefficient of thermal expansion, isobaric heat capacity, compressibility, bulk modulus, partial molar volume and water fugacity) of the H2O-NaCl solutions. As a first petrological application this EoS is used to derive water fugacity values as a function of the solution concentration. These data are used to model the mineral reaction albite + chlorite + quartz = glaucophane + paragonite + water, which takes place in the validity range of the EoS proposed in this work, showing that along slow subduction geotherms the transition from greenschist to blueschist facies will occur at shallower depths by decreasing water activity.

159

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Appendix

The EoS for H2O NaCl binary solutions (Eq. (4)) was used to determine the pressure and temperature dependence of thermodynamic properties according to the following equations:

1 - thermal expansion: P T P

C 2 - isobaric heat capacity: P T v P 2 T T P

T 2 - isothermal compressibility: 1 P T 2 C VP P

- adiabatic compressibilities: 1 s 2 VP 1 - bulk modulus: KT ,S T ,S All thermodynamic properties for pure water (0 m), 1m and 3 m aqueous NaCl solutions are derived up to 1073 K and 4.5 GPa and are listed in Table 5.A1. At temperatures up to

673 K, the maximal uncertainties on the coefficient of thermal expansion P and the isobaric heat capacity C P are estimated according to error propagation calculations to be about 1-1.5%, whereas larger uncertainties of 3.5-4% and 7-8% are estimated for the adiabatic and isothermal bulk modulus (K S and K T) and compressibility ( S and T) , respectively. For the thermodynamic properties calculated at T higher than 673 K larger maximal uncertainties are estimated: 4% for density, 8% for thermal expansion and heat capacity, 12% for adiabatic compressibility and bulk modulus, and about 25% for isothermal compressibility and bulk modulus.

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Table 5.A1. Thermodynamic properties for water and 1 m, 3 m NaCl solutions up to 1073 K and 4.5 GPa.

0m P Density VSP VP CP S KS T KT 293 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 1155.6 0.87 2186 5.2071 3766.5 1.81 0.55 1.99 0.50 0.7 1196.0 0.84 2478 4.5719 3740.3 1.36 0.73 1.50 0.67 0.9 1228.7 0.81 2709 4.1319 3721.0 1.11 0.90 1.22 0.82

1m P Density VSP VP CP S KS T KT 293 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 1183.8 0.85 2204 4.5896 3265.9 1.74 0.58 1.90 0.53 0.7 1224.8 0.82 2478 3.9643 3246.2 1.33 0.75 1.45 0.69 0.9 1257.9 0.80 2696 3.5319 3232.3 1.09 0.91 1.18 0.84 1.1 1286.1 0.78 2878 3.2073 3221.8 0.94 1.07 1.01 0.99

3m P Density VSP VP CP S KS T KT 293 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 1235.1 0.81 2261 4.1953 2943.4 1.58 0.63 1.73 0.58 0.7 1275.4 0.78 2474 3.5642 2927.8 1.28 0.78 1.38 0.72 0.9 1308.5 0.76 2680 3.1277 2917.2 1.06 0.94 1.14 0.88 1.1 1336.8 0.75 2854 2.8010 2909.4 0.92 1.09 0.98 1.02 1.3 1361.9 0.73 3006 2.5438 2903.5 0.81 1.23 0.86 1.16 1.5 1384.6 0.72 3141 2.3344 2898.9 0.73 1.37 0.77 1.30 1.7 1405.3 0.71 3262 2.1594 2895.2 0.67 1.50 0.70 1.42

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0m P Density VSP VP CP S KS T KT 373 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 1107.6 0.90 2093 5.4118 3764.3 2.06 0.49 2.32 0.43 0.7 1152.4 0.87 2390 4.7248 3726.6 1.52 0.66 1.71 0.58 0.9 1188.2 0.84 2626 4.2531 3699.4 1.22 0.82 1.37 0.73 1.1 1218.5 0.82 2822 3.9006 3678.2 1.03 0.97 1.16 0.86 1.3 1245.0 0.80 2990 3.6227 3661.0 0.90 1.11 1.01 0.99 1.5 1268.8 0.79 3137 3.3956 3646.7 0.80 1.25 0.89 1.12 1.7 1290.6 0.77 3267 3.2051 3634.5 0.73 1.38 0.81 1.24 1.9 1310.6 0.76 3385 3.0420 3623.9 0.67 1.50 0.74 1.35 2.1 1329.4 0.75 3493 2.9002 3614.7 0.62 1.62 0.68 1.47 2.3 1347.0 0.74 3591 2.7752 3606.5 0.58 1.74 0.63 1.58 2.5 1363.6 0.73 3683 2.6640 3599.1 0.54 1.85 0.59 1.68

1m P Density VSP VP CP S KS T KT 373 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 1140.5 0.88 2054 4.7436 3449.5 2.0777 0.48 2.29 0.44 0.7 1186.0 0.84 2340 4.0741 3421.7 1.5400 0.65 1.69 0.59 0.9 1222.4 0.82 2567 3.6152 3402.4 1.2413 0.81 1.36 0.74 1.1 1253.2 0.80 2757 3.2728 3387.9 1.0500 0.95 1.14 0.87 1.3 1280.2 0.78 2919 3.0036 3376.6 0.9165 1.09 0.99 1.01 1.5 1304.4 0.77 3062 2.7841 3367.4 0.8175 1.22 0.88 1.13 1.7 1326.5 0.75 3190 2.6004 3359.8 0.7409 1.35 0.80 1.25 1.9 1346.9 0.74 3305 2.4435 3353.4 0.6797 1.47 0.73 1.37 2.1 1365.9 0.73 3410 2.3073 3348.0 0.6296 1.59 0.67 1.49 2.3 1383.7 0.72 3507 2.1877 3343.4 0.5876 1.70 0.63 1.60 2.5 1400.6 0.71 3597 2.0814 3339.3 0.5519 1.81 0.59 1.71

3m P Density VSP VP CP S KS T KT 373 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 1193.7 0.84 2105 4.3210 2952.2 1.89 0.53 2.09 0.48 0.7 1239.1 0.81 2329 3.6496 2930.4 1.49 0.67 1.62 0.62 0.9 1275.8 0.78 2544 3.1894 2915.8 1.21 0.83 1.31 0.76 1.1 1306.9 0.77 2726 2.8471 2905.3 1.03 0.97 1.11 0.90 1.3 1334.2 0.75 2884 2.5790 2897.3 0.90 1.11 0.97 1.04 1.5 1358.7 0.74 3024 2.3614 2891.1 0.80 1.24 0.86 1.17 1.7 1381.1 0.72 3150 2.1803 2886.1 0.73 1.37 0.77 1.29 1.9 1401.7 0.71 3265 2.0265 2882.1 0.67 1.49 0.71 1.41 2.1 1420.8 0.70 3370 1.8940 2878.9 0.62 1.61 0.65 1.53 2.3 1438.8 0.70 3468 1.7782 2876.2 0.58 1.73 0.61 1.65 2.5 1455.8 0.69 3559 1.6760 2874.0 0.54 1.84 0.57 1.76 2.7 1471.9 0.68 3644 1.5851 2872.1 0.51 1.95 0.53 1.87

168

0m P Density VSP VP CP S KS T KT 473 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 1047.8 0.95 2001 5.6928 3746.6 2.38 0.42 2.77 0.36 0.7 1098.1 0.91 2301 4.9318 3690.6 1.72 0.58 2.00 0.50 0.9 1137.8 0.88 2540 4.4158 3650.9 1.36 0.73 1.58 0.63 1.1 1171.1 0.85 2740 4.0334 3620.7 1.14 0.88 1.32 0.76 1.3 1200.1 0.83 2912 3.7340 3596.4 0.98 1.02 1.14 0.88 1.5 1225.9 0.82 3063 3.4907 3576.3 0.87 1.15 1.00 1.00 1.7 1249.4 0.80 3197 3.2874 3559.4 0.78 1.28 0.90 1.11 1.9 1270.9 0.79 3318 3.1141 3544.8 0.71 1.40 0.82 1.22 2.1 1291.0 0.77 3428 2.9638 3532.0 0.66 1.52 0.75 1.33 2.3 1309.7 0.76 3529 2.8318 3520.8 0.61 1.63 0.70 1.44 2.5 1327.4 0.75 3623 2.7145 3510.9 0.57 1.74 0.65 1.54 2.7 1344.2 0.74 3710 2.6095 3501.9 0.54 1.85 0.61 1.64 2.9 1360.2 0.74 3791 2.5146 3493.9 0.51 1.96 0.57 1.74 3.1 1375.5 0.73 3868 2.4283 3486.6 0.49 2.06 0.54 1.84 3.3 1390.2 0.72 3940 2.3493 3479.9 0.46 2.16 0.52 1.93 3.5 1404.3 0.71 4008 2.2768 3473.8 0.44 2.26 0.49 2.03 3.7 1417.9 0.71 4073 2.2098 3468.3 0.43 2.35 0.47 2.12 3.9 1431.1 0.70 4134 2.1477 3463.1 0.41 2.45 0.45 2.21 4.1 1443.8 0.69 4193 2.0899 3458.4 0.39 2.54 0.44 2.30

1m P Density VSP VP CP S KS T KT 473 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 1086.5 0.92 1950 4.9523 3452.6 2.42 0.41 2.73 0.37 0.7 1137.8 0.88 2236 4.2209 3412.2 1.76 0.57 1.97 0.51 0.9 1178.4 0.85 2465 3.7255 3384.7 1.40 0.72 1.56 0.64 1.1 1212.4 0.82 2657 3.3590 3364.4 1.17 0.86 1.30 0.77 1.3 1241.9 0.81 2822 3.0727 3348.7 1.01 0.99 1.12 0.89 1.5 1268.3 0.79 2967 2.8405 3336.1 0.90 1.12 0.99 1.01 1.7 1292.1 0.77 3097 2.6469 3325.8 0.81 1.24 0.88 1.13 1.9 1314.1 0.76 3214 2.4821 3317.2 0.74 1.36 0.80 1.24 2.1 1334.5 0.75 3321 2.3397 3309.9 0.68 1.47 0.74 1.35 2.3 1353.6 0.74 3420 2.2148 3303.7 0.63 1.58 0.68 1.46 2.5 1371.6 0.73 3511 2.1041 3298.3 0.59 1.69 0.64 1.57 2.7 1388.6 0.72 3597 2.0052 3293.7 0.56 1.80 0.60 1.67 2.9 1404.8 0.71 3677 1.9161 3289.7 0.53 1.90 0.56 1.77 3.1 1420.3 0.70 3752 1.8352 3286.1 0.50 2.00 0.53 1.87 3.3 1435.2 0.70 3823 1.7615 3283.0 0.48 2.10 0.51 1.97 3.5 1449.5 0.69 3891 1.6938 3280.3 0.46 2.19 0.48 2.06 3.7 1463.3 0.68 3955 1.6315 3277.8 0.44 2.29 0.46 2.16 3.9 1476.6 0.68 4016 1.5739 3275.7 0.42 2.38 0.44 2.25 4.1 1489.6 0.67 4075 1.5203 3273.8 0.40 2.47 0.43 2.34

3m P Density VSP VP CP S KS T KT 473 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 1142.4 0.88 1944 4.4900 2952.2 2.32 0.43 2.60 0.38 0.7 1194.1 0.84 2210 3.7629 2920.9 1.71 0.58 1.91 0.52 0.9 1235.3 0.81 2427 3.2704 2900.5 1.37 0.73 1.52 0.66 1.1 1269.9 0.79 2611 2.9071 2885.9 1.15 0.87 1.26 0.79 1.3 1300.0 0.77 2772 2.6244 2875.0 1.00 1.00 1.09 0.92 1.5 1326.8 0.75 2914 2.3962 2866.6 0.89 1.13 0.96 1.04 1.7 1351.1 0.74 3043 2.2070 2860.0 0.80 1.25 0.86 1.16 1.9 1373.4 0.73 3160 2.0470 2854.7 0.73 1.37 0.78 1.28 2.1 1394.1 0.72 3268 1.9093 2850.4 0.67 1.49 0.72 1.40 2.3 1413.4 0.71 3368 1.7895 2846.9 0.62 1.60 0.66 1.51 2.5 1431.5 0.70 3461 1.6840 2844.0 0.58 1.71 0.62 1.62 2.7 1448.7 0.69 3548 1.5903 2841.6 0.55 1.82 0.58 1.73 2.9 1465.0 0.68 3631 1.5065 2839.6 0.52 1.93 0.54 1.84 3.1 1480.6 0.68 3709 1.4310 2837.9 0.49 2.04 0.51 1.95 3.3 1495.5 0.67 3783 1.3627 2836.6 0.47 2.14 0.49 2.05 3.5 1509.8 0.66 3854 1.3005 2835.5 0.45 2.24 0.46 2.15 3.7 1523.6 0.66 3921 1.2436 2834.6 0.43 2.34 0.44 2.25 3.9 1536.9 0.65 3986 1.1915 2833.8 0.41 2.44 0.42 2.35 4.1 1549.7 0.65 4048 1.1435 2833.3 0.39 2.54 0.41 2.45 4.3 1562.2 0.64 4108 1.0991 2832.8 0.38 2.64 0.39 2.55 4.5 1574.2 0.64 4165 1.0581 2832.5 0.37 2.73 0.38 2.65

169

0m P Density VSP VP CP S KS T KT 573 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 988.3 1.01 1928 6.0059 3751.5 2.72 0.37 3.28 0.30 0.7 1044.1 0.96 2229 5.1589 3671.3 1.93 0.52 2.33 0.43 0.9 1087.7 0.92 2471 4.5923 3615.9 1.51 0.66 1.81 0.55 1.1 1124.0 0.89 2674 4.1764 3574.3 1.24 0.80 1.49 0.67 1.3 1155.4 0.87 2849 3.8531 3541.4 1.07 0.94 1.27 0.78 1.5 1183.3 0.85 3002 3.5918 3514.5 0.94 1.07 1.12 0.90 1.7 1208.4 0.83 3139 3.3746 3491.9 0.84 1.19 0.99 1.01 1.9 1231.5 0.81 3262 3.1901 3472.6 0.76 1.31 0.90 1.11 2.1 1252.8 0.80 3374 3.0306 3455.8 0.70 1.43 0.82 1.22 2.3 1272.8 0.79 3478 2.8910 3441.2 0.65 1.54 0.76 1.32 2.5 1291.6 0.77 3573 2.7673 3428.2 0.61 1.65 0.71 1.42 2.7 1309.3 0.76 3662 2.6567 3416.6 0.57 1.76 0.66 1.52 2.9 1326.2 0.75 3745 2.5571 3406.2 0.54 1.86 0.62 1.61 3.1 1342.3 0.75 3823 2.4666 3396.8 0.51 1.96 0.59 1.71 3.3 1357.7 0.74 3896 2.3841 3388.3 0.49 2.06 0.56 1.80 3.5 1372.5 0.73 3966 2.3083 3380.5 0.46 2.16 0.53 1.89 3.7 1386.7 0.72 4032 2.2384 3373.4 0.44 2.25 0.51 1.98 3.9 1400.5 0.71 4094 2.1737 3366.8 0.43 2.35 0.48 2.07 4.1 1413.8 0.71 4154 2.1136 3360.8 0.41 2.44 0.46 2.16 4.3 1426.7 0.70 4211 2.0575 3355.2 0.40 2.53 0.45 2.24 4.5 1439.3 0.69 4266 2.0050 3350.1 0.38 2.62 0.43 2.33

1m P Density VSP VP CP S KS T KT 573 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 1032.8 0.97 1867 5.1813 3423.9 2.78 0.36 3.21 0.31 0.7 1090.0 0.92 2152 4.3795 3367.5 1.98 0.50 2.28 0.44 0.9 1134.6 0.88 2381 3.8434 3329.9 1.55 0.64 1.78 0.56 1.1 1171.8 0.85 2573 3.4504 3302.7 1.29 0.78 1.47 0.68 1.3 1203.9 0.83 2739 3.1455 3281.9 1.11 0.90 1.25 0.80 1.5 1232.4 0.81 2885 2.8994 3265.3 0.97 1.03 1.09 0.91 1.7 1258.1 0.79 3016 2.6953 3251.9 0.87 1.14 0.98 1.03 1.9 1281.6 0.78 3135 2.5222 3240.8 0.79 1.26 0.88 1.13 2.1 1303.4 0.77 3243 2.3730 3231.5 0.73 1.37 0.81 1.24 2.3 1323.7 0.76 3343 2.2426 3223.5 0.68 1.48 0.74 1.34 2.5 1342.8 0.74 3436 2.1274 3216.7 0.63 1.59 0.69 1.45 2.7 1360.9 0.73 3522 2.0246 3210.9 0.59 1.69 0.65 1.55 2.9 1378.1 0.73 3603 1.9321 3205.8 0.56 1.79 0.61 1.65 3.1 1394.4 0.72 3680 1.8484 3201.3 0.53 1.89 0.57 1.74 3.3 1410.1 0.71 3752 1.7721 3197.4 0.50 1.98 0.54 1.84 3.5 1425.1 0.70 3820 1.7023 3194.0 0.48 2.08 0.52 1.93 3.7 1439.6 0.69 3886 1.6381 3191.0 0.46 2.17 0.49 2.03 3.9 1453.5 0.69 3948 1.5787 3188.4 0.44 2.27 0.47 2.12 4.1 1467.1 0.68 4007 1.5237 3186.0 0.42 2.36 0.45 2.21 4.3 1480.1 0.68 4064 1.4726 3183.9 0.41 2.44 0.44 2.30 4.5 1492.8 0.67 4119 1.4248 3182.1 0.39 2.53 0.42 2.38

3m P Density VSP VP CP S KS T KT 573 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 1091.2 0.92 1847 4.6737 2928.4 2.68 0.37 3.08 0.33 0.7 1149.4 0.87 2113 3.8841 2885.4 1.95 0.51 2.21 0.45 0.9 1195.1 0.84 2330 3.3561 2857.8 1.54 0.65 1.73 0.58 1.1 1233.1 0.81 2514 2.9701 2838.6 1.28 0.78 1.43 0.70 1.3 1266.1 0.79 2676 2.6718 2824.4 1.10 0.91 1.22 0.82 1.5 1295.2 0.77 2819 2.4322 2813.5 0.97 1.03 1.06 0.94 1.7 1321.4 0.76 2949 2.2345 2805.1 0.87 1.15 0.95 1.06 1.9 1345.4 0.74 3067 2.0678 2798.3 0.79 1.27 0.86 1.17 2.1 1367.6 0.73 3176 1.9249 2792.9 0.72 1.38 0.78 1.28 2.3 1388.2 0.72 3278 1.8008 2788.5 0.67 1.49 0.72 1.39 2.5 1407.6 0.71 3372 1.6919 2784.9 0.62 1.60 0.67 1.50 2.7 1425.8 0.70 3461 1.5954 2781.9 0.59 1.71 0.62 1.61 2.9 1443.1 0.69 3545 1.5091 2779.4 0.55 1.81 0.58 1.71 3.1 1459.5 0.69 3625 1.4316 2777.4 0.52 1.92 0.55 1.82 3.3 1475.3 0.68 3701 1.3616 2775.8 0.49 2.02 0.52 1.92 3.5 1490.3 0.67 3773 1.2979 2774.5 0.47 2.12 0.49 2.02 3.7 1504.8 0.66 3842 1.2398 2773.4 0.45 2.22 0.47 2.12 3.9 1518.7 0.66 3908 1.1865 2772.5 0.43 2.32 0.45 2.22 4.1 1532.1 0.65 3972 1.1375 2771.8 0.41 2.42 0.43 2.32 4.3 1545.1 0.65 4033 1.0923 2771.3 0.40 2.51 0.41 2.42 4.5 1557.7 0.64 4092 1.0505 2771.0 0.38 2.61 0.40 2.51

170

0m P Density VSP VP CP S KS T KT 673 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 929.1 1.08 1873 6.3572 3746.7 3.07 0.33 3.85 0.26 0.7 990.4 1.01 2175 5.4092 3634.2 2.13 0.47 2.68 0.37 0.9 1037.9 0.96 2420 4.7845 3558.7 1.65 0.61 2.06 0.48 1.1 1077.2 0.93 2625 4.3306 3503.0 1.35 0.74 1.68 0.59 1.3 1111.0 0.90 2802 3.9806 3459.5 1.15 0.87 1.42 0.70 1.5 1140.9 0.88 2957 3.6995 3424.3 1.00 1.00 1.24 0.81 1.7 1167.8 0.86 3096 3.4670 3395.0 0.89 1.12 1.10 0.91 1.9 1192.3 0.84 3221 3.2702 3370.2 0.81 1.24 0.99 1.01 2.1 1215.0 0.82 3335 3.1009 3348.8 0.74 1.35 0.90 1.11 2.3 1236.1 0.81 3440 2.9531 3330.2 0.68 1.46 0.83 1.21 2.5 1256.0 0.80 3536 2.8225 3313.8 0.64 1.57 0.77 1.31 2.7 1274.7 0.78 3626 2.7060 3299.2 0.60 1.68 0.71 1.40 2.9 1292.4 0.77 3711 2.6013 3286.2 0.56 1.78 0.67 1.49 3.1 1309.3 0.76 3790 2.5064 3274.4 0.53 1.88 0.63 1.59 3.3 1325.4 0.75 3864 2.4200 3263.8 0.51 1.98 0.60 1.68 3.5 1340.9 0.75 3935 2.3408 3254.2 0.48 2.08 0.57 1.77 3.7 1355.8 0.74 4001 2.2678 3245.3 0.46 2.17 0.54 1.85 3.9 1370.2 0.73 4065 2.2004 3237.3 0.44 2.26 0.52 1.94 4.1 1384.1 0.72 4125 2.1378 3229.9 0.42 2.36 0.49 2.03 4.3 1397.5 0.72 4183 2.0796 3223.0 0.41 2.45 0.47 2.11 4.5 1410.6 0.71 4239 2.0251 3216.7 0.39 2.53 0.46 2.20

1m P Density VSP VP CP S KS T KT 673 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 979.5 1.02 1799 5.4337 3430.7 3.15 0.32 3.75 0.27 0.7 1042.4 0.96 2081 4.5514 3353.7 2.22 0.45 2.61 0.38 0.9 1091.2 0.92 2309 3.9697 3303.8 1.72 0.58 2.01 0.50 1.1 1131.5 0.88 2501 3.5474 3268.2 1.41 0.71 1.64 0.61 1.3 1166.2 0.86 2667 3.2221 3241.4 1.21 0.83 1.39 0.72 1.5 1196.8 0.84 2813 2.9612 3220.3 1.06 0.95 1.21 0.83 1.7 1224.3 0.82 2944 2.7457 3203.3 0.94 1.06 1.07 0.93 1.9 1249.4 0.80 3063 2.5638 3189.4 0.85 1.17 0.96 1.04 2.1 1272.6 0.79 3172 2.4074 3177.7 0.78 1.28 0.88 1.14 2.3 1294.2 0.77 3273 2.2712 3167.9 0.72 1.39 0.81 1.24 2.5 1314.4 0.76 3366 2.1511 3159.5 0.67 1.49 0.75 1.34 2.7 1333.5 0.75 3454 2.0442 3152.3 0.63 1.59 0.70 1.44 2.9 1351.6 0.74 3535 1.9483 3146.1 0.59 1.69 0.65 1.53 3.1 1368.8 0.73 3612 1.8616 3140.7 0.56 1.79 0.61 1.63 3.3 1385.2 0.72 3685 1.7828 3136.0 0.53 1.88 0.58 1.72 3.5 1401.0 0.71 3755 1.7107 3131.9 0.51 1.97 0.55 1.81 3.7 1416.1 0.71 3821 1.6445 3128.3 0.48 2.07 0.52 1.91 3.9 1430.7 0.70 3883 1.5835 3125.1 0.46 2.16 0.50 2.00 4.1 1444.8 0.69 3944 1.5269 3122.3 0.45 2.25 0.48 2.08 4.3 1458.5 0.69 4001 1.4744 3119.8 0.43 2.34 0.46 2.17 4.5 1471.7 0.68 4057 1.4254 3117.7 0.41 2.42 0.44 2.26

3m P Density VSP VP CP S KS T KT 673 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 1040.4 0.96 1768 4.8740 2929.21 3.07 0.33 3.60 0.28 0.7 1104.9 0.91 2031 4.0141 2871.4 2.19 0.46 2.54 0.39 0.9 1155.1 0.87 2246 3.4469 2835.4 1.72 0.58 1.96 0.51 1.1 1196.7 0.84 2430 3.0362 2810.6 1.42 0.71 1.60 0.62 1.3 1232.4 0.81 2591 2.7210 2792.6 1.21 0.83 1.35 0.74 1.5 1263.8 0.79 2734 2.4694 2779.0 1.06 0.94 1.18 0.85 1.7 1292.1 0.77 2864 2.2626 2768.5 0.94 1.06 1.04 0.96 1.9 1317.8 0.76 2983 2.0890 2760.2 0.85 1.17 0.93 1.07 2.1 1341.4 0.75 3093 1.9407 2753.6 0.78 1.28 0.85 1.18 2.3 1363.4 0.73 3195 1.8122 2748.2 0.72 1.39 0.78 1.29 2.5 1383.9 0.72 3291 1.6997 2743.8 0.67 1.50 0.72 1.39 2.7 1403.2 0.71 3381 1.6002 2740.3 0.62 1.60 0.67 1.50 2.9 1421.5 0.70 3466 1.5115 2737.4 0.59 1.71 0.63 1.60 3.1 1438.8 0.70 3547 1.4320 2735.0 0.55 1.81 0.59 1.70 3.3 1455.3 0.69 3623 1.3601 2733.1 0.52 1.91 0.55 1.80 3.5 1471.1 0.68 3697 1.2949 2731.5 0.50 2.01 0.53 1.90 3.7 1486.3 0.67 3767 1.2355 2730.2 0.47 2.11 0.50 2.00 3.9 1500.8 0.67 3835 1.1811 2729.3 0.45 2.21 0.48 2.10 4.1 1514.8 0.66 3900 1.1312 2728.5 0.43 2.30 0.45 2.20 4.3 1528.4 0.65 3962 1.0851 2728.0 0.42 2.40 0.44 2.30 4.5 1541.5 0.65 4023 1.0426 2727.6 0.40 2.49 0.42 2.39

171

0m P Density VSP VP CP S KS T KT 773 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 870.2 1.15 1836 6.7540 3729.8 3.41 0.29 4.50 0.22 0.7 936.9 1.07 2141 5.6864 3573.7 2.33 0.43 3.08 0.33 0.9 988.4 1.01 2387 4.9945 3472.1 1.78 0.56 2.34 0.43 1.1 1030.7 0.97 2594 4.4977 3398.7 1.44 0.69 1.89 0.53 1.3 1066.9 0.94 2773 4.1177 3342.3 1.22 0.82 1.59 0.63 1.5 1098.8 0.91 2931 3.8145 3297.1 1.06 0.94 1.37 0.73 1.7 1127.5 0.89 3071 3.5651 3259.9 0.94 1.06 1.21 0.83 1.9 1153.5 0.87 3198 3.3550 3228.6 0.85 1.18 1.08 0.92 2.1 1177.5 0.85 3313 3.1749 3201.8 0.77 1.29 0.98 1.02 2.3 1199.8 0.83 3419 3.0182 3178.6 0.71 1.40 0.90 1.11 2.5 1220.7 0.82 3517 2.8801 3158.2 0.66 1.51 0.83 1.21 2.7 1240.3 0.81 3608 2.7574 3140.3 0.62 1.61 0.77 1.30 2.9 1258.9 0.79 3693 2.6472 3124.3 0.58 1.72 0.72 1.39 3.1 1276.6 0.78 3773 2.5476 3109.9 0.55 1.82 0.68 1.48 3.3 1293.5 0.77 3848 2.4571 3096.9 0.52 1.92 0.64 1.57 3.5 1309.7 0.76 3919 2.3743 3085.2 0.50 2.01 0.61 1.65 3.7 1325.2 0.75 3986 2.2981 3074.5 0.47 2.11 0.58 1.74 3.9 1340.2 0.75 4050 2.2279 3064.8 0.45 2.20 0.55 1.82 4.1 1354.6 0.74 4111 2.1627 3055.9 0.44 2.29 0.52 1.91 4.3 1368.6 0.73 4170 2.1021 3047.6 0.42 2.38 0.50 1.99 4.5 1382.1 0.72 4225 2.0456 3040.1 0.41 2.47 0.48 2.07

1m P Density VSP VP CP S KS T KT 773 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 926.4 1.08 1744 5.7135 3445.3 3.55 0.28 4.34 0.23 0.7 995.1 1.00 2022 4.7383 3341.6 2.46 0.41 2.98 0.34 0.9 1048.0 0.95 2248 4.1053 3276.4 1.89 0.53 2.27 0.44 1.1 1091.5 0.92 2439 3.6506 3230.8 1.54 0.65 1.83 0.55 1.3 1128.7 0.89 2604 3.3031 3196.8 1.31 0.77 1.54 0.65 1.5 1161.5 0.86 2750 3.0260 3170.5 1.14 0.88 1.33 0.75 1.7 1190.9 0.84 2882 2.7983 3149.5 1.01 0.99 1.17 0.85 1.9 1217.6 0.82 3001 2.6069 3132.3 0.91 1.10 1.05 0.95 2.1 1242.1 0.81 3110 2.4430 3118.1 0.83 1.20 0.95 1.05 2.3 1264.9 0.79 3210 2.3006 3106.2 0.77 1.30 0.87 1.15 2.5 1286.3 0.78 3304 2.1754 3096.1 0.71 1.40 0.80 1.24 2.7 1306.4 0.77 3391 2.0643 3087.4 0.67 1.50 0.75 1.34 2.9 1325.4 0.75 3474 1.9647 3080.0 0.63 1.60 0.70 1.43 3.1 1343.5 0.74 3551 1.8750 3073.6 0.59 1.69 0.66 1.52 3.3 1360.7 0.73 3624 1.7935 3068.0 0.56 1.79 0.62 1.62 3.5 1377.2 0.73 3694 1.7191 3063.1 0.53 1.88 0.59 1.71 3.7 1393.0 0.72 3760 1.6509 3058.9 0.51 1.97 0.56 1.79 3.9 1408.2 0.71 3824 1.5880 3055.1 0.49 2.06 0.53 1.88 4.1 1422.9 0.70 3884 1.5299 3051.9 0.47 2.15 0.51 1.97 4.3 1437.1 0.70 3943 1.4759 3049.0 0.45 2.23 0.49 2.06 4.5 1450.9 0.69 3998 1.4257 3046.5 0.43 2.32 0.47 2.14

3m P Density VSP VP CP S KS T KT 773 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 989.8 1.01 1702 5.0934 2942.6 3.49 0.29 4.17 0.24 0.7 1060.7 0.94 1961 4.1538 2866.2 2.45 0.41 2.89 0.35 0.9 1115.4 0.90 2174 3.5433 2819.9 1.90 0.53 2.21 0.45 1.1 1160.5 0.86 2356 3.1057 2788.7 1.55 0.64 1.78 0.56 1.3 1199.0 0.83 2515 2.7724 2766.4 1.32 0.76 1.50 0.67 1.5 1232.8 0.81 2658 2.5079 2749.7 1.15 0.87 1.29 0.77 1.7 1263.0 0.79 2788 2.2916 2736.9 1.02 0.98 1.14 0.88 1.9 1290.4 0.77 2907 2.1107 2726.9 0.92 1.09 1.02 0.99 2.1 1315.5 0.76 3017 1.9566 2718.9 0.84 1.20 0.92 1.09 2.3 1338.8 0.75 3119 1.8236 2712.5 0.77 1.30 0.84 1.19 2.5 1360.5 0.74 3215 1.7074 2707.4 0.71 1.41 0.77 1.30 2.7 1380.9 0.72 3306 1.6049 2703.2 0.66 1.51 0.72 1.40 2.9 1400.1 0.71 3392 1.5137 2699.8 0.62 1.61 0.67 1.50 3.1 1418.3 0.71 3473 1.4320 2697.0 0.58 1.71 0.63 1.60 3.3 1435.7 0.70 3551 1.3584 2694.8 0.55 1.81 0.59 1.70 3.5 1452.2 0.69 3625 1.2917 2693.0 0.52 1.91 0.56 1.80 3.7 1468.0 0.68 3697 1.2309 2691.6 0.50 2.01 0.53 1.89 3.9 1483.2 0.67 3765 1.1754 2690.5 0.48 2.10 0.50 1.99 4.1 1497.9 0.67 3831 1.1245 2689.7 0.45 2.20 0.48 2.09 4.3 1512.0 0.66 3895 1.0776 2689.1 0.44 2.29 0.46 2.18 4.5 1525.6 0.66 3957 1.0343 2688.7 0.42 2.39 0.44 2.28

172

0m P Density VSP VP CP S KS T KT 873 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 811.5 1.23 1819 7.2059 3704.3 3.73 0.27 5.23 0.19 0.7 883.8 1.13 2127 5.9952 3488.7 2.50 0.40 3.52 0.28 0.9 939.2 1.06 2378 5.2252 3353.2 1.88 0.53 2.64 0.38 1.1 984.5 1.02 2588 4.6791 3257.5 1.52 0.66 2.11 0.47 1.3 1023.2 0.98 2770 4.2653 3185.1 1.27 0.78 1.76 0.57 1.5 1057.1 0.95 2929 3.9376 3127.9 1.10 0.91 1.51 0.66 1.7 1087.4 0.92 3071 3.6695 3081.2 0.97 1.03 1.33 0.75 1.9 1114.9 0.90 3200 3.4448 3042.3 0.88 1.14 1.18 0.85 2.1 1140.3 0.88 3316 3.2529 3009.2 0.80 1.25 1.07 0.94 2.3 1163.7 0.86 3423 3.0866 2980.7 0.73 1.36 0.97 1.03 2.5 1185.6 0.84 3522 2.9405 2955.9 0.68 1.47 0.90 1.12 2.7 1206.3 0.83 3613 2.8110 2934.1 0.63 1.57 0.83 1.20 2.9 1225.7 0.82 3699 2.6950 2914.7 0.60 1.68 0.77 1.29 3.1 1244.2 0.80 3779 2.5904 2897.4 0.56 1.78 0.73 1.38 3.3 1261.9 0.79 3854 2.4955 2881.9 0.53 1.87 0.68 1.46 3.5 1278.7 0.78 3926 2.4089 2867.9 0.51 1.97 0.65 1.55 3.7 1294.9 0.77 3993 2.3293 2855.1 0.48 2.06 0.61 1.63 3.9 1310.5 0.76 4057 2.2561 2843.6 0.46 2.16 0.58 1.72 4.1 1325.5 0.75 4118 2.1882 2833.0 0.44 2.25 0.56 1.80 4.3 1340.0 0.75 4177 2.1252 2823.3 0.43 2.34 0.53 1.88 4.5 1354.0 0.74 4233 2.0665 2814.3 0.41 2.43 0.51 1.96

1m P Density VSP VP CP S KS T KT 873 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 873.6 1.14 1702 6.0252 3439.7 3.95 0.25 5.01 0.20 0.7 948.1 1.05 1977 4.9424 3301.3 2.70 0.37 3.38 0.30 0.9 1005.1 0.99 2201 4.2513 3217.0 2.05 0.49 2.54 0.39 1.1 1051.8 0.95 2390 3.7606 3159.3 1.66 0.60 2.04 0.49 1.3 1091.6 0.92 2554 3.3886 3116.9 1.40 0.71 1.70 0.59 1.5 1126.5 0.89 2699 3.0941 3084.5 1.22 0.82 1.46 0.69 1.7 1157.7 0.86 2830 2.8533 3058.8 1.08 0.93 1.28 0.78 1.9 1186.0 0.84 2948 2.6517 3038.1 0.97 1.03 1.14 0.88 2.1 1211.9 0.83 3057 2.4797 3021.0 0.88 1.13 1.03 0.97 2.3 1236.0 0.81 3157 2.3308 3006.8 0.81 1.23 0.94 1.06 2.5 1258.5 0.79 3251 2.2003 2994.8 0.75 1.33 0.86 1.16 2.7 1279.6 0.78 3338 2.0847 2984.6 0.70 1.43 0.80 1.25 2.9 1299.5 0.77 3420 1.9814 2975.8 0.66 1.52 0.75 1.34 3.1 1318.4 0.76 3498 1.8884 2968.3 0.62 1.61 0.70 1.43 3.3 1336.4 0.75 3571 1.8041 2961.8 0.59 1.70 0.66 1.52 3.5 1353.6 0.74 3641 1.7274 2956.1 0.56 1.79 0.62 1.61 3.7 1370.1 0.73 3707 1.6571 2951.2 0.53 1.88 0.59 1.69 3.9 1386.0 0.72 3771 1.5924 2946.9 0.51 1.97 0.56 1.78 4.1 1401.3 0.71 3832 1.5326 2943.2 0.49 2.06 0.54 1.87 4.3 1416.1 0.71 3890 1.4772 2940.0 0.47 2.14 0.51 1.95 4.5 1430.3 0.70 3946 1.4257 2937.1 0.45 2.23 0.49 2.04

3m P Density VSP VP CP S KS T KT 873 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 939.6 1.06 1649 5.3348 2946.8 3.91 0.26 4.81 0.21 0.7 1016.7 0.98 1903 4.3044 2846.8 2.72 0.37 3.27 0.31 0.9 1076.1 0.93 2113 3.6458 2788.1 2.08 0.48 2.47 0.41 1.1 1124.6 0.89 2292 3.1788 2749.4 1.69 0.59 1.98 0.51 1.3 1165.9 0.86 2450 2.8260 2722.1 1.43 0.70 1.65 0.61 1.5 1202.0 0.83 2592 2.5478 2701.9 1.24 0.81 1.41 0.71 1.7 1234.2 0.81 2720 2.3214 2686.6 1.10 0.91 1.24 0.81 1.9 1263.3 0.79 2838 2.1328 2674.7 0.98 1.02 1.10 0.91 2.1 1289.9 0.78 2948 1.9728 2665.3 0.89 1.12 0.99 1.01 2.3 1314.5 0.76 3051 1.8350 2657.8 0.82 1.22 0.90 1.11 2.5 1337.4 0.75 3147 1.7150 2651.8 0.76 1.32 0.83 1.21 2.7 1358.9 0.74 3238 1.6094 2647.0 0.70 1.42 0.76 1.31 2.9 1379.1 0.73 3324 1.5156 2643.1 0.66 1.52 0.71 1.41 3.1 1398.2 0.72 3406 1.4317 2640.0 0.62 1.62 0.67 1.50 3.3 1416.3 0.71 3484 1.3563 2637.5 0.58 1.72 0.62 1.60 3.5 1433.6 0.70 3559 1.2880 2635.5 0.55 1.82 0.59 1.70 3.7 1450.1 0.69 3631 1.2260 2633.9 0.52 1.91 0.56 1.79 3.9 1465.9 0.68 3700 1.1693 2632.8 0.50 2.01 0.53 1.89 4.1 1481.2 0.68 3767 1.1174 2631.9 0.48 2.10 0.50 1.99 4.3 1495.8 0.67 3832 1.0697 2631.3 0.46 2.20 0.48 2.08 4.5 1509.9 0.66 3894 1.0256 2630.9 0.44 2.29 0.46 2.17

173

0m P Density VSP VP CP S KS T KT 973 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 753.2 1.33 1825 7.7251 3674.6 3.99 0.25 6.08 0.16 0.7 831.0 1.20 2143 6.3413 3376.2 2.62 0.38 4.01 0.25 0.9 890.2 1.12 2401 5.4795 3196.1 1.95 0.51 2.98 0.34 1.1 938.6 1.07 2617 4.8768 3072.0 1.56 0.64 2.36 0.42 1.3 979.7 1.02 2803 4.4249 2979.8 1.30 0.77 1.95 0.51 1.5 1015.6 0.98 2966 4.0696 2908.0 1.12 0.89 1.67 0.60 1.7 1047.6 0.95 3111 3.7808 2850.0 0.99 1.01 1.45 0.69 1.9 1076.7 0.93 3241 3.5401 2802.1 0.88 1.13 1.29 0.78 2.1 1103.3 0.91 3359 3.3354 2761.7 0.80 1.24 1.16 0.86 2.3 1127.9 0.89 3467 3.1585 2727.1 0.74 1.36 1.05 0.95 2.5 1150.9 0.87 3566 3.0038 2697.2 0.68 1.46 0.97 1.04 2.7 1172.5 0.85 3658 2.8670 2670.9 0.64 1.57 0.89 1.12 2.9 1192.9 0.84 3744 2.7448 2647.8 0.60 1.67 0.83 1.20 3.1 1212.2 0.82 3824 2.6349 2627.2 0.56 1.77 0.78 1.29 3.3 1230.5 0.81 3899 2.5353 2608.8 0.53 1.87 0.73 1.37 3.5 1248.1 0.80 3970 2.4446 2592.2 0.51 1.97 0.69 1.45 3.7 1264.9 0.79 4038 2.3615 2577.2 0.48 2.06 0.65 1.54 3.9 1281.1 0.78 4101 2.2850 2563.6 0.46 2.15 0.62 1.62 4.1 1296.6 0.77 4162 2.2144 2551.2 0.45 2.25 0.59 1.70 4.3 1311.7 0.76 4220 2.1488 2539.9 0.43 2.34 0.56 1.78 4.5 1326.2 0.75 4275 2.0878 2529.5 0.41 2.42 0.54 1.86

1m P Density VSP VP CP S KS T KT 973 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 821.1 1.22 1675 6.3748 3405.9 4.34 0.23 5.75 0.17 0.7 901.4 1.11 1947 5.1661 3221.7 2.93 0.34 3.82 0.26 0.9 962.5 1.04 2169 4.4091 3113.4 2.21 0.45 2.84 0.35 1.1 1012.4 0.99 2356 3.8781 3041.0 1.78 0.56 2.26 0.44 1.3 1054.8 0.95 2518 3.4793 2988.7 1.49 0.67 1.87 0.54 1.5 1091.8 0.92 2662 3.1657 2949.1 1.29 0.77 1.60 0.63 1.7 1124.8 0.89 2791 2.9107 2918.2 1.14 0.88 1.39 0.72 1.9 1154.7 0.87 2909 2.6983 2893.4 1.02 0.98 1.24 0.81 2.1 1182.0 0.85 3017 2.5177 2873.1 0.93 1.08 1.11 0.90 2.3 1207.3 0.83 3116 2.3620 2856.3 0.85 1.17 1.01 0.99 2.5 1230.9 0.81 3209 2.2258 2842.2 0.79 1.27 0.93 1.08 2.7 1253.0 0.80 3296 2.1055 2830.3 0.73 1.36 0.86 1.17 2.9 1273.9 0.78 3378 1.9983 2820.1 0.69 1.45 0.80 1.26 3.1 1293.7 0.77 3455 1.9019 2811.5 0.65 1.54 0.74 1.34 3.3 1312.5 0.76 3528 1.8148 2804.0 0.61 1.63 0.70 1.43 3.5 1330.4 0.75 3597 1.7356 2797.5 0.58 1.72 0.66 1.52 3.7 1347.6 0.74 3663 1.6631 2791.9 0.55 1.81 0.62 1.60 3.9 1364.1 0.73 3727 1.5965 2787.0 0.53 1.89 0.59 1.69 4.1 1380.0 0.72 3787 1.5351 2782.8 0.51 1.98 0.56 1.77 4.3 1395.3 0.72 3846 1.4783 2779.2 0.48 2.06 0.54 1.85 4.5 1410.1 0.71 3902 1.4255 2776.0 0.47 2.15 0.52 1.94

3m P Density VSP VP CP S KS T KT 973 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 889.6 1.12 1608 5.6017 2932.9 4.35 0.23 5.52 0.18 0.7 973.1 1.03 1857 4.4673 2802.8 2.98 0.34 3.69 0.27 0.9 1037.0 0.96 2063 3.7550 2729.0 2.27 0.44 2.75 0.36 1.1 1089.0 0.92 2239 3.2559 2681.3 1.83 0.55 2.18 0.46 1.3 1133.1 0.88 2395 2.8821 2648.3 1.54 0.65 1.81 0.55 1.5 1171.5 0.85 2534 2.5891 2624.2 1.33 0.75 1.54 0.65 1.7 1205.7 0.83 2662 2.3520 2606.0 1.17 0.85 1.34 0.75 1.9 1236.5 0.81 2779 2.1554 2592.1 1.05 0.95 1.19 0.84 2.1 1264.6 0.79 2888 1.9891 2581.2 0.95 1.05 1.07 0.94 2.3 1290.6 0.77 2990 1.8465 2572.5 0.87 1.15 0.97 1.03 2.5 1314.6 0.76 3086 1.7225 2565.7 0.80 1.25 0.88 1.13 2.7 1337.2 0.75 3176 1.6136 2560.2 0.74 1.35 0.82 1.23 2.9 1358.3 0.74 3262 1.5172 2555.8 0.69 1.45 0.76 1.32 3.1 1378.3 0.73 3344 1.4312 2552.3 0.65 1.54 0.71 1.42 3.3 1397.2 0.72 3423 1.3539 2549.5 0.61 1.64 0.66 1.51 3.5 1415.3 0.71 3498 1.2840 2547.3 0.58 1.73 0.62 1.61 3.7 1432.5 0.70 3571 1.2207 2545.6 0.55 1.83 0.59 1.70 3.9 1449.0 0.69 3640 1.1629 2544.3 0.52 1.92 0.56 1.80 4.1 1464.8 0.68 3708 1.1100 2543.4 0.50 2.01 0.53 1.89 4.3 1480.0 0.68 3773 1.0614 2542.8 0.47 2.11 0.50 1.98 4.5 1494.6 0.67 3836 1.0166 2542.4 0.45 2.20 0.48 2.08

174

0m P Density VSP VP CP S KS T KT 1073 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 695.2 1.44 1866 8.3280 3639.1 4.13 0.24 7.07 0.14 0.7 778.4 1.28 2206 6.7318 3223.9 2.64 0.38 4.58 0.22 0.9 841.6 1.19 2481 5.7614 2984.3 1.93 0.52 3.35 0.30 1.1 892.9 1.12 2710 5.0933 2823.9 1.52 0.66 2.63 0.38 1.3 936.5 1.07 2906 4.5978 2707.1 1.26 0.79 2.16 0.46 1.5 974.4 1.03 3077 4.2116 2617.4 1.08 0.92 1.83 0.55 1.7 1008.2 0.99 3227 3.8998 2545.9 0.95 1.05 1.59 0.63 1.9 1038.7 0.96 3361 3.6413 2487.3 0.85 1.17 1.40 0.71 2.1 1066.7 0.94 3482 3.4226 2438.4 0.77 1.29 1.26 0.80 2.3 1092.5 0.92 3592 3.2344 2396.7 0.71 1.41 1.14 0.88 2.5 1116.5 0.90 3692 3.0702 2360.9 0.66 1.52 1.04 0.96 2.7 1139.0 0.88 3785 2.9255 2329.7 0.61 1.63 0.96 1.04 2.9 1160.3 0.86 3870 2.7967 2302.3 0.58 1.74 0.89 1.12 3.1 1180.4 0.85 3950 2.6811 2278.0 0.54 1.84 0.83 1.21 3.3 1199.5 0.83 4025 2.5766 2256.4 0.51 1.94 0.78 1.29 3.5 1217.7 0.82 4095 2.4815 2237.0 0.49 2.04 0.73 1.37 3.7 1235.2 0.81 4161 2.3947 2219.5 0.47 2.14 0.69 1.44 3.9 1251.9 0.80 4223 2.3148 2203.7 0.45 2.23 0.66 1.52 4.1 1268.1 0.79 4283 2.2412 2189.4 0.43 2.33 0.62 1.60 4.3 1283.6 0.78 4339 2.1730 2176.3 0.41 2.42 0.60 1.68 4.5 1298.6 0.77 4393 2.1096 2164.3 0.40 2.51 0.57 1.76

1m P Density VSP VP CP S KS T KT 1073 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 768.9 1.30 1664 6.7695 3350.3 4.69 0.21 6.60 0.15 0.7 854.9 1.17 1935 5.4124 3105.1 3.12 0.32 4.31 0.23 0.9 920.2 1.09 2155 4.5799 2966.7 2.34 0.43 3.16 0.32 1.1 973.3 1.03 2340 4.0039 2876.2 1.88 0.53 2.49 0.40 1.3 1018.2 0.98 2500 3.5755 2812.2 1.57 0.64 2.05 0.49 1.5 1057.4 0.95 2643 3.2410 2764.4 1.35 0.74 1.74 0.57 1.7 1092.2 0.92 2770 2.9708 2727.3 1.19 0.84 1.51 0.66 1.9 1123.7 0.89 2886 2.7467 2697.9 1.07 0.94 1.34 0.75 2.1 1152.4 0.87 2992 2.5571 2674.1 0.97 1.03 1.20 0.84 2.3 1179.0 0.85 3091 2.3940 2654.5 0.89 1.13 1.08 0.92 2.5 1203.7 0.83 3182 2.2519 2638.1 0.82 1.22 0.99 1.01 2.7 1226.8 0.82 3268 2.1267 2624.4 0.76 1.31 0.91 1.09 2.9 1248.6 0.80 3348 2.0153 2612.7 0.71 1.40 0.85 1.18 3.1 1269.2 0.79 3425 1.9155 2602.8 0.67 1.49 0.79 1.26 3.3 1288.8 0.78 3497 1.8255 2594.3 0.63 1.58 0.74 1.35 3.5 1307.5 0.76 3565 1.7437 2587.0 0.60 1.66 0.70 1.43 3.7 1325.3 0.75 3631 1.6690 2580.6 0.57 1.75 0.66 1.52 3.9 1342.5 0.74 3694 1.6005 2575.2 0.55 1.83 0.63 1.60 4.1 1358.9 0.74 3754 1.5374 2570.5 0.52 1.91 0.59 1.68 4.3 1374.8 0.73 3812 1.4790 2566.4 0.50 2.00 0.57 1.76 4.5 1390.1 0.72 3867 1.4249 2562.9 0.48 2.08 0.54 1.84

3m P Density VSP VP CP S KS T KT 1073 K GPa kg/m 3 x10 3 m3/g m/s 10 -4 K-1 Jkg -1K-1 10 -1 GPa -1 10 1 GPa 10 -1 GPa -1 10 1 GPa 0.5 839.9 1.19 1580 5.8982 2901.0 4.77 0.21 6.30 0.16 0.7 929.8 1.08 1823 4.6440 2732.1 3.24 0.31 4.15 0.24 0.9 998.2 1.00 2024 3.8716 2639.8 2.44 0.41 3.05 0.33 1.1 1053.7 0.95 2197 3.3373 2581.7 1.97 0.51 2.41 0.42 1.3 1100.6 0.91 2350 2.9406 2542.0 1.65 0.61 1.98 0.51 1.5 1141.3 0.88 2487 2.6320 2513.4 1.42 0.71 1.68 0.60 1.7 1177.5 0.85 2613 2.3835 2492.2 1.24 0.80 1.45 0.69 1.9 1210.0 0.83 2728 2.1784 2476.1 1.11 0.90 1.28 0.78 2.1 1239.6 0.81 2836 2.0057 2463.5 1.00 1.00 1.14 0.87 2.3 1266.9 0.79 2937 1.8579 2453.7 0.92 1.09 1.03 0.97 2.5 1292.1 0.77 3032 1.7299 2445.9 0.84 1.19 0.94 1.06 2.7 1315.7 0.76 3122 1.6177 2439.7 0.78 1.28 0.87 1.15 2.9 1337.9 0.75 3208 1.5186 2434.8 0.73 1.38 0.80 1.25 3.1 1358.7 0.74 3290 1.4303 2430.9 0.68 1.47 0.75 1.34 3.3 1378.5 0.73 3368 1.3511 2427.8 0.64 1.56 0.70 1.43 3.5 1397.2 0.72 3443 1.2797 2425.5 0.60 1.66 0.66 1.53 3.7 1415.1 0.71 3516 1.2150 2423.6 0.57 1.75 0.62 1.62 3.9 1432.3 0.70 3586 1.1560 2422.3 0.54 1.84 0.58 1.71 4.1 1448.6 0.69 3653 1.1021 2421.4 0.52 1.93 0.55 1.80 4.3 1464.4 0.68 3719 1.0527 2420.8 0.49 2.03 0.53 1.90 4.5 1479.6 0.68 3782 1.0072 2420.4 0.47 2.12 0.50 1.99

175

176

Chapter 6

PVTx properties of a 1 m SrCl 2 solution and the effect of metal cations on the compressibility of Cl-bearing aqueous solutions

Abstract

The knowledge of the PVTx properties of Cl-bearing aqueous solutions up to geological relevant pressure and temperature conditions is a fundamental prerequisite to quantitatively model fluid involving geological processes, for instance, at the subduction settings. This Chapter 6 presents the first thermodynamic data of a 1 m H2O SrCl 2 solution up to 200 °C and 2.3 GPa, determined from acoustic velocity measurements conducted in an externally heated membrane-type diamond anvil cell (mDAC) using Brillouin scattering spectroscopy. Density values were inverted from the measured acoustic velocities and fitted with a polynomial equation of state (EoS). This EoS was successively used to derive all other thermodynamic properties of the solution investigated. The PVTx data calculated were discussed and compared with the thermodynamic properties of the NaCl-H2O solutions presented in Chapter 5. The results of this work suggest that the observed differences in the volumetric properties of the Cl- bearing aqueous solutions investigated can be explained by different effects of the dissolved Sr 2+ and Na + cations on the molecular structure of the solvent.

6.1 Introduction

Hydrothermal alteration of the oceanic lithosphere and subduction-related devolatilization reactions are two main processes controlling the global H2O and Cl cycles. For instance, the hydrothermal alteration of mantle rocks exposed to the seafloor results in the replacement of the mantle mineral assemblage with Cl-bearing hydrous phases, i.e ., serpentines, brucite and phyllosilicates (Ito et al., 1983; Scambelluri et al.,

177 1997), accompanied by the precipitation of halite and hydrated chloride minerals along grain boundaries (Sharp and Barnes, 2004). On the other side, Cl-bearing amphiboles and chlorites are produced during the hydrothermal alteration of the basaltic and gabbroic oceanic crust (Ito et al., 1983; Philippot et al., 1998). During the subduction of the hydrothermal altered oceanic slab to high pressure and temperature conditions, Cl-rich aqueous fluids can be generated through metamorphic devolatilization reactions involving Cl-bearing hydrated and soluble phases. In fact, the presence of high salinity fluids at depth has been attested by numerous fluid inclusions studies in high pressure metamorphic rock (Markl and Bucher, 1998; Philippot et al., 1998; Scambelluri et al., 1998; Becker et al., 1999; Scambelluri and Philippot, 2001), where, for instance, NaCl concentrations up to 45-50 wt% in eclogitic rocks have been observed (Philippot et al., 1998; Scambelluri et al., 1998). Experimental works (Newton and Manning, 2000; Newton and Manning, 2002; Sanchez-Valle et al., 2003; Newton and Manning, 2006; Shmulovich et al., 2006) demonstrate that the solubility of alumosilicates, SiO 2, and carbonate minerals is enhanced by the presence of dissolved NaCl in aqueous fluids at high pressure and temperature conditions. On the other hand, at elevated salt concentrations the solubility of SiO 2 and Al 2O3 decreases (Newton and Manning, 2000; Newton and Manning, 2002).

For instance, corundum solubility in H 2O-NaCl fluids at 800 °C and 1 GPa increases with NaCl up to a NaCl molar fraction of 0.15, then it slowly decreases (Newton and Manning, 2006). Is it therefore clear, that Cl-bearing aqueous fluids act as important metasomatic agents as they migrate from the subducting oceanic slab to the overlying mantle wedge (Manning, 2004), controlling the element mobilization and the precipitation of new mineral phases, and consequently, affecting the chemical composition of the surrounding rocks. For the quantitative modeling of geological processes involving Cl-bearing aqueous fluids at pressures and temperatures representative of a subduction zone setting, the knowledge of the thermodynamic properties of the phases involved at these P-T conditions is a fundamental prerequisite. While the PVTx data of H 2O-NaCl solutions up to 800 °C and 4.5 GPa are illustrated in Chapter 5, the following sections present the volumetric properties of a 1 m aqueous SrCl 2 solution determined up to 200 °C and 2.3

178 GPa from sound velocity measurements in a mDAC with performed Brillouin scattering spectroscopy. Strontium chloride is an important component of natural brines (Millero et al., 1977; Kumar, 1986), but previous works on the PVTx properties of H 2O-SrCl 2 mixtures are limited to 0.002 GPa in pressure (Ellis, 1967; Perron et al., 1974; Millero et al., 1977; Kumar, 1986; Phutela et al., 1987; Saluja and Leblanc, 1987; Holmes and Mesmer, 1996; Pena et al., 1997; Mao and Duan, 2008; Laliberte, 2009). This Chapter 6 presents the first PVTx data of 1 m SrCl 2 aqueous solution to pressure relevant for deep geological conditions. A comparison of the thermodynamic data reported here with that of NaCl aqueous solutions (Chapter 5) allows discussing briefly the effect of metal cations on the compressibility of chlorine-bearing aqueous fluids in terms of the molecular structure of the solvent.

6.2 Experimental Method

Details about the experimental methods applied to measure the acoustic velocities of the 1m aqueous SrCl 2 solution up to 200 °C and 2.3 GPa in the diamond anvil cell using Brillouin spectroscopy are provided in Chapter 2, and therefore, only a brief summary is presented here. The aqueous solution was freshly prepared by ® Aldrich ) SrCl 2 powder and deionized Milli Q water in appropriate proportions. The concentration analyzed corresponds to 1 mol of SrCl2 per kg H 2O (1 m aqueous SrCl 2 solution), equivalent to an aqueous solution with 13.7 wt% SrCl 2. All measurements were conducted using an externally heated membrane diamond anvil cell (Chervin et al., 1995) using low fluorescence type Ia diamond anvils of 500 m culet size. High temperature conditions were generated using an internal Pt heater placed around the lower diamond, and an external resistive heater, which surrounds the whole body of the cell. The temperature in the sample chamber was monitored with two calibrated K-type thermocouples, the first attached to the diamond anvil inside the mDAC close to the sample chamber and the second connected to the external heater. The sample chambers were formed by a 200 m hole drilled in a pre-indented stainless-steel gasket of

179 80 m thickness. Typically, the 1m SrCl 2 solution was loaded in the gasket together with a ruby sphere used as pressure marker for the experiments conducted up to 200 °C. The pressure was calculated using the calibrated pressure-dependent shift of the R 1 fluorescence line of ruby (Mao et al., 1978) after temperature correction (Ragan et al., 1992; Datchi et al., 2007). After loading, the cell was sealed to avoid solvent evaporation. Brillouin scattering measurements were conducted using a Fabry-Perot interferometer equipped with a photomultiplier (PMT) detector and a diode pumped laser

( 0 = 532.1 nm) as excitation source. All measurements were conducted in symmetric scattering geometry that allows direct determination of the compressional acoustic velocities (V P) in the H2O-SrCl 2 solution using the relationship (Whitfield et al., 1976):

0 P VP * (1) 2 sin( ) 2

* where, 0 is the laser wavelength, P the frequency (Brillouin) is the external scattering angle ( i.e ., angle between the incident and scattered beam outside the sample). Brillouin scattering measurements in the mDAC were performed using a 50 deg scattering geometry, while measurements at room conditions in a silica glass cuvette were conducted in 90 deg geometry. Fore more details about the Brillouin system used in this study the reader is referred to Chapter 2 and Sanchez-Valle et al. (2010). The speed of sound data in the 1m SrCl 2 solution were collected along isotherms at 20, 100 and 200 °C, in both compression and decompression experiments up to 2.3 GPa. The estimated accuracy on the measured acoustic velocities in the mDAC is 0.5-1% (Sinogeikin and Bass, 2000) but the reproducibility is generally better than 0.5%.

180 6.3 Results

6.3.1 Acoustic velocities in H 2O-SrCl 2 solution

The acoustic velocities measured along various isotherms from room pressure up to 2.3 GPa are reported in Figure 6.1 and listed in Table 6.1. The velocities obtained at room conditions in a silica glass cuvette and are identical to those measured inside the mDAC carefully closed without pressurization with an average value of 1585 ± 5 m/s (Fig. 6.1). The room condition acoustic velocities determined in this stud are also in agreement with data reported by Millero et al. (1977) at 25 °C using ultrasonic technique. The excellent agreement between sound velocities at room conditions collected with different techniques, and different scattering geometries indicates the absence of geometrical errors in the present Brillouin measurements, and that the loading procedure in the mDAC does not introduce additional errors.

The acoustic velocities VP measured in the mDAC up to 200 °C and 2.3 GPa in both compression and decompression experiments in different runs are presented in Table 6.1 and plotted in Figure 6.1. Each data point is an average of two different Brillouin measurements performed in different positions of the sample chamber to monitor the homogeneity of the fluid. Excellent agreement is found between measurements performed in different runs.

181

Figure 6.1. Acoustic velocities VP in a 1 m SrCl 2 along isotherms at 20 °C, 100 °C and 200 °C. The symbol size corresponds to 1% error in the acoustic velocities. The black dashed lines are the speeds of sound values calculated with the EoS proposed in this work (Eq. 3). The yellow triangle represents the acoustic velocity acquired at room conditions in a silica glass cuvette.

182 Table 6.1. Acoustic velocities in a 1m aqueous SrCl 2 solution measured at various pressures and temperatures. The superscript * indicates the measurement performed in the silica glass cuvette in 90 deg scattering geometry. Values in italic are speeds of sound collected upon decompression.

20 °C 100 °C 200 °C

P (GPa) VP (m/s) P (GPa) VP (m/s) P (GPa) VP (m/s) 0.00 * 1585 * 0.33 1948 0.36 1835 0.00 1584 0.38 1991 0.41 1870 0.03 1626 0.51 2083 0.41 1884 0.03 1634 0.54 2084 0.44 1919 0.06 1700 0.58 2155 0.49 1945 0.09 1708 0.64 2187 0.49 1982 0.10 1734 0.64 2226 0.69 2162 0.14 1795 0.71 2279 1.15 2464 0.15 1804 0.89 2426 1.40 2707 0.25 1971 0.99 2504 1.41 2715 0.29 1977 1.19 2687 1.77 2951 0.47 2191 1.36 2797 1.82 2965 0.48 2183 1.39 2847 1.90 3021 0.51 2230 1.47 2876 1.92 3020 0.58 2298 1.64 2957 1.94 3034 0.70 2453 2.11 3194 1.95 3054 0.77 2489 2.12 3213 2.00 3083 0.90 2610 2.03 3101 0.91 2632 2.22 3157 0.93 2651 0.94 2654 1.00 2682 1.05 2703 1.23 2850 1.30 2869 1.34 2899 1.42 2929 1.55 3018 1.65 3087

183 6.3.2 Equation of state for 1 m aqueous SrCl 2 solution to 200 °C and 2.3 GPa

The details of the inversion procedure to obtain the density of the aqueous solution from the measured acoustic velocities have been outlined in Chapter 3. The experimental acoustic velocities reported in Figure 6.1 were fitted and interpolated to produce a dense acoustic velocity grid in the pressure-temperature space using the following expression:

2 2 ln VP c1 c2 T c3 ln P c4 T ln P c5 ln P c6 T ln P (2)

where T is the temperature in Kelvin and P is the pressure in GPa. The most representative fit of the experimental VP data is obtained by splitting the data into two temperature intervals from 20 °C to 100 °C and from 100 °C to 200 °C. The ci parameters of equation (2) obtained with the least-squares fit of the experimental VP data are listed in Table 6.2. The acoustic velocities were inverted iteratively using the set of equations presented in Chapter 3 (Eq. 1a to 1c). The iteration started at an initial pressure of 0.3 GPa at each isotherm using initial values for the density and isobaric heat capacity obtained following the approximation used to process the data on sulfate-bearing aqueous solutions (Chapter 4). Briefly, the densities of the 1m SrCl 2 solution at low pressures (from 0.00001 GPa to 0.0002 GPa) and temperatures between 20 °C and 200 °C were calculated from Mao and Duan (2008) and compared to those of H2O-NaCl mixtures

(Driesner, 2007) at the same conditions to find a H2O-NaCl solution, which has similar densities. A H 2O-NaCl mixture with a NaCl molar fraction of 0.062, corresponding to

17.7 wt% NaCl, is found to reproduce the density values of a 1 m SrCl 2 solution with a maximal deviation smaller than 0.4% in the low pressure range. Therefore, the density and isobaric heat capacity for the 1 m SrCl 2 solution at 0.3 GPa are taken at those corresponding to an aqueous solution with 17.7 wt% NaCl as calculated from the EoS of Driesner (2007). The initial values of the density and heat capacity at 0.3 GPa and various temperatures are listed in Table 6.3 and the densities of the 1 m H2O-SrCl 2 solution up to 200° C and 2.3 GPa obtained in the inversion reported in Figure 6.2.

184 Table 6.2. Parameters ci for equation (2).

T range c1 c2 c3 c4 c5 c6 20 °C - 100 °C 8.1387 -8.3708 .10 -4 1.5053 .10 -1 4.1656 .10 -4 -1.3545 .10 -1 5.1326 .10 -4 100 °C - 200 °C 7.9798 -4.1111 .10 -4 2.6269 .10 -1 1.1587 .10 -4 8.3914 .10 -2 -7.4833 .10 -4

Table 6.3. Density and isobaric heat capacity at 0.3 GPa calculated from Driesner (2007) with a

NaCl molar fraction of 0.062 as equivalent for a 1m H 2O-SrCl 2 solution.

P = 0.3 GPa 20 °C 100 °C 200 °C Density (kg .m-3) 1217.4 1175.7 1117.5 . -1. -1 CP (J kg K ) 2968.8 2996.5 3010.8

The experimentally derived densities were then fitted to a polynomial equation of state (EoS) with the form:

T,P a(T) b(P) c(T,P) (3) with a(T) 1322 .43 4.3080 T b(P) .1 7984 10 3 P .9 1963 10 8 P .1 0207 10 17 P 2 c(T, P) .1 9232 10 1 T ln( P)

where, T is the temperature in Kelvin, P the pressure in Pascal and ai , bi and ci are coefficients obtained by a least squares fit of the density. Figure 6.2 displays the inverted densities at 20 °C, 100 °C and 200 °C together with the fit using equation (3); the maximal misfit is smaller than 0.4 % in density. The proposed EoS can be used to calculate the density of the 1m SrCl 2 aqueous solution at any temperature between 20 °C and 200 °C from 0.3 GPa to 2.3 GPa. The calculated densities are listed in Table 6.4 together with the thermodynamic properties of the aqueous solution, including acoustic velocity, thermal expansion coefficient, isobaric heat capacity as well as the adiabatic and

185 isothermal compressibility and bulk modulus. The acoustic velocity VP derived from equation (3) is also reported in Table 6.4 and plotted in Figure 6.1 together with the experimental data. The maximal misfit between calculated and measured VP is about 1.5% of the value.

Figure 6.2. Density values of a 1 m SrCl 2 solution. The diamonds represent the density inverted form the acoustic velocity data using equations (1a)-(1c) reported in Chapter 3, whereas the solid lines are the fit performed using equation (3).

186 Table 6.4. Thermodynamic properties of a 1m SrCl 2 solution.

T P Density VSP VP P CP S KS T KT 20°C GPa kg/m 3 cm 3/g m/s 10 -4K-1 J.kg-1.K-1 10 -10 Pa -1 10 10 Pa 10 -10 Pa -1 10 10 Pa 0.3 1217.9 0.82 1990 4.55 2968.8 2.07 0.48 2.24 0.45 0.5 1272.5 0.79 2244 3.58 2948.9 1.56 0.64 1.66 0.60 0.7 1314.8 0.76 2429 2.9 5 2937.1 1.29 0.78 1.36 0.74 0.9 1350.4 0.74 2581 2.54 2929.2 1.11 0.90 1.16 0.86 1.1 1381.7 0.72 2715 2.20 2923.6 0.98 1.02 1.02 0.98 1.3 1409.8 0.71 2840 1.93 2919.5 0.88 1.14 0.91 1.10 1.5 1435.4 0.70 2960 1.70 2916.4 0.79 1.26 0.82 1.23 1.7 1458.8 0.69 3079 1.51 2914.0 0.72 1.38 0.74 1.35

T P Density VSP VP P CP S KS T KT 100°C GPa kg/m 3 cm 3/g m/s 10 -4K-1 J.kg -1. K-1 10 -10 Pa -1 10 10 Pa 10 -10 Pa -1 10 10 Pa 0.3 1173.6 0.85 1875 4.72 2996.5 2.42 0.41 2.66 0.38 0.5 1236.0 0.81 2131 3.69 2968.2 1.78 0.56 1.92 0.52 0.7 1283.5 0.78 2319 3.0 5 2951.7 1.45 0.69 1.54 0.65 0.9 1323.0 0.76 2473 2.59 2940.9 1.24 0.81 1.30 0.77 1.1 1357.4 0.74 2608 2.24 2933.4 1.08 0.92 1.13 0.88 1.3 1388.1 0.72 2733 1.96 2927.8 0.96 1.04 1.00 1.00 1.5 1415.8 0.71 2853 1.73 2923.7 0.87 1.15 0.89 1.12 1.7 1441.2 0.69 2971 1.53 2920.6 0.79 1.27 0.81 1.24 1.9 1464.4 0.68 3089 1.36 2918.1 0.72 1.40 0.73 1.37 2.1 1485.9 0.67 3211 1.21 2916.3 0.65 1.53 0.66 1.50 2.3 1505.6 0.66 3338 1.08 2914.8 0.60 1.68 0.61 1.65

T P Density VSP VP P CP S KS T KT 200°C GPa kg/m 3 cm 3/g m/s 10 -4K-1 J.kg -1. K-1 10 -10 Pa -1 10 10 Pa 10 -10 Pa -1 10 10 Pa 0.3 1118.2 0.89 1760 4.96 3010.8 2.89 0.35 3.23 0.31 0.5 1190.4 0.84 2015 3.83 2969.2 2.07 0.48 2.26 0.44 0.7 1244.4 0.80 2204 3.14 2945.9 1.65 0.60 1.78 0.56 0.9 1288.7 0.78 2358 2.66 2930.9 1.40 0.72 1.48 0.67 1.1 1327.0 0.75 2493 2.29 2920.5 1.21 0.82 1.28 0.78 1.3 1360.9 0.73 2617 1.99 2913.0 1.07 0.93 1.12 0.89 1.5 1391.4 0.72 2735 1.76 2907.5 0.96 1.04 1.00 1.00 1.7 1419.1 0.70 2850 1.55 2903.3 0.87 1.15 0.89 1.12 1.9 1444.5 0.69 2966 1.38 2900.0 0.79 1.27 0.81 1.24 2.1 1467.9 0.68 3084 1.22 2897.5 0.72 1.40 0.73 1.36 2.3 1489.4 0.67 3206 1.09 2895.6 0.65 1.53 0.67 1.50

187 6.4 Discussion

Figure 6.3 compares the density of various Cl-bearing aqueous solutions and water at 200 °C. The data include the present results on SrCl 2 aqueous solutions and the data for 1m and 3m aqueous NaCl solutions reported in Chapter 5. The density values of pure water are from Chapter 5 and (Sanchez-Valle et al., in prep.) (see Appendix B). The 1m

H2O-SrCl 2 solution is 13.6% denser than pure water at 0.5 GPa and 200 °C and the density contrast remains constant in the investigated pressure range (Fig. 6.4). In comparison to a 1 m NaCl aqueous solution, the 1m SrCl 2 solution is 9.6% and 10 % denser at 0.5 GPa and 2.3 GPa, respectively. Similarly, the negative density contrast between the 3m NaCl and 1m SrCl 2 solution changes from 4.2% at 0.5 GPa to 5.4% at 2.3 GPa. Although in some cases the density differences are close to the accuracy of the respective EoS (0.3-0.5% for the 1 m SrCl 2 solution and 0.7% for the H 2O-NaCl mixtures), the comparison show that the density difference between pure water and the

1m SrCl 2 solution stays constant along the P-range investigated, whereas between the

NaCl solutions and the SrCl 2 aqueous solution the difference increases with increasing pressure. This observation suggests that the pressure-induced density change of a 1m

SrCl 2 aqueous solution is more similar to that of pure water than to that of the NaCl-H2O solution.

The differences in the behavior under pressure of the SrCl 2 and NaCl aqueous solutions could be explained in terms of the differences in the hydration strength of divalent Sr 2+ and monovalent Na + cations. Strontium is considered as a structure-maker ion (Marcus, 1994; Marcus, 2009) due to its relatively large ionic radius (118 pm) and small ionic potential (Hribar et al., 2002), and hence favors the formation of hydrogen bonds in the water molecules forming its hydration shells. Contrary to Sr 2+ , monovalent Na + and Cl - inhibit the formation of the hydrogen-bonding network in water, being respectively, a border line ion and a structure breaker ion (Marcus, 1994; Marcus, 2009).

In a H 2O-SrCl 2 solution, the disruption of the water H-bond network induced by the presence of Cl - ions is partially counterbalanced by the structure-maker character of Sr 2+ cations. Therefore, the molecular structure of a SrCl 2 solution is more similar to the three- dimensional hydrogen-bonded open structure of pure water (Saitta and Datchi, 2003),

188 than in the case of the NaCl solution, where the H-bonded network is more significantly perturbed by the presence of both Na + and Cl - ions (Mancinelli et al., 2007). For this reason, a 1 m SrCl 2 solution and pure water show a similar density increment as a function of the pressure (e.g., d / dP ), and consequently, the density difference between the two solutions remains constant with pressure (Fig. 6.3). Using the same argument, a higher NaCl concentration in the aqueous solution will result in a larger disruption of the H- bonded network of water (Walrafen, 1962; Leberman and Soper, 1995; Cavaille et al., 1996), leading to a different pressure-response of the density, as observed in Chapter 5.

189

Figure 6.3. Densities of Cl-bearing aqueous solutions as a function of pressure at 200 °C. Data for the 1 m and 3 m H2O-NaCl solutions and water are calculated with equation (4) of Chapter 5

(this work), whereas the values of the 1 m SrCl 2 solution are calculated with equation (3) of this Chapter. The water densities are from equation (4) of Chapter 5 (light blue solid line) and from Sanchez-Valle et al. (2012) (dashed dotted line, labeled as SV et al).

Figure 6.4 compares the isothermal compressibility T at 200 °C of the same aqueous solutions reported in Figure 6.3 with additional data of pure water from (Wagner and Pruss, 2002). The differences in the compressibility of the different fluids are significant in the low pressure range, with water being less compressible than the NaCl- bearing aqueous solutions and more compressible than the 1 m aqueous SrCl 2 mixture. However, as pressure increases, the compressibility contrast decreases and differences are not appreciable between the 4 solutions above 1.3 GPa.

190 The fractional volume change, that describes the changes in volume with pressure, is defined as:

dV d 1 V 1 V dP dT T dP P dT (4) V V P T V T P

where, V is the volume, T is the isothermal compressibility and P the thermal expansion coefficient. Along an isotherm, the temperature is per definition constant, and therefore, equation (4) becomes:

dV d dP (5) V T

Rearranging equation (5):

d (6) dP T

At low pressure, pure water has lower T than the NaCl aqueous solutions (Fig 5.5). This observation is a consequence of the intermolecular three dimensional H-bound structure of water (Saitta and Datchi, 2003) that is disrupted to solvate the Na ions (structure-breakers) in solution (Walrafen, 1962; Cavaille et al., 1996; Mancinelli et al., 2007). Sr ions however behave as structure makers in solution and would thus enhance the the formation of an H-bound structure in the solvent. For this reason, the compressibility of pure water and the 1 m SrCl 2 solution should be similar, and smaller than that of the NaCl aqueous solutions. On the other hand, the differences in density between Cl-bearing aqueous solutions discussed above (Fig. 6.3) suggest that pure water and the 1 m SrCl 2 aqueous solution have also a similar d / dP . Therefore, as the Sr- bearing solution has the highest density (Fig. 6.3) and considering equation (5), it follows that the H 2O-SrCl 2 solution has the smallest isothermal compressibility T as observed in

191 Figure 6.4. This observation is also in agreement with the larger ionic radius of Sr 2+ compared to Na + (Marcus, 1988). Upon increasing pressure and temperature, all investigated solutions would experience a weakening or a rupture of the intermolecular H-bonds between the water molecules (Cavaille et al., 1996; Soper and Ricci, 2000; Strassle et al., 2006), and therefore they approach similar isothermal compressibility values (Fig. 6.4).

Figure 6.4. Isothermal compressibility of Cl-bearing aqueous solutions plotted at 200°C. The data of the H 2O-NaCl solutions and pure water are taken from equation (9) of Chapter 5 (this work). Data of pure water are form Sanchez-Valle et al. (2012) (labeled as SV et al) and Wagner and Pruss (2002) (labeled as IAPWS-95).

192 The values of isobaric heat capacity CP and coefficient of thermal expansion P at 200 °C for different Cl-bearing solutions are plotted in Figure 5a and 5b, respectively. At

0.5 GPa, the CP of the Sr-bearing solution is respectively 21% and 14% smaller that for pure water and the 1 m NaCl aqueous solution, but about 1% bigger than the CP of 3m NaCl aqueous solutions. These differences become 18 %, 12% and 2% at 2.3 GPa respectively. The coefficient of thermal expansion P of the 1 m SrCl 2 aqueous solution is

33%, 23% and 15% smaller than P of pure water, 1 m and 3 m NaCl aqueous solutions, respectively at 0.5 GPa. At 2.3 GPa, differences increase to 61%, 51% and 39%.

193 Figure 6.5. a) Isobaric heat capacity CP and b) coefficient of thermal expansion P of Cl- bearing aqueous solutions as a function of pressure at 200 °C. The values of the

1m H2O-SrCl 2 solution (purple solid line) are calculated from equation (3) following equation (4) and (5) in chapter 3. The data of pure water (light blue solid line), 1 m H2O- NaCl (red solid line) and

3m H2O-NaCl (black solid line) are taken from Chapter5.

194 6.5 Conclusions

The equation of state and thermodynamic properties of a 1 m SrCl 2 aqueous solution have been determined up to 200 °C and 2.3 GPa from acoustic velocity measurements in a mDAC performed using Brillouin scattering spectroscopy. The proposed equation of state allows deriving the thermodynamic properties of the fluid, including isobaric heat capacity, coefficient of thermal expansion and compressibility that are important to model fluid-mineral interactions in natural systems.

The PVTx properties of the 1 m SrCl 2 aqueous solution were compared to data for

H2O-NaCl mixtures presented in Chapter 5 and with the data of pure water to discuss the effect of metal cations (Sr and Na) on the density and compressibility of chlorine-bearing aqueous solutions at high pressure and temperature. The comparisons indicated that differences in the volumetric data can be explained by different effect of Sr and Na cations on the molecular structure of the aqueous solution. The structure-making nature 2+ + - of Sr ions (Marcus, 1994), in contrast to Na and Cl ions, suggests that a H 2O-SrCl 2 mixture has an intermolecular structure more similar to pure water than to a NaCl aqueous solution, where the H-bonded network of the water molecules is more largely disrupted by the formation of solvation shells around the ions (Mancinelli et al., 2007).

195 6.6 References

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Ellis A. J. (1967) Partial Molal Volumes of MgCl 2 CaCl 2 SrCl 2 and BaCl 2 in Aqueous Solution to 200 Degrees. Journal of the Chemical Society a -Inorganic Physical Theoretical (4), 660-&. Holmes H. F. and Mesmer R. E. (1996) Aqueous solutions of the alkaline-earth metal chlorides at elevated temperatures. Isopiestic molalities and thermodynamic properties. Journal of Chemical Thermodynamics 28 (12), 1325-1358. Hribar B., Southall N. T., Vlachy V., and Dill K. A. (2002) How ions affect the structure of water. J. Am. Chem. Soc. 124 (41), 12302-12311. Ito E., Harris D. M., and Anderson A. T. (1983) Alteration of Oceanic-Crust and Geologic Cycling of Chlorine and Water. Geochimica Et Cosmochimica Acta 47 (9), 1613-1624. Kumar A. (1986) Densities of Aqueous Strontium Chloride Solutions up to 200-Degrees- C and at 20 Bar. J. Chem. Eng. Data 31 (3), 347-349. Laliberte M. (2009) A Model for Calculating the Heat Capacity of Aqueous Solutions, with Updated Density and Viscosity Data. J. Chem. Eng. Data 54 (6), 1725-1760.

196 Leberman R. and Soper A. K. (1995) Effect of High-Salt Concentrations on Water- Structure. Nature 378 (6555), 364-366. Mancinelli R., Botti A., Bruni F., Ricci M. A., and Soper A. K. (2007) Hydration of sodium, potassium, and chloride ions in solution and the concept of structure maker/breaker. J. Phys. Chem. B 111 (48), 13570-13577. Manning C. E. (2004) The chemistry of subduction-zone fluids. Earth Planet. Sci. Lett. 223 (1-2), 1-16. Mao H. K., Bell P. M., Shaner J. W., and Steinberg D. J. (1978) Specific Volume Measurements of Cu, Mo, Pd, and Ag and Calibration of Ruby R1 Fluorescence Pressure Gauge from 0.06 to 1 Mbar. Journal of Applied Physics 49 (6), 3276- 3283. Mao S. and Duan Z. H. (2008) The P,V,T,x properties of binary aqueous chloride solutions up to T=573 K and 100 MPa. Journal of Chemical Thermodynamics 40 (7), 1046-1063. Marcus Y. (1988) Ionic-Radii in Aqueous-Solutions. Chem. Rev. 88 (8), 1475-1498. Marcus Y. (1994) Viscosity B-Coefficients, Structural Entropies and Heat-Capacities, and the Effects of Ions on the Structure of Water. J. Solut. Chem. 23 (7), 831-848. Marcus Y. (2009) Effect of Ions on the Structure of Water: Structure Making and Breaking. Chem. Rev. 109 (3), 1346-1370. Markl G. and Bucher K. (1998) Composition of fluids in the lower crust inferred from metamorphic salt in lower crustal rocks. Nature 391 (6669), 781-783. Millero F. J., Ward G. K., and Chetirkin P. V. (1977) Relative Sound Velocities of Sea Salts at 25°C. J. Acoust. Soc. Am. 61 (6), 1492-1498.

in H 2O-NaCl solutions at deep crust/upper mantle pressures and temperatures: Implications for metasomatic processes in shear zones. Am. Miner. 87 (10), 1401- 1409.

197 Newton R. C. and Manning C. E. (2006) Solubilities of corundum, wollastonite and quartz in H2O-NaCl solutions at 800 degrees C and 10 kbar: Interaction of simple minerals with brines at high pressure and temperature. Geochimica Et Cosmochimica Acta 70 (22), 5571-5582. Pena M. P., Vercher E., and MartinezAndreu A. (1997) Apparent molar volumes of strontium chloride in ethanol plus water at 298.15 K. J. Chem. Eng. Data 42 (1), 187-189. Perron G., Desnoyer.Je, and Millero F. J. (1974) Apparent Molal Volumes and Heat- Capacities of Alkaline-Earth Chlorides in Water at 25 Degreesc. Can. J. Chem.- Rev. Can. Chim. 52 (22), 3738-3741. Philippot P., Agrinier P., and Scambelluri M. (1998) Chlorine cycling during subduction of altered oceanic crust. Earth Planet. Sci. Lett. 161 (1-4), 33-44. Phutela R. C., Pitzer K. S., and Saluja P. P. S. (1987) Thermodynamics of Aqueous Magnesium-Chloride, Calcium-Chloride, and Strontium Chloride at Elevated- Temperatures. J. Chem. Eng. Data 32 (1), 76-80. Ragan D. D., Gustavsen R., and Schiferl D. (1992) Calibration of the Ruby R(1) and R(2) Fluorescence Shifts as a Function of Temperature from 0 to 600-K. Journal of Applied Physics 72 (12), 5539-5544. Saitta A. M. and Datchi F. (2003) Structure and phase diagram of high-density water: The role of interstitial molecules. Phys. Rev. E 67 (2). Saluja P. P. S. and Leblanc J. C. (1987) Apparent Molar Heat-Capacities and Volumes of Aqueous-Solutions of Mgcl2, Cacl2, and Srcl2 at Elevated-Temperatures. J. Chem. Eng. Data 32 (1), 72-76. Sanchez-Valle C., Chio C.-H., and Gatta G. D. (2010) Single-crystal elastic properties of . (Cs,Na)AlS 2O6 H2O pollucite: A zeolite with potential use for long-term storage of Cs radioisotopes. Journal of Applied Physics 108 (9), 093509. Sanchez-Valle C., Mantegazzi D., Bass. J. D. and Reusser E. (in prep.) Equation of state, refractive index and polarizability of compressed water to 673 K and 7 GPa. Sanchez-Valle C., Martinez I., Daniel I., Philippot P., Bohic S., and Simionovici A. (2003) Dissolution of strontianite at high P-T conditions: An in-situ synchrotron X-ray fluorescence study. Am. Miner. 88 (7), 978-985.

198 Scambelluri M., Pennacchioni G., and Philippot P. (1998) Salt-rich aqueous fluids formed during eclogitization of metabasites in the Alpine continental crust (Austroalpine Mt. Emilius unit, Italian western Alps). Lithos 43 (3), 151-167. Scambelluri M. and Philippot P. (2001) Deep fluids in subduction zones. Lithos 55 (1-4), 213-227. Scambelluri M., Piccardo G. B., Philippot P., Robbiano A., and Negretti L. (1997) High salinity fluid inclusions formed from recycled seawater in deeply subducted alpine serpentinite. Earth Planet. Sci. Lett. 148 (3-4), 485-499. Sharp Z. D. and Barnes J. D. (2004) Water-soluble chlorides in massive seafloor serpentinites: a source of chloride in subduction zones. Earth Planet. Sci. Lett. 226 (1-2), 243-254. Shmulovich K. I., Yardley B. W. D., and Graham C. M. (2006) Solubility of quartz in

crustal fluids: experiments and general equations for salt solutions and H 2O-CO 2 mixtures at 400-800°C and 0.1-0.9 GPa. Geofluids 6(2), 154-167. Sinogeikin S. V. and Bass J. D. (2000) Single-crystal elasticity of pyrope and MgO to 20 GPa by Brillouin scattering in the diamond cell. Physics of the Earth and Planetary Interiors 120 (1-2), 43-62. Soper A. K. and Ricci M. A. (2000) Structures of high-density and low-density water. Phys. Rev. Lett. 84 (13), 2881-2884. Strassle T., Saitta A. M., Le Godec Y., Hamel G., Klotz S., Loveday J. S., and Nelmes R. J. (2006) Structure of dense liquid water by neutron scattering to 6.5 GPa and 670 K. Phys. Rev. Lett. 96 (6). Wagner W. and Pruss A. (2002) The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 31 (2), 387-535. Walrafen G. E. (1962) Raman Spectral Studies of Effects of Electrolytes on Water. J. Chem. Phys. 36 (4), 1035-&. Whitfield C. H., Brody E. M., and Bassett W. A. (1976) Elastic-Moduli of NaCl by Brillouin-Scattering at High-Pressure in a Diamond Anvil Cell. Review of Scientific Instruments 47 (8), 942-947.

199

200 Chapter 7

Thermodynamic properties of carbon-bearing aqueous solutions and the 2 nd dissociation constant of carbonic acid at high pressure and temperature conditions

Abstract

The PVTx properties of carbonate and bicarbonate- bearing aqueous solutions in the 0.1 m to 1 m concentration range were determined up to 400 °C and 3 GPa from Brillouin scattering measurements in a membrane-type diamond anvil cell (mDAC). The calculated partial molar volume and compressibility of carbonate and bicarbonate ions in solution have been used to evaluate the effect of pressure in the reaction volume and equilibrium nd - 2- + constant of the 2 dissociation reaction of carbonic acid (HCO 3 = CO 3 + H ) up to 300

°C and 3 GPa. The volume of reaction Vr has negative values in the investigate P-T 2- - range, indicating that carbonate ions CO 3 are favoured over the bicarbonate ions HCO 3 at high pressure and temperature conditions, in agreement with the results of speciation studies using Raman spectroscopy. The stability of carbonate species and the efficient dissolution of carbonate mineral at high pressures indicate that carbonate ions may be major aqueous species in high pressure natural fluids.

7.1 Introduction

The fluids released from subducted slabs are mainly composed of H 2O, CO 2 and mantle (Jarrard, 2003; Manning, 2004). Carbonate minerals are sequestered in rocks and veins in the upper oceanic crust during hydrothermal alteration processes (Alt and Teagle,

201 1999). Most of these carbonates are believed to survive subduction-related dehydration and silicate melting reactions in the upper mantle (Biellmann et al., 1993; Molina and Poli, 2000; Kerrick and Connolly, 2001; Dasgupta et al., 2004; Grassi and Schmidt, 2011), resulting in a recycling of carbon to deeper mantle levels. However, experimental studies (Newton and Manning, 2002; Caciagli and Manning, 2003; Sanchez-Valle et al., 2003) and thermodynamic calculations (Kerrick and Connolly, 2001; Dolejs and Manning, 2010) show that the solubility of carbonate minerals is significantly enhanced by the presence of aqueous fluids released at depth during dehydration metamorphic reactions at subduction zones (Schmidt and Poli, 1998). This fact suggests that aqueous fluids in the upper mantle may be enriched in carbon-bearing species as they migrate from the subducting oceanic slab into the overlying mantle wedge. The occurrence of

CO 2 (Roedder, 1984; Philippot et al., 1995) and carbonate daughter-minerals in fluid and melt inclusions in high pressure minerals (Wang et al., 1996; Korsakov and Hermann, 2006) confirms that C-bearing fluid phases are mobile at such mantle conditions. The aqueous fluids released during the subduction of the oceanic lithosphere may therefore play an important role in the transfer of carbon at depth, and knowledge of their thermodynamic properties is important to understand the global carbon cycle. Additionally, the carbonate system is the predominant buffering system in natural aqueous fluids, and therefore, the knowledge of the dissociation constant for the carbonic + - - 2- + acids reactions (CO 2 + H 2O = H + HCO 3 and HCO 3 = CO 3 + H ) over a wide range of pressures and temperatures is essential for understanding the chemistry of natural waters (Hershey et al., 1983). Speciation studies in carbon-bearing aqueous fluids using diamond anvil cells and Raman spectroscopy (Frantz, 1998; Martinez et al., 2004) have shown that 2- carbonate CO 3 ions are the dominant species in high pressure fluids up to at least 400 °C - and 10 GPa with minor amounts of bicarbonate HCO 3 ions only observed at pressures below 0.2 GPa (Frantz, 1998). The presence of carbonate ions in high pressure fluids nd - suggest that the negative volume of the 2 dissociation reaction of carbonic acid (HCO 3 2- + = CO 3 + H ) reported at low pressures (Hershey et al., 1983; Shock and Helgeson, 1988) is maintained to pressures relevant for the shallow parts of the upper mantle. However, there are no experimental data on the reaction volume of the dissociation reaction to confirm these observations.

202 Despite the great importance of the carbonate-bicarbonate system, very little is know about its thermodynamic properties at high pressure and temperature conditions.

The volumetric data for H2O Na 2CO 3 solutions are limited to 0.052 GPa and 350 °C

(Hershey et al., 1983; Apelblat et al., 2009), while the PVTx values in H2O NaHCO 3 mixtures (e.g., proxy for bicarbonate-bearing solutions) are provided only up to 0.028 GPa and 350 °C (Perron et al., 1974; Sharygin and Wood, 1998). The effect of pressure and temperature on the equilibrium constants of carbonic acid have been determined by Hershey et al. (1983) up to 0.1 GPa and 45 °C, while the Helgeson-Kirkham-Flowers (HKF) equation of state (Helgeson et al., 1981; Shock and Helgeson, 1988) for aqueous species can be used to predict these dissociation constants up to 1000 °C at pressure conditions corresponding to crustal settings (P to 0.5 GPa). The aim of this study was to determine the equation of state and thermodynamic properties of carbonate- and bicarbonate-bearing aqueous solutions for carbonate- and bicarbonate-bearing aqueous solutions with various concentrations (0.1 m to 1 m) up to 400 °C and 3 GPa. The equations of state (P, T, x) were obtained from the acoustic velocity (V P) measured in the membrane diamond anvil cell using Brillouin scattering spectroscopy as described in Chapters 2 and 3. The partial molal volumes of the

nd solutions investigated were then used to determine the Vr of the 2 dissociation reaction of carbonic acid in aqueous solutions. The partial molar volume of reaction Vr values were successively used to estimate the effect of pressure on the 2nd ionization constants for carbonic acid from 25 to 300 °C up to 3 GPa. The implications of these results for the equilibrium and speciation of bicarbonate/carbonates fluids at high pressure are discussed.

7.2 Experimental Method

The experimental approach used in this work is extensively explained in Chapter 2, and therefore, only a brief description of specific details is provided.

7.2.1 Sample preparation

203 The carbonate and bicarbonate bearing aqueous solutions investigated in this work are all prepared mixing the accurately weighted amount of Milli Q water and high purity ® NaHCO 3 and NaCO 3 powder (Sigma Aldrich ). Table 7.1 summarizes the solutions and the respective molalities investigated in this study.

Table 7.1. Composition and molality of the samples investigated.

Composition Molality m (mol/kg H 2O) Reagent powder ® H2O Na 2CO 3 1, 0.5, 0.1 Na 2CO 3 (99.995%, Sigma Aldrich ) ® H2O NaHCO 3 0.5, 0.1 NaHCO 3 (99.7 -100.3%, Sigma Aldrich )

7.2.2 Diamond Anvil Cell technique

All measurements were conducted in a membrane-type diamond anvil cell (mDAC) with large optical opening and mounted with two low fluorescence type Ia diamonds of 500 m culet diameter (Chervin et al., 1995). A ring-shaped resistive heater surrounding the body of the cell and an internal Pt resistive heater placed around the lower diamond were used simultaneously to generate high temperature conditions up to 400 °C. The temperature was monitored to ±2 °C with a K-type thermocouple attached to one of the diamonds close to the sample chamber. An additional thermocouple is included in the external heater and was calibrated against the internal thermocouple before the experiments (Chervin et al., 2005). The pressure in the sample chamber was monitored with two solid pressure sensors (namely, ruby spheres and cubic boron nitride chips), depending on the temperature conditions. During experimental measurements up to 200 °C the pressure was calculated from the calibrated pressure dependent shift of the R1 fluorescence line of ruby (Mao et al., 1978) after temperature correction (Ragan et al., 1992; Datchi et al., 2007b). As extensively discussed in Chapter 2, at temperature > 280 °C the use of ruby spheres as pressure sensor become problematic due to the decreasing reliability in the pressure calculation (Datchi et al., 1997). For this reason, experiments at 300 °C and 400 °C were conducted using chips of the chemically inert cubic boron nitride (cBN) as pressure marker. In this case, the pressure is calculated from the

204 calibrated pressure dependent frequency shift of the 1054 cm -1 Raman transverse optical mode (TO) (Datchi et al., 2007a). Some experiments at 20 °C, 100 °C and 300 °C were repeated using both ruby spheres and cBN chips as pressure markers, a good agreement better than 0.05 GPa at high pressure and temperature was always observed. Pressure monitoring with ruby spheres at T < 300 °C showed a precision better than 0.02 GPa, while at 300°C this value increased to 0.04 GPa. For the cBN chips the reproducibility of the pressure measured was better than 0.03 GPa at any temperature. Raman and fluorescence spectra were fitted to voigt or pearson functions using the software Peakfit version 4.12 (© Seasolve Incorporation). After the loading of the pressure sensor and the aqueous solution in a 250 to 300 m hole drilled in a pre-indented stainless steel or rhenium gasket of about 80-100 m thickness, the mDAC was immediately closed and pressurized to avoid fluid evaporation and/or solute precipitation that would modify the concentration of the solution. The reliability of the loading procedure was confirmed by the reproducibility of the acoustic data collected in repeated loadings, and by the agreement with the data collected outside the mDAC at room conditions and with literature values (Hershey et al., 1983; Apelblat et al., 2009).

7.2.3 Brillouin scattering spectroscopy

Brillouin scattering measurements were conducted at ETH Zurich using a Nd:YVO 4

0 = 532.1 nm) as a light source and a six-pass tandem Fabry-Perot interferometer of Sandercock type (Sandercock, 1982), equipped with a photomultiplayer (PMT) detector to analyze the scattered light. The Brillouin system is coupled to a Raman system installed on the same optical bench that enables collection of Raman and fluorescence spectra from the pressure standards (ruby and c-BN) without changing the position of the mDAC. Additional details of this experimental setup are provided in Sanchez-Valle et al. (2010) and Chapter 2. All measurements were conducted in symmetric scattering geometry that allows direct determination of the compressional acoustic velocities in the fluid ( VP ) using the following relationship (Whitfield et al., 1976):

205 V 0 P (1) P * 2 sin( ) 2

* where, 0 is the laser wavelength, P is the Brillouin shift and is the external scattering angle ( i.e ., angle between the incident and scattered beam outside the sample). The measurements in the mDAC were always conducted using a 50 deg scattering angle, whereas reference spectra for the carbonate and bicarbonate-bearing aqueous solutions were acquired at room conditions in 90 deg scattering geometry in a silica glass cuvette which has lateral dimensions of 20 mm x 25 mm and a thickness of 1 mm. According to the system calibration reported in Chapter 2, the accuracy in the acoustic velocities measured is calculated to be between 0.5 and 1% at high pressure and temperature conditions. Acoustic velocity measurements were conducted during compression and decompression experiments in isothermal runs at 20 °C, 100 °C, 200 °C and 300 °C for the 0.1 m, 0.5 m aqueous Na 2CO 3 and the 0.1 m, 0.5 m aqueous NaHCO 3 solutions, whereas measurements in the 1 m aqueous Na 2CO 3 solution were performed up to 400 °C. More than two spectra were collected at each isothermal pressure point, in different positions of the compression chamber, to verify the homogeneity of the fluid. Typical collection time per spectrum is between 5 to 10 minutes with the output power of the laser kept below 80 mW. All collected spectra were of excellent quality with high signal- to-noise ratio (Fig. 7.1).

206

Figure 7.1. Example of Brillouin spectra of a 1 m H2O Na 2CO 3 mixture collected in the mDAC at different temperature and pressure conditions. The compressional acoustic velocity and the backscattered compressional acoustic velocity are labeled VP and nV P , respectively, where n refers to the refractive index of the carbonate-bearing aqueous solution. The backscattered acoustic velocity nV P is generated by the interaction of some backscattered light (e.g. backscattered from the culet of the lower diamond) with the acoustic phonons in the sample. The collecting time for each spectrum is 5 to 10 minutes. The rayleigh peak have been suppressed for clarity.

7.3 Results

7.3.1 Acoustic velocities in H2O Na 2CO 3 and H 2O NaHCO 3 solutions

207

Representative Brillouin spectra of the 1m aqueous Na 2CO 3 solution collected at different pressure and temperature conditions inside the mDAC are displayed in Figure 7.1. The speeds of sound data collected at room conditions in the mDAC, carefully closed without pressurization, and in a silica glass cuvette are shown in Figure 7.2a-b together with literature data for the different compositions (Hershey et al., 1983; Apelblat et al., 2009).

Figure 7.2. Acoustic velocities measured at room conditions in the a) H2O Na 2CO 3 and b) H2O

NaHCO 3 system. The black dots and the yellow square are measurements performed in this work in the mDAC (50 deg scattering geometry) and in the silica glass cuvette (90 deg scattering geometry), respectively. The white square and the green diamond are the ultrasound measurements collected in a larger volume by (Hershey et al., 1983) and (Apelblat et al., 2009), respectively. The white diamond is the speed of sound in pure water acquired in a diamond anvil cell by Sanchez-Valle et al. (2012) with the same method of this work.

208 All speeds of sound data at room conditions collected in the mDAC and in the silica glass cuvette are identical within a maximal deviation smaller than 0.5% in velocity.

These VP values are reported in Table 7.2. The excellent agreement in the acoustic velocity results shows that the use of the mDAC does not introduce geometrical or systematic errors, and that fluid evaporation and solute precipitation during the loading procedures is negligible. Additionally, the sound velocities at room conditions collected in this work perfectly agree with the ultrasonic data of Hershey et al. (1983) and Apelblat et al. (2009) measured in a larger volume, confirming the good reproducibility of the VP acquired with the experimental setup used in this work. The averaged values for the 0.1 m,

0.5 m and 1 m Na 2CO 3 solutions are respectively, 1496 m/s, 1555 m/s and 1645 m/s; whereas for the 0.1 m and 0.5 m NaHCO 3 solutions are 1490 m/s and 1523 m/s. At room pressure and temperature conditions the VP in water is about 1483 ± 1 m/s (Wagner and Pruss, 2002, Sanchez-Valle et al., 2012). The acoustic velocities collected in the carbonate- and bicarbonate-bearing aqueous solutions up to high pressure and temperature conditions are reported in Table 7.2. The

Figures 7.3a-c display the speeds of sound data measured in the 0.1 m, 1 m Na 2CO 3 and the 0.5 m aqueous NaHCO 3 solutions, respectively. Excellent agreement between the measurements performed in compression and decompression experiments (Fig. 7.3a and c) is always observed. Additionally, the acoustic velocities acquired during repeated loadings and with different pressure sensors (Fig. 7.3b) are identical within the range of overlapping.

Figure 7.4 show the acoustic velocities in the H2O-Na 2CO 3 and H 2O-NaHCO 3 system collected at 20 °C in this work and in pure water by Sanchez-Valle et al. (2012)

(Appendix B). At room temperature the 1 m H2O-Na 2CO 3 mixture has clearly the highest

VP values, whereas 0.5 m and 0.1 m Na 2CO 3 and NaHCO 3 aqueous solutions are almost identical within a deviation of 1.0% of the acoustic velocity. The VP data of pure water (Sanchez-Valle et al., 2012) also plot in the region of overlapping. Although a trend for the acoustic velocities in the different aqueous solutions is still distinguishable, with 0.5 m

Na 2CO 3 and NaHCO 3 aqueous solutions having higher values than the respective 0.1 m mixtures and pure water, the lowest molality that allows a clear distinction between the

209 acoustic velocities in aqueous solutions and pure water is about 0.1 mol/kg H 2O.

Therefore, a molality of 0.1 mol/ kg H 2O represents a sort of lower detection limit for the acoustic velocity in saline aqueous fluids measured with Brillouin scattering spectroscopy.

Within errors, the VP values for the different aqueous solutions and molality plotted in Figure 7.4 become more similar at high pressure due to differences in compressibility.

210

Figure 7.3. Speed of sound data collected in a) 0.1 m H2O Na 2CO 3, b) 1m H2O Na 2CO 3 and c)

0.5 m H2O NaHCO 3 aqueous solutions. Diamonds, dots, triangles, square and reversed triangles indicate experiments performed at 20, 100, 200, 300 and 400 °C, respectively. Same symbols with different colors in a) and c) correspond to compression and decompression experiments. Black symbols in b) and grey squares in a) and c) represent experiments performed using cBN chips as pressure sensor. The symbol size is less than 2% error in velocity at high pressure. The black dashed lines are the acoustic velocities calculated with the EoS for the different solutions proposed in this work.

211 Table 7.2. Acoustic velocities measured in the H 2O-Na 2CO 3 and H 2O-NaHCO 3 aqueous solutions. The superscript * indicates data acquired at room conditions in a silica glass cuvette using a 90 deg scattering geometry. Numbers in italic represent data collected during decompression experiments. Bold values are measured during experiments using cBN chips as a pressure sensor. Every value is an average of at least 2 measurements performed in different regions of the compression chamber.

0.1 m H2O-Na 2CO 3 20 °C 100 °C 200 °C 300 °C P (GPa) VP (m/s) P (GPa) VP (m/s) P (GPa) VP (m/s) P (GPa) VP (m/s) 0.00 * 1497 * 0.33 1951 0.48 2101 0.83 2395 0.00 1494 0.61 2296 1.35 2910 0.91 2463 0.01 1512 0.99 2633 1.44 2941 1.05 2598 0.03 1533 1.25 2876 1.47 2977 0.25 1938 1.29 2888 1.71 3146 0.33 2031 1.42 2967 2.26 3383 0.36 2050 3.24 3791 0.40 2102 0.41 2129 0.44 2171 0.54 2283 0.63 2373 0.74 2453 0.89 2643 1.04 2763 1.13 2840

0.5 m H2O-Na 2CO 3 20 °C 100 °C 200 °C 300 °C P (GPa) VP (m/s) P (GPa) VP (m/s) P (GPa) VP (m/s) P (GPa) VP (m/s) 0.00 * 1559 * 0.49 2168 0.59 2247 2.12 3232 0.00 1551 0.51 2202 1.27 2846 2.34 3324 0.16 1835 0.57 2281 1.94 3180 2.37 3326 0.22 1912 0.76 2470 2.05 3263 2.46 3379 0.25 1900 1.10 2744 2.45 3441 0.33 2067 1.49 3009 3.07 3665 0.49 2204 0.55 2280 0.66 2351 0.69 2401 0.91 2568 1.02 2717 1.04 2748 1.13 2806 1.24 2865

212 1 m H2O-Na 2CO 3 20 °C 100 °C 200 °C 300 °C 400 °C P Vp P Vp P Vp P Vp P Vp (GPa) (m/s) (GPa) (m/s) (GPa) (m/s) (GPa) (m/s) (GPa) (m/s) 0.00 * 1639 * 0.19 1972 0.54 2249 2.30 3322 2.33 3272 0.00 1651 0.26 2040 0.58 2307 2.33 3347 2.21 3245 0.03 1695 0.48 2329 0.80 2463 2.54 3445 2.95 3561 0.03 1707 0.51 2355 1.02 2672 3.17 3687 2.50 3357 0.03 1711 0.67 2512 1.06 2690 3.77 3921 0.04 1746 0.97 2741 1.08 2700 0.05 1787 1.14 2821 1.16 2743 0.05 1784 1.55 3029 1.68 3090 0.05 1771 1.58 3068 2.09 3247 0.14 1886 1.73 3118 2.12 3275 0.25 2034 1.78 3132 2.20 3302 0.36 2179 2.18 3300 2.23 3339 0.52 2354 2.39 3454 2.37 3412 0.74 2543 2.92 3622 0.91 2681 3.06 3689 1.15 2846 3.28 3769 1.35 2935 3.70 3919 1.40 3009

0.1 m H2O-NaHCO 3 20 °C 100 °C 200 °C 300 °C P (GPa) VP (m/s) P (GPa) VP (m/s) P (GPa) VP (m/s) P (GPa) VP (m/s) 0.00 * 1489 * 0.44 2017 0.34 1874 1.31 2686 0.00 1491 0.82 2436 1.00 2573 1.34 2701 0.05 1551 0.93 2565 1.44 2867 1.62 2876 0.11 1664 1.29 2843 2.07 3270 2.03 3133 0.16 1742 1.43 2945 2.37 3445 0.25 1859 2.93 3647 0.30 1891 0.32 1973 0.49 2205 0.71 2434 0.73 2475 0.87 2595 1.04 2753

0.5 m H2O-NaHCO 3 20 °C 100 °C 200 °C 300 °C P (GPa) VP (m/s) P (GPa) VP (m/s) P (GPa) VP (m/s) P (GPa) VP (m/s) 0.00 * 1523 * 0.54 2102 0.88 2450 1.39 2797 0.00 1522 0.57 2136 1.31 2803 1.50 2864 0.11 1644 0.87 2450 1.98 3166 1.59 2908 0.25 1877 1.05 2622 2.33 3367 1.72 3009 0.26 1914 1.35 2807 2.80 3582 0.34 2005 1.46 2900 3.34 3809 0.48 2127 0.66 2322 0.77 2466 1.04 2685 1.28 2866 1.40 2928

213

Figure 7.4. Acoustic velocities collected at 20 °C. The diamonds and the dots represent the VP data measured in this work in the H 2O Na 2CO 3 and the H 2O NaHCO 3, respectively. The colors refer to different molalities. The blue triangles are VP data in pure water collected by

Sanchez-Valle et al. (2012). The symbols size is about 1.0% error in VP

7.3.2 Inversion of the acoustic velocity data

The density (P, T, x) and the acoustic velocity VP (P,T,x) in aqueous fluids are related through the thermodynamic relationships:

T 2 1 P (2a) P 2 C T VP P

214 1 P (2b) T P

C 2 P T v T 2 P 2 P (2c) P T T P T P

3 where VP is the acoustic velocity (m/s) measured, is the density (kg/m ), P the -1 -1 -1 coefficient of thermal expansion (K ), CP the isobaric heat capacity (Jkg K ) and v the specific volume (m 3/kg). As explained in Chapter 2 and following previous studies on pure water (Wiryana et al., 1998; Abramson and Brown, 2004; Asahara et al., 2010) the density of the solutions investigated in this work are inverted from the respective speeds of sound data VP . The iteration procedure is explained in detail in Chapter 3, and starts at

0.5 GPa for the 1 m H2O-Na 2CO 3, while for all other aqueous solutions a reference pressure of 0.4 GPa was taken. Therefore, values of density and isobaric heat capacity at these starting pressures are needed. As it was explained in the introduction, these values are not available yet, and therefore, the strategy adopted in this study is to find

2O-NaCl solutions that has similar densities than the carbonate- and bicarbonate-bearing aqueous solution in the low pressure region, where thermodynamic data are known (Perron et al., 1974; Hershey et al., 1983; Sharygin and Wood, 1998 ;

Abdulagatov et al., 2007; Apelblat et al., 2009). For the system H 2O-NaCl the thermodynamic properties are provided up to 0.5 GPa and 1000 °C (Driesner, 2007). This approximation was successfully applied in the inversion of the data collected on sulfate- bearing aqueous solutions and additional details are provided in Chapter 5.

2O-NaCl aqueous solutions the low pressure density data of the H 2O-Na 2CO 3 system (Abdulagatov et al., 2007), interpolated for molalities of 0.1, 0.5 and 1, and the density values of 0.1 m and 0.5 m H2O-NaHCO 3 solutions (Sharygin and Wood, 1998), are compared with the densities of H 2O-NaCl solutions (Driesner, 2007). The results of these comparisons are reported in Table 7.3 together with initial values for the density and isobaric heat capacity for the aqueous solutions investigated in this work.

215 The acoustic velocity data measured in each composition were fitted using the following equation:

2 2 ln VP c1 c2 T c3 ln P c4 T ln P c5 ln P c6 T ln P (3)

where T is the temperature in Kelvin and P is the pressure in GPa. The values of the ci fitting coefficients for all the investigated aqueous solutions are reported in Table 7.4. In some cases ( e.g ., 1 m H2O-Na 2CO 3 solutions), the most representative fit of the VP data is obtained with the fit of the 20 °C data separated from the values collected at higher temperatures. Using this approach, all the acoustic velocity values are modeled with a misfit between measured and calculated velocities smaller than 1.5%, which corresponds to the upper limit of the experimental uncertainty expected for the acoustic velocities at high pressure and temperature conditions, including error in the acoustic velocity, temperature and pressure determination.

216 Table 7.3 Equivalent H 2O-NaCl solutions for the carbonate and bicarbonate-bearing aqueous solutions investigated in this work and initial values of density and isobaric heat capacity Cp used for the iterations of equation (2a)-(2c) along the isotherms investigated in this work. The data are taken from Driesner (2007). Values for the 1m H 2O-Na 2CO 3 solution are at 0.5 GPa, while for the other concentrations and compositions the data are at 0.4 GPa.

2O-NaCl solution Molar fraction NaCl Wt.% NaCl

H2O-Na 2CO 3 1m 0.047 13.75 0.5 m 0.021 6.51 0.1 m 0.005 1.60

H2O-NaHCO 3 0.5 m 0.011 3.48 0.1 m 0.003 0.97

H2O-Na 2CO 3 H2O-NaHCO 3 Density (kg/m 3) 0.1 m 0.5 m 1 m 0.1 m 0.5 m 20°C 1137.0 1167.1 1231.9 1133.1 1148.5 100°C 1097.4 1126.8 1191.5 1093.6 1108.5 200°C 1040.0 1070.0 1138.0 1036.2 1051.4 300°C 977.5 1008.7 1082.6 973.5 989.3 400°C 1024.1 Cp (J .kg -1. K-1) 0.1 m 0.5 m 1 m 0.1 m 0.5 m 20°C 3538.3 3352.7 2995.2 3561.3 3469.1 100°C 3713.7 3456.2 3012.4 3747.9 3614.0 200°C 3720.2 3462.5 3012.8 3754.4 3620.5 300°C 3710.0 3450.9 2988.4 3744.4 3609.6 400°C 2989.8

Table 7.4. Numerical coefficients for equation (3).

H2O-Na 2CO 3 H2O-NaHCO 3 Molality 0.1 m 0.5m 1m 0.1m 0.5m 20 - 20 - 20°C 100 - 20 - 20 - T - range 300 °C 300°C 400°C 300°C 300°C r2 0.999999 0.999999 0.999999 0.999999 0.999998 0.999999

c1 7.9705 7.9122 7.9150 8.0321 7.9891 7.9438 4 c2 10 -2.1511 -0.6781 0.0143 -3.2552 -3.0771 -2.3626 1 c3 10 3.2890 0.2961 3.0083 1.2455 3.7350 1.9830 4 c4 10 -0.2915 0.1100 -1.7032 3.1057 -1.1262 3.4704 1 c5 10 1.2740 1.3830 0.8428 0.5773 0.9998 1.400 4 c6 10 -2.5812 -3.0283 -1.9250 -0.7555 -1.5799 -3.4030

217 The densities resulted by the recursive integration of equations (2a)-(2c) using the initial values of Table 7.3b are displayed in Figure 7.5a-e.

7.3.3 Polynomial equation of state (EoS) for carbon-bearing aqueous fluids

The experimentally derived density values were fitted with polynomial equations of state (EoS) as described in Chapter 3. The 0.1 m and 0.5 m H2O-Na 2CO 3 solutions were fitted with a single EoS together with values of pure water taken from Sanchez-Valle et al. (2012), and the IPAWS-95 EoS (Wagner and Pruss, 2002) at the lower most pressure of 0.4 GPa. The same procedure is applied to the 0.1 m and 0.5 m H2O-NaHCO 3 mixtures and pure water. The 1 m Na 2CO 3 aqueous solution was fitted independently because the experimental data for this aqueous mixture cover a larger temperature range up to 400 °C. The EoS used in this work has the following general form:

T, P, X a(T) b(P) c(T, P) d(X ) e(T, P, X ) H2O H2O H2O (4) where, T is the temperature in Kelvin, P is the pressure in Pascal and X is the molar H2O X fraction of water (i.e., a molality of 0.1 m corresponds to a H2O =0.998, a 0.5 m to X =0.998). For the different solutions the polynomial expressions (from this point H2O referred as Eq. 4a, 4b and 4c) are the following:

a) 1m Na 2CO 3 aqueous solution: 20 400 °C and 0.5 - 3.7 GPa

a(T) a1 a2 T

2 b(P) b1 P b2 P b3 P b4 / P (4a)

c(T, P) c1 T ln( P)

218 b) H2O-Na 2CO 3 aqueous solutions: 0 m - 0.5 m, 20 300 °C and 0.4 - 3 GPa

2 a(T ) a1 a2 T a3 T

b(P) b1 P b2 P

c(T,P) c1 T P c2 T ln( P) (4b)

d(X ) d X d X 2 d 1( X )3 d 1( X )4 H2O 1 H2O 2 H2O 3 H2O 4 H2O

2 e(T, P, X H O ) e1 T X H O ln( P) e2 T 1( X H O ) ln( P) 2 2 2 e T 1( X )2 P e T 1( X )2 / log( P) e T 1( X )2 / P 3 H2O 4 H2O 5 H2O

c) H2O-NaHCO 3 solutions: 0 m - 0.5 m, 20 - 300°C and 0.4 - 3 GPa

2 a(T ) a1 a2 T a3 T

b(P) b1 P b2 P (4c)

c(T,P) c1 T P c2 T ln( P)

d(X ) d X d X 2 d 1( X )4 H2O 1 H2O 2 H2O 3 H2O

2 e(T, P, X H O ) e1 T X H O ln( P) e2 T X H O ln( P) 2 2 2 e T 1( X )2 P e T 1( X )2 / ln( P) e 1( X )2 / P 3 H2O 4 H2O 5 H2O

The coefficient for the different EoS obtained by the least squares fit of the experimentally derived density data are listed in Table 7.5. The densities calculated with the proposed EoS are plotted in Figure 7.5a-e and reported in Table 7.6 together with the derived thermodynamic properties for the aqueous compositions investigated in this study (see Eq. 4-9 in Chapter 3).

219 Table 7.5. Numerical coefficients for equation (4).

H2O-Na 2CO 3 H2O-NaHCO 3 Molality-range 1m 0m-0.5 m 0m-0.5 m P-T range 20 - 400°C 20 - 300°C 20 - 300°C 0.5 - 3.7 GPa 0.4 - 3 GPa 0.4 - 3 GPa r2 0.999992 0.999994 0.999991 . 3 a1 1.2591 10 44.1892 -7637.88

a2 -2.5606 -1.8966 -5.0699 . -4 . -5 a3 -1.2085 10 -8.8089 10 . -8 . -3 . -3 b1 3.6466 10 9.0154 10 9.7198 10 . -3 . -8 . -8 b2 5.2891 10 -4.2306 10 -5.7756 10 . -18 b3 2.5241 10 . 9 b4 -5.8641 10 . -1 . -11 . -11 c1 1.0168 10 6.0606 10 9.24874 10

c2 -4.8747 3.7877

d1 373.355 342.901

d2 706.767 8426.4 . 9 . 10 d3 -2.8943 10 2.13296 10 . 11 d4 3.3035 10

e1 4.9443 -3.4068 . -3 e2 0.3677 -7.8175 10 . -7 . -7 e 3 -3.9186 10 -2.9394 10 . 5 . 4 e 4 -1.27261 10 -1.3495 10 . 11 . 13 e5 5.9386 10 4.7305 10

Figure 7.5 (next page). Density of a) 0.1 m Na 2CO 3, b) 0.5 m Na 2CO 3, c) 1m Na 2CO 3, d) 0.1 m

NaHCO 3 and e) 0.5 m NaHCO 3 aqueous solutions. The diamonds are the values calculated with the recursive integration of equations (2a)-(2c). Solid lines are the densities calculate with the respective EoS proposed in this work. Symbol size represents less than 1% deviation in density at high pressure. f) Comparison at 200°C between all the solutions investigated in this work and values for pure water (Sanchez-Valle et al., 2012). Symbols are the data obtained by equations (2a)-(2c), while the black solid line, the black dashed and the dot dashed line are the values of pure water calculated from the respective EoS (see text). The IAPWS-95 EoS of pure water (Wagner and Pruss, 2002) is also plotted for comparison.

220

221 Table 7.6. PVTx data for all carbonate- and bicarbonate-bearing aqueous solutions investigated in this work.

20°C

H2O - Na 2CO 3 P V Vsp Cp K K P S S T T GPa m/s kg/m 3 cm 3/g 10 -4 K-1 JKg -1K-1 10 -10 Pa -1 10 10 Pa 10 -10 Pa -1 10 10 Pa 0.4 2096 1132.3 0.88 4.35 3538.3 2.01 0.50 2.15 0.47 0.6 2362 1178.0 0.85 3.79 3507.7 1.52 0.66 1.62 0.62 0.1 m 0.8 2577 1214.5 0.82 3.37 3483.2 1.24 0.81 1.32 0.76 1 2760 1245.4 0.80 3.03 3462.7 1.05 0.95 1.12 0.90 1.2 2922 1272.4 0.79 2.75 3444.9 0.92 1.09 0.97 1.03 0.4 2192 1175.3 0.85 4.77 3352.7 1.77 0.56 1.94 0.52 0.6 2379 1219.1 0.82 4.27 3319.7 1.45 0.69 1.58 0.63 0.5 m 0.8 2563 1256.2 0.80 3.84 3292.7 1.21 0.83 1.32 0.76 1 2734 1288.1 0.78 3.47 3270.0 1.04 0.96 1.12 0.89 1.2 2892 1316.2 0.76 3.15 3250.5 0.91 1.10 0.98 1.02 0.5 2289 1229.7 0.81 4.26 2995.2 1.55 0.64 1.70 0.59 0.7 2514 1271.5 0.79 3.85 2977.9 1.24 0.80 1.36 0.74 0.9 2687 1306.1 0.77 3.55 2964.2 1.06 0.94 1.16 0.87 1 m 1.1 2830 1336.2 0.75 3.32 2952.9 0.93 1.07 1.02 0.98 1.3 2953 1363.4 0.73 3.13 2943.2 0.84 1.19 0.91 1.10 1.5 3062 1388.3 0.72 2.97 2934.8 0.77 1.30 0.83 1.20

20°C

H2O NaHCO 3 P V Vsp Cp K K P S S T T GPa m/s kg/m 3 cm 3/g 10 -4 K-1 JKg -1K-1 10 -10 Pa -1 10 10 Pa 10 -10 Pa -1 10 10 Pa 0.4 2030 1131.8 0.88 4.37 3561.3 2.14 0.47 2.28 0.44 0.6 2323 1178.2 0.85 3.78 3533.5 1.57 0.64 1.67 0.60 0.1 m 0.8 2557 1214.8 0.82 3.35 3511.8 1.26 0.79 1.34 0.75 1 2755 1245.4 0.80 3.00 3494.0 1.06 0.95 1.12 0.89 1.2 2930 1271.9 0.79 2.70 3478.9 0.92 1.09 0.96 1.04 0.4 2003 1149.1 0.87 4.65 3469.1 2.17 0.46 2.33 0.43 0.6 2281 1197.4 0.84 3.91 3439.2 1.61 0.62 1.71 0.58 0.5 m 0.8 2512 1235.4 0.81 3.40 3417.0 1.28 0.78 1.36 0.73 1 2714 1267.1 0.79 3.00 3399.3 1.07 0.93 1.13 0.88 1.2 2894 1294.3 0.77 2.67 3384.6 0.92 1.08 0.97 1.03

222 100°C

H2O - Na 2CO 3 P V Vsp Cp K K P S S T T GPa m/s kg/m 3 cm 3/g 10 -4 K-1 JKg -1K-1 10 -10 Pa -1 10 10 Pa 10 -10 Pa -1 10 10 Pa 0.4 2036 1092.2 0.92 4.69 3713.7 2.21 0.45 2.41 0.41 0.6 2295 1141.6 0.88 4.08 3668.6 1.66 0.60 1.81 0.55 0.8 2502 1181.1 0.85 3.63 3633.0 1.35 0.74 1.47 0.68 1 2677 1214.5 0.82 3.27 3603.5 1.15 0.87 1.24 0.81 1.2 2830 1243.7 0.80 2.96 3578.1 1.00 1.00 1.08 0.93 0.1 m 1.4 2966 1269.8 0.79 2.70 3555.9 0.90 1.12 0.96 1.05 1.6 3090 1293.6 0.77 2.47 3536.2 0.81 1.23 0.86 1.16 1.8 3203 1315.4 0.76 2.26 3518.4 0.74 1.35 0.78 1.28 2 3309 1335.6 0.75 2.06 3502.2 0.68 1.46 0.72 1.39 2.2 3408 1354.4 0.74 1.88 3487.3 0.64 1.57 0.66 1.51 2.4 3501 1372.2 0.73 1.71 3473.6 0.59 1.68 0.62 1.62 0.4 2155 1129.7 0.89 5.13 3456.2 1.91 0.52 2.16 0.46 0.6 2321 1176.6 0.85 4.59 3407.2 1.58 0.63 1.77 0.56 0.8 2493 1216.8 0.82 4.12 3367.5 1.32 0.76 1.48 0.68 1 2653 1251.6 0.80 3.72 3334.5 1.14 0.88 1.26 0.79 1.2 2801 1282.2 0.78 3.39 3306.5 0.99 1.01 1.09 0.91 0.5 m 1.4 2939 1309.6 0.76 3.09 3282.2 0.88 1.13 0.97 1.03 1.6 3068 1334.3 0.75 2.84 3260.7 0.80 1.26 0.87 1.16 1.8 3190 1356.9 0.74 2.61 3241.6 0.72 1.38 0.78 1.28 2 3305 1377.7 0.73 2.40 3224.3 0.66 1.50 0.71 1.40 2.2 3415 1397.0 0.72 2.21 3208.6 0.61 1.63 0.65 1.53 2.4 3521 1415.0 0.71 2.04 3194.1 0.57 1.75 0.60 1.65 0.5 2246 1187.8 0.84 4.41 3012.4 1.67 0.60 1.87 0.53 0.7 2474 1232.3 0.81 3.97 2988.0 1.33 0.75 1.49 0.67 0.9 2651 1268.9 0.79 3.66 2968.8 1.12 0.89 1.25 0.80 1.1 2796 1300.7 0.77 3.41 2953.1 0.98 1.02 1.10 0.91 1.3 2921 1329.3 0.75 3.21 2939.7 0.88 1.13 0.98 1.02 1 m 1.5 3032 1355.3 0.74 3.04 2928.2 0.80 1.25 0.89 1.12 1.7 3132 1379.4 0.72 2.90 2918.0 0.74 1.35 0.82 1.22 1.9 3225 1402.0 0.71 2.77 2908.9 0.69 1.46 0.76 1.32 2.1 3312 1423.1 0.70 2.66 2900.7 0.64 1.56 0.70 1.42 2.3 3395 1443.2 0.69 2.56 2893.3 0.60 1.66 0.66 1.52 2.5 3475 1462.2 0.68 2.46 2886.6 0.57 1.77 0.62 1.61

223

100°C

H2O NaHCO 3 P V Vsp Cp K K P S S T T GPa m/s kg/m 3 cm 3/g 10 -4 K-1 JKg -1K-1 10 -10 Pa -1 10 10 Pa 10 -10 Pa -1 10 10 Pa 0.4 2007 1091.6 0.92 4.66 3747.9 2.27 0.44 2.47 0.40 0.6 2282 1142.1 0.88 4.02 3707.2 1.68 0.59 1.82 0.55 0.8 2501 1181.7 0.85 3.56 3676.0 1.35 0.74 1.46 0.68 1 2684 1215.0 0.82 3.19 3650.6 1.14 0.88 1.23 0.81 1.2 2843 1243.9 0.80 2.87 3629.2 0.99 1.01 1.06 0.94 0.1 m 1.4 2985 1269.7 0.79 2.60 3610.8 0.88 1.13 0.94 1.06 1.6 3113 1293.0 0.77 2.35 3594.7 0.80 1.25 0.84 1.19 1.8 3230 1314.3 0.76 2.12 3580.5 0.73 1.37 0.76 1.31 2 3339 1334.1 0.75 1.91 3567.8 0.67 1.49 0.70 1.43 2.2 3442 1352.4 0.74 1.71 3556.3 0.62 1.60 0.65 1.55 2.4 3538 1369.7 0.73 1.52 3545.9 0.58 1.71 0.60 1.66 0.4 1916 1105.8 0.90 4.96 3614.0 2.46 0.41 2.69 0.37 0.6 2189 1159.3 0.86 4.16 3570.0 1.80 0.56 1.96 0.51 0.8 2414 1201.3 0.83 3.61 3537.9 1.43 0.70 1.54 0.65 1 2606 1236.1 0.81 3.18 3512.6 1.19 0.84 1.28 0.78 1.2 2776 1266.2 0.79 2.84 3491.8 1.02 0.98 1.09 0.92 0.5 m 1.4 2930 1292.7 0.77 2.54 3474.1 0.90 1.11 0.95 1.05 1.6 3072 1316.4 0.76 2.28 3458.8 0.81 1.24 0.85 1.18 1.8 3204 1338.0 0.75 2.05 3445.3 0.73 1.37 0.76 1.31 2 3328 1357.8 0.74 1.83 3433.3 0.67 1.50 0.69 1.45 2.2 3446 1376.0 0.73 1.64 3422.5 0.61 1.63 0.63 1.58 2.4 3558 1393.0 0.72 1.46 3412.6 0.57 1.76 0.58 1.71

224 200°C

H2O - Na 2CO 3 P V Vsp Cp K K P S S T T GPa m/s kg/m 3 cm 3/g 10 -4 K-1 JKg -1K-1 10 -10 Pa -1 10 10 Pa 10 -10 Pa -1 10 10 Pa 0.4 2057 1039.8 0.96 5.15 3720.2 2.27 0.44 2.60 0.38 0.6 2294 1093.8 0.91 4.48 3650.7 1.74 0.58 1.97 0.51 0.8 2484 1137.0 0.88 3.98 3597.0 1.42 0.70 1.61 0.62 1 2644 1173.6 0.85 3.59 3552.9 1.22 0.82 1.36 0.73 1.2 2782 1205.6 0.83 3.26 3515.6 1.07 0.93 1.19 0.84 1.4 2904 1234.3 0.81 2.98 3483.2 0.96 1.04 1.06 0.95 1.6 3014 1260.4 0.79 2.72 3454.6 0.87 1.14 0.95 1.05 0.1 m 1.8 3114 1284.5 0.78 2.50 3429.1 0.80 1.25 0.87 1.15 2 3206 1306.8 0.77 2.29 3406.1 0.74 1.34 0.80 1.25 2.2 3292 1327.7 0.75 2.10 3385.1 0.70 1.44 0.74 1.35 2.4 3372 1347.4 0.74 1.92 3365.8 0.65 1.53 0.69 1.45 2.6 3448 1366.1 0.73 1.76 3348.0 0.62 1.62 0.65 1.54 2.8 3520 1383.8 0.72 1.60 3331.5 0.58 1.71 0.61 1.64 3 3589 1400.6 0.71 1.45 3316.1 0.55 1.80 0.58 1.74 0.4 2175 1070.4 0.93 5.64 3462.5 1.97 0.51 2.38 0.42 0.6 2325 1121.4 0.89 5.03 3386.3 1.65 0.61 1.97 0.51 0.8 2481 1165.5 0.86 4.51 3325.4 1.39 0.72 1.64 0.61 1 2626 1203.8 0.83 4.07 3275.6 1.20 0.83 1.40 0.71 1.2 2761 1237.6 0.81 3.70 3233.7 1.06 0.94 1.22 0.82 1.4 2886 1267.8 0.79 3.39 3197.9 0.95 1.06 1.08 0.93 1.6 3003 1295.2 0.77 3.11 3166.5 0.86 1.17 0.97 1.03 0.5 m 1.8 3113 1320.3 0.76 2.86 3138.8 0.78 1.28 0.88 1.14 2 3216 1343.4 0.74 2.64 3113.9 0.72 1.39 0.80 1.25 2.2 3315 1364.9 0.73 2.44 3091.4 0.67 1.50 0.73 1.36 2.4 3409 1384.9 0.72 2.26 3070.9 0.62 1.61 0.68 1.47 2.6 3500 1403.7 0.71 2.09 3052.0 0.58 1.72 0.63 1.59 2.8 3588 1421.4 0.70 1.93 3034.5 0.55 1.83 0.59 1.70 3 3673 1438.1 0.70 1.79 3018.2 0.52 1.94 0.55 1.82 0.5 2203 1135.4 0.88 4.62 3012.8 1.81 0.55 2.11 0.47 0.7 2435 1183.3 0.85 4.14 2977.3 1.43 0.70 1.66 0.60 0.9 2615 1222.5 0.82 3.80 2949.9 1.20 0.84 1.39 0.72 1.1 2764 1256.4 0.80 3.53 2927.6 1.04 0.96 1.20 0.83 1.3 2891 1286.6 0.78 3.32 2908.8 0.93 1.08 1.07 0.94 1.5 3004 1314.1 0.76 3.14 2892.6 0.84 1.19 0.97 1.04 1.7 3106 1339.5 0.75 2.98 2878.4 0.77 1.29 0.88 1.13 1.9 3200 1363.1 0.73 2.85 2865.9 0.72 1.40 0.81 1.23 1 m 2.1 3288 1385.3 0.72 2.73 2854.6 0.67 1.50 0.76 1.32 2.3 3371 1406.3 0.71 2.62 2844.4 0.63 1.60 0.71 1.41 2.5 3452 1426.2 0.70 2.53 2835.2 0.59 1.70 0.66 1.51 2.7 3529 1445.1 0.69 2.44 2826.7 0.56 1.80 0.62 1.60 2.9 3605 1463.2 0.68 2.36 2818.9 0.53 1.90 0.59 1.70 3.1 3679 1480.4 0.68 2.29 2811.7 0.50 2.00 0.56 1.79 3.3 3752 1497.0 0.67 2.22 2805.0 0.47 2.11 0.53 1.89 3.5 3825 1512.8 0.66 2.16 2798.8 0.45 2.21 0.50 1.99 3.7 3898 1528.1 0.65 2.10 2793.0 0.43 2.32 0.48 2.09

225 200°C

H2O NaHCO 3 P V Vsp Cp K K P S S T T GPa m/s kg/m 3 cm 3/g 10 -4 K-1 JKg -1K-1 10 -10 Pa -1 10 10 Pa 10 -10 Pa -1 10 10 Pa 0.4 2023 1039.9 0.96 5.06 3754.4 2.35 0.43 2.66 0.38 0.6 2274 1095.2 0.91 4.36 3692.4 1.77 0.57 1.99 0.50 0.8 2471 1138.8 0.88 3.85 3645.7 1.44 0.70 1.61 0.62 1 2635 1175.4 0.85 3.45 3608.2 1.23 0.82 1.36 0.74 1.2 2775 1207.3 0.83 3.11 3577.1 1.08 0.93 1.18 0.85 1.4 2898 1235.8 0.81 2.81 3550.5 0.96 1.04 1.05 0.95 1.6 3008 1261.7 0.79 2.54 3527.5 0.88 1.14 0.95 1.06 0.1 m 1.8 3107 1285.6 0.78 2.30 3507.3 0.81 1.24 0.86 1.16 2 3198 1307.7 0.76 2.08 3489.4 0.75 1.34 0.79 1.26 2.2 3283 1328.5 0.75 1.87 3473.4 0.70 1.43 0.73 1.36 2.4 3362 1348.0 0.74 1.67 3459.0 0.66 1.52 0.68 1.46 2.6 3437 1366.4 0.73 1.49 3445.9 0.62 1.61 0.64 1.56 2.8 3508 1384.0 0.72 1.31 3433.9 0.59 1.70 0.60 1.65 3 3576 1400.7 0.71 1.14 3422.8 0.56 1.79 0.57 1.75 0.4 1951 1050.0 0.95 5.39 3620.5 2.50 0.40 2.86 0.35 0.6 2197 1110.2 0.90 4.51 3553.0 1.87 0.54 2.11 0.47 0.8 2398 1157.0 0.86 3.90 3504.9 1.50 0.67 1.68 0.60 1 2571 1195.9 0.84 3.44 3467.5 1.27 0.79 1.40 0.71 1.2 2722 1229.4 0.81 3.06 3437.2 1.10 0.91 1.20 0.83 1.4 2858 1259.0 0.79 2.75 3411.7 0.97 1.03 1.06 0.95 1.6 2982 1285.5 0.78 2.47 3389.8 0.87 1.14 0.94 1.06 0.5 m 1.8 3097 1309.7 0.76 2.22 3370.7 0.80 1.26 0.85 1.18 2 3204 1332.0 0.75 2.00 3353.9 0.73 1.37 0.77 1.29 2.2 3304 1352.6 0.74 1.80 3338.8 0.68 1.48 0.71 1.41 2.4 3400 1371.8 0.73 1.61 3325.2 0.63 1.59 0.66 1.52 2.6 3491 1389.9 0.72 1.43 3312.7 0.59 1.69 0.61 1.64 2.8 3579 1406.9 0.71 1.26 3301.3 0.55 1.80 0.57 1.75 3 3664 1422.9 0.70 1.11 3290.8 0.52 1.91 0.54 1.87

226 300°C

H2O - Na 2CO 3 P V Vsp Cp K K P S S T T GPa m/s kg/m 3 cm 3/g 10 -4 K-1 JKg -1K-1 10 -10 Pa -1 10 10 Pa 10 -10 Pa -1 10 10 Pa 0.4 1950 985.0 1.02 5.69 3710.0 2.67 0.37 3.18 0.31 0.6 2198 1043.7 0.96 4.92 3606.2 1.98 0.50 2.35 0.43 0.8 2392 1090.5 0.92 4.37 3527.6 1.60 0.62 1.89 0.53 1 2551 1130.3 0.88 3.94 3464.1 1.36 0.74 1.59 0.63 1.2 2685 1165.1 0.86 3.58 3411.0 1.19 0.84 1.38 0.73 1.4 2802 1196.4 0.84 3.27 3365.4 1.06 0.94 1.22 0.82 1.6 2905 1224.9 0.82 3.00 3325.5 0.97 1.03 1.09 0.91 0.1 m 1.8 2998 1251.2 0.80 2.76 3290.2 0.89 1.12 1.00 1.00 2 3082 1275.7 0.78 2.54 3258.6 0.83 1.21 0.91 1.09 2.2 3159 1298.6 0.77 2.33 3230.0 0.77 1.30 0.85 1.18 2.4 3231 1320.3 0.76 2.15 3204.0 0.73 1.38 0.79 1.27 2.6 3298 1340.9 0.75 1.97 3180.1 0.69 1.46 0.74 1.36 2.8 3361 1360.4 0.74 1.81 3158.0 0.65 1.54 0.69 1.44 3 3420 1379.1 0.73 1.65 3137.6 0.62 1.61 0.66 1.52 0.4 2139 1008.8 0.99 6.23 3450.9 2.17 0.46 2.81 0.36 0.6 2260 1063.8 0.94 5.53 3335.5 1.84 0.54 2.34 0.43 0.8 2406 1111.8 0.90 4.94 3245.1 1.55 0.64 1.94 0.52 1 2546 1153.6 0.87 4.46 3172.3 1.34 0.75 1.65 0.61 1.2 2676 1190.5 0.84 4.05 3112.0 1.17 0.85 1.43 0.70 1.4 2795 1223.7 0.82 3.71 3060.8 1.05 0.96 1.26 0.80 1.6 2905 1253.7 0.80 3.41 3016.6 0.95 1.06 1.12 0.89 0.5 m 1.8 3008 1281.3 0.78 3.14 2977.8 0.86 1.16 1.01 0.99 2 3104 1306.7 0.77 2.90 2943.3 0.79 1.26 0.92 1.09 2.2 3195 1330.3 0.75 2.69 2912.3 0.74 1.36 0.84 1.19 2.4 3282 1352.4 0.74 2.49 2884.1 0.69 1.46 0.78 1.29 2.6 3364 1373.1 0.73 2.31 2858.5 0.64 1.55 0.72 1.39 2.8 3443 1392.7 0.72 2.15 2834.8 0.61 1.65 0.67 1.49 3 3520 1411.1 0.71 1.99 2812.9 0.57 1.75 0.63 1.59 0.5 2097 1083.0 0.92 4.84 2988.4 2.10 0.48 2.51 0.40 0.7 2349 1134.3 0.88 4.32 2938.9 1.60 0.63 1.92 0.52 0.9 2543 1176.1 0.85 3.95 2901.2 1.31 0.76 1.58 0.63 1.1 2701 1212.0 0.83 3.66 2870.8 1.13 0.88 1.35 0.74 1.3 2836 1243.9 0.80 3.43 2845.4 1.00 1.00 1.19 0.84 1.5 2954 1272.8 0.79 3.24 2823.7 0.90 1.11 1.07 0.94 1.7 3061 1299.5 0.77 3.07 2804.8 0.82 1.22 0.97 1.03 1.9 3158 1324.3 0.76 2.93 2788.2 0.76 1.32 0.89 1.12 1 m 2.1 3249 1347.5 0.74 2.81 2773.3 0.70 1.42 0.82 1.21 2.3 3334 1369.4 0.73 2.69 2759.9 0.66 1.52 0.77 1.30 2.5 3416 1390.2 0.72 2.59 2747.8 0.62 1.62 0.72 1.39 2.7 3495 1409.9 0.71 2.50 2736.7 0.58 1.72 0.67 1.48 2.9 3571 1428.6 0.70 2.42 2726.5 0.55 1.82 0.63 1.58 3.1 3646 1446.6 0.69 2.34 2717.1 0.52 1.92 0.60 1.67 3.3 3720 1463.7 0.68 2.27 2708.5 0.49 2.03 0.57 1.76 3.5 3793 1480.2 0.68 2.20 2700.4 0.47 2.13 0.54 1.85 3.7 3866 1496.0 0.67 2.14 2692.9 0.45 2.24 0.51 1.95

227

300°C

H2O NaHCO 3 P V Vsp Cp K K P S S T T GPa m/s kg/m 3 cm 3/g 10 -4 K-1 JKg -1K-1 10 -10 Pa -1 10 10 Pa 10 -10 Pa -1 10 10 Pa 0.4 1981 986.4 1.01 5.52 3744.4 2.58 0.39 3.06 0.33 0.6 2225 1046.7 0.96 4.73 3653.0 1.93 0.52 2.27 0.44 0.8 2412 1094.1 0.91 4.17 3585.6 1.57 0.64 1.82 0.55 1 2564 1134.0 0.88 3.73 3532.4 1.34 0.75 1.54 0.65 1.2 2692 1168.9 0.86 3.36 3488.6 1.18 0.85 1.34 0.75 1.4 2802 1200.2 0.83 3.04 3451.7 1.06 0.94 1.19 0.84 1.6 2899 1228.8 0.81 2.76 3420.1 0.97 1.03 1.07 0.93 0.1 m 1.8 2985 1255.1 0.80 2.50 3392.5 0.89 1.12 0.98 1.02 2 3063 1279.7 0.78 2.26 3368.3 0.83 1.20 0.90 1.11 2.2 3134 1302.7 0.77 2.04 3346.8 0.78 1.28 0.84 1.20 2.4 3200 1324.5 0.75 1.84 3327.5 0.74 1.36 0.78 1.28 2.6 3261 1345.2 0.74 1.64 3310.2 0.70 1.43 0.73 1.36 2.8 3319 1365.0 0.73 1.46 3294.4 0.66 1.50 0.69 1.45 3 3375 1383.8 0.72 1.28 3280.0 0.63 1.58 0.66 1.53 0.4 1894 992.5 1.01 5.88 3609.6 2.81 0.36 3.36 0.30 0.6 2134 1059.3 0.94 4.89 3509.2 2.07 0.48 2.44 0.41 0.8 2327 1111.0 0.90 4.22 3439.5 1.66 0.60 1.93 0.52 1 2489 1153.9 0.87 3.72 3386.4 1.40 0.72 1.60 0.62 1.2 2630 1190.8 0.84 3.31 3343.7 1.21 0.82 1.37 0.73 1.4 2755 1223.5 0.82 2.97 3308.4 1.08 0.93 1.20 0.83 1.6 2868 1252.9 0.80 2.68 3278.4 0.97 1.03 1.07 0.93 0.5 m 1.8 2971 1279.7 0.78 2.41 3252.4 0.89 1.13 0.97 1.04 2 3065 1304.4 0.77 2.18 3229.6 0.82 1.23 0.88 1.14 2.2 3154 1327.4 0.75 1.96 3209.4 0.76 1.32 0.81 1.24 2.4 3237 1348.9 0.74 1.77 3191.3 0.71 1.41 0.75 1.34 2.6 3316 1369.1 0.73 1.58 3174.9 0.66 1.51 0.70 1.43 2.8 3391 1388.2 0.72 1.41 3159.9 0.63 1.60 0.65 1.53 3 3463 1406.3 0.71 1.24 3146.2 0.59 1.69 0.61 1.63

400 °C

H2O - Na 2CO 3 P V V Cp K K P SP S S T T GPa m/s kg/m 3 cm 3/g 10 -4 K-1 JKg -1K-1 10 -10 Pa -1 10 10 Pa 10 -10 Pa -1 10 10 Pa 0.5 1992 1030.6 0.97 5.08 2989.8 2.44 0.41 3.01 0.33 0.7 2268 1085.4 0.92 4.51 2922.3 1.79 0.56 2.22 0.45 0.9 2477 1129.6 0.89 4.11 2871.8 1.44 0.69 1.79 0.56 1.1 2646 1167.6 0.86 3.80 2831.5 1.22 0.82 1.52 0.66 1.3 2789 1201.2 0.83 3.55 2798.2 1.07 0.93 1.32 0.76 1.5 2913 1231.6 0.81 3.35 2769.9 0.96 1.04 1.18 0.85 1.7 3024 1259.6 0.79 3.17 2745.4 0.87 1.15 1.06 0.94 1.9 3124 1285.5 0.78 3.02 2723.9 0.80 1.25 0.97 1.03 1 m 2.1 3218 1309.7 0.76 2.89 2704.8 0.74 1.36 0.90 1.12 2.3 3306 1332.5 0.75 2.77 2687.6 0.69 1.46 0.83 1.20 2.5 3389 1354.1 0.74 2.66 2672.1 0.64 1.56 0.77 1.29 2.7 3469 1374.6 0.73 2.56 2658.1 0.60 1.65 0.73 1.38 2.9 3546 1394.1 0.72 2.48 2645.2 0.57 1.75 0.68 1.47 3.1 3622 1412.7 0.71 2.40 2633.3 0.54 1.85 0.64 1.55 3.3 3696 1430.5 0.70 2.32 2622.4 0.51 1.95 0.61 1.64 3.5 3770 1447.6 0.69 2.25 2612.3 0.49 2.06 0.58 1.73 3.7 3843 1464.0 0.68 2.19 2602.8 0.46 2.16 0.55 1.83

228

Figure 7.6. a) Coefficient of thermal expansion, b) isobaric heat capacity and c) adiabatic compressibility at 200 °C calculated from the EoS proposed in this work (Eq.4). Data of pure water from Sanchez-Valle et al (2012), the IAPWS-96 EoS (Wagner and Pruss, 2002) and Wiryana et al. (1998) are also plotted for comparison.

229 7.3.4 The effect of pressure on the 2nd ionization constant of carbonic acid

In the water-carbonate system the two main dissociation reactions are the following:

- H 2O CO 2 H HCO 3 (11)

- -2 HCO 3 H CO 3 (12)

The effect of pressure and temperature on the 1st and 2 nd dissociation constants of carbonic acid was determined by Hershey et al. (1983) up to 45 °C and 0.1 GPa, and by Shock and Helgeson (1988) up to 1000 °C and 0.5 GPa using the HKF equation of state for the properties of electrolytes (Helgeson et al., 1981)). The pressure dependence of the of the 2 nd dissociation constant for carbonic acid can be determined from the change in the in the partial molar volume of reaction (12) (Hershey et al., 1983; Millero et al., 2012):

2 V r V (CO 3 ) V (H ) V (HCO 3 ) (13)

where V indicates the partial molar volume at infinite dilution (cm 3/mol). According to the additivity relations (Hershey et al., 1983; O'connell et al., 1999), the values of V r for the dissociation of the bicarbonate ions can be estimated as:

V r V (Na 2CO 3 ) V (HCl ) V (NaHCO 3 ) V (NaCl ) (14)

where V is the partial molar volume at infinite dilution of the components in pure water.

The V values for the components NaCl, Na 2CO 3 and NaHCO 3 in water were derived from the respective EoS proposed in this manuscript (see Chapter 5 for the NaCl solutions). In fact, the partial molar volumes V i of the components i = NaCl, Na 2CO 3

230 and NaHCO 3 in an aqueous mixture are derived according to the thermodynamic relationship (Cemic, 1988):

Vm Vm V i V X (15) n m H2O X i P,T ,n H2O P,T

where, ni are the moles of component i and Vm is the average molar volume of the aqueous mixture (cm 3/mol for 1 mol of the solution), which is calculated with:

M (X ) V (T, P) H2O i H 2O (16) m (T, P, X ) H 2O

where, M (X ) is the molar mass of the H O - i mixture as a function of the H2O i H2O 2 (T, P, X ) concentration, and H2O is the density calculated with the respective EoS (e.g.,

Eq. 4 in this work for H2O-Na 2CO 3 and the H 2O-NaHCO 3 mixtures). The values of partial molar volume at infinite dilution ( ni 0) for the components NaCl, Na 2CO 3 and

NaHCO 3 in water at 25, 100, 200 and 300 °C up to 3 GPa are reported in Table 7.7. The EoS used for calculating the V values is valid from 0.5 GPa for the NaCl aqueous solution and from 0.4 GPa for Na 2CO 3 and NaHCO 3 aqueous mixtures, for this reason, the V data are provided from a starting pressure of 0.5 GPa. In order to obtain the V data for HCl in the pressure range of interest (0.5 to 3 GPa), the available literature data were extrapolated in pressure adopting the following procedure. The V (HCl ) values were calculated to 300 °C and 0.028 GPa with the equation proposed by Sharygin and Wood

(1997) and then used to obtain the dimensionless Krichevskii parameter A12 (O'connell et al., 1996; Trevani et al., 2007) according to the relationship A12 V (HCl /() kW ater R T ) , where kwater is the compressibility of water calculated with the IAPWS-95 EoS (Wagner and Pruss, 2002) and R the gas constant. The Krichevskii parameter A12 calculated at 25, 100, 200 and 300 °C were then fitted as a function of the water density with 2 nd grade

231 2 polynomial functions ( e.g., A12 a b water c water ) and successively, extrapolated to 3 GPa. The V (HCl )values to 3 GPa were then recalculated from the extrapolated A12 data. The V (HCl )data are reported in Table 7.7.

The values of V r for reaction (12) calculated up to 3 GPa from the partial molar volume of the components HCl, NaCl, Na 2CO 3 and NaHCO 3 following equation (14) are reported in Table 7.7.

232 Table 7.7. Partial molar volume at infinite dilution V for the components NaCl, NaHCO 3,

HCl and Na 2CO 3 and V r data for reaction (12) as a function of the pressure up to 300°C.

20 °C 100 °C P 3 3 (GPa) V (cm /mol) 3 V (cm /mol) 3 Vr (cm /mol) Vr (cm /mol) NaCl NaHCO 3 Na 2CO 3 HCl NaCl NaHCO 3 Na 2CO 3 HCl 0.5 29.11 22.57 -79.59 19.47 -111.80 24.84 -62.29 -142.21 18.74 -86.01 0.6 28.64 20.46 -82.24 19.51 -111.84 24.46 -61.85 -144.32 18.81 -88.11 0.7 28.25 18.82 -84.14 19.50 -111.70 24.14 -61.29 -145.62 18.82 -89.65 0.8 27.91 17.48 -85.54 19.46 -111.47 23.87 -60.68 -146.39 18.77 -90.81 0.9 27.61 16.38 -86.59 19.40 -111.18 23.63 -60.04 -146.80 18.69 -91.70 1 27.35 15.44 -87.37 19.30 -110.86 23.42 -59.39 -146.96 18.58 -92.40 1.1 27.11 14.64 -87.96 19.19 -110.52 23.23 -58.75 -146.93 18.45 -92.96 1.2 23.07 -58.12 -146.76 18.31 -93.40 1.3 22.91 -57.50 -146.50 18.16 -93.75 1.4 22.77 -56.90 -146.16 18.00 -94.03 1.5 22.64 -56.31 -145.76 17.84 -94.25 1.6 22.51 -55.74 -145.32 17.68 -94.42 1.7 22.40 -55.19 -144.85 17.51 -94.54 1.8 22.29 -54.65 -144.35 17.35 -94.64 1.9 22.19 -54.13 -143.84 17.19 -94.70 2 22.09 -53.63 -143.31 17.03 -94.74 2.1 22.00 -53.14 -142.78 16.88 -94.76 2.2 21.92 -52.67 -142.24 16.73 -94.75 2.3 21.83 -52.21 -141.69 16.58 -94.73 2.4 21.75 -51.77 -141.15 16.44 -94.70 200 °C 300 °C P 3 3 (GPa) V (cm /mol) 3 V (cm /mol) 3 Vr (cm /mol) Vr (cm /mol) NaCl NaHCO 3 Na 2CO 3 HCl NaCl NaHCO 3 Na 2CO 3 HCl 0.5 17.81 -191.25 -242.18 14.57 -54.17 8.86 -353.78 -366.97 8.60 -13.44 0.6 17.68 -185.62 -242.57 15.16 -59.46 9.20 -339.65 -363.87 9.63 -23.79 0.7 17.57 -180.65 -242.18 15.57 -63.52 9.47 -327.59 -360.28 10.34 -31.81 0.8 17.47 -176.20 -241.32 15.86 -66.73 9.68 -317.08 -356.48 10.85 -38.24 0.9 17.38 -172.17 -240.17 16.06 -69.33 9.86 -307.75 -352.61 11.21 -43.50 1 17.31 -168.49 -238.84 16.19 -71.47 10.01 -299.38 -348.75 11.47 -47.90 1.1 17.24 -165.09 -237.39 16.27 -73.27 10.14 -291.78 -344.94 11.66 -51.64 1.2 17.18 -161.95 -235.88 16.31 -74.79 10.25 -284.82 -341.21 11.80 -54.84 1.3 17.12 -159.02 -234.32 16.33 -76.09 10.35 -278.42 -337.57 11.89 -57.62 1.4 17.07 -156.28 -232.75 16.32 -77.22 10.45 -272.48 -334.04 11.96 -60.04 1.5 17.02 -153.71 -231.17 16.29 -78.19 10.53 -266.96 -330.61 12.00 -62.18 1.6 16.98 -151.29 -229.60 16.25 -79.05 10.61 -261.79 -327.28 12.02 -64.08 1.7 16.94 -148.99 -228.04 16.20 -79.79 10.68 -256.93 -324.05 12.02 -65.77 1.8 16.90 -146.82 -226.50 16.14 -80.45 10.74 -252.36 -320.92 12.01 -67.29 1.9 16.86 -144.75 -224.99 16.07 -81.03 10.80 -248.04 -317.88 12.00 -68.65 2 16.83 -142.79 -223.49 16.00 -81.54 10.86 -243.95 -314.94 11.97 -69.87 2.1 16.80 -140.91 -222.03 15.92 -81.99 10.91 -240.06 -312.08 11.94 -70.99 2.2 16.77 -139.12 -220.59 15.84 -82.39 10.96 -236.36 -309.31 11.90 -72.00 2.3 16.74 -137.40 -219.18 15.76 -82.75 11.00 -232.84 -306.61 11.86 -72.92 2.4 16.71 -135.75 -217.79 15.68 -83.07 11.05 -229.46 -303.99 11.82 -73.76 2.5 16.68 -134.17 -216.44 15.60 -83.35 11.09 -226.24 -301.45 11.77 -74.53 2.6 16.66 -132.65 -215.11 15.52 -83.60 11.13 -223.15 -298.97 11.73 -75.23 2.7 16.63 -131.18 -213.81 15.44 -83.82 11.17 -220.18 -296.56 11.68 -75.88 2.8 16.61 -129.77 -212.53 15.36 -84.01 11.20 -217.32 -294.22 11.63 -76.47 2.9 16.58 -128.41 -211.28 15.28 -84.18 11.24 -214.58 -291.93 11.58 -77.01 3 16.56 -127.09 -210.06 15.20 -84.33 11.27 -211.93 -289.71 11.53 -77.52

233 According to the thermodynamic relationship (Cemic, 1988; Anderson, 2005):

ln( K ) V P r (17) P T R T

where, KP is the equilibrium constant and R the gas constant, the equilibrium constant

KP at any pressure P can be calculated from:

P 1 ln( K ) V r P ln( K ) (18) P R T P0

In this case, the initial pressure P0 is imposed by the validity range of the EoS for the components NaCl, Na 2CO 3 and NaHCO 3 and therefore, corresponds to 0.5 GPa. To solve equation (18) an expression for the V r values as a function of the pressure is

2 needed. The following equation reproduces well (r = 0.99998) the V r data of Table 7.8 from 25 °C to 300 °C up to 3 GPa:

152 .264 3 V r T, P 396 67. .2 005 T .6 795 10 P .4 503 P T (19) P .2 427 10 6 T P .8 831 10 3 T P .0 178 T ln( P) .4 055 T .7 973 10 9 T 2 P .6 367 10 6 T 2 P

with the pressure in bar.

ln( K ) The P0 value at 0.5 GPa are calculated using the HFK equation of state for aqueous species (Helgeson et al., 1981; Shock and Helgeson, 1988), which is valid up to 1000°C and 0.5 GPa. According to (Shock and Helgeson, 1988):

0 G T, P log (K ) r (20) 10 P 2.303 R T

234 where KP is the equilibrium constant at any pressure up to 0.5 GPa, R the gas

0 0 constant, T the temperature in K and Gr (T, P) n ,ri G T, P is the Gibbs free i energy of reaction, with ni,r the reaction coefficients of the species i in the reaction and

0 G T, P denotes the apparent standard partial molal Gibbs free energy of formation of the species i given by:

0 0 T G T, P G f S ref (T Tref ) c1(T ln( ) T Tref ) Tref P a1(P Pref ) a2 ln( ) Pref

1 T T T Tref (T ) c ((( ) ( ))( ) ln( )) (21) 2 2 T T(Tref ) 1 P 1 1 ( )( a3 (P Pref ) a4 ln( )) ( )1 ref ( )1 T Pref ref

ref Yref (T Tref )

where P is the pressure in bar, T the temperature in K, the subscript ref denotes 25°C and 1 bar, and all other parameters and constants are given in Table 7.8. At the temperature and pressure of interest the parameters is equal to the parameter ref (Shock et al., 1992). log (K ) The 10 P0 value at 0.5 GPa from 25°C to 300°C calculated with equations (20) and (21) are reported in Table 7.9. Equation (19) is then used to derive the 2 nd dissociation constant of carbonic acid (Eq. 12) from 25°C to 300°C up to 3 GPa (Table 7.9).

23 5 Table 7.8. Summary of the parameters for equations (20) and (21) taken from Shock and Helgeson (1988) and references therein. The water dielectric constant and the Y Born function are taken from Shock et al. ( 1992).

0 .10 .10 -2 .10 -4 .10 -4 .10 -5 G f Sref a1 a2 a3 a4 c1 c2 ref cal .K cal .g cal cal .g Units cal .mol -1 cal .mol -1. K-1 cal .mol -1. bar -1 cal .mol -1 cal .mol -1 .mol -1 .K.mol -1 .mol -1. K-1 .K.mol -1 H+ 0 0 0 0 0 0 0 0 0 - HCO 3 -140282 23.53 7.5621 1.1505 1.2346 -2.8266 12.9395 -4.7579 1.2733 2- CO 3 -126191 -11.95 2.8524 -3.9844 6.4142 -2.6143 -3.3206 -17.1917 3.3914 Constants 228 K 2600 bars R 1.98719 cal .mol -1. K-1 Shock et al. (1992) Yref Shock et al. (1992) ref 25°C 1bar

236 Table 7.9. Summary of the log 10 (K P ) values for reaction (12). The data at 0.5 GPa are calculated with equations (20) and (21), and the data of Table 7.8 (Shock and Helgeson, 1988; Shock et al., 1992).

20 °C 100 °C 200 °C 300 °C P (GPa) log 10 (K P ) log 10 (K P ) log 10 (K P ) log 10 (K P ) 0.5 -8.22 -8.12 -8.51 -9.05 0.6 -6.26 -6.89 -7.90 -8.87 0.7 -4.30 -5.64 -7.23 -8.62 0.8 -2.35 -4.37 -6.51 -8.30 0.9 -0.40 -3.08 -5.76 -7.93 1.0 1.55 -1.79 -4.98 -7.51 1.1 3.49 -0.49 -4.18 -7.06 1.2 0.81 -3.36 -6.58 1.3 2.12 -2.52 -6.06 1.4 3.43 -1.67 -5.53 1.5 4.74 -0.80 -4.97 1.6 6.05 0.07 -4.40 1.7 7.37 0.95 -3.80 1.8 8.69 1.83 -3.20 1.9 10.01 2.73 -2.58 2.0 11.34 3.63 -1.95 2.1 12.66 4.53 -1.30 2.2 13.99 5.44 -0.65 2.3 15.32 6.35 0.01 2.4 16.66 7.27 0.68 2.5 8.02 1.35 2.6 9.10 2.04 2.7 10.03 2.73 2.8 10.95 3.42 2.9 11.88 4.12 3.0 12.81 4.83

According to Anderson et al. (1991) and Dolejs and Manning (2010) the equilibrium constant KP at high pressure can be modeled with simple relationships including the density of the solvent. The model proposed in this work has the following form:

2 3 log 10 (K P ) a(T) b(T) log 10 ( water ) c(T) log 10 ( water ) d(T) log 10 ( water ) (22)

237 3 where, T is the temperature in Kelvin, water the density of water (g/cm ) taken from the IAPWS-95 EoS (Wagner and Pruss, 2002) and a(T ) , b(T ) , c(T ) and d(T) are polynomial expansions in temperature, all with the same form:

2 3 a(T) a1 a2 T a3 T a4 T .

The numerical values of the coefficients ai , bi , ci and di for the components a(T ) , b(T ), c(T ) and d(T) are reported in Table 7.10, and are calculated by the least squares fit of the KP data derived in this work, the KP values up to 0.5 GPa calculated from the HKF EoS (Helgeson et al., 1981; Shock and Helgeson, 1988) and the density data of water from the IAPWS-95 EoS (Wagner and Pruss, 2002). Equation (22) is valid for temperatures between 25°C and 300°C and pressures from 0 GPa to 3 GPa. nd Figure 7.7 illustrates the fit with equation (22) of the log 10 (K P ) values for the 2 dissociation reaction of carbonic acid calculated in this work, together with literature data (Hershey et al., 1983; Shock and Helgeson, 1988; Millero et al., 2006) at different pressure and temperature conditions and values of the dissociation constant of water up to 100°C (Bandura and Lvov, 2006). The fit with equation (22) is excellent, with r2 of 0.9995. At 25°C the model proposed here reproduces the room pressure data of (Millero et al., 2006) perfectly, also the low pressure values of (Hershey et al., 1983) are in good agreement with the model presented here. Equation (22) can therefore be used to derive the 2 nd dissociation constant of carbonic acid from room pressure to 3 GPa for temperatures between 25 and 300°C.

Table 7.10. Numerical parameters for equation (22).

Parameters . 1 . 4 a1 -1.0940 10 c1 -8.0763 10 . -3 . 2 a2 -5.5406 10 c2 5.4827 10 4.0445 .10 -5 c . 1 a3 3 -1.2032 10 -4.4844 .10 -8 . -4 a4 c4 8.6144 10 . 3 . 5 b1 2.2226 10 d1 6.0966 10 . 1 . 3 b2 -1.5624 10 d 2 -3.9642 10 . -2 . 1 b3 3.5714 10 d 3 8.5203 10 . -5 . -3 b4 -2.6454 10 d4 -6.0195 10

238

Figure 7.7. Second dissociation constants of carbonic acid and self-ionization constant of water as a function of the solvent density (Wagner and Pruss, 2002). The diamonds, dots, triangles and squares are data at 25, 100, 200 and 300 °C, respectively. The different colors for the same symbol differentiate the databases: light grey are data from this work, blue (labeled SH88) are calculated with the HFK EoS of Shock and Helgeson (1988), yellow (labeled H83) are the low pressure data of Hershey et al. (1983) and red (labeled M06) are room pressure data at 25 °C taken from Millero et al. (2006). The solid lines are the fit performed with equation (22), while the black dashed lines (labeled BL06) are the water dissociation constant values from Bandura and Lvov (2006).

239 7.4 Discussion

7.4.1 Thermodynamic properties of carbonate-bicarbonate aqueous solutions.

The equations of state for carbonate- and bicarbonate-bearing aqueous solutions proposed in this work (Eq. 4a-c) predict their thermodynamic properties over a broad range of pressure, temperature and concentrations (Table 7.6) The agreement between the densities calculated with the EoS proposed (Eq. 4a-c) and the experimentally derived data is always excellent, with a maximal deviation of

1.3% in density at 300 °C for the 0.1m NaHCO 3 solution. The data of pure water calculated with the EoS for the H2O-Na 2CO 3 (Eq. 4b) and the H 2O-NaHCO 3 (Eq. 4c) systems are reported in Table 7.11, together with the literature data (Wagner and Pruss, 2002 at 0.4 GPa and Sanchez-Valle et al., 2012, from 0.6 to 3 GPa) used for the fit with equation (4b-c). Equations (4b) and (4c) reproduce the densities of pure water with a maximum deviation of 0.3% and 1%, respectively. Apart from this relatively large difference at 0.4 GPa and 300 °C, corresponding to a density value taken from the

IAPWS-95 EoS (Wagner and Pruss, 2002), the EoS for H2O-NaHCO 3 aqueous solutions provide densities with differences smaller than 0.4%, which is within the expected maximal uncertainty for the density using the inversion procedure applied here (see Chapter 3). We should point out that the water density values of Sanchez-Valle et al. (2012) were determined with the same experimental method and numerical approach of this work (see Appendix B). The density data at 200 °C are plotted in Figure 7.5f together with the values of the other investigated concentrations and compositions. At 1 GPa, the 1m H2O-Na 2CO 3 mixture is 5.6%, 3% and 7% denser than the 0.1 m, 0.5 m H2O-Na 2CO 3 solution and pure water, respectively. The differences are 5.2% and 3.6% relative to a 0.1 m and 0.5 m H2O-

NaHCO 3 solution, respectively. At 3 GPa these values decrease to 5.1%, 2.5%, 7 %, 4.8% and 3.3%. From Figure 7.5f is evident that the 0.5 m carbonate- and bicarbonate- bearing solutions have very similar densities (the maximal difference of 2% is at 0.4 GPa. At other pressures this value is smaller than 1%) in agreement with the almost equivalent speed of sound data measured in the mDAC (Table 7.2).

240

Table 7.11. Comparison between the density of pure water at different temperatures up to 200 °C. The literature data (Lit.) are taken from Sanchez-Valle et al. (2012) and the IAPWS-95 EoS (Wagner and Pruss, 2002) at 0.4 GPa ( *). The columns labeled as Eq. 4b and Eq. 4c are the data

calculated from the EoS for the H 2O-Na 2CO 3 and the H 2O-NaHCO 3 system, respectively.

Density of pure water (kg/m 3) 20 °C 100 °C 200 °C 300 °C P Lit. Eq. Eq. Lit. Eq. Eq. Lit. Eq. Eq. Lit. Eq. Eq. (GPa) 4b 4c 4b 4c 4b 4c 4b 4c 0.4 1129.1 * 1132.6 1132.1 1088.0 * 1086.7 1082.9 1029.8 * 1027.0 1019.8 965.1 * 965.0 955.0 0.6 1175.5 1176.5 1177.8 1130.8 1133.8 1132.2 1075.6 1078.2 1073.7 1020.9 1020.2 1013.5 0.8 1212.1 1211.6 1213.7 1170.0 1171.5 1171.1 1117.8 1119.1 1116.3 1066.3 1064.3 1059.7 1 1243.0 1241.3 1243.9 1202.9 1203.4 1203.8 1153.3 1153.8 1152.1 1104.3 1101.8 1098.7 1.2 1231.7 1231.4 1232.3 1184.2 1184.3 1183.4 1137.3 1134.8 1132.8 1.4 1257.4 1256.5 1257.6 1211.8 1211.7 1211.5 1166.7 1164.4 1163.5 1.6 1280.7 1279.3 1280.6 1236.7 1236.6 1237.0 1193.4 1191.5 1191.6 1.8 1302.1 1300.3 1301.7 1259.7 1259.6 1260.4 1217.8 1216.6 1217.5 2 1322.0 1319.8 1321.1 1280.9 1281.1 1282.3 1240.4 1239.9 1241.6 2.2 1340.5 1338.0 1339.3 1300.7 1301.2 1302.7 1261.5 1261.9 1264.4 2.4 1357.9 1355.1 1356.4 1319.3 1320.1 1322.0 1281.3 1282.7 1285.9 2.6 1336.9 1338.0 1340.3 1300.0 1302.4 1306.3 2.8 1353.5 1355.1 1357.6 1317.7 1321.2 1325.8 3 1369.4 1371.4 1374.2 1334.6 1339.1 1344.5

The acoustic velocities VP derived from the polynomial equations of state are reported in Table 7.6 and plotted in Figure 7.3. The agreement is excellent, with a difference between

experimentally measured and derived VP data smaller than 2%. It has been already pointed out that a maximal misfit of 1.5-2% between measured and derived speed of sound data is expected when the density data have an associated uncertainty between 0.3- 0.5%, confirming the maximal density misfit reported above (Chapter 3). For the EoS of

the 1 m H2O-Na 2CO 3 solution (Eq. 4a) the same associated uncertainty of 0.3-0.5% for the

density is valid, because also in this case, the VP values generated by the EoS proposed match the experimentally measured acoustic velocities up to 400°C and 3.7 GPa with a maximal misfit smaller than 1.5-2% (Fig. 7.3b). In summary, equations (4a)-(4c) provide the density of carbonate- and bicarbonate- bearing aqueous fluids with uncertainties between 0.3 and 0.5 % at pressures and temperatures up to 400 °C and 3 GPa.

241

The coefficient of thermal expansion, isobaric heat capacity and adiabatic compressibility at 300 °C calculated from the EoS proposed here are plotted in Figure 7.7a-c, together with data for pure water. These derived PVTx properties have larger associated uncertainties because they are derivative of the density and typically range from 3 to 8% as discussed in Chapter 3 and 4. A small difference in density will thus propagate to larger uncertainties in the derived thermodynamic properties (Wagner and Pruss, 2002; Abramson and Brown, 2004) as illustrated from the deviation in thermal expansion and heat capacity for water using different EoS (Fig. 7.7a-b). According to error propagation calculations (Caporaloni et al., 1987) an uncertainty of 0.5% in density generates a maximal misfit in P and CP values of 1%, which propagates to 4.5% and 8% in adiabatic and isothermal elastic properties (compressibility and bulk modulus), respectively.

The adiabatic compressibility of the carbonate- and bicarbonate-bearing aqueous solutions are reported in Table 7.6 and plotted in Figure 7.7c together with values for pure water. Within the maximal associate error of 4.5%, the comparisons in Figure 7.7c suggest that bicarbonate-bearing aqueous solutions have larger compressibility than carbonate-bearing aqueous solutions, with the 1 m H2O-Na 2CO 3 mixture showing the lowest values. Pure water (Wagner and Pruss, 2002; Sanchez-Valle et al., 2012) have in general a compressibility smaller than the bicarbonate-bearing aqueous solutions and slightly larger or similar to the carbonate-bearing aqueous solutions. Within the same composition, the difference between a 0.1 m and a 0.5 m solution are very small, and in most of the cases lower than the associate uncertainty of 4.5%. In the H 2O-Na 2CO 3 system, the 1 m solution has the lowest compressibility. In most of the cases, the differences between the aqueous solutions decrease with the pressure. If the structure making/breaking behaviors (Marcus, 1994) of the ions dissolved are considered, the differences between the aqueous solutions can be interpreted from a molecular point of view. Pure water has a 3-dimensional hydrogen-bond network with tetrahedral arrangement of the nearest neighbors (Saitta and Datchi, 2003). The dissolution in water of ions with structure breaking behavior, like Cl -, induces the rupture

242 of the H-bonds between the water molecules (Walrafen, 1962; Marcus, 1994; Cavaille et al., 1996); the same effect, or at least a weakening of the H-bonds, is induced by a pressure and temperature increase (Cavaille et al., 1996; Soper and Ricci, 2000; Strassle et al., 2006). In the aqueous systems investigated in this work, the dissolved species are + - 2- + Na , HCO 3 and CO 3 . The Na are present in both H 2O-Na 2CO 3 and H 2O-NaHCO 3 system, and therefore, they cannot represent the source of the differences between carbonate- and bicarbonate-bearing aqueous solutions observed in Figure 7.7c. In - 2- addition, HCO 3 and CO 3 are respectively, border line and structure making ions (Marcus, 1994). Thus, the presence of dissolved carbonate ions enhances the formation of a 3 dimensional hydrogen-bond network, inducing a decrease in the adiabatic compressibility. The higher the concentration of the dissolved carbonate ions is the lower the compressibility (i.e. , 1 m respective to 0.5 m and 0.1 m). The combined effect of + - dissolved Na (weak structure breaker; Marcus, 1994) and HCO 3 ions damages the H- bonds network, explaining the larger compressibility for bicarbonate-bearing aqueous solutions. At high pressure the differences between the aqueous solutions decrease, because a pressure increase induces the rupture or the weakening of the hydrogen-bond network in water (Cavaille et al., 1996; Soper and Ricci, 2000; Strassle et al., 2006).

7.4.2 Implications for the carbonate-bicarbonate equilibrium in high pressure fluids

The negative values of the volume of reaction V r reported in Table 7.7 imply that the carbonate ions species are favored over the bicarbonate ions at high pressure. The results of this work are in agreement with previous experimental studies (Frantz, 1998; Martinez et al., 2004), which demonstrated that carbonate ions are stable in aqueous fluid up to high pressure conditions. Additionally, experimental studies on the solubility of strontianite (Sanchez-Valle et al., 2003) and calcite (Newton and Manning, 2002; Caciagli and Manning, 2003) in water show that the solubility of carbonate minerals is significantly enhanced by the presence of water-rich fluids at high pressure and temperature conditions. These experimental findings are supported by thermodynamic calculations (Kerrick and Connolly, 2001; Dolejs and Manning, 2010). Combined, these

243 observations suggest that carbonate ions may be major aqueous species in water-rich high pressure fluids at subduction zones.

7.5 Conclusions

The thermodynamic properties of carbonate- and bicarbonate-bearing aqueous solutions in the 0.1 m to 1 m concentration range were determined up to 400 °C and 3 GPa from acoustic velocity measurements in the diamond anvil cell using Brillouin scattering spectroscopy. The proposed equations of state are able to predict the densities of carbonate and bicarbonate aqueous fluids with an accuracy of 0.3-0.5% while the thermal expansion, heat capacity and compressibility of the fluid are obtained with a total error of 3-8%. The EoS was used to calculate the partial molar volume and compressibility of carbonate and bicarbonate ions in solution and applied to evaluate the effect of pressure in the reaction volume and equilibrium constant of the 2nd dissociation reaction of - 2- + carbonic acid (HCO 3 = CO 3 + H ). The results, together with low pressure data (< 0.5 GPa) calculated from the Helgeson-Kirkham-Flowers (HKF) equation of state (Helgeson et al., 1981; Shock and Helgeson, 1988) were fitted as a function of the solvent density (Wagner and Pruss, 2002) to formulate a predictive model for the equilibrium constant of the dissociation reaction valid from room pressure up to 3 GPa for temperatures between

25 °C and 200 °C. The volume of reaction Vr has negative values in the investigate P- 2- T range, indicating that carbonate ions CO 3 are favoured over the bicarbonate ions - HCO 3 at high pressure and temperature conditions, in agreement with the results of speciation studies using Raman spectroscopy. The stability of carbonate species and the efficient dissolution of carbonate mineral at high pressures indicate that carbonate ions may be major aqueous species in high pressure natural fluids.

244 7.6 References

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247 Millero F. J., Graham T. B., Huang F., Bustos-Serrano H., and Pierrot D. (2006) Dissociation constants of carbonic acid in seawater as a function of salinity and temperature. Mar. Chem. 100 (1-2), 80-94. Millero F. J., Ward G. K., Lo Surdo A., and Huang F. (2012) Effect of pressure on the dissociation constant of boric acid in water and seawater. Geochim. Cosmochim. Acta 76 , 83-92. Molina J. F. and Poli S. (2000) Carbonate stability and fluid composition in subducted

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248 Saitta A. M. and Datchi F. (2003) Structure and phase diagram of high-density water: The role of interstitial molecules. Phys. Rev. E 67 (2). Sanchez-Valle C., Chio C.-H., and Gatta G. D. (2010) Single-crystal elastic properties of . (Cs,Na)AlSi 2O6 H2O pollucite: A zeolite with potential use for long-term storage of Cs radioisotopes. Journal of Applied Physics 108 (9), 093509. Sanchez-Valle C., Martinez I., Daniel I., Philippot P., Bohic S., and Simionovici A. (2003) Dissolution of strontianite at high P-T conditions: An in-situ synchrotron X-ray fluorescence study. Am. Miner. 88 (7), 978-985. Sandercock J. R. (1982) Trends in Brillouin-Scattering - Studies of Opaque Materials, Supported Films, and Central Modes. Topics in Applied Physics 51 , 173-206. Schmidt M. W. and Poli S. (1998) Experimentally based water budgets for dehydrating slabs and consequences for arc magma generation. Earth and Planetary Science Letters 163 (1-4), 361-379. Sharygin A. V. and Wood R. H. (1997) Volumes and heat capacities of aqueous solutions of hydrochloric acid at temperatures from 298.15 K to 623 K and pressures to 28 MPa. J. Chem. Thermodyn. 29 (2), 125-148. Sharygin A. V. and Wood R. H. (1998) Densities of aqueous solutions of sodium carbonate and sodium bicarbonate at temperatures from (298 to 623) K and pressures to 28 MPa. J. Chem. Thermodyn. 30 (12), 1555-1570. Shock E. L. and Helgeson H. C. (1988) Calculation of the Thermodynamic and Transport-Properties of Aqueous Species at High-Pressures and Temperatures - Correlation Algorithms for Ionic Species and Equation of State Predictions to 5 Kbar and 1000 °C. Geochim. Cosmochim. Acta 52 (8), 2009-2036. Shock E. L., Oelkers E. H., Johnson J. W., Sverjensky D. A., and Helgeson H. C. (1992) Calculation of the Thermodynamic Properties of Aqueous Species at High- Pressures and Temperatures - Effective Electrostatic Radii, Dissociation- Constants and Standard Partial Molal Properties to 1000 °C and 5 Kbar. J. Chem. Soc.-Faraday Trans. 88 (6), 803-826. Soper A. K. and Ricci M. A. (2000) Structures of high-density and low-density water. Phys. Rev. Lett. 84 (13), 2881-2884.

249 Strassle T., Saitta A. M., Le Godec Y., Hamel G., Klotz S., Loveday J. S., and Nelmes R. J. (2006) Structure of dense liquid water by neutron scattering to 6.5 GPa and 670 K. Phys. Rev. Lett. 96 (6). Trevani L. N., Balodis E. C., and Tremaine P. R. (2007) Apparent and standard partial molar volumes of NaCl, NaOH, and HCl in water and heavy water at T=523 K and 573 K at P=14 MPa. J. Phys. Chem. B 111 (8), 2015-2024. Wagner W. and Pruss A. (2002) The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 31 (2), 387-535. Walrafen G. E. (1962) Raman Spectral Studies of Effects of Electrolytes on Water. J. Chem. Phys. 36 (4), 1035-&. Wang A., Pasteris J. D., Meyer H. O. A., and DeleDuboi M. L. (1996) Magnesite-bearing inclusion assemblage in natural diamond. Earth and Planetary Science Letters 141 (1-4), 293-306. Whitfield C. H., Brody E. M., and Bassett W. A. (1976) Elastic-Moduli of Nacl by Brillouin-Scattering at High-Pressure in a Diamond Anvil Cell. Rev. Sci. Instrum. 47 (8), 942-947. Wiryana S., Slutsky L. J., and Brown J. M. (1998) The equation of state of water to 200 °C and 3.5 GPa: model potentials and the experimental pressure scale. Earth and Planetary Science Letters 163 (1-4), 123-130.

250 Chapter 8

Conclusions and outlook

In this last chapter of the thesis the main conclusions are summarized, and possible fields for future researches are proposed.

8.1 Conclusions

This work provides the first constrains on the equation of state and thermodynamic properties of model saline aqueous fluids at pressure at temperature conditions relevant for cold subduction zone settings at shallow to intermediate depths (up to 800 °C and 4.5 GPa). The PVTx properties of the fluids have been determined from acoustic velocity measurements using Brillouin scattering spectroscopy combined with an externally heated membrane-type diamond anvil cell (mDAC).

The investigated compositions includes H 2O NaCl, H 2O SrCl 2, H 2O Na 2SO 4,

H2O Na 2CO 3 and H 2O NaHCO 3 mixtures which are reasonable analogs for saline water-rich geological fluids. For each composition one or more concentrations were investigated (see Table 2.1 in Chapter 2), in a molality range between 0 m and 3 m also representative for dilute water-rich subduction zone fluids at shallow to intermediate depths (Manning, 2004; Scambelluri et al., 2004).

The experimental approach adopted in this work allows determining the PVTx properties of fluids at P-T conditions previously uncharted (Chapter 1). The membrane- type diamond anvil cell (mDAC) (Chervin et al., 1995) used here combined the use of an external and internal resistive heater that allows reaching temperatures up to 500 °C and pressures up to 5 GPa at least. Several solid pressure sensors were used to monitor pressure in the sample chamber and to ensure the accuracy required in the determination of the experimental equations of state (Chapter 2).

251 A method for the numerical processing of the acoustic velocity data to obtain the density of the aqueous fluids has been developed, and the code used was implemented in Matlab ® (Appendix A). Using this method, the density of the fluid can be retrieved with an accuracy of 0.3-0.5% (Chapter 3). The experimentally derived densities were fitted using polynomial equations of state (EoS) that describe the thermodynamic properties of the fluid in the P-T and composition ranges investigated in this study. From the proposed equations of state, the coefficient of thermal expansion and the isobaric heat capacity of the fluids can be determined with an accuracy of 1.5-2%, whereas the adiabatic and isothermal bulk modulus and compressibility have larger associated uncertainties of 4.5- 5% and 7-8%, respectively.

In the H 2O-Na 2SO 4 system (Chapter 4) the liquid-liquid transition from sparse water to dense water (Li et al., 2005; Strassle et al., 2006) were observed at 20 °C in the pressure interval between 0.2 and 0.4 GPa. This result is in accord with a previous spectroscopy study (Schmidt, 2009) in a similar sulfate-bearing aqueous system. The

PVTx properties of a 1 m Na 2SO 4 aqueous solution were provided up to 500 °C and 3 GPa and compared with the data of the pure solvent and with literature data on similar aqueous systems (Abramson et al., 2001). The structure making behavior of the sulfate ions dissolved in water (Walrafen, 1971; Vchirawongkwin et al., 2007) enhances the formation of a three dimensional H-bonding network in the solvent. This behavior is reflected by a decrease in the compressibility of the sulfate bearing solutions relative to water, and confirmed by the different pressure response of density and specific volume relative to the pure solvent.

For the first time, an equation of state for H 2O NaCl solutions (0 m to 3 m NaCl) valid to 800 °C and 4.5 GPa has been proposed (Chapter 5). This polynomial EoS was used to calculate all the PVTx properties of NaCl-bearing aqueous solutions up to pressure and temperature conditions relevant for cold subduction zones at shallow to intermediate depths (800 °C and 4.5 GPa). The derived values of water partial molar volume and water fugacity were successively used to constrain the composition dependence of dehydration reaction boundaries in a subducting oceanic crust. The results

252 indicated that the transition from greeschists to blueschists metamorphic facies in the mafic rocks of the oceanic crust takes place at shallower depths, when the water activity is decreased by the presence of NaCl dissolved in the fluid.

In the carbonate-bicarbonate aqueous system the 2 nd dissociation constant of - 2- + carbonic acid (HCO 3 = CO 3 + H ) were determined up to 300 °C and 3 GPa. The dissociation reactions of carbonic acid are extremely important in natural waters, because they represent the predominant acid-base buffering system (Hershey et al., 1983). The K P values determined in this work were fitted together with the low pressure values calculated from the HFK EoS for aqueous species (Shock and Helgeson, 1988) in order to provide a model for the 2 nd dissociation constant of carbonic acid valid from room pressure to 3 GPa for temperatures between 25 °C and 300 °C.

nd The negative values of the volume of reaction V r for the 2 dissociation of carbonic acid (Table 7.7 in Chapter 7) imply that at high pressure the carbonate ions species are favored over the bicarbonate ions. These results are in agreement with previous experimental studies (Frantz, 1998; Martinez et al., 2004), which demonstrated that carbonate ions are the dominant carbon species in aqueous fluids up to high pressure conditions. These observations, combined with the high solubility of carbonate minerals in aqueous fluids at high pressure and temperature conditions (Newton and Manning, 2002; Caciagli and Manning, 2003; Sanchez-Valle et al., 2003; Dolejs and Manning, 2010), suggests that carbon species may be present in subduction zone fluids and that the carbon speciation is dominated by the carbonate ions.

8.2 Outlook

Following the lead of the studies presented in this manuscript (Chapter 4-7), the experimental set-up and the numerical data treatment explained here can be adopted to determine the PVTx properties up to high pressure and temperature of all other binary electrolyte solutions. The use of diamond anvils with smaller culet diameter would allow the achievement of higher pressure conditions during the Brillouin measurements, in order to extend the

253 EoS presented here and/or the EoS for new systems to deeper Earth conditions. Additionally, the combination of Brillouin scattering spectroscopy with other types of diamond anvil cells, like hydrothermal diamond anvil cell (HDAC) (Bassett et al., 1993), would permit performing experiments in the lower pressure region, namely at pressure below 0.4-0.5 GPa, in order to complete the gap between available literature data and the measurements performed in this work. Additionally, the use of a HDAC would allow the achievement of higher experimental temperatures. As it was pointed out in the introduction, geological fluids at subduction zones may also contain non-saline dissolved species, like dissolved alumosilicates polymers and non polar gases. Among the different solutes, two binary systems that could be matter of interest to better characterize water-rich subduction zone fluids are the H 2O SiO 2 system and the H 2O CO 2 system.

While the H 2O SiO 2 system up to high pressure and temperature conditions is part of the research field covered by the PhD thesis of Alexandra Tsay at ETH Zurich under the supervision of Prof. Carmen Sanchez-Valle, a H2O CO 2 system with 95% mole fraction H 2O and 5 % mole fraction CO 2 has been investigated by Brillouin scattering spectroscopy measurements in a DAC up to 300 °C and freezing point pressure at ca. 6

GPa (Qin et al., 2010). In this study, the CO 2 was cryogenically loaded in deionized water, and the cell successively warmed up with resistance heating (Qin et al., 2010). The fluid composition was determined from visual estimations of the water volume in the sample chamber at 0.5 GPa, and known CO 2 solubility in water at these conditions (Qin et al., 2010).

An alternative way to generate a H 2O-CO 2 mixture with a better constrained composition is to decompose powder of oxalic acid dehydrate (OAD) (Holloway et al., 1968; Morgan et al., 1992). In fact, OAD decomposes following the reaction:

. . . . H2C2O4 2 H2O = 2 H2O + 2 CO 2 + H2

therefore, producing a 50:50 H 2O-CO 2 solution and with H 2 that is supposed to escape from the sample chamber (Morgan et al., 1992). After the decomposition, the homogenization conditions of the H 2O-CO 2 mixture should then be achieved with an

254 increase of the temperature in the sample chamber, in order to perform Brillouin measurements in the single phase region of the H2O-CO 2 solution. The thermodynamic properties ( i.e. and CP values) required to start the data treatment could be provided from different EoS (Churakov and Gottschalk, 2003; Duan and Zhang, 2006) valid up to high pressure and temperature conditions.

255 8.3 References

Abramson E. H., Brown J. M., Slutsky L. J., and Wiryana S. (2001) Measuring speed of sound and thermal diffusivity in the diamond-anvil cell. Int. J. Thermophys. 22(2), 405-414. Bassett W. A., Shen A. H., Bucknum M., and Chou I. M. (1993) A New Diamond-Anvil Cell for Hydrothermal Studies to 2.5 GPa and from - 190 °C to 1200 °C. Rev. Sci. Instrum. 64(8), 2340-2345. Caciagli N. C. and Manning C. E. (2003) The solubility of calcite in water at 6-16 kbar and 500-800 °C. Contrib. Mineral. Petrol. 146(3), 275-285. Chervin J. C., Canny B., Besson J. M., and Pruzan P. (1995) A Diamond-Anvil Cell for Ir Microspectroscopy. Rev. Sci. Instrum. 66(3), 2595-2598. Churakov S. V. and Gottschalk M. (2003) Perturbation theory based equation of state for polar molecular fluids: II. Fluid mixtures. Geochimica Et Cosmochimica Acta 67(13), 2415-2425.

Duan Z. H. and Zhang Z. G. (2006) Equation of state of the H 2O, CO 2, and H 2O-CO 2 systems up to 10 GPa and 2573.15 K: Molecular dynamics simulations with ab initio potential surface. Geochimica Et Cosmochimica Acta 70(9), 2311-2324. Frantz J. D. (1998) Raman spectra of potassium carbonate and bicarbonate aqueous fluids at elevated temperatures and pressures: comparison with theoretical simulations. Chem. Geol. 152(3-4), 211-225. Hershey J. P., Sotolongo S., and Millero F. J. (1983) Densities and Compressibilities of Aqueous Sodium-Carbonate and Bicarbonate from 0 °C to 45 °C. J. Solut. Chem. 12(4), 233-254.

Holloway J. R., Burnham C. W., and Millholl.Gl. (1968) Generation of H 2O-CO 2 Mixtures for Use in Hydrothermal Experimentation. Journal of Geophysical Research 73(20), 6598-&. Li F. F., Cui Q. L., He Z., Cui T., Zhang J., Zhou Q., Zou G. T., and Sasaki S. (2005) High pressure-temperature Brillouin study of liquid water: Evidence of the structural transition from low-density water to high-density water. J. Chem. Phys. 123(17).

256 Manning C. E. (2004) The chemistry of subduction-zone fluids. Earth and Planetary Science Letters 223(1-2), 1-16. Martinez I., Sanchez-Valle C., Daniel I., and Reynard B. (2004) High-pressure and high- temperature Raman spectroscopy of carbonate ions in aqueous solution. Chem. Geol. 207(1-2), 47-58. Morgan G. B., Chou I. M., and Pasteris J. D. (1992) Speciation in Experimental C-O-H Fluids Produced by the Thermal-Dissociation of Oxalic-Acid Dihydrate. Geochimica Et Cosmochimica Acta 56(1), 281-294. Newton R. C. and Manning C. E. (2002) Experimental determination of calcite solubility

in H 2O-NaCl solutions at deep crust/upper mantle pressures and temperatures: Implications for metasomatic processes in shear zones. Am. Miner. 87(10), 1401- 1409. Qin J. F., Li M., Li J., Chen R. Y., Duan Z. H., Zhou Q. A., Li F. F., and Cui Q. L. (2010) High temperatures and high pressures Brillouin scattering studies of liquid

H2O+CO 2 mixtures. J. Chem. Phys. 133(15). Sanchez-Valle C., Martinez I., Daniel I., Philippot P., Bohic S., and Simionovici A. (2003) Dissolution of strontianite at high P-T conditions: An in-situ synchrotron X-ray fluorescence study. Am. Miner. 88(7), 978-985. Scambelluri M., Muntener O., Ottolini L., Pettke T. T., and Vannucci R. (2004) The fate of B, Cl and Li in the subducted oceanic mantle and in the antigorite breakdown fluids. Earth and Planetary Science Letters 222(1), 217-234.

Schmidt C. (2009) Raman spectroscopic study of a H 2O + Na 2SO 4 solution at 21-600°C 2- and 0.1 MPa to 1.1 GPa: Relative differential -SO 4 Raman scattering cross sections and evidence of the liquid-liquid transition. Geochimica Et Cosmochimica Acta 73(2), 425-437. Shock E. L. and Helgeson H. C. (1988) Calculation of the Thermodynamic and Transport-Properties of Aqueous Species at High-Pressures and Temperatures - Correlation Algorithms for Ionic Species and Equation of State Predictions to 5 Kbar and 1000 °C. Geochimica Et Cosmochimica Acta 52(8), 2009-2036.

257 Strassle T., Saitta A. M., Le Godec Y., Hamel G., Klotz S., Loveday J. S., and Nelmes R. J. (2006) Structure of dense liquid water by neutron scattering to 6.5 GPa and 670 K. Phys. Rev. Lett. 96(6). Vchirawongkwin V., Rode B. M., and Persson I. (2007) Structure and dynamics of sulfate ion in aqueous solution - An ab initio QMCF MD simulation and large angle X-ray scattering study. J. Phys. Chem. B 111(16), 4150-4155. Walrafen G. E. (1971) Raman Spectral Studies of Effects of Solutes and Pressure on Water Structure. J. Chem. Phys. 55(2), 768-&.

258 Appendix A

Matlab® code for the inversion of the acoustic velocity VP data

i ii iii iv v

vi Appendix B

Thermodynamic properties of water up to 673 K and 7 GPa

This appendix presents the sound velocities and equation of state of water up to 400 °C and 7 GPa used as reference for discussion of the thermodynamic properties of aqueous solutions reported in this study. The acoustic velocity data was collected by C. Sanchez-Valle at the University of Illinois at Urbana-Champaign and processed at the ETH Zürich using the methodology described in this dissertation (see Chapters 2 and 3). The results are being edited for publication in Journal of Chemical Physics and referred to as Sanchez-Valle et al.(in prep.) in this manuscript.

vii Equation of state, refractive index and polarizability of compressed water to 7 GPa and 673 K

Carmen Sanchez-Valle 1, Davide Mantegazzi 1, Jay D. Bass 2 and Eric Reusser 1

Institute for Geochemistry and Petrology, ETH Zurich, Switzerland Department of Geology, University of Illinois at Urbana-Champaign, USA

To be submitted to J. Chem. Phys.

Abstract

The equation of state, refractive index and polarizability of water have been determined up to 673 K and 7 GPa from acoustic velocity measurements conducted in a resistively-heated diamond anvil cell using Brillouin scattering spectroscopy. Measured acoustic velocities compare favorably with previous experimental studies but they are lower than velocities calculated from the extrapolation of the IAPWS95 equation of state (EoS) above 3 GPa at 673 K and deviations increase up to 6% at 7 GPa. Densities calculated from the velocity data were used to propose an empirical EoS suitable in the 0.6 7 GPa and 293 673 K and accurate within 0.5%. The density model and thermodynamic properties derived from the experimental EoS have been compared to several EoS proposed in the literature. The IAPWS95 EoS provides good agreement, although underestimates density by up to 1.2% at 7 GPa and 673 K and the thermodynamic properties deviate largely (10-20%) outside the uncertainties above 4 GPa. The refractive index n of liquid water increases linearly with density and do not depend intrinsically on temperature. The polarizability decreases with pressure by less than 4% within the investigated P-T range, suggesting strong intermolecular interactions in H 2O that are consistent with the prevalence of the hydrogen bond network in the fluid. The results will allow the refinement of interaction potentials that consider polarization effects for a better understanding of solvent-solvent and ion- solvent interactions in aqueous fluids at high pressure and temperature conditions.

1 Corresponding author: [email protected]

viii 1. INTRODUCTION

Knowledge of the thermodynamic properties of water over a broad range of pressure and temperature conditions is important in a range of scientific disciplines, including Earth, planetary and physical sciences 1. In th high pressure water-rich fluids mediate heat and mass transfer processes that ultimately shape its evolution and internal dynamics 2. Significant efforts have been thus dedicated to determine accurate PVT equations of state (EoS) of water to predict its thermodynamic properties over a broad range of pressure (P) and temperature (T) conditions. However, the experimental data for the density of water is mainly restricted to pressures below 1 GPa 3-6 or to the extreme densities achieved above 200 GPa in shock wave experiments 7,8, with very few experimental constraints at intermediate pressures 9-11 . The equations of state (EoS) for water at high pressure are thus based on empirical extrapolations of low pressure (< 1 GPa) experimental data 12-17 and on molecular dynamic (MD) simulations using interaction potentials 18-20 whose accuracy is difficult to test due to the lack of high pressure experimental constraints. Among these EoS, the Saul and Wagner (1989) and more recently the Wagner and Pruss EoS (IAPWS95) 17, fitted to an extensive experimental dataset at low pressure, are considered the most accurate EoS at pressures below 1 GPa and temperatures up to 1273 K. However, the thermodynamic properties predicted by these EoS outside the calibration range largely deviate when compared to experimental studies 9. A more reliable extrapolation of the EoS of water beyond the experimental P-T range of calibration thus requires additional experimental constrains that will in turn allow for the refinement of interatomic potentials describing the evolution of atomic/molecular scale interactions in the fluid with pressure and temperature. In the recent years, significant effort have been dedicated to the development of interaction potentials for water 21-23 , with particular attention to those including polarization effects between water molecules that enhance intermolecular interactions. Therefore, polarization effects have to be considered for an accurate description of the structural, dynamic and thermodynamic properties of water at extreme high pressures and temperatures. The electronic polarization of water molecules is a measure of the relative

ix tendency of its electron cloud to be distorted in an electrical field that is manifested macroscopically by changes in the refractive index n. Direct measurements of the refractive index of water at high pressure and temperature will thus provide important information on the polarizability of water molecules and on the microscopic scale interactions that are used for the refinement of interaction potentials. Although the refractive index and polarizability of room temperature water and ice phases has been accurately determined using first principle calculations 24 and reflectivity methods in the diamond anvil cell up to 120 GPa 25,26 , the polarizability of water molecules in high temperature compressed liquid water remain undetermined. Here we report Brillouin scattering measurements of the acoustic velocities of liquid water to 7 GPa and 673 K conducted using externally heated diamond anvil cells. The velocity data has been used to determine an empirical EoS of water valid in the measured P-T range and compare the derived thermodynamic properties to several EoS in the literature. Furthermore, the acoustic velocity data provide the first experimental constraints on the refractive index n and the polarizability of water molecules in the fluid phase over a broad range of pressure-temperature conditions.

2. EXPERIMENTAL METHODS

2.1. Diamond anvil cell techniques Acoustic velocity measurements at room temperature were conducted in a three-pin Merrill Basset DAC modified for Brillouin scattering with large angular aperture. All high temperature measurements were conducted in a membrane-type diamond anvil cell 27 using two types of external resistance heating designs. A miniaturized platinum-wire resistive heater winded around the diamond anvils was used to achieve temperature conditions up to 473 K. The internal heater was powered with a digital DC power supply rated to a maximum of 18 V and 10 A and temperature was controlled to 0.5 K by controlling the output voltage. At higher temperatures, an additional ring-shaped Watlow ® resistive heater surrounding the body of the cell was added to minimize heat loss and thermal gradients across the cell, and to ensure thermal stability during the measurements 28,29 . The temperature was measured by two K-type chromel-alumel

x thermocouples placed in contact with the side face of one of the diamond anvils very close to the compression chamber and attached with high-temperature ceramic cement. Temperature was also monitored by a K-type thermocouple attached to the external heater and calibrated against the temperature in the sample chamber before the experiments. Sample chambers for measurements conducted between 293 and 473 K were formed from stainless-steel foils preindented to a final thickness of 60-80 m and drilled with 185-200 m holes in the center of the indentation. At higher temperature, and in order to avoid chemical reaction between the gasket and/or the pressure calibrants and the fluid, stainless-steel/platinum composite gaskets with two separated compression chambers were prepared following Datchi et al . (1999) 28 . The larger compression chamber (~150- -pure water whereas the second chamber (~ 60- hosts the pressure calibrants embedded in paraffin oil. Pressure at temperature below 473 K was determined from the calibrated frequency shift of the R1 fluorescence line of ruby 30 after temperature correction 31,32 . At higher temperatures, as the ruby fluorescence lines broaden and becomes more difficult to resolve 32,33, pressure 5 7 was calibrated using the D0 F0 luminescence line samarium-doped tetraborate 2+ 31 (Sm :SrB 4O7) . Spectra from the pressure calibrants were recorded before and after each Brillouin measurement using the same laser light and the signal was recorded through an optical fiber and sent to a dispersive spectrometer mounted in the same optical bench. Estimated uncertainties in pressure are about 0.02 GPa at 297 K, 0.05 GPa at 473 K and 0.15 GPa at 673 K.

2.2. Brillouin scattering measurements

Brillouin scattering measurements were performed by using an Ar ion laser 0 = 514.5 nm as a light source and a six-pass tandem Fabry Pérot interferometer equipped with a solid-state photon detector to analyze the frequency of the scattered light. All spectra were collected in symmetric/platelet scattering geometry in which the acoustic velocities are calculated from the measured frequency shifts using the following relationship 34:

xi 0 i Vi (1) 2sin( i )2/ where Vi is the compressional (V P) phonon velocity, i is the measured Brillouin shift,

0 is the laser wavelength ( 0=514.5 nm) and is the external scattering angle, i.e ., the angle between the incident and the scattered light outside the DAC ( ). At high pressures, and in order to avoid vignetting effects 35 , experiments were conducted either in 80 or 50 degrees scattering depending on the diamond-anvil-cell (DAC) employed. To reduce geometric or other possible systematic errors in the velocity measurements, the Brillouin system was calibrated using an MgO single-crystal standard. The accuracy in the determined acoustic velocities is within 0.5-0.8% at high pressure although the precision is better than 0.4% at all investigated conditions. Reference Brillouin spectra of water at ambient conditions were measured in a glass cuvette (1mm length path) using a 90° scattering geometry. An additional set of measurements at room conditions were performed in glass cuvettes in 90, 80 and 50 degrees scattering geometry at ETH Zurich using a solid-state laser 0=532.1 nm), a Fabry Perot interferometer and a photomultiplier tube (PMT) detector as described in detail in Ref.[ 36]. Acoustic measurements were performed as a function of pressure along isotherms at 293, 373, 423, 473, 573 and 673 K. Measurements were extended up to the ice crystallization pressure unless for the 673 K isotherm in which experiments were prematurely finished due to gasket failure (Fig. 1). High pressure acoustic velocities were collected at room temperature in two independent runs, on both increasing and decreasing pressure, in the Merrill-Basset DAC using 80° scattering geometry. Redundant measurements were performed at selected pressures to check for internal consistency among the datasets. The reference velocities measured in glass cuvettes were crosschecked with measurements conducted inside the diamond anvil cell carefully closed without pressurization at the beginning of each run. Additional measurements at room temperature were conducted using 50° scattering geometry before the high temperature runs to confirm the accurate control of the scattering geometry. Typical acquisition times were less than 1 minute per spectrum and at a least two spectra were collected at each P-T point to increase the precision on the velocity determination.

xii Fig1. Phase diagram of

H2O and P-T conditions investigated in this study. Brillouin measurements were collected along isotherms upon compression from the liquid phase up to the crystallization of ice. The dashed line corresponds to the melting curve of ice VII reported in Ref.[ 28].

3. RESULTS AND DISCUSSION

3.1. Sound velocities in H 2O at high P-T conditions

Figure 2 shows representative Brillouin spectra of H 2O collected at 293 K and 0.3 GPa and 673 K and 1.84 GPa in the externally heated diamond anvil cell. The strongest feature in the spectra corresponds to the compressional wave-velocities VP in water in symmetric scattering. The lower intensity feature labeled as nV P, where n is the refractive index of the fluid, corresponds to the backscattering signal (180 degrees scattering) arising from light partially reflected from the output diamond anvil and that acts as a secondary excitation light. Acoustic velocities measured in water as a function of pressure up to 7 GPa along several isotherms from 293 to 673 K are reported in Fig.3 and 4 and Table I. Fig.3 displays the acoustic velocities measured as a function of pressure at 293 K in several runs in both compression and decompression experiments, together with available literature data. Very good agreement is found between velocities measured inside and outside the diamond anvil cell and using different scattering geometries, demonstrating that the results are not affected by geometric or any other systematic errors 35. The

xiii Brillouin results are also in excellent agreement with literature data, including early ultrasonic 37,38 and optical interferometry 39 and the most recent measurements using light- scattering methods 9,10 , as well as acoustic velocities calculated from the EoS given in Ref.[ 15,17]. We observe however a subtle change in the pressure dependence of the acoustic velocities of water between 0.3-0.4 GPa that is most likely associated to the low- density (LDW) to high-density (HDW) transition in water 40 , as identified by previous Brillouin, Raman and theoretical studies 40-42. The evolution of the acoustic velocities with pressure and temperature is reported in Fig.4. Acoustic velocities increase monotonously with pressure along each isotherm but the temperature dependence remains moderate compared to the pressure dependence at the investigated conditions. The inset in Fig.4 compares the acoustic velocities in water determined at 673 K in this work with available experimental data 10,43 and velocities derived from the EoS of Ref.[ 15,17]. The present measurements reproduce very well previous ISS and Brillouin measurements performed in the diamond anvil cell using the double-hole gasketing technique 10,28,43, with maximum deviation of 0.5% below 3 GPa, that is within overall experimental errors. Although the acoustic velocities derived from the EoS of Ref.[ 15] and Ref.[ 17] compares well with experimental results within errors below 3 GPa, a systematic deviation toward higher velocities is observed above this pressure as found previously 10 . At 7 GPa and 673 K, the velocities predicted by the IAPWS95 EoS 17 are larger than the experimental values by 6%.

xiv

Fig. 2. Selected Brillouin spectra of H 2O collected in the diamond anvil cell at the indicated pressure and temperature conditions. The compressional wave velocity ( Vp) and the backscattering (n VP) signal are labeled. Typical acquisition times were less than 1 minute. Differences in V P intensities are due to different laser power outputs. The Rayleigh elastic scattering (R) has been suppressed for clarity.

Fig. 3. Acoustic velocities (V P) in H 2O as a function of pressure at 293 K. ( DAC (this work); ( , 50° scattering geometry (this work); ( , ): ultrasonic measurements 37,38; ( ): optical interferometry 39; ( ): Impulsive Stimulated Scattering (ISS) 10 ; ( ): calculated from the Equations of state of Ref.[ 15,17]. Errors in the present Brillouin data do not exceed the size of the symbols (< 0.5%). The solid line is a guide for the eyes and shows changes in the pressure dependence of the acoustic velocities above 0.3-0.4 GPa, consistent with the liquid-liquid phases transition in water (LDW to HDW).

xvi

Fig. 4. Acoustic velocities (V P) in water as a function of pressure from 373 to 673 K. Symbols are measured acoustic velocities in this work at 373 K ( K and ( ) 673 K. Dashed lines are acoustic velocities calculated from the equation of state given in Eq.(6). Inset: comparison between measured acoustic velocities in H 2O at 673 K [( ) this work, ( ) Ref.[ 10 43] and velocities calculated from the equations of state of Ref.[ 17] ( ) and Ref.[ 15

xvii Table I. Measured acoustic velocities in H 2O to 7 GPa and 673 K. Velocities are determined with a precision of 0.5% below 473 K and with a precision of 0.8-1% at higher temperature.

293 K 373 K 423 K 473 K 573 K 673 K

P VP P VP P VP P VP P VP P VP (GPa) (m/s) (GPa) (m/s) (GPa) (m/s) (GPa) (m/s) (GPa) (m/s) (GPa) (m/s) 0.00 a 1483 0.60 2378 0.41 2100 0.61 2388 0.89 2530 1.30 2763 0.00 b 1488 0.73 2475 0.73 2504 0.66 2461 1.10 2692 1.37 2802 0.00 c 1479 0.97 2725 1.07 2752 0.72 2505 1.20 2755 1.84 3070 0.00 d 1490 1.15 2816 1.24 2893 1.14 2874 1.33 2930 3.52 3850 0.09 1610 1.33 2970 1.72 3204 1.44 2979 1.58 3068 3.80 3960 0.16 1746 1.34 2960 1.86 3301 1.85 3316 1.93 3220 4.13 4070 0.17 1742 1.37 2994 2.03 3398 2.50 3615 2.25 3380 4.52 4166 0.23 1849 1.38 3002 2.16 3448 2.68 3671 2.65 3541 4.85 4291 0.27 1900 1.62 3150 2.75 3740 3.12 3843 3.24 3790 5.20 4352 0.39 2090 1.86 3278 3.44 3970 3.30 3827 5.40 4401 0.39 2090 2.36 3540 4.19 4222 3.71 3970 5.51 4422 0.39 2093 2.52 3602 4.18 4120 5.55 4432 0.41 2100 4.57 4236 5.62 4450 0.45 2157 4.82 4336 6.17 4560 0.45 2157 6.80 4636 0.47 2180 7.10 4680 0.60 2378 0.61 2353 0.61 2388 0.65 2390 0.66 2461 0.69 2429 1.00 2680 1.00 2685 0.90 2608 0.73 2454 0.98 2696 1.15 2824 1.17 2835

a glass cuvette (90° scattering); b DAC (50° scattering); c glass cuvette (90° geometry, ETH Zurich); d glass cuvette (50° geometry, ETH Zurich)

xviii 3.2. Equation of state of H 2O to 7 GPa and 673 K

The experimentally determined acoustic velocities, V P, in the fluid are related to the density of the fluid through the thermodynamic relations:

T 2 1 P P 2 C T VP P (2)

1 P T P (3)

C 2 P T v T 2 P 2 P P T T P T P (4)

3 where VP is the measured acoustic velocity (m/s), is the density (kg/m ), P the -1 -1 -1 coefficient of thermal expansion (K ), CP the isobaric specific heat capacity (Jkg K ) and v the specific volume (m 3/kg). The measured acoustic velocities were inverted using the iterative procedure outlined in Ref.[ 10 ,44] to obtain the density of water at high pressure-temperature conditions. The integration of these equations requires the sound velocities as a function of pressure and temperature, and the densities and specific heat capacities at one reference pressure. In the first step, the acoustic velocities as a function of pressure and temperature are integrated neglecting the isothermal-adiabatic correction 2 (T. /C P). The resulting density is used to calculate a first approximation for P and CP (Eq. 3 and 4) that are further used in the next iteration of Eq.(2). This process is reiterated until convergence. The inversion was first tested using the acoustic velocity data derived from the IAPWS95 EoS 16 and data reported in previous Brilloun scattering studies 9,10 .

The inversion reproduces the , and C P with a maximal relative deviation of 0.3-0.4%.

For the integration, the experimental acoustic velocities measured above 373 K and 1 GPa were interpolated to produce a mesh of acoustic velocity values in the pressure- temperature space using the following analytical expression:

xix 3 3 (5) VP, this work (P,T ) VP, IAPWS 95- (P,T /() 1 ( .8 1246 10 P .4 1926 10 )) where T is the temperature in Kelvin and P the pressure in GPa. The room temperature and low pressure (< 1 GPa) data were excluded to optimize the fit in the high pressure- high temperature region. Eq. (5) reproduces the experimental VP data with a maximal deviation of 0.5% at 673 K. The integration of Eq. (2) started at 1 GPa at each isotherm from 373 to 673 K using initial values of density and isobaric heat capacity CP at 1 GPa at the corresponding temperature from the IAPWS95 EoS 17. The inversion procedure allows retrieving the densities with uncertainties smaller than 0.5% as estimated from the propagation of experimental errors (Fig.5) 44 . The inverted densities were combined with data at pressure below 1 GPa and 373 K from the Ref.[ 17] to generate a best-fit empirical equation of state of the type:

T,P,x a(T) b(P) c(T,P) (6) with:

2 a(T) a1 a2 T a3 T b(P) b1 P b2 P c(T,P) c1 T P c2 T ln (P) where, T is the temperature in Kelvin, P is the pressure in Pascal. The best-fit coefficients ai ,bi and ci are tabulated in Table II. The proposed equation of state (Eq.6) reproduces the inverted densities with an average deviation of 0.3% (Fig.5) and the experimental acoustic velocities with a maximal misfit of 1.2% at 673 K (Fig 4). This indicates that our equation of state is fairly satisfactory and that can be confidently used to predict the density and properties of water in the 0.6 7 GPa and 293 673 K range.

xx Table II. Best-fit parameters for Eq.(6).

Parameters 1.148187 .10 3 a1 -2.540804 a2 . -5 a3 2.917138 10 8.507742 .10 -3 b1 -2.412079 .10 -8 b2 1.811854 .10 -11 c1 9.660446 .10 -2 c2

Figure 5 compares the density of water calculated along various isotherms from Eq.(6) with literature data, including densities from previous light-scattering measurements 9,10 , empirical EoS 12,15,17 and the most recent EoS derived from Molecular Dynamic (MD) simulations 20 . Data derived from other theoretical studies 18,19 have been excluded from the comparison because their accuracy to predict the density of water has been discussed previously 9-11 . Densities obtained from the present Brillouin study are in fairly good agreement with results from ISS measurements 9,10 and theoretical EoS 19 , with differences smaller than 0.4-0.5% in the investigated P-T range. However, H 2O is denser than predicted by the extrapolation of the IAPWS-95 above 3 GPa and the deviation increases with temperature, reaching up to 1.2% at 7 GPa and 673 K. It is also worth noting that the empirical EoS of Ref.[ 12] displays a non-systematic deviation on density, reaching differences of up to 1.3% at 5 GPa.

xxi

Fig5. a) Density of H 2O as a function of pressure along isotherms. Symbols denote density determined through inversion of the acoustic velocity data and the solid lines are densities calculated using the best-fit EoS given in Eq.(6) with the best fit parameters listed in Table II. Errors in the inverted densities are within the symbol size (0.5%). b) Comparison between densities determined from Eq.(6) with data from selected equations of state for H 2 ) Ref.[ 15]; (+) Ref.[ 12 17 Ref.[ 20 9,10 ]. Deviations of density datasets respect to the equation of state obtained in this study are reported as [( - EoS )/ ](%), where denotes the datasets listed above and EoS refers to Eq.(6).

xxii 3.4. Thermodynamic properties of H 2O and comparison with previous studies

Using the EoS (Eq.6), we calculate the thermodynamic properties of water in the

0.6 7 GPa range up to 673 K, including the isobaric thermal expansion coefficient ( P) , specific heat capacity (C P) as well as the isothermal and adiabatic compressibility ( T and

S) and bulk modulus (K T and K S). According to error propagation calculations, estimated maximal uncertainties on the coefficient of thermal expansion P and the isobaric heat capacity C P are about 2-3%, whereas larger uncertainties of 4% and 6% are estimated for the adiabatic and isothermal bulk modulus (K S and K T) and compressibility 45 ( S and T) , respectively. The results are tabulated in Supplementary Table AI and plotted at selected temperatures in Fig.6, together with data from commonly used EoS 15,17 and previous experimental studies 9. The figure illustrates that although densities predicted from the present work and the IAPSW95 EoS are in relatively good agreement (<1.2%), the derived thermodynamic properties significantly deviate at high pressure.

This is most noticeable in the isothermal evolution with pressure of the heat capacity C P at 673 K at pressures above 2 GPa. While the C P derived from this study continuously decreases with pressure until it approaches a constant value above 4 GPa, that derived from the IAPWS95 EoS 17 15 slightly increases above 2 GPa.

These two EoS thus IAPWS95 overestimates the C P by about 10% at 673 K and 7 GPa. A similar behavior is observed on the thermal expansion, although differences with the IAPWS95 EoS 17 are most noticeable at pressures above 4 GPa at 673 K, reaching values of up to 20% at 7 GPa. These differences are well outside the present uncertainties, indicating that the accuracy of the IAPWS95 EoS 17 to predict the thermodynamic properties of water rapidly decreases when extrapolated above 4 GPa. The new experimental constrains on the EoS of water derived from this study thus may allow further refinement of the theoretical approaches to provide a more reliable extrapolation of the properties of water over a broader range of P-T conditions.

xxiii

Fig6. Pressure dependence of the thermodynamic properties at H 2O along isotherms at 473 (solid grey lines) and 673 K (solid black lines) calculated from the best-fit EoS proposed in Eq.(6): a) Thermal expansion coefficient P; b) isobaric heat capacity C P; c) isothermal compressibility T; and d) isothermal bulk modulus K T. Dashed, short dashed and dot-dashed lines denote properties derived from the EoS reported in Ref.[ 17] (W&P02), Ref.[ 15] (S&W89) and Ref.[ 9] (W98), respectively.

3.5. Refractive index n and polarizability of H 2O The acoustic velocities measured in water in 50 and 180 (backscattering) degrees scattering geometry (Fig.2) were used to determine the refractive index n of water at 0 to 6 GPa and 293 to 673 K. In an isotropic medium, the measured Brillouin shifts in 50 and

180 geometries ( i) are related to the refractive index n through the relationship:

xxiv 180 50 n sin (7) 2 50

The calculated refractive index n for water are listed in Table III and displayed as a function of pressure at various temperatures from 293 to 673 K in Fig. 7. The refractive index smoothly increases with pressure along an isotherm but decreases with increasing 46-48 temperature, as observed for other molecular liquids such as CO 2, NH 3 and CH 4 . The refractive index of H 2O determined in this study at room conditions for the 514.5 nm wavelength, n = 1.332 0.002, is consistent with the value of 1.336 reported in Ref.[ 49] within experimental errors. The room temperature data is also in agreement with measurements using the interferometry method in the diamond anvil cell with a laser wavelength of 632.8 nm 25. This is consistent with the weak dispersion in the refractive 25,50 index of H 2O previously reported . In Fig.8, the refractive index n of water is reported as a function of density, together with previous room temperature data 25,49. The refractive index n increases linearly with density and a fit to the Gladstone-Dale relation 51 , n = a + b. , provides best-fit coefficients of a = 1.00 ± 0.01 and b = 3.3 10 -4 ± 8 10 -5 m3/kg. The coefficients compare well with those reported for room temperature liquid water data 25, indicating little temperature effect on n in the investigated range, as expected for a property related to the electronic structure of the material. This indicates that the linear relationship can be confidently used at higher pressure and temperatures to determine the refractive index of liquid water.

xxv Table III. Refractive index n and polarizability of water to 673 K and 5.6 GPa. The estimated error in n and are 1 and 1.5%, respectively.

293 K 373 K 473 K 573 K 673 K

(10 -30 (10 -30 (10 -30 (10 -30 (10 -30 P n P n P n P n P n m3) m3) m3) m3) m3)

0.00 a 1.332 1.455 0.60 1.370 1.428 0.61 1.359 1.458 0.89 1.358 1.446 1.30 1.364 1.438 0.03 1.327 1.428 0.73 1.379 1.426 0.66 1.364 1.461 1.10 1.369 1.437 1.37 1.363 1.420 0.08 1.332 1.419 0.97 1.396 1.432 0.72 1.366 1.452 1.20 1.375 1.437 1.84 1.399 1.462 0.09 1.339 1.441 1.05 1.394 1.411 1.14 1.386 1.427 1.33 1.385 1.447 3.80 1.451 1.409 0.16 1.358 1.478 1.15 1.395 1.398 1.44 1.398 1.416 1.58 1.393 1.431 4.13 1.458 1.403 0.27 1.359 1.435 1.33 1.400 1.386 1.85 1.416 1.416 2.25 1.422 1.433 4.52 1.471 1.410 0.39 1.367 1.423 1.34 1.401 1.388 2.65 1.422 1.391 4.85 1.476 1.402 0.45 1.371 1.419 1.37 1.402 1.387 5.51 1.492 1.404 0.47 1.378 1.437 1.38 1.412 1.416 5.55 1.478 1.368 0.61 1.408 1.496 5.62 1.489 1.391 0.65 1.385 1.412 0.69 1.393 1.429 0.98 1.412 1.433 1.00 1.420 1.454 1.17 1.434 1.468 0.00 b 1.338 1.467

xxvi

Fig7. Refractive index n of H2O measured at 0 = 514.5 nm as a function of pressure along various isotherms from 293 to 673 K. ( ) 293 K; ( ) 573 K;

( ) 673 K. Dashed lines are guides for the eyes.

The polarizability of water molecules was determined from the refractive index n using the Lorentz-Lorenz relation:

2 (8) n 1 4 N A n2 2 3 M

23 where NA 10 , and and M the density and molar mass (M = 18.01528 g/mol) of water, respectively. Calculated polarizabilities using our measured refractive index and inverted densities are reported in Table III and shown as a function of density in Figure 8. At room conditions, we find a value of 1.455(20)x10 -30 m3 that compares favorably with the average polarizability reported for room P-T water byfirst-principle calculations 24. We note a very subtle decrease of the polarizability of -30 3 individual H 2O molecules with density, reaching a value of 1.391x10 m at a density of 1.489 g/cm 3 (5.92 GPa 673 K). The decrease in the polarizability upon compression

xxvii may be explained by the reduction in the distortion of the electron cloud of the individual water molecules, leading in turn to a decrease of the intermolecular interactions with neighboring molecules. The moderate change by 4% in the polarizability of water in the investigated density range contrasts with the evolution observed in other molecular 52 systems such as H 2 , where the polarizability decreases by 12% when density changes by only 0.2 g/cm 3. This observation indicates that the interactions between water molecules remain relatively strong, in agreement with the prevalence of the hydrogen bond network in hot compressed water in the investigated P-T range 53 . The dataset reported in Fig.8 and Table III is, to the best of our knowledge, the first determination of the refractive index and polarizability of liquid water at high pressure- temperature conditions. It is expected that the present results will assist in the validation of computational studies of the properties of hot compressed water and on the refinement of interaction potentials which include polarization effects 21-23. This will in turn contribute to better the understanding of ion solvation processes and solvent-solute interactions in aqueous fluids at high pressure and temperature conditions.

xxviii

Fig. 8. a) Refractive index n and b) polarizability of H 2O as a function of density at 0 < P < 5 GPa and 293 < T < 673 K. Red and blue dots in a) are experimental data from Ref.[ 49] and Ref.[ 25], respectively. The polarizability was calculated from n and (P,T) using the Lorentz-Lorenz relation [Eq.(8)]. The red diamond shows the polarizability determined at room P-T in Ref.[ 24] from first principle calculations. The solid line in a) is a fit to data using the Gladstone-Dale relation 51 , n = a + b. , with best- fit coefficients a = 1.00 ± 0.01 and b = 3.3 10 -4 ± 8 10 -5 m3/kg.

xxix 5. CONCLUSIONS

Acoustic velocity measurements in water have been performed up to 7 GPa and 673 K in externally heated diamond anvil cells using Brillouin scattering spectroscopy. The measurements compare favorably with previous experimental studies but deviations of up to 2% from velocities calculated from commonly used EoS 15,17 are observed at pressure above 3 GPa at 673 K. The acoustic velocity data was used to determine the density of water and an empirical EoS suitable in the 0.6 7 GPa and 293 673 K and accurate within 0.5% has been proposed. The density model and thermodynamic properties derived from the experimental EoS have been compared to several EoS proposed in the literature. The IAPWS95 EoS provides the best agreement, although underestimates density by up to 1.2% at 7 GPa and 673 K and the thermodynamic properties deviate at pressure above 4 GPa. The present Brillouin measurements also provide first constraints on the refractive index n and polarizability of liquid water at high pressure and temperature conditions. The refractive index increases linearly with pressure and do not depend intrinsically on temperature. The polarizability of water at room conditions is in good agreement with values reported from first principles and decreases with pressure by less than 4% within the investigated P-T range. This observation indicates that interactions between water molecules remain strong, in agreement with the prevalence of the hydrogen bond network in hot compressed water in the investigated P-T range. The results reported here will assist in the refinement of interaction potentials which include polarization effects, contributing to advance our understanding of solvent-solvent and ion-solvent interaction in aqueous fluids at high pressure and temperature conditions.

Acknowledgement- We would like to thank A.G. Kalinichev for providing the code for solving the Saul and Wagner (1989) EoS. This work was partially supported by the ETHIIRA program of ETH Zurich (grant ETH-30 08-2 to CSV).

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xxxi 31 D.R. Ragan, R. Gustacsen and D. Schiferl, J. Appl. Phys. 72(12), 5539 (1992). 32 F. Datchi, A. Dewaele, P. Loubeyre, R. Letoullec, Y. Le Godec and B. Canny, High Pres. Res. 27, 447 (2007). 33 C. Sanchez-Valle, I. Daniel, B. Reynard, R. Abraham and C. Goutaudier, J. Appl. Phys. 92, 4349 (2002). 34 C.H. Whitfield, E.M. Brody and W.A. Bassett, Rev. Sci. Instrum. 47(8), 942 (1976). 35 S.V. Sinogeikin and J.D. Bass, Phys. Earth Planet. Interiors 120, 43 (2000). 36 C. Sanchez-Valle, C-H. Chio and G.D. Gatta, J. Appl. Phys. 108, 093509 (2010). 37 A.H. Smith and A.W. Lawson, J. Chem. Phys. 22, 351 (1953). 38 W.D. Wilson, J. Acoust. Soc. Am. 31(8), 1067 (1959). 39 P.L.M. Heydemann and J. C. Houck, J. Appl. Phys., 40, 1609 (1969). 40 A. K. Soper and M. A. Ricci, Phys. Rev. Lett. 84, 2881 (2000) . 41 T. Kawamoto, S. Ochiai and H. Kagi, J. Chem. Phys. 120, 5867 (2004). 42 F. Li, W. Cui, Z. He, T. Cui, J. Zhang, Q. Zhou, Q., and G. Zou, J. Chem. Phys. 123, 174511 (2005). 43 F. Decremps, F. Datchi and A. Polian, Ultrasonics 44, 1495 (2006). 44 D. Mantegazzi, C. Sanchez-Valle, E. Reusser and T. Driesner, J. Chem. Phys. in press (2012) 45 See Supplementary Material Document No.______for a compilation of the PVT properties of water to 673 K and 7 GPa derived from acoustic velocity measurements in the diamond anvil cell using Brillouin scattering spectroscopy. For information on Supplementary Material, see http://www.aip.org/pubservs/epaps.html

46 H.Shimizu, T. Kitagawa, and S. Sasaki, Phys. Rev. B 47(17), 11 567 (1993). 47F. Li et al., J. Chem. Phys., 131, 134502 (2009). 48 M. Li et al., J. Chem. Phys., 133, 044503 (2010). 49A. H. Harvey, J.S. Gallagher and J.M.H Levelt-Sengers, J. Phys. Chem. Ref. Data 27, 761 (1998). 50 L. Weiss, A. Tazibt, A. Tidu and M. Aillerie, J. Chem. Phys., 136, 124201 (2012). 51 R. Setchell, J. Appl. Phys. 91, 2833 (2002). 52K. Matsuishi, E. Gregoryanz, H-k. Mao and R.J. Hemley, J. Chem. Phys. 118, 10683 (2003). 53 T. Strassle et al., Phys. Rev. Lett. 96, 067801 (2006).

xxxii APPENDIX Table A1: PVT properties of water to 673 K and 7 GPa derived from acoustic velocity measurements in the diamond anvil cell using Brillouin scattering spectroscopy.

T 293 K P VP VSP CP S KS T KT (GPa) (m/s) (kg/m 3) (m 3/kg) (K -1) (J .kg -1.K-1) (GPa -1) (GPa) (GPa -1) (GPa) 10 -3 10 -4 0.6 2337 1175.5 0.85 4.77 3751.0 0.156 6.4 0.171 5.9 0.8 2571 1212.1 0.83 4.36 3730.9 0.125 8.0 0.137 7.3 1 2767 1243.0 0.80 4.05 3714.8 0.105 9.5 0.115 8.7

T 373 K P VP VSP CP S KS T KT (GPa) (m/s) (kg/m 3) (m 3/kg) (K -1) (J .kg -1.K-1) (GPa -1) (GPa) (GPa -1) (GPa) 10 -3 10 -4 0.6 2288 1130.8 0.88 4.91 3737.3 0.169 5.9 0.190 5.3 0.8 2523 1170.0 0.85 4.48 3708.8 0.134 7.4 0.152 6.6 1 2719 1202.9 0.83 4.15 3686.4 0.112 8.9 0.127 7.9 1.2 2889 1231.7 0.81 3.88 3668.1 0.097 10.3 0.110 9.1 1.4 3041 1257.4 0.80 3.65 3652.7 0.086 11.6 0.097 10.3 1.6 3178 1280.7 0.78 3.46 3639.6 0.077 12.9 0.087 11.5 1.8 3304 1302.1 0.77 3.28 3628.4 0.070 14.2 0.079 12.7 2 3420 1322.0 0.76 3.13 3618.6 0.065 15.5 0.072 13.8 2.2 3529 1340.5 0.75 2.99 3610.0 0.060 16.7 0.067 15.0 2.4 3631 1357.9 0.74 2.86 3602.5 0.056 17.9 0.062 16.1

T 423 K P VP VSP CP S KS T KT (GPa) (m/s) (kg/m 3) (m 3/kg) (K -1) (J .kg -1.K-1) (GPa -1) (GPa) (GPa -1) (GPa) 10 -3 10 -4 0.6 2262 1103.1 0.91 5.01 3711.6 0.177 5.6 0.203 4.9 0.8 2497 1143.8 0.87 4.56 3677.2 0.140 7.1 0.161 6.2 1 2694 1178.1 0.85 4.21 3650.2 0.117 8.5 0.134 7.4 1.2 2863 1207.9 0.83 3.93 3628.3 0.101 9.9 0.116 8.6 1.4 3014 1234.5 0.81 3.70 3610.0 0.089 11.2 0.102 9.8 1.6 3149 1258.7 0.79 3.49 3594.6 0.080 12.5 0.092 10.9 1.8 3274 1280.8 0.78 3.32 3581.3 0.073 13.7 0.083 12.0 2 3388 1301.4 0.77 3.16 3569.7 0.067 14.9 0.076 13.2 2.2 3495 1320.5 0.76 3.01 3559.7 0.062 16.1 0.070 14.3 2.4 3595 1338.5 0.75 2.88 3550.9 0.058 17.3 0.065 15.3 2.6 3690 1355.5 0.74 2.76 3543.1 0.054 18.5 0.061 16.4 2.8 3780 1371.7 0.73 2.65 3536.2 0.051 19.6 0.057 17.5 3 3865 1387.0 0.72 2.55 3530.2 0.048 20.7 0.054 18.6

xxxiii T 473 K P VP VSP CP S KS T KT (GPa) (m/s) (kg/m 3) (m 3/kg) (K -1) (J .kg -1.K-1) (GPa -1) (GPa) (GPa -1) (GPa) 10 -3 10 -4 0.6 2238 1075.6 0.93 5.11 3705.6 0.186 5.4 0.217 4.6 0.8 2474 1117.8 0.89 4.64 3664.5 0.146 6.8 0.171 5.8 1 2670 1153.3 0.87 4.28 3632.5 0.122 8.2 0.142 7.0 1.2 2839 1184.2 0.84 3.98 3606.6 0.105 9.5 0.122 8.2 1.4 2988 1211.8 0.83 3.74 3585.2 0.092 10.8 0.108 9.3 1.6 3123 1236.7 0.81 3.53 3567.1 0.083 12.1 0.096 10.4 1.8 3245 1259.7 0.79 3.35 3551.6 0.075 13.3 0.087 11.5 2 3358 1280.9 0.78 3.19 3538.2 0.069 14.4 0.080 12.5 2.2 3463 1300.7 0.77 3.04 3526.6 0.064 15.6 0.074 13.6 2.4 3561 1319.3 0.76 2.90 3516.5 0.060 16.7 0.068 14.6 2.6 3654 1336.9 0.75 2.78 3507.5 0.056 17.8 0.064 15.7 2.8 3741 1353.5 0.74 2.67 3499.7 0.053 18.9 0.060 16.7 3 3825 1369.4 0.73 2.56 3492.7 0.050 20.0 0.056 17.7 3.2 3904 1384.5 0.72 2.46 3486.6 0.047 21.1 0.053 18.7 3.4 3980 1399.0 0.71 2.37 3481.2 0.045 22.2 0.051 19.8 3.6 4052 1412.9 0.71 2.28 3476.4 0.043 23.2 0.048 20.8 3.8 4123 1426.2 0.70 2.20 3472.2 0.041 24.2 0.046 21.8 4 4190 1439.1 0.69 2.12 3468.5 0.040 25.3 0.044 22.8

T 573 K P VP VSP CP S KS T KT (GPa) (m/s) (kg/m 3) (m 3/kg) (K-1) (J .kg -1.K-1) (GPa -1) (GPa) (GPa -1) (GPa) 10 -3 10 -4 0.6 2199 1020.9 0.98 5.33 3702.7 0.203 4.9 0.246 4.1 0.8 2435 1066.3 0.94 4.81 3645.4 0.158 6.3 0.192 5.2 1 2630 1104.3 0.91 4.41 3601.6 0.131 7.6 0.159 6.3 1.2 2798 1137.3 0.88 4.10 3566.7 0.112 8.9 0.136 7.3 1.4 2945 1166.7 0.86 3.84 3538.0 0.099 10.1 0.119 8.4 1.6 3077 1193.4 0.84 3.61 3514.0 0.089 11.3 0.106 9.4 1.8 3196 1217.8 0.82 3.42 3493.7 0.080 12.4 0.096 10.4 2 3305 1240.4 0.81 3.24 3476.2 0.074 13.6 0.088 11.4 2.2 3406 1261.5 0.79 3.09 3461.1 0.068 14.6 0.081 12.4 2.4 3501 1281.3 0.78 2.95 3448.0 0.064 15.7 0.075 13.3 2.6 3589 1300.0 0.77 2.82 3436.6 0.060 16.7 0.070 14.3 2.8 3672 1317.7 0.76 2.70 3426.6 0.056 17.8 0.066 15.3 3 3751 1334.6 0.75 2.58 3417.8 0.053 18.8 0.062 16.2 3.2 3826 1350.7 0.74 2.48 3410.0 0.051 19.8 0.058 17.2 3.4 3897 1366.1 0.73 2.38 3403.3 0.048 20.7 0.055 18.1 3.6 3965 1380.9 0.72 2.29 3397.3 0.046 21.7 0.052 19.1 3.8 4031 1395.1 0.72 2.20 3392.1 0.044 22.7 0.050 20.0 4 4093 1408.9 0.71 2.12 3387.6 0.042 23.6 0.048 20.9 4.2 4154 1422.1 0.70 2.04 3383.6 0.041 24.5 0.046 21.9 4.4 4213 1434.9 0.70 1.97 3380.2 0.039 25.5 0.044 22.8 4.6 4270 1447.3 0.69 1.90 3377.2 0.038 26.4 0.042 23.7 4.8 4325 1459.3 0.69 1.83 3374.7 0.037 27.3 0.041 24.7 5 4378 1471.0 0.68 1.76 3372.6 0.035 28.2 0.039 25.6 5.2 4430 1482.3 0.67 1.70 3370.8 0.034 29.1 0.038 26.5

xxxiv 5.4 4481 1493.4 0.67 1.64 3369.4 0.033 30.0 0.036 27.5 5.6 4531 1504.1 0.66 1.58 3368.3 0.032 30.9 0.035 28.4 5.8 4579 1514.6 0.66 1.52 3367.5 0.031 31.8 0.034 29.3 6 4627 1524.8 0.66 1.47 3366.9 0.031 32.6 0.033 30.3 6.2 4673 1534.7 0.65 1.41 3366.5 0.030 33.5 0.032 31.2 6.4 4719 1544.5 0.65 1.36 3366.4 0.029 34.4 0.031 32.1 6.6 4764 1554.0 0.64 1.31 3366.4 0.028 35.3 0.030 33.1 6.8 4808 1563.3 0.64 1.26 3366.7 0.028 36.1 0.029 34.0 7 4851 1572.4 0.64 1.21 3367.1 0.027 37.0 0.029 35.0

T 673 K P VP VSP CP S KS T KT (GPa) (m/s) (kg/m 3) (m 3/kg) (K -1) (J .kg -1.K-1) (GPa -1) (GPa) (GPa -1) (GPa) 10 -3 10 -4 0.6 2172 966.8 1.03 5.57 3689.7 0.219 4.6 0.278 3.6 0.8 2409 1015.3 0.98 4.99 3611.9 0.170 5.9 0.215 4.6 1 2603 1055.9 0.95 4.56 3553.5 0.140 7.2 0.177 5.6 1.2 2769 1091.0 0.92 4.22 3507.5 0.120 8.4 0.151 6.6 1.4 2914 1122.3 0.89 3.94 3470.2 0.105 9.5 0.132 7.6 1.6 3042 1150.5 0.87 3.70 3439.3 0.094 10.6 0.117 8.5 1.8 3158 1176.5 0.85 3.49 3413.2 0.085 11.7 0.106 9.5 2 3264 1200.4 0.83 3.30 3391.1 0.078 12.8 0.096 10.4 2.2 3361 1222.8 0.82 3.14 3372.1 0.072 13.8 0.088 11.3 2.4 3451 1243.8 0.80 2.99 3355.7 0.067 14.8 0.082 12.2 2.6 3535 1263.7 0.79 2.85 3341.4 0.063 15.8 0.076 13.1 2.8 3614 1282.5 0.78 2.72 3329.1 0.060 16.8 0.071 14.0 3 3688 1300.4 0.77 2.61 3318.3 0.057 17.7 0.067 14.9 3.2 3758 1317.5 0.76 2.50 3308.8 0.054 18.6 0.063 15.8 3.4 3825 1333.9 0.75 2.40 3300.6 0.051 19.5 0.060 16.7 3.6 3889 1349.6 0.74 2.30 3293.4 0.049 20.4 0.057 17.5 3.8 3949 1364.7 0.73 2.21 3287.1 0.047 21.3 0.054 18.4 4 4008 1379.3 0.73 2.13 3281.7 0.045 22.2 0.052 19.3 4.2 4064 1393.3 0.72 2.04 3277.0 0.043 23.0 0.050 20.2 4.4 4118 1406.9 0.71 1.97 3273.0 0.042 23.9 0.048 21.0 4.6 4170 1420.1 0.70 1.89 3269.6 0.040 24.7 0.046 21.9 4.8 4221 1432.9 0.70 1.82 3266.7 0.039 25.5 0.044 22.8 5 4270 1445.3 0.69 1.75 3264.3 0.038 26.4 0.042 23.6 5.2 4318 1457.4 0.69 1.69 3262.3 0.037 27.2 0.041 24.5 5.4 4364 1469.2 0.68 1.63 3260.7 0.036 28.0 0.039 25.3 5.6 4409 1480.6 0.68 1.56 3259.5 0.035 28.8 0.038 26.2 5.8 4453 1491.8 0.67 1.51 3258.6 0.034 29.6 0.037 27.1 6 4497 1502.7 0.67 1.45 3258.1 0.033 30.4 0.036 27.9 6.2 4539 1513.3 0.66 1.39 3257.8 0.032 31.2 0.035 28.8 6.4 4581 1523.7 0.66 1.34 3257.8 0.031 32.0 0.034 29.7 6.6 4621 1533.9 0.65 1.29 3258.0 0.031 32.8 0.033 30.5 6.8 4661 1543.8 0.65 1.24 3258.4 0.030 33.5 0.032 31.4 7 4701 1553.6 0.64 1.19 3259.0 0.029 34.3 0.031 32.2

xxxv

xxxvi Acknowledgments

At the beginning of a PhD you think that a long way stays in front of you, that you have now your own project, that you will do your own experiments and that you will write your own papers. At the beginning of a PhD you imagine your PhD as something that is only for you. After your PhD, you look back and you realize first that the time has passed extremely fast and second that without the help of a lot of people you would never have been able to finish your PhD. For this reason I would like to thank all the people who in different ways helped me during the 4.5 years.

nt my last 4.5 years. Second, I thank my two office mates, Marion and Angelika for sharing this experience with me, and also all other members of the Group: Sasha, Rita, Wim, Zoltan, Denis, Ingrid, Chloè and Jingyung. Then I would like to thank Thomas, who knows a lot about fluids, and Eric for his precious help with Matlab, and Dave and Mark for their support in the fantastic world of the Thermodynamic of mineral reactions. For all other special moments, not necessarily related to the PhD, but to my preferred part of the last 4.5 years, including Apèros, Partys, Excursions, Running Trainings, Lunch, Coffee Breaks or just normal days, I would like to say thank you to: Bona, Omar, Erica, Vicky, Monica, Ettore, Rohit, Galli, Nene, Pippo and Claudio, Lukas, Mattia, Remco, Ute, Esther and Tamara, Ethan, Max and Neil, Nastia, Marianne, Stefania, Enrico, Stefanie, Sharzad and Claudia Büchel. Of course, without the support of my Family, my parents Eliana and Antonio, and my his was not possible. Grazie mille!

Thank you everybody again and Forza Ambrì Forever!

Ciao Davide

xxxvii

xxxviii Davide Mantegazzi Date of Birth: January 8, 1983 Via industria 18a Citizenship: Swiss 6826 Riva San Vitale (TI) Hometown: Riva San Vitale (TI)

Education

2007-2012 PhD student , ETH Zurich, Switzerland. Thesis: The PVTx properties of saline aqueous fluids at high P-T conditions from acoustic velocity measurements using Brillouin scattering spectroscopy. Supervised by Prof. Carmen Sanchez-Valle.

Presentation at national and international conferences: Swiss Geoscience Meeting 2008, 2009 and 2011, EMPG XII 2008, Goldschmidt 2009 and 2010, ECROFI 2009, AGU 2010.

2002-2007 Diploma in Naturwissenschaften an der ETH Zurich , Departement Erdwissenschaften, Institute of geochemistry and petrology. Thesis: Petrographie im Gebiet vom Passo San Giacomo (Val Bedretto, TI). Supervised by Prof. Max W. Schmidt and Dr. Eric Reusser.

1998-2002 Gymnasialmatura , Liceo Cantonale di Mendrisio (TI).

1994-1998 Secondary school in Riva San Vitale (TI).

1989-1994 Primary school in Riva San Vitale (TI).

Professional Experience

2007-2011 ETH Zurich , Departement Erdwissenschaften Organization of the Verzasca Exkursion Assistant for the lecture Assistant for the lecture

2002-2007 ETH Zurich , Departement Erdwissenschaften Assistant for the lecture Assistant for the lecture Assistant for the lecture

Assistant during field trips

Experimental Skills

Brillouin und Raman Spectroscopy

Diamond Anvil Cell techniques (DAC) Elektron Microprobe Analysis (EMPA)

X-Ray Fluorescence (XRF), X-Ray Diffraction (XRD)

Mikroskopie

Languages

Italian: mother tongue

German: fluent

English: fluent

French: basic knwoledge

Zürich, March 2012 Davide Mantegazzi

xxxix