Sound Velocity, Density, and Equation of State of Silicate

SOUND VELOCITY, DENSITY, AND EQUATION OF STATE OF SILICATE

AND CARBONATE MELTS IN THE EARTH’S MANTLE

MAN XU

Submitted in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

Department of Earth, Environmental, and Planetary Sciences

CASE WESTERN RESERVE UNIVERSITY

May, 2020

CASE WESTERN RESERVE UNIVERSITY

SCHOOL OF GRADUATE STUDIES

We hereby approve the thesis/dissertation of

Man Xu

Candidate for the degree of Doctor of Philosophy*.

Committee Chair

James A. Van Orman

Committee member

Steven A. Hauck, II

Committee member

Ralph P. Harvey

Committee member

Daniel Lacks

Date of Defense

March 4, 2020

*We also certify that written approval has been obtained for any

proprietary material contained therein.

 2020

Man Xu

LIST OF TABLES ...... V

LIST OF FIGURES ...... VI

ACKNOWLEDGEMENTS ...... XIV

ABSTRACT ...... XVI

CHAPTER I INTRODUCTION ...... 1

REFERENCES...... 9

CHAPTER II ULTRASONIC VELOCITY OF DIOPSIDE LIQUID AT HIGH PRESSURE AND

TEMPERATURE: CONSTRAINTS ON VELOCITY REDUCTION IN THE UPPER MANTLE

DUE TO PARTIAL MELTS ...... 17

ABSTRACT ...... 17

INTRODUCTION ...... 18

EXPERIMENTAL METHODS ...... 21

Starting materials ...... 21

High-pressure ultrasonic measurements ...... 22

RESULTS ...... 28

Ultrasonic signals and detection of partial melting ...... 28

Sound velocity and EOS of diopside liquid ...... 31

DISCUSSION ...... 37

Adiabatic temperature profile and stability of diopside liquid in the upper mantle...... 37

Sound velocity and compressibility of diopside liquid versus diopside glass ...... 39

Velocity reduction in the mantle due to the presence of melts ...... 42

CONCLUSIONS ...... 44

ACKNOWLEDGEMENTS ...... 45

SUPPLEMENTARY MATERIALS ...... 46

REFERENCES...... 49

i CHAPTER III DISTINCT ACOUSTIC BEHAVIORS BETWEEN COLD AND HEATED

DIOPSIDE GLASS AT HIGH PRESSURES REVEALED BY IN-SITU ULTRASONIC

MEASUREMENTS ...... 60

ABSTRACT ...... 60

INTRODUCTION ...... 61

MATERIALS AND METHODS ...... 64

RESULTS ...... 68

DISCUSSION ...... 75

Effect of temperature on glass velocity and compression mechanism...... 75

Comparison with diopside liquid ...... 81

IMPLICATIONS ...... 85

ACKNOWLEDGEMENTS ...... 86

REFERENCES...... 86

CHAPTER IV ACOUSTIC VELOCITY AND COMPRESSIBILITY IN THE MOLTEN

HEDENBERGITE (CAFESI2O6)-DIOPSIDE (CAMGSI2O6) JOIN AT HIGH PRESSURES:

IMPLICATIONS FOR THE STABILITY AND SEISMIC SIGNATURE OF IRON-RICH MELT IN

THE MANTLE ...... 96

ABSTRACT ...... 96

INTRODUCTION ...... 97

MATERIALS AND METHODS ...... 99

Starting materials ...... 99

High-pressure ultrasonic measurements ...... 100

RESULTS ...... 103

Hd melt sound velocity ...... 103

Hd50Di50 melt sound velocity ...... 104

DISCUSSIONS ...... 107

Velocity and density comparison in the molten Hd-Di join and test of linear mixing ...... 107

ii Implications for the upper mantle low-velocity zone (LVZ) and low-velocity layer (LVL) ...... 109

CONCLUSIONS ...... 113

ACKNOWLEDGEMENTS ...... 114

APPENDIX A. MONTE-CARLO FITTING OF THE SOUND VELOCITY DATA ...... 114

APPENDIX B. CALCULATION OF S-WAVE VELOCITY CHANGE (푑푙푛푉푠) AND DENSITY CHANGE (푑푙푛𝜌) FOR

PARTIALLY MOLTEN ASSEMBLAGES ...... 116

REFERENCES...... 117

CHAPTER V DENSITY OF NAALSI2O6 MELT AT HIGH PRESSURE AND TEMPERATURE

MEASURED BY IN-SITU X-RAY MICROTOMOGRAPHY...... 125

ABSTRACT ...... 125

INTRODUCTION ...... 125

MATERIALS AND METHODS ...... 129

Starting materials ...... 129

High-pressure experiments ...... 130

X-ray microtomography measurements ...... 132

Tomographic reconstruction and 3D volume rendering ...... 133

RESULTS AND DISCUSSIONS ...... 138

Density of jadeite melt at high pressures ...... 138

Comparison of the compressibility with other silicate melts and geological implications ...... 143

CONCLUSIONS ...... 147

ACKNOWLEDGMENTS...... 148

SUPPLEMENTARY MATERIALS ...... 149

REFERENCES...... 151

CHAPTER VI HIGH-PRESSURE ELASTIC PROPERTIES OF DOLOMITE MELT

SUPPORTING CARBONATE-INDUCED MELTING IN DEEP UPPER MANTLE ...... 161

ABSTRACT ...... 161

INTRODUCTION ...... 162

iii RESULTS ...... 164

Sound velocity of dolomite melt ...... 164

Density and EOS for dolomite melt ...... 166

FPMD simulation results and comparison with experimental results and previous studies ...... 168

DISCUSSION ...... 170

MATERIALS AND METHODS ...... 175

Starting materials ...... 175

High-pressure ultrasonic measurements ...... 176

Sink-float density measurements...... 177

SEM analysis of quenched samples ...... 179

First-principles molecular dynamics simulations ...... 180

ACKNOWLEDGMENTS...... 181

SUPPLEMENTARY INFORMATION...... 181

Text S1. Criteria for detecting melting using ultrasonic signals...... 182

Text S2. EOS fitting procedure ...... 183

Text S3. Calculation of velocity reductions for partially molten assemblages ...... 186

REFERENCES...... 198

BIBLIOGRAPHY ...... 210

iv LIST OF TABLES

Table I.1. Comparison between different methods to determine the EOS of mantle melts at high pressures . 3

Table I.2 Compositions studied and techniques used in this dissertation ...... 8

Table II.1 Experimental conditions and results for sound velocity measurements of diopside liquid ...... 27

Table II.2 Fitting results and comparison with previous studies ...... 35

Supplementary Table II.3 Compositions of the quenched liquid samples from the experiments measured by

EDS (recalculated as oxides wt%)...... 49

Table III.1 Experimental conditions and results of sound velocity measurements on diopside glass at different P-T paths ...... 71

Table IV.1 Sound velocity data measured for Hd and Hd50Di50 melt...... 105

Table IV.2 Fitting results for melts in the Hd-Di join...... 107

Table V.1 Experimental P-T conditions and measured densities for jadeite melt...... 139

Table V.2 Fitting results on bulk modulus and its pressure derivative and comparison with previous studies.

...... 143

Supplementary Table V.3 Compositions of the quenched sample measured by EDS (atomic %)...... 151

Table VI.1 Fitting results for the EOS of dolomite melt ...... 170

Supplementary Table VI.2 Composition of the quenched samples measured by EDS (atomic %)...... 194

Supplementary Table VI.3 Sound velocity data measured for dolomite melt...... 194

Supplementary Table VI.4 FPMD simulation results for dolomite melt. Time refers to the simulation time.

...... 197

v LIST OF FIGURES

Figure II.1 Schematic drawing of the cell assembly used in the multi-anvil experiments for ultrasonic measurements. BR: buffer rod; BP: backing plate...... 23

Figure II.2 (a) Schematic diagram for travel time measurements. (b) A representative radiographic image of the sample. The sample length can be measured by plotting the derivative of image gray values vs. pixel distances...... 27

Figure II.3 (a) Representative P-wave ultrasonic signals obtained in the experiments and the corresponding sketches of the sample status (BR-buffer rod, BP-backing plate, GS-glass sample, SS-solid sample, LS-liquid sample). (b) P-wave velocity vs. temperature at constant load (100 tons) showing the different states of the sample during a heating cycle (PM-partial melting). (c) SEM Si element mapping of a partially molten sample quenched from ~5 GPa and 2193 K showing distinct textures between quenched glass and remaining solid.

...... 31

Figure II.4 (a) Frequency dependence of the measured sound velocities at different pressures. (b) Fitting results for the sound velocities of diopside liquid and the comparison with the sound velocities of diopside glass and crystal. (c) The correlation between fitted K and K’. The ellipse defines the uncertainties in the fitting parameters...... 36

(EOS parameters from this study) and solid (EOS parameters from Li & Neuville (2010) and thermal expansion coefficient from Finger & Ohashi (1976)) along the adiabat in (a). The density profile from PREM

(Dziewonski & Anderson, 1981) is shown for reference. The shock temperatures of the shock wave points at high pressures estimated by Rigden et al. (1989) are close to the adiabatic temperatures...... 39

Valle & Bass, 2010 and magenta from Liu & Lin, 2014). The dashed line corresponds to the Birch’s law. (b)

Compressibility variation with pressure for Di liquid (this study), glass (Sakamaki et al., 2014) and solid (Li

& Neuville, 2010)...... 42

vi Figure II.7 P-wave velocity reductions as a function of pressure and melt fraction. Solid curve – calculated based on the sound velocity of diopside liquid at high P-T measured in this study, dashed curve – calculated from the model in Clark et al. (2016) based on the sound velocity of cold-compressed basalt glass...... 44

Supplementary Figure II.8 Comparison of the pressures estimated by the two different methods. The pressures at high temperatures (>~1873 K) estimated by extrapolating the pressures determined by X-ray diffraction of MgO at relatively low temperatures (~1273 to 1773 K) are in agreements with the pressures estimated from the melting curve of diopside (Williams & Kennedy, 1969 (blue); Gasparik, 1996 (red)) where the melting temperature of diopside can be deduced from the ultrasonic signals...... 46

University (CWRU). The cell used in the calibration experiment is identical to that used in the ultrasonic measurements except that the sample was replaced by a MgO disk sandwiched by two Al2O3 disks and pressure marker was replaced by pure MgO, respectively. MgO will react with Al2O3 at high temperatures and form a well-defined spinel layer whose thickness is a function of pressure, temperature and reaction time

(Van Westrenen et al., 2003). Therefore, knowing the pressure and experimental run duration, the temperature at any location where spinel layer forms can be estimated. (a) The calculated temperature profile based on spinel layer thickness (Van Westrenen et al., 2003). (b) The cell assembly for the calibration experiment. (c) SEM mapping of the spinel layers...... 47

Supplementary Figure II.10 Representative S-wave signals for the experiments. The S-wave signal for the sample can be clearly detected when the sample is in glass and crystalline solid state. After the sample becomes partially molten, the S-wave energy is largely dissipated by the irregular surface between the melt and remaining solid, so the S-wave signal for the sample and backing plate is hardly seen. When the sample is fully molten, the S-wave signal for the sample disappears completely, consistent with the fact that S-wave cannot propagate through liquids. (BR-buffer rod, BP-backing plate)...... 48

S-sample...... 66

vii Figure III.2 Pressure-temperature paths of the experiment. Solid square: measurements along the cooling, open circle: initial cold compression, star: cold compression after one heating cycle, cross: cold compression after two heating cycles...... 68

Figure III.3 (a) P-wave sound velocity Vp, (b) S-wave sound velocity Vs and (c) bulk sound velocity Vb as a function of pressure. Open circles are data from initial cold compression corresponding to the open circles in

Figure III.2, stars and crosses are cold compression data after one and two heating cycles, respectively, open squares are data collected during cooling of the sample, and open diamonds are cold compression data from

Sakamaki et al. (2014a). The dashed lines are linear fittings to the data...... 73

Figure III.4 Calculated (a) density, (b) Poisson’s ratio, (c) bulk modulus and (d) shear modulus as a function of pressure. The symbols are the same as in Figure III.3...... 75

Figure III.7 (a) Vp and density systematics for diopside glass from this study (same symbols as in Figure III.3 and Figure III.4), diopside liquid (red solid line, from Xu et al. (2018)) and diopside crystal (solid triangles, from Li & Neuville (2010), colors represent the same temperatures as in the glass case). (b) Compressibility as a function of pressure for diopside liquid (red line, from Xu et al. (2018)), cold-compressed diopside glass

(blue line, calculated from Sakamaki et al. (2014a)) and diopside crystal (black line, calculated from Li &

Neuville (2010)). The glass data from this study are also plotted as symbols same as in Figure III.3...... 84

Figure IV.1 Diagram showing the experimental setup and cell assembly for high-pressure ultrasonic measurements on silicate melts...... 101

viii Figure IV.2 (a) A representative radiographic image of Hd50Di50 melt sample at ~3.6 GPa and 2010 K. (b)

Ultrasonic signals for Hd50Di50 at a constant load of 200 tons with increasing temperature. BR-buffer rod,

BP-backing plate, SS-solid sample, LS-liquid sample...... 103

1571-1879 K, and room-pressure velocity data for Hd50Di50 melt is from Guo et al. (2014) and is measured in the temperature range of 1653-1847 K...... 105

Figure IV.4 Comparison of sound velocity (a) and density (b) as a function of pressure among melts in the

Hd-Di join and test of linear mixing. PREM model for density is from Dziewonski and Anderson (1981).

...... 109

Figure IV.5 S-wave velocity reduction (푑푙푛푉푠) as a function of density change (푑푙푛𝜌) and melt fraction for

Hd-Di melts-bearing mantle in the (a) LVZ at 2.5 GPa and (b) LVL at 12 GPa based on the theoretical model for partially model assemblages (Takei, 2002). The shaded area in (a) is based on seismic observations from

Kawakatsu et al. (2009) and Schmerr (2012) for the velocity reductions in LVZ. The shaded area in (b) represents seismic velocity reduction reported in Tauzin et al. (2010) and buoyancy constraints for LVL.

Colorbar represents the melt fraction...... 113

Figure V.1 Cross section of the PE cell assembly used for X-ray microtomography experiments on silicate melts...... 131

Sinogram showing the stack of line integrals of the pixel values at a given row height within the sample. (c)

Reconstructed horizontal slice (viewed from the top) using the TOMO_DISPLAY program. The inset shows the reconstructed vertical slice (viewed from the side). The rectangular area is zoomed in Figure V.3 showing the filtering and separation processes. (d) 3D volume rendering of the sample using Blob3D. The Mo capsule was removed for clarity in this view...... 135

ix processes. (a) Reconstructed slice after adjusting contrast and brightness. (b) Slice after applying the mean filter. (c) Slice showing the separated sample based on specifying the GTR and SR. (d) Slice showing the separated sample after applying the Remove Islands/Holes filter and the Majority filter...... 137

B19-Bajgain et al. (2019), Sa17-Sakamaki (2017) and Su11-Suzuki et al. (2011)...... 140

Malfait et al. (2014b), Seifert et al. (2013), Ai and Lange (2008) and Sakamaki et al. (2010), respectively.

The compressibility curve for jadeite melt was calculated using the best-fit values from BM-EOS. Blue curves are for polymerized melts based on the NBO/T ratios, and red curves are for depolymerized melts.

...... 145

Figure V.6 Comparison of the density profile of jadeite melt obtained in this study with that of jadeite solid

(Zhao et al., 1997), PREM model (Dziewonski and Anderson, 1981) and Di, An, model basalt (Di64An36) melts (Asimow and Ahrens, 2010). The Jd melt and solid are compared at 1673 K isotherm, while the Di, An and model basalt liquids from shock-wave studies are along their respective adiabats with a potential temperature of 1673 K. The shaded area represents the uncertainty in the compression curve for jadeite melt.

...... 147

Supplementary Figure V.7 Temperature-power relationships calibrated at different loads for the PE cell assembly used for tomographic measurements on silicate melts...... 149

Supplementary Figure V.8 (a) Secondary electron (SE) image (left) and backscattered electron (BSE) image

(right) of the quenched sample. (b) Composition mapping of the quenched sample...... 150

K’<3. See discussions in the main text. (b) Correlations between fitted K0 and K’ using Murnaghan EOS in the parameter spaces of 5 to 25 GPa for K0 and -1 to 15 for K’. Red circles indicate the best-fit values. .. 151

x Figure VI.1 (a) A representative radiographic image of the liquid sample at 4.1 GPa and 1733 K. Red lines indicate the positions of the buffer rod (BR)-sample and sample-backing plate (BP) boundaries. (b)

Corresponding P-wave ultrasonic signals obtained for the dolomite melt sample...... 166

K, but the temperature effect on the velocity of diopside melt at high pressures is negligible (Xu et al., 2018).

(b) Density as a function of pressure for dolomite melt obtained from experiments and FPMD simulations in this study, and comparison with previous studies. Blue asterisk-neutral point, blue upward-pointing triangle- floatation point, blue solid line-EOS fitting based on experimental data at 1773 K, blue dotted line-EOS fitting at 2000 K, red circle-density data obtained by LDA, red square-density data obtained by GGA, red dashed line-EOS fitting at 2000 K for LDA, red dash-dot line-EOS fitting at 2000 K for GGA, green diamond- classical MD simulations data at 2073 K from Desmaele et al. (2019), dark green diamond-GGA simulation data at 1773 K from Desmaele et al. (2019), cyan cross-classical MD simulations data at 1100 K from Hurt

(2018)...... 169

(2018). PREM model is from Dziewonski and Anderson (1981), IASP91 model from Kennett and Engdahl

(1991) and AK135 model from Kennett et al. (1995). All the calculations were performed along a plausible mantle adiabatic temperature profile (Katsura et al., 2010)...... 175

Supplementary Figure VI.4 (a) Cell assembly for ultrasonic experiments and a schematic drawing for travel time measurements. Black arrows indicate directions of sound waves in the cell. BR-buffer rod, BP-backing

xi plate. (b) Cell assembly for sink-float density measurements and schematic drawings of sample capsules showing the sink, neutral, and float scenarios, respectively...... 189

Supplementary Figure VI.5 Representative ultrasonic signals obtained for the dolomite sample at a constant load of 150 tons, showing the change of sample P- (left) and S-wave (right) signals with increasing temperature from the solid state (top), to the partially molten state (middle), and then to the fully molten state

(bottom)...... 190

Supplementary Figure VI.6 Sink-float experimental results for dolomite melt. (a) The dolomite sample decomposes at 1 GPa and 1773 K, preventing the sink of B4C markers. (b) Neutral buoyancy of B4C spheres in dolomite melt at 3 GPa and 1773 K. (c) Flotation of B4C spheres in dolomite melt at 5 GPa and 1873 K.

...... 191

Supplementary Figure VI.7 (a) Backscattered electron (BSE) image (left) and secondary electron (SE) image of the quenched sample from ultrasonic measurements (T2261), BR-buffer rod, BP-backing plate. The sample shows the typical quench texture for carbonate melts, indicating that the sample was fully molten during the experiments. (b) Composition mapping of the quenched sample. At low pressures (<2.5 GPa), the dolomite melt sample may partly decompose to MgO plus a vapor phase. The MgO blobs then sank to the bottom of the liquid sample and reacted with Al2O3 buffer rod to form spinels. Due to the fact that velocity is a bulk property of a material, and most of the blobs are at the bottom of the sample, it is unlikely that they can affect the velocity results of the melt significantly...... 192

Supplementary Figure VI.8 Correlations between fitted K and K’ for Birch-Murnaghan equation of state using the experimental velocity and density data...... 193

Supplementary Figure VI.9 FPMD simulation results for the density of dolomite melt based on (a) GGA and

(b) LDA, respectively...... 193

Supplementary Figure VI.10 . (a) P-wave velocity reduction (푑푙푛푉푝) and (b) S-wave velocity reduction

(푑푙푉푠) as a function of melt fraction and equivalent aspect ratio  based on the model of Takei (2002). Solid black lines-SC olivine + dolomite melt, dashed black lines-SC olivine + diopside melt and the numbers labelled are corresponding aspect ratio . The data used for SC olivine is from Liu et al. (2005). Red squares- experimental data from Chantel et al. (2016) for SC olivine + basaltic melt and thin red lines-modeled results by correcting the anelastic effects expected for seismic waves using a range of values for the anelastic factor

xii (See details in Chantel et al. (2016)). Purple shaded areas-seismic velocity reductions observed for the low- velocity zone (Fischer et al., 2010; Kawakatsu et al., 2009; Rychert and Shearer, 2009). Pink shaded areas- melt fractions for the low-velocity zone constrained from petrologic studies (Hirschmann, 2010a; Presnall and Gudfinnsson, 2005) and space-time distribution of seamounts (Conrad et al., 2017). For low-degree partial melts, the experimental results, seismic observations and petrologic constraints can only be satisfied when the melt aspect ratio  is ~0.01, corresponding to the melt film geometry...... 194

xiii ACKNOWLEDGEMENTS

There are so many people that I would like to thank during the creation of this dissertation. First, I would like to express my sincere gratitude to my advisors, Drs.

Zhicheng Jing and Jim Van Orman. Zhicheng is such a nice and great person who lead me to the field of mineral physics, provided me valuable guidance and support, and shared with me his time, enthusiasm and wisdom throughout my PhD study at Case Western. Jim, being an amazing-talent with great patience, helped me a lot from small things like data fitting in Matlab to larger things like career planning. For both of you, I owe a deep debt of gratitude. I would also like to thank my committee members, Drs. Steven Hauck, Ralph

Harvey and Daniel Lacks, for their time and encourage throughout the course of this research and the constructive comments on my dissertation. Particular thanks for Steve, who provided me general academic guidance and organized the weekly Earth and Planetary

Interiors group meeting which helped me learn a lot.

In addition, I would like to thank Drs. Tony Yu and Yanbin Wang for their excellent support and collaboration for beamline experiments carried out in this research. Thanks to

Drs. Suraj Bajgain and Mainak Mookherjee for willing to collaborate in the carbonate melt project. Thanks to Nanthawan Avishai for her assistance in SEM analysis and Dr. Caleb

Holyoke for providing the dolomite samples in this study. I would also like to thank our lab manager Dr. George Amulele, former Case Western student and postdoc researchers

Drs. Jian Han, Julien Chantel, Ludovic Huguet and Jeff Pigott for their help with my experiments and useful discussions. Thanks also go to our office staff Linda Day and Karen

Payne for their kind helps with financial and academic affairs. Thanks to all my fellow graduate student peers and friends here at Case Western. I have spent five wonderful years

xiv here with everyone, and I am really appreciated for everything the university has offered to me. I would also like to thank for the funding support from NSF (EAR-1619964) which makes this research possible.

Last but not least, I would like to thank my lovely wife Sisi Lai and my mom and dad back in China. Because of their continuous love and support, I can go through the difficult times and finally make it.

xv Sound Velocity, Density, and Equation of State of Silicate and Carbonate

Melts in the Earth’s Mantle

Abstract

MAN XU

Silicate and carbonate melts in the Earth’s mantle play a crucial role in the chemical differentiation and heat transfer of the planet, and are largely responsible for the mantle heterogeneities observed geochemically and geophysically. In order to better model mantle melting, magma differentiation and solidification, and to understand the stability, transport of mantle melts and their effects on seismic observations, the knowledge of the physical properties (e.g., sound velocity, density) and equation of state (EOS) of melts are essential.

However, the sound velocity and density of melts relevant to mantle processes are still poorly constrained due to experimental challenges to measure these properties of melts at extreme conditions. In this dissertation, I have studied the EOS of silicate and carbonate melts at high pressure and temperature conditions, with a focus on Mg, Fe and Na-rich

xvi silicate melts as well as pure carbonate melts, by developing new techniques for high- pressure sound velocity and density measurements on melts, including the in-situ ultrasonic technique and high-pressure X-ray microtomography. Various high-pressure cell designs combined with synchrotron techniques allow us to obtain the first high-pressure sound velocity dataset for silicate melts in the diopside (CaMgSi2O6)-hedenbergite (CaFeSi2O6) join (Chapters II and IV), and for carbonate melts in the MgCO3-CaCO3 join (Chapter VI).

The differences of the elastic properties between silicate glasses and their corresponding liquids are revealed (Chapter III). New high-pressure density data using X-ray microtomographic reconstruction for sodium-rich jadeite melt are also reported (Chapter

V). The results of these studies have significant implications for several geophysical problems, including the stability and possible density crossover of melts in the Earth’s mantle, the origin of the seismic low-velocity regions in the mantle, the solidification of early magma oceans, and the fate of subducted carbonates, etc.

xvii Chapter I

Introduction

Magmas with different compositions widely exist in Earth and some other terrestrial planets (e.g., Moon, Mars), and play an important role in the planets’ differentiation, as they are the major agent to transfer heat and chemical species (Sanloup, 2016) either to the planet’s surface or to the deep mantle, resulting in the volcanism and formation of crust or chemical heterogeneities in the mantle. The density contrast between the magmas and surrounding mantle materials exerts a first order control of these differentiation processes.

For magmas that erupt to the surface, knowing their density vs. pressure is required to model their segregation from source regions and subsequent migration to the surface. As for melts trapped in the mantle, such as those in the lithosphere-asthenosphere boundary

(LAB) (Schmerr, 2012) and atop the 410 km and 660 km discontinuities as suggested by geophysical observations (Schmandt et al., 2014; Tauzin et al., 2010), the knowledge of density at high pressures is needed to understand their stability in the mantle. In addition, the early history of the Earth and the Moon is believed to be characterized by at least one stage of nearly entirely molten state, namely, the magma ocean, formed in the aftermath of the giant Moon forming impact event (Hosono et al., 2019; Nakajima and Stevenson, 2015).

In order to thermodynamically model the solidification of the early magma ocean, we need to know the density of the magmas. Thus, the equation of state (EOS) for melts of different compositions is fundamental to the understanding of the evolution of our Earth and other terrestrial planets.

Despite this importance, the density of magmatic liquids is still poorly constrained due to the difficulties in direct experimental measurements at high pressure and high

1 temperature conditions, as well as the fact that the natural magmatic liquids comprise a potentially infinite, multi-dimensional continuum of compositions (Thomas and Asimow,

2013a), which requires us to develop a reliable tool to interpolate the melt density based on limited experimental data. The challenging nature of the experimental measurements is reflected by the various approaches that have been applied to determine the melt density at high pressure, including sink-float experiments (Agee, 1998; Agee and Walker, 1993;

Ghosh et al., 2007; Jing and Karato, 2012; Knoche and Luth, 1996; Matsukage et al., 2005),

X-ray absorption (Malfait et al., 2014b; Sakamaki et al., 2010; Seifert et al., 2013), X-ray diffraction (Hudspeth et al., 2018; Sanloup et al., 2013) and shock-wave technique

(Asimow and Ahrens, 2010; Rigden et al., 1989; Thomas and Asimow, 2013a). All these methods have some shortcomings with respect to accuracy, precision, cost or complexity.

A comparison of these methods together with the in-situ high pressure ultrasonic technique and the high-pressure X-ray tomographic technique developed in this study is listed in Table I.1. The ultrasonic measurements of magmatic liquids are important in the aspect that they can directly provide us the bulk modulus (퐾) information of the melts, and thus can help uniquely constrain the pressure dependence of the bulk modulus (퐾′), while there exists a strong trade-off between the fitted bulk modulus (퐾) and the pressure dependence of bulk modulus (퐾′) if we only have density data in a limited pressure range but no sound velocity data (Jing and Karato, 2008). In addition, the relaxed sound velocity from ultrasonic measurements can be directly compared with seismic observation to infer the existence of melts in the mantle (Chantel et al., 2016; Xu et al., 2018), and to make constraints on the internal structure of the planets (Jing et al., 2014). Although the 1-bar sound velocity data for both silicate melts (Ai and Lange, 2008; Rivers and Carmichael,

2 1987) and some carbonate melts (O’Leary et al., 2015) have been established, no sound velocity data exist for magmatic liquids at high pressures due to the experimental challenges. One of the major goals of this dissertation is to develop the ultrasonic technique for silicate and carbonate liquids at high pressure to fill this data gap.

As for the high-pressure X-ray microtomography technique, which measures the 3D volume of the liquid sample directly from a series of radiographic images, though in its incipient stage, it is a very straightforward and promising method compared to other techniques for density measurements, and it is suitable for volatile-rich and high viscosity melts (e.g., alkali-rich melts) whose density cannot be determined by commonly used techniques such as the sink-float experiments and X-ray absorption method. This technique has the potential to significantly expand the density dataset for melts in the pressure- composition relevant to the Earth’s mantle.

Table I.1. Comparison between different methods to determine the EOS of mantle melts at high pressures

Technique P-T upper limits Pros Cons Suitable marker is often hard to find; Only works for low-viscosity melts and melts that can have a Relatively density crossover with straightforward; Sink-float 24 GPa-2500 K the solid marker within Experimental the experimental configuration is simple pressure range; Few points along the EOS; Accuracy depends on the EOS of the solid marker Temperature measurement may be an issue; Need pre-melting of the sample which Shock wave 200 GPa-8000 K Undefeated P-T range may not be suitable for some melt compositions; High- cost experiments

3 Fine P-T mesh; Not suitable for low- Relatively absorption materials; X-ray absorption 10 GPa-2300 K straightforward Cell instability; Limited diagnostic pressure range

Challenging experiments; Long Fine P-T mesh; experimental duration; X-ray diffraction 70 GPa-3000 K Simultaneous structural Delicate data data processing; Sensitive to background signals

Direct information on Challenging compressibility and its experiments; Need a pressure dependence; reference density point Ultrasonic technique 20 GPa-2500 K Sensitive to melting; to get the EOS; Not Straightforward suitable for highly diagnostic viscous melt

Suitable for nearly any silicate melts; Relatively Limited pressure range; straightforward No thermocouple to X-ray microtomography 10 GPa-2500 K diagnostic; Can directly directly measure the measure the volume temperature change upon melting Adapted from Sanloup (2016). The P-T upper limits correspond to the maximum values that can be reached according to the literature.

Due to the extensive appearance of silicate melts in Earth, the density for silicate melts has been widely studied for a range of compositions, from ultramafic peridotite melts

(Sakamaki et al., 2010), MORB (Agee, 1998; Ohtani and Maeda, 2001) to silica-rich melt

(Malfait et al., 2014b) and hydrous melt (Jing and Karato, 2012; Matsukage et al., 2005) by a variety of techniques. Nevertheless, all the EOS obtained in these studies are empirical and can only be applied to calculate the density of the specific melt compositions studied at conditions covered by the experimental pressure ranges. Cautions should be taken when using these EOS for a different melt composition or extrapolating the density to higher pressures that exceed the experimental pressure range. Obviously, this kind of EOS is far

4 from sufficient for silicate melts relevant to planets’ differentiations. Another approach is to determine the density of the end-member compositions (e.g., diopside, anorthite) and some intermediate compositions (e.g., model basalt), and by employing appropriate mixing models, the density of any melt compositions in between can be calculated. This has been demonstrated by some pioneer works for silicate melts at 1-bar conditions using the linear mixing model (Bottinga et al., 1982; Kress and Carmichael, 1991; Lange and Carmichael,

1987; Rivers and Carmichael, 1987), which can let us calculate the density and compressibility of silicate melts with most compositions at ambient pressure. Some of these data have also been successfully used in the thermodynamic model pMELTS

(Ghiorso et al., 2002) to calculate the phase equilibria during magma crystallization in a low pressure range. Since magmas may also exist in the deep mantle, there is an urgent need to extend the dataset to high pressures in order to better model magmatic processes in the interior of the Earth. In this context, shock-wave studies have been carried out on some end-member liquid phases (Asimow and Ahrens, 2010; Rigden et al., 1989; Thomas and

Asimow, 2013a, 2013b). However, there still exists a large data gap, especially for sound velocity, for silicate liquids between ambient pressure and shock wave pressure. This dissertation intends to fill this data gap by overcoming the experimental challenges. The new data provided here can help us better understand the existence and buoyancy of silicate melts in the mantle, thus providing valuable constraints on the reason why some melts can be trapped in certain layers of the Earth, and how the early magma ocean solidified.

Carbonate melts, although volumetrically sparse compared to silicate melts, are also very important in understanding the dynamic and magmatic history of the Earth, as substantial carbonates that could be molten under mantle conditions are subducted into the

5 deep Earth (Hammouda and Keshav, 2015). Petrologic studies have shown that the presence of carbonates in the mantle can dramatically lower the solidus of mantle rocks

(Dasgupta et al., 2013; Dasgupta and Hirschmann, 2006; Hammouda, 2003; Litasov and

Ohtani, 2010; Poli, 2015), producing carbonate-rich melt (or carbonatite melt) as the near- solidus partial melts. These carbonate-rich melts play a crucial role in regulating the deep carbon cycle (Dasgupta and Hirschmann, 2010) and strongly affect the mantle redox state

(Rohrbach and Schmidt, 2011). Many important geological problems are related to the properties of carbonate melts. Firstly, carbonatites widely occur in Earth from Archean to the present day and are thought to be produced from carbonate-dominant magmatism

(Jones et al., 2013). Studies have demonstrated that partial melting of carbonated lithologies just above the solidus could generate carbonatite melts in the mantle (Dasgupta and Hirschmann, 2006; Litasov and Ohtani, 2010). These carbonatite melts could be highly reactive with reduced ambient mantle, producing diamonds and creating a barrier to the deep carbon subduction (Thomson et al., 2016). The presence of a small amount of carbonate-rich melts in the asthenosphere were also suggested to be responsible for the seismic low-velocity zone (Hirschmann, 2010a; Presnall and Gudfinnsson, 2005) and electrical conductivity anomalies (Gaillard et al., 2008; Sifré et al., 2014). In addition, CO2 is also one of the major volatile species in silicate melts and can affect the melt properties significantly. Experimental petrology studies (Dasgupta et al., 2013) have shown that carbonate-rich melts are likely present in the asthenosphere beneath the mid-ocean ridges and can be strongly reactive with silicate mantle, leading to a progressive change in the melt composition from carbonate-rich to silicate-rich. Some carbonate-rich melts, like kimberlites, are also very important in diamond formation. The mechanism for the fast

6 ascent of kimberlite magma is still not well-known. It is suggested that the buoyancy of kimberlite melt plays an important role at depth, which is dictated by the unique physical properties of its carbonatitic composition (Russell et al., 2012; Sharygin et al., 2017).

Despite the importance of carbonate melts in many aspects, the knowledge of the density and compressibility of carbonate melts are extremely lacking. Until now, only a few experimental data are available for carbonate melts, most of which were measured at ambient pressure (Dobson et al., 1996; Liu and Lange, 2003). However, ambient-pressure density data are not readily applicable to carbonate melts at mantle conditions, and for

CaCO3 (calcite), MgCO3 (magnesite) and CaMg(CO3)2 (dolomite), carbonates that most relevant to Earth’s mantle (Dasgupta and Hirschmann, 2010), their density and sound velocity cannot be measured at ambient pressure because they decarbonate and degas prior to melting. This study provides the first comprehensive density and elastic dataset for dolomite melt, which are important to understanding carbonate-induced mantle melting and its role in deep carbon cycles.

In this dissertation, I will mainly focus on Mg, Fe and Na-rich silicate melts and

MgCO3-CaCO3 carbonate melts. Table I.2 shows the melt compositions that have been studied in this dissertation. For silicate melts, Mg, Fe and Na-rich pyroxene end-member joins are chosen because: (1) Pyroxenes are one of the most important minerals in the mantle and they are thought to be the last major phase to crystallize during the solidification of the magma ocean (Gasparik, 1992); (2) Mg, Fe, Na-rich end-member compositions are much less well-studied due to experimental difficulties and they often possess unique characteristics (e.g., high viscosity for Na-rich melt, changing valences for iron-bearing melt) and therefore does not always obey the linear mixing behavior; (3) Including these

7 compositions can help expend the dataset for silicate melts and improve the EOS model to a larger composition space; and (4) Fe, Na-rich compositions themselves are important in many aspects, for example, sodium may play an important role in melt generation in the deep mantle (Takazawa et al., 1998), and iron can strongly affect the melt density and is an indicator of the oxygen fugacity in the melts (Sanloup et al., 2013). For carbonate melts, dolomite melt is chosen to study because it is close to the primary near-solidus carbonatite melt compositions at upper mantle conditions by melting of carbonated mantle lithologies

(Dasgupta and Hirschmann, 2010).

Table I.2 Compositions studied and techniques used in this dissertation

Composition Technique

Mg-rich silicate melt Di (CaMgSi2O6) Ultrasonic

Fe-rich silicate melt Hd (CaFeSi2O6) and Hd50Di50 Ultrasonic

Na-rich silicate melt Jd (NaAlSi2O6) X-ray microtomography

Carbonate melt Dol (CaMg(CO3)2) Ultrasonic and sink/float

Silicate glass Di (CaMgSi2O6) Ultrasonic

In Chapter II, the technical developments on ultrasonic measurements of silicate melts are reported and applied to diopside melt (CaMgSi2O6), allowing us to obtain the first high- pressure sound velocity dataset for a silicate melt. The sound velocity of diopside melt increases with pressure and is nearly independent of temperature. The results suggest that the amount of seismic wave velocity reduction in the mantle increases with melt fraction and decreases with pressure.

In Chapter III, the differences of the elastic properties among cold-compressed silicate glass, high-pressure heated silicate glass and the corresponding silicate liquid are revealed,

8 suggesting that silicate glasses may not be good analogs for studying the elastic properties of corresponding liquids.

In Chapter IV, the sound velocity of iron-rich melt in the hedenbergite-diopside join

(CaFeSi2O6-CaMgSi2O6) is reported. Experimental results show that iron can significantly reduce the sound speed while increase the density in silicate liquids, and the mixing behaviors in iron-rich melts are complicated. The presence of iron-rich melt above the mantle transition zone may be responsible for the seismically observed low-velocity layer.

In Chapter V, the X-ray microtomography technique is presented and for the first time applied to determine the density of sodium-rich jadeite melt (NaAlSi2O6). The results show that alkali contents in silicate melt can significantly affect the melt compressibility. Sodium aluminosilicate melts, if generated by low-degree partial melting of mantle peridotite in the deep upper mantle, are highly compressible and may become denser than surrounding mantle materials and gravitationally stable.

In Chapter VI, the first experimental high-pressure density and sound velocity data are reported for dolomite melt (CaMg(CO3)2). Using these data, the calculated VP/VS ratio of the upper mantle and its comparison with global seismic observations suggest that a low- degree carbonate-rich partial melt (~0.05%) is likely present pervasively in the deep upper mantle at the depths of ~180 to 330 km, which has significant implications for the deep carbon cycle.

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16 Chapter II

Ultrasonic velocity of diopside liquid at high pressure and temperature:

Constraints on velocity reduction in the upper mantle due to partial

melts

(Published in Journal of Geophysical Research: Solid Earth)

Abstract

Sound velocities of diopside liquid were determined at high pressures and temperatures up to 3.8 GPa and 2375 K, using the ultrasonic technique combined with synchrotron X-ray diffraction and imaging in a multi-anvil apparatus. Our results show that the sound velocity increases with pressure but is nearly independent of temperature. Using a Monte-Carlo approach, the measured high-pressure sound velocities combined with ambient-pressure density provide tight constraints for the equation of state of diopside liquid, with a best-fit adiabatic bulk modulus (Ks) of 23.8 ± 0.4 GPa and its pressure derivative (Ks’) of 7.5 ± 0.5. The calculated adiabatic temperature and density profile of diopside liquid suggest that a melt layer with diopside composition in the upper mantle would be gravitationally unstable and start to crystallize from the bottom of the layer during cooling. By comparing our results with previous acoustic measurements on silicate glasses, we demonstrate the important differences in sound velocities between silicate liquids and glasses and conclude that silicate glasses may not work as a good analog material for studying the acoustic properties of silicate liquids, as measurements on unrelaxed glasses do not capture the entropic contribution to the compressional properties of liquids. We modeled velocity reductions due to partial melts in the upper mantle using our results and

17 found that for a given velocity reduction, the deeper the low velocity region, the larger the melt fraction is required. Using silicate glass data for such estimation would result in a significant underestimation of melt fractions at high pressures.

Introduction

Melting of silicate rocks is common to the mantles and crusts of the Earth and other terrestrial planets in the solar system and has played an important role in the differentiation of these planetary bodies. Silicate melts are a major agent to transfer chemical species to either the surface or the deep mantle depending on the density contrast between the melts and the surrounding materials (e.g., Sanloup, 2016; Stolper et al., 1981), resulting in volcanism and formation of crusts or chemical heterogeneities in the mantle. In order to thermodynamically model processes related to mantle melting, magma differentiation and solidification, it is necessary to obtain an accurate equation of state (EOS) for silicate liquids (e.g., Ghiorso, 2004). Although density and compressibility of silicate liquids at ambient pressure have been well established by the linear mixing model (e.g., Ai & Lange,

2008; Bottinga et al., 1982; Kress & Carmichael, 1991; Lange & Carmichael, 1987; Lange,

1997; Rivers & Carmichael, 1987), high pressure data are far from sufficient to construct a unified model (e.g., Jing & Karato, 2011). Previously, the EOS for silicate liquids at high pressures relevant to the Earth’s upper mantle and transition zone was mainly constrained using the density data obtained by static compression such as sink-float (e.g., Agee, 1998;

Agee & Walker, 1993; Ghosh et al., 2007; Jing & Karato, 2012; Matsukage et al., 2005) and X-ray absorption experiments (e.g., Malfait et al., 2014; Sakamaki et al., 2010; Seifert et al., 2013). However, the obtained EOS often have large uncertainties due to the scarcity of data from sink-float measurements and the limited pressure range for X-ray absorption

18 method (e.g., Agee, 1998; Agee & Walker, 1993; Malfait et al., 2014): There exists a large trade-off between the fitted bulk modulus (K) and its pressure derivative (K’) due to the strong correlation between these two EOS parameters (Bass et al., 1981; Jing and Karato,

2008). Hugoniot data obtained by shock compression (e.g., Asimow & Ahrens, 2010;

Rigden et al., 1989; Thomas & Asimow, 2013) can help place tighter constraints on K and

K’ due to the wider pressure range in the measurements, but the reduction of shock-wave data requires assumptions on high-pressure thermal properties since shock temperatures were not determined directly in these experiments.

Sound velocity measurements are often used to provide direct information on the bulk modulus and its pressure derivative of a material and hence can tightly constrain the EOS of the material (e.g., Chantel et al., 2012; Irifune et al., 2008; Jing et al., 2014; Li et al.,

2004; Li & Liebermann, 2014). Sound velocities of minerals and melts are also important to the interpretation of seismic data. Global seismic velocity profiles generally increase with depth, with abrupt changes associated with lithological boundaries or mineral phase transitions (e.g., PREM, AK135) (Dziewonski and Anderson, 1981; Kennett et al., 1995).

There are also some regions in the crust and mantle where the velocities are slower than the global average (e.g., Hawaii, Japan arc, lithosphere-asthenosphere boundary, top of core-mantle boundary). One possible explanation for such velocity reduction is the presence of partial melts (Anderson & Spetzler, 1970; Chantel et al., 2016; Hirschmann,

2010; Kawakatsu et al., 2009; Williams & Garnero, 1996). Thus, sound velocity measurements of silicate liquids at high pressures can not only provide better constraints on the EOS, but also on the existence of melts in the mantle and the amount of melt needed to interpret a given velocity reduction. However, sound velocity measurements on silicate

19 liquids at high-pressure and high-temperature conditions are extremely challenging. Until now, there are no reported high-pressure experimental data, to our best knowledge, on the sound velocity of any silicate liquid. Due to this limitation, many studies have used silicate glasses as analogs for liquids to infer the acoustic behavior of silicate liquids at high pressures (e.g., Clark et al., 2016; Liu & Lin, 2014; Malfait et al., 2011; Meister et al., 1980;

Murakami & Bass, 2011; Sakamaki et al., 2014; Sanchez-Valle & Bass, 2010; Suito et al.,

1992). These studies have shown that many silicate glasses exhibit an elastic anomaly with weak or even negative pressure dependence of sound velocity within the pressure range of a few GPa. For example, Liu & Lin (2014) determined the sound velocities of a (Fe, Al)- bearing MgSiO3 glass and a basalt glass using the Brillouin scattering spectroscopy in a diamond anvil cell and found that the velocity profiles of these two glasses display decreasing VP and VS with velocity minima at about 5 and 2 GPa, respectively. Clark et al.

(2016) also observed anomalous sound velocity behavior by applying the gigahertz ultrasonic interferometry on the Columbia River basalt glass where the VP displayed a minimum at about 4.5 GPa. They further modeled the melt sound velocity at high pressures by assuming that the pressure dependence of sound velocity in silicate melts has similar anomalies to those in basalt glass. However, silicate glasses and liquids may be fundamentally different in their compressional properties (Jing and Karato, 2011). Whether silicate liquids have similar pressure dependence of sound velocity as their glass counterparts or not needs to be tested.

In this study, we report the first direct high-pressure and high-temperature ultrasonic sound velocity measurements on a silicate liquid, i.e., diopside liquid (CaMgSi2O6).

20 Results of the measurements were used to determine the EOS of diopside liquid and place constraints on the velocity reduction in the upper mantle due to partial melts.

Experimental methods

We conducted ultrasonic sound velocity measurements on diopside liquid in a multi- anvil apparatus under pressure and temperature conditions ranging from ~0.5 to 4 GPa and

2010 to 2375 K, with the help of synchrotron X-ray imaging and diffraction techniques.

Diopside was chosen to study because it is not only one of the most important phases in the Earth’s upper mantle, but also an end-member composition of the model basalt. It is thus an ideal simplified melt composition in the upper mantle. Furthermore, the viscosity of diopside liquid is relatively low (e.g., Reid et al., 2003), which ensures the measured sound velocities to be fully relaxed within the experimental time frame. In addition, diopside liquid has been studied by ultrasonic measurements at ambient pressure (Ai and

Lange, 2008) and by shock-wave experiments at much higher pressures (Asimow and

Ahrens, 2010). These allow comparison with our results over a wide pressure range.

Starting materials

The starting materials were prepared by mixing appropriate proportions of reagent grade powders of MgCO3, CaCO3 and SiO2 in ethanol for ~2 hours. The mixed powders were first dried and decarbonated at 1173 K in a high temperature box furnace for ~24 hours and then fused at 1773 K for ~1 hour and finally quenched to a glass. The weight of the mixture was checked before and after decarbonation to confirm full release of CO2 and no contamination of hydroxyls in the starting carbonates. The fusion process was repeated twice to ensure homogeneity of the glass. The glass was then crushed and ground to a fine powder, loaded into a piston cylinder apparatus, and fused for the third time at 1973 K and

21 1 GPa. After quenching, transparent, bubble-free, and homogeneous glass pellets with the desired outer diameter were obtained. The top and bottom surfaces of the glass pellets were polished down to 1 m with nearly perfect parallelism. The glass pellets were then used as the starting materials for high-pressure and temperature ultrasonic measurements.

High-pressure ultrasonic measurements

High-pressure ultrasonic measurements were carried out in a 10 MN multi-anvil press at the GSECARS Beamline 13-ID-D of the Advanced Photon Source (APS), Argonne

National Laboratory (ANL), with a double-stage Kawai-type multi-anvil module (T-25)

(Wang et al., 2009). Tungsten carbide (WC) anvils were used as the second-stage anvils with a truncation edge length (TEL) of 8 mm. The design of the cell assembly is similar to that used in Jing et al. (2014), and is shown in Figure II.1. An MgO-MgAl2O4 octahedron with 14-mm edge length was used as the pressure medium in each experiment. A graphite sleeve was used as the heater inserted into a ZrO2 thermal insulator with a transverse MgO

X-ray window. Pressure of the experiments was determined by the energy-dispersive X- ray diffraction of the pressure marker (PM) consisting of a mixture of MgO and h-BN

(MgO:BN = 4:1 by weight) using the EOS of MgO (Tange et al., 2009). However, MgO diffraction peaks became too weak when temperature was higher than ~1873 K, likely due to the grain growth at high temperatures. We estimated the pressure at higher temperatures

(~1873 to 2473 K) by linearly extrapolating the MgO pressures determined by X-ray diffraction at lower temperatures (~1273 to 1773 K). The pressures estimated by this method are in excellent agreement with the pressures estimated by the high-pressure melting curve of diopside (Williams & Kennedy, 1969; Gasparik, 1996). In our

22 experiments, the melting temperature was determined from ultrasonic signals (described in detail below in Section 3.1) (Table II.1 and Supplementary Figure II.8).

MgO + MgAl2O4 MgO

ZrO2 Al2O3 Graphite Mullite

Figure II.1 Schematic drawing of the cell assembly used in the multi-anvil experiments for ultrasonic measurements. BR: buffer rod; BP: backing plate. The temperature of the experiments was monitored by a W5Re-W26Re thermocouple.

A large temperature gradient was observed during heating the sample: The sample exhibits a partially molten state over a wide temperature interval despite the fact that diopside melts congruently. This was expected, as the sample was directly connected to the anvil by the molybdenum buffer rod which is a good thermal conductor. To better estimate the temperature distribution in the cell assembly, we conducted an offline temperature calibration experiment using the spinel layer growth method described in Van Westrenen et al. (2003) and Watson et al. (2002). The experimental details and calibration results are shown in Supplementary Figure II.9. Our calibration results show that (1) the temperature of the pressure marker is ~58 K lower than the temperature measured by the thermocouple;

(2) the top and bottom part of the sample are at least ~114 K and ~212 K lower than the temperature measured by the thermocouple, respectively; (3) there is a ~100 K gradient in the sample region, which can cause progressive melting from the high temperature end to

23 the low temperature end of the sample while increasing the sample temperature. We then corrected the temperatures in our experimental runs according to our calibration results

(Supplementary Figure II.9), assuming that the temperature difference between any two points in the cell assembly should increase with the thermocouple temperature as a linear function with zero difference at ambient temperature. The corrected temperatures are listed in Table II.1.

The principles for ultrasonic measurements have been described in detail by Jing et al.

(2014). A 10° Y-cut LiNbO3 piezoelectric transducer with a resonant frequency of 50 MHz for compressional waves (P-waves) and 30 MHz for shear waves (S-waves) was attached to the back of the bottom WC anvil using high temperature epoxy resin. Electrical signals of sine waves in the frequency range of 20-60 MHz were generated by an arbitrary waveform generator and were converted to compressional (P) and shear (S) waves by the transducer. The elastic waves then travel through the cell assembly and are reflected at the anvil-buffer rod (BR), buffer rod-sample and sample-backing plate (BP) interfaces (see

Figure II.1 for the position of various interfaces) and received by the same transducer which then converts elastic waves back to electrical signals that are displayed and recorded by a digital oscilloscope at a sampling rate of 5  109 sample/s. In our experiments, all these interfaces were carefully polished to 1 m to ensure good contact. Travel time through the sample was determined by the pulse-overlap method (Jing et al., 2014; Kono et al., 2012) using the reflected signals from BR-sample and sample-BP interfaces (Figure II.2a). The travel time is the time delay that results in the maximum cross correlation between the two signals. The cross-correlation method has been shown to be valid for determining time delay for attenuating media and generally gives consistent results with other methods such

24 as the Fourier method (Molyneux and Schmitt, 2000). Uncertainty in the travel time determination is within 0.2 ns, corresponding to a relatively uncertainty of 0.16%. Sample length was determined by X-ray radiographic imaging (Figure II.2b) using a CCD camera.

Uncertainty in determined sample length is within 2.431 m (1 pixel), corresponding to a relatively uncertainty of 0.67%. Then the sound velocity of the sample was calculated from travel time and sample length, with a total propagated uncertainty of less than ~1%.

Molybdenum was used as the buffer rod (BR)/backing plate (BP) and the sample capsule material because (1) it has a very high melting temperature (~2900 K at room pressure);

(2) it has little chemical reactivity with the diopside liquid at high pressures; (3) it has a much higher density and X-ray absorption than silicate melts and results in large acoustic impedance and X-ray imaging contrasts. The successful use of molybdenum as a buffer rod or sample capsule material has also been demonstrated in ambient-pressure ultrasonic measurements for silicate liquids (Ai and Lange, 2008; Guo et al., 2014), sink-float density measurements (Agee, 2008; Agee and Walker, 1988), and shock wave experiments

(Asimow and Ahrens, 2010; Thomas et al., 2012).

For each experiment, the sound velocity of the liquid was measured at one to three different fixed hydraulic ram loads, corresponding to pressures from 0.3 to 3.8 GPa, and at temperatures from 2010 to 2375 K. After the target load was reached in each experiment, the temperature was then increased at a rate of ~50 K/min. We measured the pressure every

200 K using the energy-dispersive diffraction setup, with a Ge solid state detector and a fixed two-theta angle at ~6° (Wang et al., 2009). During heating, ultrasonic signals were constantly monitored until the sample reached the fully molten state (Figure II.3). Then, we continued increasing the temperature at least 100 K higher before taking the ultrasonic

25 measurements. Two sample images were taken for each ultrasonic measurement using the charge coupled device (CCD) camera, with one taken before the ultrasonic measurement and one after, to check if the sample length had changed during the measurement (which usually takes less than 10 min). For each experiment, 2 to 3 heating cycles were performed and finally the sample was quenched by turning off the heater power. The quench products from the experiments were sectioned, polished, and mounted in epoxy to be observed in a field emission scanning electron microscope (FE-SEM) in backscattered electron (BSE) mode for texture imaging and in the energy-dispersive spectroscopy (EDS) mode for chemical analysis. The SEM analyses were carried out at the Swagelok Center for Surface

Analysis of Materials (SCSAM) of Case Western Reserve University (CWRU). The acceleration voltage and probe current were set at 10 kV and 15 nA, respectively. These analyses show that the run products were homogeneous in composition with little molybdenum contamination. The bulk compositions of the run products are listed in

Supplementary Table II.3.

26 (a) (b) Anvil Buffer rod Sample

c Backing plate

)

(

Mo t

Anvil echo i

Buffer rod echo capsule D

Sample echo Input Buffer rod

Derivative of image gray value ∆t (travel time)

Table II.1 Experimental conditions and results for sound velocity measurements of diopside liquid

푊퐾 퐺 Run # PMgO 푃푚 푃푚 T (K) 푇푚 (K) f c (m/s) Average 1 SD (GPa) (GPa) (GPa) (MHz) c (m/s) (m/s) T2019 2.46 2.3 2.1 2101 1919 20 3730 3675 40 T2019 2.46 2.3 2.1 2101 1919 25 3709 T2019 2.46 2.3 2.1 2101 1919 30 3691 T2019 2.46 2.3 2.1 2101 1919 40 3652 T2019 2.46 2.3 2.1 2101 1919 50 3638 T2019 2.46 2.3 2.1 2101 1919 60 3632 T2019 2.47 2.3 2.1 2147 1919 20 3662 3678 18 T2019 2.47 2.3 2.1 2147 1919 25 3653 T2019 2.47 2.3 2.1 2147 1919 30 3677 T2019 2.47 2.3 2.1 2147 1919 40 3691 T2019 2.47 2.3 2.1 2147 1919 50 3697 T2019 2.47 2.3 2.1 2147 1919 60 3688 T2019 3.26 2.8 2.7 2284 1964 20 3965 3962 6 T2019 3.26 2.8 2.7 2284 1964 25 3957 T2019 3.26 2.8 2.7 2284 1964 30 3954 T2019 3.26 2.8 2.7 2284 1964 40 3961 T2019 3.26 2.8 2.7 2284 1964 50 3965 T2019 3.26 2.8 2.7 2284 1964 60 3969 T2019 3.74 3.8 4.0 2375 2056 20 4192 4175 12

27 T2019 3.74 3.8 4.0 2375 2056 25 4179 T2019 3.74 3.8 4.0 2375 2056 30 4175 T2019 3.74 3.8 4.0 2375 2056 40 4179 T2019 3.74 3.8 4.0 2375 2056 50 4167 T2019 3.74 3.8 4.0 2375 2056 60 4158 T2023 0.30 0.3 0.2 2010 1690 20 3088 3082 7 T2023 0.30 0.3 0.2 2010 1690 25 3082 T2023 0.30 0.3 0.2 2010 1690 30 3075 T2023 0.30 0.3 0.2 2101 1690 20 3096 3084 10 T2023 0.30 0.3 0.2 2101 1690 25 3077 T2023 0.30 0.3 0.2 2101 1690 30 3079 T2027 3.18 3.3 3.3 2284 2010 20 3853 3853 0 T2027 3.18 3.3 3.3 2284 2010 25 3853 T2027 3.18 3.3 3.3 2284 2010 30 3853 T2027 3.70 3.8 4.0 2284 2056 20 4148 4165 26 T2027 3.70 3.8 4.0 2284 2056 25 4152 T2027 3.70 3.8 4.0 2284 2056 30 4195 T2027 3.70 3.8 4.0 2375 2056 20 4110 4131 31 T2027 3.70 3.8 4.0 2375 2056 25 4115 T2027 3.70 3.8 4.0 2375 2056 30 4166 Note:

PMgO – pressure estimated by extrapolating the pressures obtained by the X-ray diffraction of MgO standard at 1273 to 1773 K. The uncertainties are about 10%. This pressure was used in the EOS fitting of K and K’. 푊퐾 푃푚 – pressure estimated by the melting curve of diopside from Williams and Kennedy (1969). The uncertainties are about 0.5 GPa. 퐺 푃푚 – pressure estimated by the melting curve of diopside from Gasparik (1996). The uncertainties are about 0.3 GPa. T – corrected average sample temperature based on the calibration experiment. The uncertainties are about 50 K.

푇푚 – melting temperature of diopside deduced from the ultrasonic signals. The uncertainties are about 50 K. f – frequency of the signal used in the ultrasonic measurements. c – sound velocities for diopside liquid. The uncertainties in measured sound velocities are about 1%.

Results

Ultrasonic signals and detection of partial melting

Some typical P-wave ultrasonic signals obtained in the experiments are shown in

Figure II.3a. Although S-wave signals are also observed at some conditions

(Supplementary Figure II.10), here we focus our discussion on the P-wave signals since S-

28 waves cannot propagate through liquids. Ultrasonic sound wave signals and sound velocities have been demonstrated to be very sensitive to melting and other phase transitions, and can thus be used to detect the change of sample state at high pressures

(Chantel et al., 2018). As shown in Figure II.3b, the state of the sample during a typical heating cycle (the load was at 100 tons for this particular case) can be clearly divided into four regimes: glass, crystal, partial melt (PM), and liquid, based on the changes in the measured sound velocities. The jump in sound velocity from ~6700 m/s to ~7500 m/s between 1188 K and 1371 K likely corresponds to the recrystallization of the glass starting material, consistent with the ambient-pressure glass transition temperature of diopside glass which is about 1013 K (Lange, 1997). With further heating, the sample remains in the crystalline form for a few hundred degrees before it starts to melt, as indicated by the dramatic decrease in sound velocity starting at ~1780 K. A partial melt is present in the temperature range of ~1750 K to ~2010 K because the crystalline sample can only melt progressively under the large temperature gradient in the cell as discussed in Section 2.2.

That is, melting starts close to the center of the cell assembly while the remaining portion of the sample adjacent to the buffer rod stays in the solid state. A sample in the partially molten state (~5 GPa and ~2193 K) was quenched and analyzed by SEM. Si element mapping of the run product showed distinct solid (crystallized from the starting glass) and quenched melt layers with different textures (Figure II.3c). As a result, upon melting we can detect two separate P-wave ultrasonic signals reflected from the back of both the solid and the liquid layers of the sample (Figure II.3a), denoted as SS and LS, respectively, with the SS signal arriving earlier since the solid layer is closer to the buffer rod. The average sound velocity of the whole sample can be calculated using the travel time difference

29 between the LS signal and the buffer rod signal (BR) (Figure II.3a) and displays a sharp drop in the partially molten state (Figure II.3b). Meanwhile, echo amplitudes for both sample (that is, the echo reflected at the back of the sample) and backing plate (BP) decrease significantly from solid state to partially molten state as the irregular solid-melt interface dissipates a significant amount of P-wave energy. At a certain stage, the energy dissipation was so great that nearly no energy could reach the backing plate (BP), so the

BP signal almost completely disappeared. In addition, travel time of the molten sample signal increases gradually with increasing temperature, as the sound wave travel distance in the liquid portion of the sample increases with temperature (Figure II.3a), until the sample is in the fully molten state, which is indicated by the complete disappearance of solid sample signals and the appearance of clear liquid and BP signals. Once the sample is fully molten, the measured sound velocities do not change much with temperature (Figure

II.3b).

The ultrasonic signals obtained can thus be used to estimate the melting temperature of diopside. After correcting the effect of thermal gradient in the cell, the average temperature of the sample when both solid and liquid signals coexist is used as the estimation for the melting temperature. The results of the estimated melting temperature are shown in Table II.1 (as Tm). The temperature intervals for our ultrasonic measurements are ~100 K, so the uncertainties in the estimated melting temperatures should be at least

~50 K. The melting temperatures estimated from the ultrasonic signals can then be compared with the melting curves of diopside determined by Williams and Kennedy (1969) and Gasparik (1996), respectively, to estimate the pressures of the experiments. The estimated pressures using the above two different melting curves are generally in

30 agreement with each other (Table II.1), and are also within the uncertainties of the pressures estimated by the X-ray diffraction of the MgO pressure standard in our cell assembly

(Supplementary Figure II.8).

(a) Glass

Backing plate Solid

Liquid

Buffer rod (b)

9000 Crystal 8000 Glass

7000 Backing plate PM ) 6000

(

i 5000

)

v V Liquid

Buffer rod

e 4000

(

i 3000

t 2000

1000

0 0 500 1000 1500 2000 2500 Temperature (K)

Quenched glass (c)

Time (s) Remaining solid

Sound velocity and EOS of diopside liquid

The sound velocities obtained are shown in Table II.1 and Figure II.4. The uncertainties in the measured sound velocities are less than ~1%, coming mostly from uncertainties in sample length measurements as discussed above. The contamination of the liquid sample by molybdenum at high temperatures was minor as shown in Supplementary

Table II.3, so its effect on the sound velocities is negligible. It is also important to make

31 sure that the measured sound velocities for the silicate liquid are fully relaxed (e.g., Rivers

& Carmichael, 1987), so that they can be directly compared with seismic wave velocities.

As shown in Figure II.4a, there is no significant frequency dependence from 20 to 60 MHz of the measured liquid sound velocities and the S-wave signals were not observed for the liquid (Supplementary Figure II.10), indicating that the sound velocities are fully relaxed.

Our sound velocity results are consistent with the ambient-pressure ultrasonic measurements (Ai and Lange, 2008) and show a monotonic increase with pressure from

~3083 m/s at 0.3 GPa to ~4148 m/s at 3.8 GPa (Figure II.4b). Velocity data determined at different temperatures but at the same pressures of either 2.5 GPa or 3.8 GPa (Table II.1) show essentially no temperature dependence within the uncertainties of our experiments.

Using these data, the temperature dependence is estimated to be -0.13 ± 0.52 m s-1 K-1.

Ambient-pressure ultrasonic measurements on silicate liquids (Rivers and Carmichael,

1987) showed that the temperature dependence of sound velocity of silicate liquids in the fully relaxed region is generally small (e.g., ~ -0.09 m s-1 K-1 for basalt liquid). Also, ambient-pressure sound velocity measurements on diopside liquid by Ai and Lange (2008) showed a velocity decrease of about 50 m s-1 over a 188 K temperature range from 1699 K to 1887 K (or ~ -0.27 m s-1 K-1). It is possible that there is a very weak but nonzero temperature dependence of sound velocity at high pressures similar to that at ambient- pressure, but the temperature range of our experiments was too small to resolve such a small effect. Given the 1% uncertainty in velocity measurements, a temperature dependence with an absolute value less than ~0.4 m s-1 K-1 would not be resolved in our experiments. In addition, results from first principles molecular dynamics simulations

(FPMD) (Sun et al., 2011) show that calculated velocity profiles of diopside liquid at 1773

32 K, 1900 K and 2000 K over the entire mantle pressure range are nearly identical, also implying that there is little temperature effect on the sound velocity of diopside liquid.

Based on the above reasons, we assume that the effect of temperature on the sound velocity of diopside liquid is negligible in the following EOS calculations.

Compared to density data, our sound velocity data can tightly constrain both bulk modulus (K) and its pressure derivative (K’), and hence the EOS of diopside liquid, provided that the ambient-pressure density of the liquid is known. We fit our data using the third-order Birch-Murnaghan EOS along an adiabat (e.g., Birch, 1952). It should be noted that using an adiabatic EOS with our isothermal sound velocity data implicitly includes the result of negligible temperature dependence as discussed above. The Birch-Murnaghan

EOS (BM-EOS) is given as

7 5 2 3퐾푆0 𝜌 3 𝜌 3 3 ′ 𝜌 3 푃 = [( ) − ( ) ] {1 + (퐾푆 − 4) [( ) − 1]} (1) 2 𝜌0 𝜌0 4 𝜌0

′ where 퐾푆0 is the ambient-pressure adiabatic bulk modulus, 퐾푆 is the pressure derivative of the adiabatic bulk modulus, 𝜌 is density at high pressures and 𝜌0 is the ambient-pressure density. Based on the Eulerian finite strain theory, the high-pressure bulk modulus is given as (Anderson, 1995)

5 2 2 𝜌 3 1 𝜌 3 ′ 27 ′ 𝜌 3 퐾푆 = 퐾푆0 ( ) {1 + (1 − ( ) ) [5 − 3퐾푆 − (4 − 퐾푆) (1 − ( ) )]}. (2) 𝜌0 2 𝜌0 4 𝜌0

The sound velocity (c) at high pressures is related to the adiabatic bulk modulus (퐾푆) and density () via

푐 = √퐾푆/𝜌 . (3)

The ambient-pressure density (0) of diopside liquid at a temperature of T is given as

𝜌0 = 𝜌0,푇푟푒푓 exp[−훼0(푇 − 푇푟푒푓)], (4)

33 where 푇푟푒푓 is the reference temperature and is chosen to be 1673 K. The density of diopside liquid at 1673 K (𝜌0,1673퐾 ) and the thermal expansion coefficient at ambient pressure (훼0) have been determined by Lange (1997) to be 2.643 g cm-3 and 8.58  10-5 K-1, respectively, and are used as fixed parameters in this study.

A Monte-Carlo approach, which can help better estimate the fitting uncertainties (e.g.,

′ Bevington & Robinson, 2002), was used to find the best fit values of 퐾푆0 and 퐾푆. A million sets of random number pairs were generated as initial guesses in the parameter space of

′ 18-30 GPa for 퐾푆0 and 2 to 10 for 퐾푆, respectively. For a given set of randomly generated

′ ′ ′ 퐾푆0 and 퐾푆 , we calculated density 𝜌푖(𝜌0, 퐾푆0, 퐾푆) and bulk modulus 퐾푆푖(𝜌0, 퐾푆0, 퐾푆) at each experimental pressure 푃푖, using Eqs. (1) and (2), respectively. Then, the modeled

푚표푑푒푙 sound velocity 푐푖 was calculated using Eq. (3). The same calculations are repeated for

2 ′ each experimental condition, and then the  for a certain set of 퐾푆0 and 퐾푆 was calculated as

2 (푐푑푎푡푎−푐푚표푑푒푙) 2 ∑ 푖 푖 휒 = 푖 푐 2 (5) (𝜎푖 )

푑푎푡푎 푐 where 푐푖 is the measured sound velocity for experiment i and 𝜎푖 is the total uncertainty in the sound velocity, which is the sum of the uncertainty in the sound velocity measurements and the propagated equivalent uncertainty in sound velocity due to the uncertainty in pressure determination. The 2 calculations were performed for all of the

′ ′ one million randomly generated pairs of 퐾푆0 and 퐾푆. The best-fit value for 퐾푆0 and 퐾푆 can be found as the pair that produces the minimum 2.

The fitting results are shown in Figure II.4 and Table II.2. Our best fit values for the

′ adiabatic bulk modulus (퐾푆0) and its pressure derivative (퐾푆) are 23.8 ± 0.4 GPa and 7.5 ±

34 0.5 (1), respectively, with a reduced 2 = 0.92. The values obtained are generally consistent with the results from previous studies using different techniques (Table II.2). It can be seen from Figure II.4c that there is a negative correlation between the fitted bulk modulus (K) and its pressure derivative (K’). If only density data were used, it would be difficult to constrain both K and K’ due to the limited number of data points when using the sink-float method for density measurements or limited pressure range when using the

X-ray absorption method. A large family of K and K’ pairs could recover the experimental data (e.g., Agee & Walker, 1993) equally well, but this would mean large uncertainties in the fitting parameters (e.g., Seifert et al., 2013) and large uncertainties in extrapolations of the EOS. Unlike density data, sound velocity at high pressures provides direct information on bulk modulus and its pressure dependence, thereby uniquely constraining both K and K’ within relatively small uncertainties, as shown in this study (Figure II.4c). The calculated density profile for diopside liquid using our fitting results are shown in Figure II.5b. The density calculated at higher pressures beyond the pressure range of our experiments is consistent with previous shock wave data at similar temperatures (Asimow and Ahrens,

2010), indicating that the EOS for diopside liquid obtained from sound velocity measurements can be extrapolated to pressures at least to the bottom of the upper mantle.

Table II.2 Fitting results and comparison with previous studies

K K’ This study 23.8 (0.4) 7.5 (0.5) Ai and Lange (2008) 22.5# 6.8# Rigden et al. (1989) 22.4 6.9 Asimow and Ahrens (2010) 24.57 6.98 Sun et al. (2011)* 20.1 (3) 6.04 (11) Matsui (1996)* 20 (2)# 6.1 (9)# * MD simulations. # isothermal bulk modulus and its pressure derivative. 1773 K for Ai and Lange (2008) and 1900 K for Matsui (1996).

35 (a) 4300

3.74 GPa 4200

4100

)

s 3.26 GPa / 4000

(

e 3900

3800 2.47 GPa 3700

3600 20 25 30 35 40 45 50 55 60 Frequency (MHz) (b) 9000

8000

7000

)

s / 6000

(

e 5000

4000

This study high pressure 3000 Ai and Lange (2008) room pressure EOS fitting Di glass from Sakamaki et al. (2014) Di solid from Li and Neuville (2010) 2000 0123456789 Pressure (GPa) (c) 9

8.5

' 7.5

6.5

6 22 22.5 23 23.5 24 24.5 25 25.5 26 K (GPa)

36 glass and crystal. (c) The correlation between fitted K and K’. The ellipse defines the uncertainties in the fitting parameters.

Discussion

Adiabatic temperature profile and stability of diopside liquid in the upper mantle

The EOS obtained from sound velocity measurements allows us to evaluate gravitational stability of diopside liquid in the upper mantle. Because thermal expansion coefficients of solids and liquids are different, it is necessary to compare density profiles at similar temperatures (e.g., Asimow & Ahrens, 2010). We first estimate density profile of diopside liquid using our EOS, noting that this profile is along an adiabat for diopside liquid, which may be different from the mantle adiabat or solid adiabat. Such adiabatic temperatures of silicate liquids are of crucial importance in modeling the solidification of the early magma oceans (e.g., Monteux et al., 2016; Stixrude et al., 2009), since the slope difference between the melting curve and the liquid adiabat determines the depth at which the crystallization is initiated.

The adiabatic temperature gradient is related to the adiabatic Anderson-Gruneisen parameter, which is given as (Stacey, 2005)

훿푆 ≡ (휕푙푛(훼푇/퐶푃)/휕 ln 푉)푆 = −(휕 ln 퐾푠/휕푇)푃/훼 = 1 − 2(휕푙푛푐/휕푇)푃/훼 (6) where T is the absolute temperature,  is the thermal expansion coefficient, Ks is the adiabatic bulk modulus and c is the sound velocity. Assuming that temperature dependence of sound velocity for diopside liquid is negligible as discussed above, 훿푆 should be close to ~1. In a convecting liquid layer, the adiabatic temperature gradient can be calculated by integrating equation (6) (e.g., Jing et al., 2014), yielding

훿푆+1 (휕푇) = 훼푇 = ( 훼0푇0 ) (𝜌0) (7) 휕푃 푆 𝜌퐶푃 𝜌0퐶푃0 𝜌

37 where 훼0 is the thermal expansion coefficient at ambient pressure and its value is ~8.58 

-5 -1 10 K (Lange, 1997), 퐶푃 is the isobaric heat capacity and its ambient-pressure value for

-1 -1 diopside liquid is ~1613 J K kg (Lange & Navrotsky, 1992; Thomas et al., 2012), 푇0 is the potential temperature and is set to 1610 K which is the estimated mantle potential temperature (Katsura et al., 2010), and  is the density which can be calculated using our

EOS. The estimated average adiabatic temperature gradient for diopside liquid using Eq.

(7) is ~23 K GPa-1, a little higher than the adiabatic temperature gradient in the upper mantle (~16 K GPa-1) as estimated by Katsura et al. (2010). The adiabatic temperature profile for diopside liquid can then be obtained by integrating Eq. (7). Figure II.5a shows the calculated adiabatic temperature profile for diopside liquid and its comparison with the melting curve of diopside (Gasparik, 1996; Williams & Kennedy, 1969). The slope of the melting curve is significantly larger than that of the liquid adiabat, implying that a magma ocean with diopside composition extending into the upper mantle (e.g., Hofmeister, 1983) would crystallize from the bottom and proceed upwards. As the solid is denser than the liquid in the upper mantle (Figure II.5b discussed below), this bottom-up crystallization could cause stratification in the upper mantle in the early Earth (e.g., Ohtani, 1985).

The calculated density profiles for both diopside liquid and solid along the same

(liquid) adiabat are shown in Figure II.5b. Due to the higher compressibility of the liquid, there could be a density crossover between diopside solid and liquid at ~20 GPa if extrapolating the profiles to higher pressures, consistent with previous study by Ai and

Lange (2008) who estimated a density inversion between diopside solid and liquid at ~17

GPa and 1900 K. However, solid diopside breaks down to garnet and CaSiO3 perovskite at a pressure (~16-17 GPa (Gasparik, 1996)) lower than this crossover pressure. Therefore, it

38 is unlikely for pure diopside liquid to become denser than the solid upper mantle based on our EOS, and diopside liquid would thus migrate upwards if generated in the upper mantle.

However, it should be noted that in the real Earth, the compositions of magmatic liquids are more complex and generally differ from those of coexisting crystalline phases, and the heaviest major element Fe in silicates prefers to partition into melts (Mibe et al., 2006), as a result, silicate melts could become denser than surrounding mantle minerals at the bottom of the upper mantle (e.g., Agee & Walker, 1993; Stolper et al., 1981).

(a) 2600 (b) 4 Adiabat Melting curve (Gasparik, 1996) Melting curve (Williams and Kennedy, 1969) 2400 3.5

2200 3

)

(

m e 2000

(

a 2.5

1800 n

T 2 1600 PREM Di liquid this study Di solid Li and Neuville (2010) 1.5 Di liquid room pressure 1400 Lange (1997) Di liquid shock wave Asimow and Ahrens (2010) 1200 1 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 Pressure (GPa) Pressure (GPa)

Figure II.5 (a) Calculated adiabatic temperature profile (potential temperature 1610 K) for diopside liquid and its comparison with the melting curve of diopside. (b) Calculated density profiles for diopside liquid (EOS parameters from this study) and solid (EOS parameters from Li & Neuville (2010) and thermal expansion coefficient from Finger & Ohashi (1976)) along the adiabat in (a). The density profile from PREM (Dziewonski & Anderson, 1981) is shown for reference. The shock temperatures of the shock wave points at high pressures estimated by Rigden et al. (1989) are close to the adiabatic temperatures.

Sound velocity and compressibility of diopside liquid versus diopside glass

Our data show no obvious abnormal pressure dependence (i.e., negative dependence or a change of slope in the velocity-pressure curve) of sound velocity for diopside liquid up to ~4 GPa (Figure II.4b), consistent with the prediction based on FPMD simulation results (Sun et al., 2011), but contradictory to previous studies on various silicate glasses where both 푉푃 and 푉푆 exhibit a change in slope at a pressure of a few GPa (Clark et al.,

2016; Liu & Lin, 2014; Sakamaki et al., 2014; Sanchez-Valle & Bass, 2010; Zha et al.,

39 1994). Figure II.6a shows the density vs. 푉푃 for diopside liquid, glass and crystal as well as other depolymerized silicate glasses from experimental measurements. Clearly, high pressure glasses and liquid exhibit different velocity-density relationships than that for the diopside crystal (Figure II.6a). For diopside glass, the pressure or density dependence of

푉푃 is very weak, with the velocity increasing slightly up to ~4 GPa and then remaining nearly constant to ~8 GPa (Sakamaki et al., 2014). MgSiO3 and basalt glasses also have a weak or even negative pressure or density dependence of the sound velocity up to a few

GPa (Figure II.6a), with different studies showing some inconsistencies in the pressure range of this anomalous behavior. Some of the inconsistencies may be attributable to the different pressure media used in the experiments (Clark et al., 2016). For diopside liquid, the velocity increases smoothly with pressure and density, and the 푉푃 - trend is nearly subparallel to the slope for diopside solid (Figure II.6a). FPMD simulations on MgSiO3 liquid (Stixrude et al., 2009) also show that the acoustic velocities increase monotonically with pressures in the deep mantle with no visible anomaly, in contrast to the anomalous acoustic behavior reported in MgSiO3 glass by Brillouin scattering (Liu and Lin, 2014;

Sanchez-Valle and Bass, 2010). Another important difference in acoustic properties between liquids and glasses is that shear waves can propagate through glasses (Clark et al.,

2016; Liu and Lin, 2014; Sakamaki et al., 2014) but not through liquids (Supplementary

Figure II.10).

Thermodynamically, the discrepancy in acoustic properties between silicate liquids and glasses may be explained by the difference in their compression mechanisms. For silicate liquids, it has been suggested that the configurational or entropic contribution to compression plays an important role in addition to the vibrational or energetic contribution

40 (Jing and Karato, 2011; Richet and Neuville, 1992). This entropic contribution is due to the fact that the atoms in a liquid are free to change their geometrical configurations as long as they do not overlap or get too close to each other. Using a model based on hard sphere mixtures, Jing and Karato (2011) showed that the entropic contribution could quantitatively explain the much higher compressibility of silicate liquids than that of silicate glasses and crystals. Glasses, on the other hand, can be considered as a frozen liquid that has only one fixed configurational state. At the frequencies in Brillouin scattering measurements (a few GHz) or ultrasonic measurements (a few to tens of MHz), the timescales of the experiments are much shorter than the relaxation time of glasses as the viscosity of glasses are orders of magnitude higher than that of liquids. As a result, the measured acoustic properties on glasses are unrelaxed (e.g., Rivers & Carmichael, 1987) and only reflect the vibrational contribution of a particular frozen configurational state which depends on the thermal history of the glass (Askarpour & Manghnani, 1993; Ghosh

& Karki, 2018; Stebbins, 2016). As seen in Figure II.6b, the relative difference between the compressibility of diopside liquid and those of diopside glass and solid decreases with increasing pressure, suggesting the less important role of the entropic contribution relative to energetic contribution at higher pressures. However, it should be noted again that for a relaxed liquid, there is no shear velocity and shear modulus (Supplementary Figure II.10) even at very high pressure, but glasses always have shear properties (e.g., Sanchez-Valle

& Bass, 2010). Meanwhile, simulations results have shown that compression of a room- pressure quenched glass and a glass quenched in-situ at high pressure behaves very differently in the elastic behaviors (Ghosh et al., 2014; Ghosh & Karki, 2018), suggesting the kinetic effects for glass at low temperatures are prominent. Consequently, despite

41 sharing some similar structural features with silicate liquids, silicate glasses may not be a good analog material to study the acoustic and elastic properties of the corresponding liquids, especially at relatively low pressures such as upper mantle pressures, as the unrelaxed glasses cannot capture the entropic contributions which are very important to liquids.

(a) 9000 (b)0.045 Di liquid Di glass 0.04 Di solid 8000 Di solid

0.035

)

En glass 1

) 7000 -

/ Di glass a

P 0.03

(

Basalt glass t

i l 6000 0.025

w 0.02

o P 5000

C 0.015

4000 Di liquid 0.01

3000 0.005 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 0123456789 Density (g/cm3) Pressure (GPa)

Figure II.6 (a) P-wave velocity and density systematics for Di liquid (blue curve this study), Di glass (red square, from Sakamaki et al., 2014), Di solid (green triangle, from Li & Neuville, 2010), basalt glass (star, black from Clark et al., 2016 and gray from Liu & Lin, 2014) and En glass (diamond, orange from Sanchez- Valle & Bass, 2010 and magenta from Liu & Lin, 2014). The dashed line corresponds to the Birch’s law. (b) Compressibility variation with pressure for Di liquid (this study), glass (Sakamaki et al., 2014) and solid (Li & Neuville, 2010).

Velocity reduction in the mantle due to the presence of melts

Based on the observations that silicate glasses have a weak pressure or density dependence of acoustic velocities up to the upper mantle pressures, previous studies (e.g.,

Clark et al., 2016; Liu & Lin, 2014) suggest that the melt fraction needed for a given velocity reduction in the crust and mantle may be significantly overestimated. But as demonstrated by our results, silicate liquids have much lower sound velocities than glasses do and do not exhibit any abnormal pressure dependence of velocity similar to that of glasses. In order to better evaluate the effect of partial melts on velocity reductions in the

Earth’s upper mantle, our sound velocities measured directly on diopside liquid are used

42 here to calculate the aggregate velocity of a simplified partial melt (PREM + various fractions of diopside liquid, where PREM is used to represent the solid mantle). Although melt geometry can also affect acoustic properties of the partially molten mantle assemblage

(e.g., Faul et al., 2004; Hammond & Humphreys, 2000), our main focus currently is on the effect of melt fraction, so a simple additive model (the Voigt limit) which was also used in

Clark et al. (2016) is employed here to calculate the aggregate velocity as a function of pressure and melt fraction for the partial melt. Although the exact melt fraction needed for a given velocity reduction cannot be determined by this simple additive model as it depends on realistic melt geometries and can be different when using different methods or model parameters, the simple model can still provide instructive information on the relative effect of pressure and melt fraction on the velocity reductions.

Figure II.7 shows the calculated velocity reductions relative to PREM as a function of pressure and melt fraction using our measured sound velocities for diopside liquid (solid curve) and melt velocities modeled from results on cold-compressed basalt glass (Clark et al., 2016) (dashed curve). Our results show that the degree of velocity reduction increases significantly with the fraction of melt present in the mantle, while it decreases with pressure meaning that more melts are needed at higher pressures in order to reduce the velocity by a few percent. If this is true, velocity anomalies in deep parts of the mantle requires a higher melt fraction than those at shallower depths. In contrast, the velocity reduction calculated from basalt glass show little variation with pressures, thereby underestimating the melt fraction needed to account for the same degree of velocity reduction, especially at higher pressures. More high-pressure and high-temperature sound velocity data measured directly on silicate/basaltic liquids are needed to better resolve the differences between liquids and

43 glasses and understand the role of silicate melts relevant to the low velocity regions in the mantle.

3.5

) 5% melt % 3

(

P 2.5

i t 2

o 2% melt

t 1.5

p 1

V 1% melt

0.5

0 2 4 6 8 10 12 Pressure (GPa)

Figure II.7 P-wave velocity reductions as a function of pressure and melt fraction. Solid curve – calculated based on the sound velocity of diopside liquid at high P-T measured in this study, dashed curve – calculated from the model in Clark et al. (2016) based on the sound velocity of cold-compressed basalt glass.

Conclusions

1. The sound velocities of diopside liquid increase smoothly with pressure and the effect of temperature on the sound velocity is negligible within the uncertainty of our experimental measurements. Fitting our data to the adiabatic Birch-Murnaghan EOS gives

′ the adiabatic bulk modulus 퐾푆 of 23.8 ± 0.4 GPa and its pressure derivative 퐾푆 of 7.5 ± 0.5.

Although there is a correlation between K and K’, our results show that sound velocities measured at high pressures can tightly constrain both the K and K’.

44 2. The calculated adiabatic temperature gradient in a diopside liquid layer is lower than the slope of its melting curve, so a magma ocean of diopside composition extending into the upper mantle would be crystallized from the bottom. The calculated density profile shows that diopside liquid may not become denser than surrounding mantle materials under upper mantle conditions.

3. In contrast to the anomalous acoustic behavior in diopside glass and other silicate glasses, the diopside liquid shows no abnormal behavior in the pressure dependence of the sound velocities. We conclude that silicate glasses may not be a good analog material to study the acoustic and elastic properties of silicate liquids, especially at relatively low pressures such as in the Earth’s upper mantle, as the entropic contribution important to liquids may not be fully captured by measurements on unrelaxed glasses.

4. The modeled velocity reduction in the mantle using the data on diopside liquid increases with melt fraction and decreases with pressure. If using silicate glass data to model melt acoustic properties, the melt fraction needed to satisfy a given velocity reduction could be significantly underestimated. More high P-T experimental data on sound velocity of silicate liquids are needed to further understand the low velocity regions in the mantle as well as the differences between silicate liquids and glasses.

Acknowledgements

All the data for this paper are reported in Table II.1 and are available upon request from Man Xu at [email protected]. We thank two anonymous reviewers, editor Douglas

Schmitt and one anonymous associate editor for their constructive comments which helped improve the manuscript substantially. This research was supported by the National Science

Foundation (EAR-1619964) to ZJ and YW. The ultrasonic measurements were performed

45 at GSECARS beamline 13-ID-D, Advanced Photon Source (APS), Argonne National

Laboratory. GSECARS is supported by the National Science Foundation - Earth Sciences

(EAR-1634415) and Department of Energy - GeoSciences (DE-FG02-94ER14466). This research used resources of the Advanced Photon Source, a U.S. Department of Energy

(DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne

National Laboratory under Contract No. DE-AC02-06CH11357. We thank James A. Van

Orman for access to his piston-cylinder and multi-anvil devices at Case Western Reserve

University (CWRU) and for his help on Monte-Carlo analysis. We also thank Nanthawan

Avishai for her assistance on the SEM analysis of the quenched samples at the Swagelok

Center for Surface Analysis of Materials (SCSAM) of CWRU.

Supplementary Materials

Chemical compositions of the experimental products, additional information on the pressure comparison using different methods, the thermal gradient calibration results and typical S-wave signals are provided here.

4.5

)

G 3.5

(

c 3

e 2.5

d 2

s 1.5

s 1

P 0.5

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Pressure estimated by extrapolating from lower temperatures (GPa)

46 estimated from the melting curve of diopside (Williams & Kennedy, 1969 (blue); Gasparik, 1996 (red)) where the melting temperature of diopside can be deduced from the ultrasonic signals.

Supplementary Figure II.9 Thermal gradient calibration of the ultrasonic cell assembly. The experiment was carried out at ~2 GPa and 2173 K for 0.5 h in a Walker-type multi-anvil press at Case Western Reserve University (CWRU). The cell used in the calibration experiment is identical to that used in the ultrasonic measurements except that the sample was replaced by a MgO disk sandwiched by two Al2O3 disks and pressure marker was replaced by pure MgO, respectively. MgO will react with Al2O3 at high temperatures and form a well-defined spinel layer whose thickness is a function of pressure, temperature and reaction time (Van Westrenen et al., 2003). Therefore, knowing the pressure and experimental run duration, the temperature at any location where spinel layer forms can be estimated. (a) The calculated temperature profile

47 based on spinel layer thickness (Van Westrenen et al., 2003). (b) The cell assembly for the calibration experiment. (c) SEM mapping of the spinel layers.

48 is fully molten, the S-wave signal for the sample disappears completely, consistent with the fact that S-wave cannot propagate through liquids. (BR-buffer rod, BP-backing plate).

Supplementary Table II.3 Compositions of the quenched liquid samples from the experiments measured by EDS (recalculated as oxides wt%).

T2019 T2023 T2027

SiO2 53.7 53.4 55.3 MgO 18.9 20.5 19.4 CaO 25.9 26.0 25.4

MoO2 1.5 0 0

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59 Chapter III

Distinct acoustic behaviors between cold and heated diopside glass at

high pressures revealed by in-situ ultrasonic measurements

(In preparation for submission)

Abstract

Sound velocities of a diopside glass were measured up to 5.3 GPa and 1006 K along different P-T paths including compression at room temperature (cold compression), heating at constant loads (high P-T), and cold compression after experiencing one and two heating cycles (cold compression after heating), using a synchrotron-based ultrasonic technique in a multi-anvil apparatus. The experimental results show that the high-pressure heated glass displays distinct acoustic behaviors with the glass in the cold compression, with the heated glass having higher acoustic velocities than the cold-compressed glass at similar pressures, and the velocities of the heated glass exhibit smooth increase with pressure in contrast with the weak pressure dependence of velocities observed in the cold- compressed glass. We show that these distinct acoustic behaviors between cold and heated glass at high pressures may arise from their different pressure responses of the intermediate-range order. For the heated glass, its intermediate-range structure is thermally relaxed to a denser and more homogeneous one, whereas the cold-compressed glass has a more heterogeneous intermediate-range order with different regions responding differently to compression. The cold-compressed glass after experiencing the heating cycles also shows higher velocities than the initial cold-compressed glass, indicating the kinetic effect in the glass is likely to be prominent. Our results point out the importance of temperature during compression in order to fundamentally understand the behaviors of silicate glasses.

60 By comparing with diopside liquid, we show that both the high-pressure heated and cold- compressed glass cannot fully capture the configurational contributions to compression which are important in liquids, but the heated glass can better mimic the pressure dependence of sound velocities in the liquid than the cold-compressed glass. If using the abnormal acoustic behavior observed in the cold-compressed glass to model the melt fractions in the mantle low-velocity regions, the melt fractions needed to explain a given velocity reduction can be significantly underestimated at high pressures.

Introduction

Seismically detected low-velocity regions in the interior of the Earth are commonly interpreted to suggest the presence of silicate melts in the mantle (e.g., Anderson and

Spetzler 1970; Williams and Garnero 1996; Kawakatsu et al. 2009; Hirschmann 2010;

Schmerr 2012; Naif et al. 2013; Stern et al. 2015; Chantel et al. 2016). These deep-seated partial melts may have played a very important role in controlling the chemical differentiation and heat transfer in the deep Earth. Depending on the density contrast between silicate melts and the ambient mantle, the melts can either migrate upwards or sink into the deep interior (Agee, 1998; Sanloup, 2016; Stolper et al., 1981), resulting in quite different geodynamical scenarios. The knowledge of the elastic and acoustic properties of silicate liquids are essential in thermodynamic modelling of mantle melting

(e.g., Ghiorso 2004) and better constraining of the melt fractions in the low-velocity regions in the mantle (e.g., Takei 2002; Clark and Lesher 2017).

While the density of silicate liquids can be directly measured at simultaneous high pressure and temperature by static compression such as sink-float (e.g., Agee and Walker

1993; Agee 1998; Matsukage et al. 2005) and X-ray absorption method (e.g., Sakamaki et

61 al. 2010; Seifert et al. 2013; Malfait et al. 2014) as well as by Hugoniot data obtained by shock compression (e.g., Rigden et al. 1989; Asimow and Ahrens 2010; Thomas and

Asimow 2013), measurements of the acoustic velocity and elastic properties at high P-T conditions for silicate liquids are very challenging and limited. Until now, only one study

(Xu et al., 2018) has reported the sound velocity data measured directly on a silicate liquid at simultaneous high pressure and temperature. As an alternative to this limitation, many studies have used the chemically related glasses as analogs for silicate liquids to infer the acoustic and elastic behaviors of melts at high pressures (Clark et al., 2016; Clark and

Lesher, 2017; Liu and Lin, 2014; Malfait et al., 2011; Meister et al., 1980; Murakami and

Bass, 2011; Sakamaki et al., 2014a; Sanchez-Valle and Bass, 2010; Suito et al., 1992; Wu et al., 2014). These studies have revealed that silicate glasses have an anomalous acoustic behavior with weak or negative pressure dependence of sound velocity in a certain pressure range (usually a few GPa), showing a change of slope in the velocity-pressure or velocity- density space. For example, the sound velocity of a basalt glass at high pressures has been determined by Liu and Lin (2014) using Brillouin scattering spectroscopy in a diamond anvil cell and displays decreasing Vp and Vs with velocity minima at about 5 and 2 GPa, respectively. This acoustic softening behavior in glasses has also been used to model the melt velocities in mantle low-velocity zones (Clark and Lesher, 2017). However, a recent ultrasonic study directly on a diopside liquid at high pressures (Xu et al., 2018) shows that diopside liquid velocity increases smoothly with pressure with no obvious anomaly, in sharp contrast with its glass counterpart, suggesting glasses may not be good analogs to study the acoustic and elastic properties of corresponding liquids. We note that most of previous velocity measurements on silicate glasses were carried out by compression at

62 room temperature without any heating, while the effect of temperature on glass velocities has not been well studied.

Previous first-principles molecular dynamics (FPMD) simulations on silicate glasses with different compression paths have demonstrated that cold-compressed glasses (glasses compressed at 300 K) behave quite differently with hot-compressed glasses (glasses quenched in situ from high pressure and high temperature), with the hot compression producing higher density, higher sound velocity and greater coordination numbers than cold compression (Ghosh et al., 2014; Ghosh and Karki, 2018). Meanwhile, the pressure response of sound velocity in the cold-compressed glass is sluggish as opposed to the smooth increase in the hot-compressed one (Ghosh and Karki, 2018), suggesting the hot- compressed glass may be a better analog to study the high-pressure silicate melts. Whether temperature can substantially modify the acoustic behavior in silicate glasses at high pressures and make them better mimic the high-pressure liquids or not has not been experimentally verified. Here we report in-situ ultrasonic measurements on a diopside glass along different P-T paths including compression at room temperature (300 K) (cold compression), heating experiments at constant loads (simultaneously high P-T) and room- temperature compression after experiencing heating cycles (cold compression after heating) to investigate the effect of temperature on glass acoustic and elastic properties. The results were then compared with our previous measurements directly performed on a diopside liquid (Xu et al., 2018) to give insight to the similarities and differences between silicate glasses and liquids.

63 Materials and Methods

Reagent-grade powders of MgO, CaCO3 and SiO2 were mixed in appropriate proportions according to the diopside composition in ethanol for ~2 hrs. The mixtures were then dried and decarbonated at 1173 K in a high-temperature box furnace for ~24 hrs. The full release of CO2 was confirmed by checking the mixture weight before and after decarbonation. Then the decarbonated mixture was fused at 1773 K for ~1 hr, and finally quenched to a glass. The fusion process was repeated twice to ensure homogeneity of the glass. The resulted glass is transparent, bubble-free and homogeneous. A perfect cylindrical glass disk with desired outer diameter was machined from the quenched glass patch by using a CNC-milling machine. The top and bottom surface of the cylindrical glass was polished to 1m with nearly perfect parallelism and was used as the sample for high- pressure ultrasonic measurements.

The high-pressure experiment was performed in a 1000-ton large volume press with a

Kawai-type multi-anvil module (Wang et al., 2009) at the GSECARS beamline 13-ID-D of the Advanced Photon Source, Argonne National Laboratory. The cell assembly used and the experimental details have been described previously in Xu et al. (2018), and are only briefly summarized here. An MgO-MgAl2O4 octahedron with 14 mm edge length was used as the pressure medium. A graphite sleeve inserted into a MgO X-ray window and

ZrO2 thermal insulators was used as the heater. Molybdenum buffer rod (BR) and backing plate (BP) were placed at the bottom and top of the sample, respectively, to generate the impedance contrast with the sample. The sample, BR and BP were separated from the heater by an Al2O3 sleeve. Pressure of the experiment was determined by the energy- dispersive X-ray diffraction of the pressure marker in the cell assembly consisting of a

64 mixture of MgO and h-BN (MgO:BN = 4:1 by weight) using the high temperature equation of state (EOS) of MgO (Tange et al., 2009). The uncertainty in the determined pressures mainly comes from the uncertainty of the EOS of MgO and is estimated to be less than

0.5%. The temperature was monitored by a W5Re-W26Re thermocouple, and is accurate to ±10 K. The temperature gradient in the ultrasonic cell assembly has been previously calibrated by Xu et al. (2018). All the temperatures reported in this study have been corrected for the thermal gradient.

For the ultrasonic measurements, a 10° Y-cut LiNbO3 piezoelectric transducer with a resonant frequency of 50 MHz for P-waves and 30 MHz for S-waves was attached to the back of the bottom tungsten carbide anvil. An arbitrary waveform generator was used to generate electrical signals of sine waves in the frequency range of 20-60 MHz. The electrical signals were then converted to P and S elastic waves by the transducer. The converted elastic waves then traveled through the bottom anvil and the cell assembly and were reflected back at the anvil-buffer rod (BR), BR-sample, and sample-backing plate

(BP) interfaces. The reflected elastic waves were received by the same transducer which converts them back to electrical signals that were recorded by a digital oscilloscope at a sampling rate of 5  109 sample/s. The two-way travel time through the sample was determined by the pulse-overlap method (Jing et al., 2014; Kono et al., 2012) using the reflected signals from BR-sample and sample-BP interfaces. Uncertainty in the travel time is within ±0.2 ns, corresponding to a relative uncertainty of about 0.1%. The sample length was determined from radiographic imaging by plotting the derivative of the image gray value versus pixel distances. Uncertainty of the sample length is within ±1.775 m (±1 pixel), translating to a relative uncertainty of less than 0.5%. The sound velocity was then

65 calculated from the travel time and sample length, with a total uncertainty less than ~0.6%.

An example of the sample image and ultrasonic signals for P and S waves at 2.0 GPa and

823 K is shown in Figure III.1.

Figure III.1 An example of the (a) X-ray radiographic image, (b) P-wave and S-wave ultrasonic signals for diopside glass at 2.0 GPa and 823 K. Mo-molybdenum, BR-buffer rod, BP-backing plate, EN-electric noise, S-sample. The experimental P-T paths are shown in Figure III.2. The P-T paths contain room- temperature cold compression (initial cold-compressed glass), heating and cooling at fixed loads (heated glass at simultaneously high P-T) and cold compression after heating cycles

66 (cold-compressed glass after experiencing heating cycles) in the same experimental run.

The sample was first compressed at 300 K (room temperature) to a hydraulic ram load of

100 tons, corresponding to a pressure of 3.4 GPa, with ultrasonic measurements taken in a step of every 25 tons (open circles in Figure III.2). At 100 tons, a heating cycle was performed. The temperature was first increased at a rate of 100 K/min to the highest target temperature 1006 K which is just below the glass transition temperature for diopside glass

(~1013 K at ambient pressure (Lange, 1997) and estimated to be ~1200 K at around 2 GPa

(Xu et al., 2018). Then we measured the sound velocities with decreasing temperature at every ~200 K. The data were collected along cooling rather than heating is because: (1) increasing to high temperature first can help release the deviatoric stress accumulated along cold compression and provide better hydrostatic conditions (Liu et al., 2009); (2) the glass in cooling process also somewhat mimics the glass quenched in-situ at high pressure and high temperature used in the FPMD simulations (e.g., Ghosh et al. 2014), although the cooling rate is much slower than the quench rate. After the first heating cycle, we performed another cold compression from 100 tons to 150 tons, with ultrasonic measurements taken at 300 K, 125 tons and 150 tons (stars in Figure III.2). Then, a second heating cycle was performed at 150 tons with the same procedure as the first heating cycle.

A third heating cycle was performed at 200 tons following the cold compression from 150 tons to 200 tons (crosses in Figure III.2). Totally, three compression-heating cycles were carried out, corresponding to a pressure range from 0.4 to 5.3 GPa and temperature range from 300 to 1006 K.

Figure III.2 Pressure-temperature paths of the experiment. Solid square: measurements along the cooling, open circle: initial cold compression, star: cold compression after one heating cycle, cross: cold compression after two heating cycles.

Results

The experimental conditions and measured sound velocities are shown in Table 1. The

P- and S-wave velocity as a function of pressure for both the cold-compressed and heated glass together with the cold compression data for diopside glass from Sakamaki et al.

(2014a) are shown in Figure III.3. The data obtained in the initial cold compression in this study (open circles) are consistent with the cold compression data from Sakamaki et al.

(2014a) (open diamonds) in which the diopside glass was compressed continuously to 8.4

GPa at room temperature without any heating. It can be clearly seen from Figure III.3 that the heated glass demonstrates very different acoustic behaviors with the cold compressed one. Firstly, for both P and S wave velocities (Vp and Vs, respectively), data collected during the heating cycles (open squares) and after the heating cycles (stars and crosses) are higher than those collected along cold compression without experiencing any heating cycles. At same pressures, the Vp and Vs measured at 300 K cooled from high temperatures

68 are about 5% and 7% higher than those measured at 300 K without experiencing heating.

Secondly, the cold-compressed glass after experiencing one heating cycle (stars) displays higher Vp and Vs than the initial cold-compressed glass (open circles) but still lower than the heated glass cooled from high temperatures (blue open squares). While the velocities of the cold-compressed glass experiencing two heating cycles (crosses) are higher than those of cold-compressed glass experiencing one heating cycle (stars) and approach the values of the heated glass at 300 K (blue open squares). These observations indicate that a heating cycle can greatly increase the sound velocities of the cold-compressed glass and this high velocity feature can be partly retained during subsequent cold compression. In addition, the pressure dependences of the sound velocities are also quite different between the cold-compressed glass and the heated glass. For cold compression without experiencing heating, the Vp initially increases from ambient pressure to ~4 GPa and then remains nearly constant up to ~8 GPa, and the Vs generally decreases with pressure up to ~8 GPa with some small increases around 2-3 GPa. In contrast, the Vp and Vs of the heated glass increase smoothly with pressure, and the pressure dependence of Vp is much stronger than that of

Vs, similar to its crystalline solid counterpart (Li and Neuville, 2010). Basically, the acoustic behavior of the heated glass is more similar to normal solid materials with the acoustic velocities increasing with pressure and decreasing with temperature. For cold- compressed glass experiencing one and two heating cycles, it is not possible to make a definite statement about the velocity pressure dependences since there are only two data points for each path, but a close observation of Figure III.3 implies that experiencing more heating cycles in cold-compressed glass does not change the pressure dependence of the velocities significantly, but it changes the velocities to higher values.

69 All the above observations indicate that temperature can substantially modify the acoustic behaviors of silicate glass and the glass velocity strongly depends on its thermal history. Therefore, the anomalous acoustic behaviors found in previous cold-compressed silicate glasses (e.g., Sanchez-Valle and Bass 2010; Liu and Lin 2014; Clark et al. 2016) may not be directly applied to liquids without knowing the effect of temperatures as the glass itself is rather complex. In order to further investigate the elastic properties of the heated glass, we fit our high-temperature Vp and Vs to a linear model with pressure and temperature considering the limited pressure range of the data:

푐 = 푐 + 휕푐 푃 + 휕푐 (푇 − 300) (1) 0 휕푃 휕푇 where 푐 is the sound velocity, and can be either Vp or Vs, 푐0 is the ambient-pressure sound velocity, 휕푐 is the pressure dependence of the sound velocity, 휕푐 is the temperature 휕푃 휕푇 dependence of sound velocity and P, T are pressures and temperatures, respectively. The

휕푉푝 휕푉푝 fitting results for Vp are 푉 = 6825 ± 31 m/s, = 83.3 ± 8.6 m/s/GPa and = -0.306 ± 푝0 휕푃 휕푇

휕푉푠 휕푉푠 0.044 m/s/K, and for Vs are 푉 = 3849 ± 17 m/s, = 12.5 ± 4.5 m/s/GPa and = -0.318 푠0 휕푃 휕푇

± 0.024 m/s/K. Clearly, Vp has a stronger pressure dependence than Vs but the temperature dependences are about the same in both Vp and Vs. The bulk sound velocity (Vb) of the glass can be calculated from Vp and Vs through

1 푉 = (푉 2 − 4 푉 2)2 (2). 푏 푝 3 푠

The calculated Vb for the glass at different P-T paths are shown in Figure III.3c. Unlike Vp and Vs, the differences of the calculated Vb between heated glass and cold-compressed glass are much smaller and only evident at higher pressures. This is because that although both Vp and Vs are higher in the heated glass than the cold-compressed glass, the difference

70 between Vp and Vs according to Eqn. 2 may not change very much, suggesting that the effect of heating on the changes of Vp and Vs may be roughly similar. At pressures higher than ~4 GPa, the Vb of the heated glass become higher than those of the cold-compressed one.

Table III.1 Experimental conditions and results of sound velocity measurements on diopside glass at different P-T paths

Load P T Vp Vs Vb  Ks Gs Poisson’s (ton) (GPa) (K) (m/s) (m/s) (m/s) (g/cm3) (GPa) (GPa) ratio 25 0.40 300 6532 3662 4978 2.937 72.8 39.4 0.271 50 1.23 300 6705 3636 5228 2.969 81.2 39.3 0.292 75 2.22 300 6749 3585 5331 3.005 85.4 38.6 0.303 100 3.43 300 6765 3596 5340 3.045 86.8 39.4 0.303 100 2.26 1006 6776 3620 5333 2.952 83.9 38.7 0.300 100 2.00 823 6861 3730 5340 2.955 84.3 41.1 0.290 100 1.81 641 6874 3783 5308 2.961 83.4 42.4 0.283 100 1.60 458 6910 3822 5318 2.966 83.9 43.3 0.280 100 1.44 300 6973 3876 5347 2.972 85.0 44.7 0.276 125 2.43 300 6872 3793 5296 3.007 84.3 43.3 0.281 150 3.66 300 6959 3789 5412 3.050 89.3 43.8 0.289 150 3.95 1006 6911 3658 5471 3.010 90.1 40.3 0.305 150 3.69 823 6944 3731 5445 3.013 89.3 41.9 0.297 150 3.48 641 6994 3778 5467 3.018 90.2 43.1 0.294 150 3.32 458 7025 3825 5464 3.025 90.3 44.3 0.289 150 3.11 300 7084 3881 5486 3.030 91.2 45.6 0.286 175 3.93 300 7130 3876 5550 3.059 94.2 46.0 0.290 200 4.80 300 7190 3874 5629 3.087 97.8 46.3 0.295 200 5.32 1006 7081 3702 5645 3.054 97.3 41.9 0.312 200 5.02 823 7142 3769 5662 3.056 98.0 43.4 0.307 200 5.03 641 7124 3814 5600 3.069 96.2 44.6 0.299 200 4.59 458 7129 3838 5584 3.067 95.6 45.2 0.296 200 4.43 300 7205 3898 5626 3.073 97.2 46.7 0.293 Note: Uncertainty in measured velocities is about 0.6%. Uncertainty in pressure and temperature is about 0.5% and 10 K, respectively. Uncertainties in calculated density and moduli are about 1%.

72 Figure III.3 (a) P-wave sound velocity Vp, (b) S-wave sound velocity Vs and (c) bulk sound velocity Vb as a function of pressure. Open circles are data from initial cold compression corresponding to the open circles in Figure III.2, stars and crosses are cold compression data after one and two heating cycles, respectively, open squares are data collected during cooling of the sample, and open diamonds are cold compression data from Sakamaki et al. (2014a). The dashed lines are linear fittings to the data.

The density () of the glass can be calculated from the following equation assuming that all the deformation is elastic (e.g., Sanchez-Valle and Bass 2010; Liu and Lin 2014;

Wu et al. 2014):

휕𝜌 1 1 = 2 2 = 2 (3). 휕푃 푉푝 −4푉푠 ⁄3 푉푏

Integrating Eqn. (3), we can obtain

푃 1 𝜌 − 𝜌0 = ∫ 2 푑푃 (4) 푃0 푉푏

Using the same ambient-pressure density for diopside glass (2.920 g/cm3) from Sakamaki et al. (2014a) and a thermal expansion coefficient of 2.498  10-5 K-1 for diopside glass from Lange (1997), the density of diopside glass at each pressure and temperature can be calculated from the measured sound velocities. The adiabatic bulk modulus (Ks), adiabatic shear modulus (Gs) and adiabatic compressibility 훽푠 can be calculated using the

2 2 2 relationships of 퐾푠 = 𝜌(푉푝 − 4푉푠 ⁄3), 퐺푠 = 𝜌푉푠 and 훽푠 = 1/퐾푠. The Poisson’s ratio can also be directly calculated from the measured sound velocities through

2 2 푉푝 −2푉푠 휈 = 2 2 (5). 2(푉푝 −푉푠 )

The results for the calculated density, bulk modulus, shear modulus and Poisson’s ratio are shown in Figure III.4. For the calculated density, there is nearly no difference between the heated glass and the cold-compressed one, with the density increasing smoothly with pressure and decreasing with temperature. This is probably partly due to the integration method used to calculate the density. The density calculated by Eqn. (4) is only a function of pressure, temperature and the pressure dependence of the bulk sound velocity. Since the

73 pressure dependences of Vb in both heated and cold-compressed glass are not so different as described above (Figure III.3c), the calculated density is similar in both the heated and cold-compressed glass. The smooth increase in density with pressure in contrast with the complicated and anomalous acoustic behavior suggesting a decoupling between these two physical properties in silicate glasses, as previous studies suggested (Clark et al., 2016;

Sanchez-Valle and Bass, 2010; Tkachev et al., 2005; Wu et al., 2014). The Poisson’s ratio for both heated and cold-compressed glass increases with pressure. However, the pressure dependences of Poisson’s ratio are distinct between the cold compressed and thermally treated glasses. For the cold-compressed glass without experiencing heating, the Poisson’s ratio initially increases very rapidly from ambient condition to ~1.5 GPa, and then the pressure derivative of Poisson’s ratio becomes smaller and similar to the trend observed in the heated glass as well as the cold-compressed glass after heating cycles. The Poisson’s ratio for heated glass is generally smaller than the cold-compressed glass without heating at similar pressures, and decreases with decreasing temperature. For the calculated bulk modulus and shear modulus, they mimic the behaviors of Vb and Vs, respectively, as the difference in density is small. Both of these two moduli generally increase with pressure, with the shear modulus showing much larger difference between the heated glass and the cold-compressed glass than bulk modulus.

Figure III.4 Calculated (a) density, (b) Poisson’s ratio, (c) bulk modulus and (d) shear modulus as a function of pressure. The symbols are the same as in Figure III.3.

Discussion

Effect of temperature on glass velocity and compression mechanism

Previous high-temperature and room-pressure Brillouin scattering studies on diopside glass have shown that the velocities (both Vp and Vs) decreases almost linearly with temperature in both glassy state and supercooled liquid state, with a sharp change of the temperature derivative of velocities around the glass transition temperature Tg (Askarpour et al., 1993; Schilling et al., 2003). A comparison between our high-pressure and high- temperature data with those measured previously at room pressure and high temperatures below Tg is shown in Figure III.5. Our results are consistent with the high-temperature

Brillouin scattering studies, showing a decrease of Vp and Vs with temperature at a rate of

75 about -0.31 m/s/K and -0.32 m/s/K for Vp and Vs, respectively, similar to the values (e.g.,

~-0.37 m/s/K and -0.26 m/s/K for Vp and Vs, respectively) obtained by previous studies

(Schilling et al., 2003), indicating that pressure has no effect on the temperature dependence of the glass velocity. This degree of temperature dependence in sound velocities of diopside glass is also similar to that observed in diopside crystal (-0.35 m/s/K and -0.27 m/s/K for Vp and Vs, respectively) (Li and Neuville, 2010). Therefore, in terms of the heated glass, the temperature’s effect on the acoustic behaviors should be similar to those in crystalline solid.

Figure III.5 (a) P-wave sound velocity and (b) S-wave sound velocity as a function of temperature. Colored squares are high P-T data from this study at constant loads corrected to the same pressures using the linear fitting results of Eqn (1), and dashed colored lines are the corresponding fittings. Black squares are the measured room-pressure data on diopside glass from Schilling et al. (2013) and dashed black lines are the linear fitting results on the Di-1 sample measured at room pressure from Askarpour et al. (1993). However, besides the direct effect of temperature on sound velocities through affecting the phonon vibrations in the glass just like in the crystal, temperature must have a significant effect on the compression mechanism or high-pressure structural properties which ultimately control the acoustic and elastic behavior of the thermodynamically metastable glass, as evidenced in the distinct acoustic behaviors between the cold and heated glass shown in Figure III.3. Although no direct relationship has been established between the acoustic velocity and the structure of the glass, the canonical explanation for

76 the observed acoustic anomalies in cold-compressed silicate glasses involves the reduction of the interstitial voids as well as the topological rearrangement of the silicate network such as bending of the Si-O-Si bond, changing of the bonding angles, mutual rotation of the local SiO4 tetrahedra, compaction on the intermediate-range structure and likely decrease of the silicate ring size (Clark et al., 2016; Liu and Lin, 2014; Sakamaki et al., 2014a;

Sanchez-Valle and Bass, 2010; Tkachev et al., 2005; Wu et al., 2014) based on the results on extensively studied silica glass in which the elastic anomalies with pressure are well- known (e.g., Hemley et al. 1986; Meade and Jeanloz 1987; Zha et al. 1994; Huang et al.

2004; Deschamps et al. 2009). The anomalous acoustic behaviors observed in the cold- compressed diopside glass in this study are lost during the heating cycle suggesting that the structural response to pressure of the heated glass at high pressures may be different with the cold-compressed glass. Indeed, a recent study on silica glass (Guerette et al., 2015) using multiple approaches revealed that the intermediate-range order of the silica glass annealed at high pressures and high temperatures below the Tg is different from the cold- compressed one at room temperature. For silica glass, it has been shown that temperature can facilitate its densification and elevate its acoustic velocities compared to the room- temperature compressed silica glass (Guerette et al., 2015; Hofler and Seifert, 1984;

Yokoyama et al., 2010). For example, Yokoyama et al. (2010) measured the elastic wave velocities of silica glass at simultaneous high pressure and high temperature and found that the velocities measured at both high pressure and high temperature are higher than those measured at room-temperature compression, and the resulted density increases with temperature, implying a negative thermal expansion for silica glass at high pressures.

Guerette et al. (2015) using high-pressure quench experiments demonstrate that the

77 densification of silica glass strongly depends on the temperature with the high P-T conditions being much more efficient in increasing the density than just cold compression without heating, and temperature can help eliminate the elastic anomalies observed in silica glass. These distinct behaviors between cold-compressed and high P-T silica glass is also supported by the total structure factor S(q) measured by X-ray diffraction (Guerette et al.,

2015; Inamura et al., 2004). The first sharp diffraction peak (FSDP) position of the structure factor, which is typically interpreted as the intermediate-range order of the network (Elliott, 1991; Sakamaki et al., 2014b), increases with temperature to higher q values in a specific temperature-pressure range (Inamura et al., 2004; Katayama and

Inamura, 2005), indicating the intermediate-range structure of silica glass is thermally relaxed to a denser one. Meanwhile, contrary to the broadening and decrease in intensity of the FSDP in the room-temperature compressed silica glass (Benmore et al., 2010; Sato and Funamori, 2010; Tan and Arndt, 1999), the FSDP of high P-T silica glass narrows and its intensity does not change much with pressure (Guerette et al., 2015; Inamura et al.,

2004), suggesting the intermediate-range structure has been substantially altered with temperature. A similar narrowing and temperature dependence of FSDP for high P-T jadeite glass has also been observed by in-situ X-ray structural measurements (Sakamaki et al., 2014b).

78 2.4

2.35

Slope = 0.019 2.3

2.25

2.2

Slope = 0.008 2.15

2.1 012345678 Pressure (GPa)

Figure III.6 The FSDP position as a function of pressure for cold-compressed diopside glass (open diamond) from Sakamaki et al. (2014a) compared with that of annealed diopside glass recovered from high pressures and 773 K (solid square) from Shimoda et al. (2005). The dashed lines are linear fittings of the data. Figure III.6 shows the FSDP position changes with pressure measured on a cold- compressed diopside glass without heating (Sakamaki et al., 2014a) and a diopside glass recovered from 773 K and high pressures up to 7.5 GPa (Shimoda et al., 2005). The position of FSDP in the cold-compressed glass increases with pressure more than two times faster than that in the high P-T annealed glass, indicating a faster shrink of the intermediate-range order in the cold-compressed glass than in the high-pressure heated one. The shrink of intermediate-range order can result in a more compact structure and thus a higher density.

However, as shown previously in Figure III.4a, the densities of the cold-compressed glass and the high-pressure heated glass are about similar. This suggests that temperature may also have a significant effect on the intermediate-range order of diopside glass, probably

79 similar to those observed in silica and jadeite glass (Inamura et al., 2004; Sakamaki et al.,

2014b) and the structure of high-pressure heated diopside glass is thermally relaxed to an initially denser one which may be different to that in the cold-compressed glass. This thermally relaxed denser intermediate-range structure may be responsible for the higher acoustic velocities observed in the heated diopside glass. In addition, this denser structure may be partially retained during cooling as the cold-compressed glass after the heating cycles has higher velocities than the glass in the initial cold compression. This may also reflect the kinetic behavior of the glass at high temperatures since this thermal relaxation in intermediate-range structure is very likely time-dependent. Kono et al. (2012) observed a shift of acoustic velocities of silica glass to higher values after keeping it at high temperature and high pressure for ~2-3 hrs compared to the values obtained at same pressure and temperature before the annealing, similar to the shifts obtained in our diopside glass after heating cycles, indicating a time-dependent relaxation behavior. It is expected that with sufficient annealing time or equivalently experiencing enough heating cycles, the behavior of the cold compressed glass will finally become the same as the one cooled from high temperatures. This may be the reason that the cold-compressed glass after experiencing two heating cycles (crosses in Figure III.3) have velocities higher than the cold-compressed glass experiencing only one heating cycle (stars in Figure III.3) and approaching the values obtained for high-pressure heated glass (Figure III.3).

The structure factor obtained for the high P-T diopside glass (Figure 1b in Shimoda et al., 2005) also shows narrowing of the FSDP compared with the structure factor of the cold-compressed diopside glass (Figure 4c in Sakamaki et al. 2014a). The full width half maximum (FWHM) of FSDP is believed to relate to atomic density fluctuation in the

80 structure and estimate the range over which the periodicity survives with a correlation length of 2/FWHM (Du and Corrales, 2005; Guerette et al., 2015). The sharpening of

FWHM results in a longer correlation length, meaning the intermediate-range structure is more ordered and homogeneous. On the contrary, the broadening of FWHM observed in the cold-compressed glass indicates the intermediate-range order becomes more heterogeneous (Guerette et al., 2015; Katayama and Inamura, 2005). This different intermediate-range ordering between the high P-T glass and the cold-compressed glass is probably the cause of their different pressure dependences of the sound velocity. The heterogenous intermediate-range order in the cold-compressed glass may allow different regions respond to pressure differently: some regions are likely deformed more than others, thus resulting in larger structural rearrangement locally which is likely responsible for the anomalous pressure dependence of the sound velocities in the cold-compressed glass. In contrast, the denser and more homogenous intermediate-range order in the heated glass will respond to compression more uniformly, hence the sound velocities increase steadily with pressure with no anomalies observed. More direct in-situ measurements on silicate glasses at simultaneous high pressure and high temperature are needed to validate this hypothesis and to map out the complicated pressure-temperature-time dependent behaviors in silicate glasses.

Comparison with diopside liquid

In order to further investigate whether the high P-T glass can better mimic the acoustic behavior of the corresponding liquid than the cold-compressed glass or not as well as to better understand the differences and similarities between glass and liquid, we plot the systematics of Vp vs. density of our glass data from this study and diopside liquid results

81 from a previous study (Xu et al., 2018) together with the diopside crystal data from (Li and

Neuville, 2010) in Figure III.7a. Several observations can be made from Figure III.7a: (1) both the high P-T glass and cold-compressed glass possess much higher P-wave velocities than those of the liquid; (2) the Vp- trend in the high P-T glass is very similar to that in the crystal and close to the linear trend defined by the Birch’s law (Birch, 1961) with only a small offset; (3) the density derivative of Vp in the liquid is similar to that in the crystal and high P-T glass and is nearly subparallel to the Birch’s law but with a very large offset;

(4) cold-compressed glass has a weak density dependence of Vp in contrast with the high

P-T glass, crystal and liquid. The observations (1), (2) and (3) implies that the entropic or configurational contribution to compression must be important for the liquid in addition to the internal energy contribution (vibrational) to compression which is the dominate compression mechanism in the crystal and glass (Jing and Karato, 2011; Richet and

Neuville, 1992; Schilling et al., 2003; Xu et al., 2018). For the vibrational contribution, as the atom vibration is an intrinsic phenomenon of a material, the vibrational contribution to compression is likely to be similar regardless of the material state. This probably is the reason for the similar density derivatives of Vp observed in the crystal, high P-T glass and the liquid in Figure III.7a. While the atoms in the liquid can change their geometrical configuration freely as long as they do not overlap or get too close with each other as described in the liquid hard-sphere models (Jing and Karato, 2011), giving rise to the various configuration states for the liquid. This configurational contribution to compression can quantitatively explain the much higher compressibility observed in liquid than that in glass and crystal (Figure III.7b) (Jing and Karato, 2011), and for diopside liquid this configurational compressibility has been estimated to account for ~30% of its total

82 compressibility at room pressure (Askarpour et al., 1993; Schilling et al., 2003). The much lower velocity of the liquid than that in the crystal is also believed to result from the entropic effect in the liquid structure (Xu et al., 2018).

For measurements on glass, a thermodynamically metastable product, since the megahertz probe frequency induced by ultrasonic signals in this study is much higher than the relaxation frequency of the glass whose viscosity can be orders of magnitude higher than the viscosity of the liquid, the measured velocities on glass are unrelaxed (e.g., Rivers and Carmichael 1987), while the low viscosity of the liquid at very high temperatures enables us to measure the relaxed velocity of the liquid at ultrasonic frequencies (Xu et al.,

2018). In addition, for relaxed liquid, there is no shear velocity observed (Rivers and

Carmichael, 1987; Xu et al., 2018), while for both the cold-compressed and high P-T glass in this study, shear velocities are measured. These differences between glass and liquid is because that frozen glass cannot fully capture the configurational contribution to compression that are only available in liquids as described above. For the glass frozen from the liquid below Tg, the vibrational or energetic contribution dominates in its compressional properties. Thus, the measurements on unrelaxed glass can only reflect the vibrational contribution of a particular frozen configurational state which also depends on the thermal history of the glass (e.g., Askarpour et al. 1993). The vibrational dominated glass is more like its crystal counterpart, with only a very small offset corresponding to the frozen one fixed configurational state in the Vp-density space (Figure III.7a). Therefore, measurements on unrelaxed glasses cannot fully capture the configurational properties in liquids, and the velocity values measured on silicate glasses can by no means be directly applied to their chemically related silicate liquids.

83 The different pressure dependence of sound velocities in the cold-compressed and high

P-T glass has been discussed previously and is also evident from the Vp vs density plot

(Figure III.7a). The cold-compressed glass has a weak pressure or density dependence of the sound velocity, while the high P-T glass exhibits larger and more smooth pressure or density dependence of sound velocity, similar to the behavior observed in diopside liquid where the sound velocity increases smoothly with pressure (Xu et al., 2018). This probably indicates that the liquid at high temperatures may also possess more homogeneous intermediate-range order and the pressure response of this homogeneous structure may be similar to that in the high P-T glass. Therefore, in terms of the pressure dependence of sound velocity and the intermediate-range structure, high P-T glasses may be more similar to the liquids than the cold-compressed glasses without experiencing heating, similar to the conclusions drawn from FPMD simulations on silicate glasses (Ghosh et al., 2014; Ghosh and Karki, 2018) as well as in-situ structural measurements on a jadeite glass and liquid

(Sakamaki et al., 2014b).

84 (blue line, calculated from Sakamaki et al. (2014a)) and diopside crystal (black line, calculated from Li & Neuville (2010)). The glass data from this study are also plotted as symbols same as in Figure III.3.

Implications

Our study has clearly shown the distinct acoustic behaviors between cold-compressed and high-pressure heated glass and pointed out the importance of temperature during compression in order to fundamentally understand the behavior of silicate glasses. Since the measured acoustic velocities on silicate glasses are unrelaxed, they cannot be directly compared with the seismic wave velocities that are measured at much lower and relaxed frequency to constrain the composition and structure of possible melt layers in the Earth’s interior. Based on the anomalous pressure dependence of sound velocity observed in many silicate glasses that are compressed at room temperature, previous models and experimental studies argue that the melt fractions needed to account for the velocity reduction in the upper mantle low-velocity zones could be much smaller than conventionally thought (e.g., Liu and Lin 2014; Clark et al. 2016; Clark and Lesher 2017).

This is because that the velocity of cold-compressed glass does not increase significantly or even decrease with pressure due to its weak pressure dependence. This weak pressure dependence also means that the melt fractions needed to explain a given velocity reduction is similar in both the shallower part of the mantle and the deeper part of the mantle regardless of pressure. However, the pressure dependence of the sound velocities in the high-pressure heated glass and liquid shows no anomalous behavior and the velocities increase smoothly with pressure. These results indicate that the degree of velocity reduction actually decreases with pressure, meaning that more melt fractions are needed at higher pressures to explain a similar amount of velocity reductions than those observed at lower pressures. Likewise, velocity anomalies observed in the deeper parts of the mantle may

85 suggest the existence of a larger melt layer than those at shallower depths. Using the acoustic behavior from cold-compressed silicate glasses can result in a significant underestimate of the melt fractions needed to explain a given velocity reduction, especially at high pressures. The high-pressure heated glasses can better mimic the pressure dependence of velocities in liquids despite the fact that they cannot fully capture the configurational properties which are important in liquids. More experiments performed at simultaneous high pressures and high temperatures on silicate glasses and liquids are needed to elucidate the complex behaviors in silicate glasses as well as the differences between glasses and liquids during compression.

Acknowledgements

This research was supported by the National Science Foundation (EAR-1619964) to

ZJ and YW. The experiments were performed at GSECARS beamline 13-ID-D, Advanced

Photon Source (APS), Argonne National Laboratory. GSECARS is supported by the

National Science Foundation-Earth Sciences (EAR-1634415) and Department of Energy-

GeoSciences (DE-FG02-94ER14466). This work used resources of the Advanced Photon

Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-

06CH11357.

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95 Chapter IV

Acoustic velocity and compressibility in the molten hedenbergite

(CaFeSi2O6)-diopside (CaMgSi2O6) join at high pressures: Implications

for the stability and seismic signature of iron-rich melt in the mantle

(In preparation for submission)

Abstract

Iron-rich melt plays an important role in the magmatic history of the Earth and the

Moon. However, its elastic properties at high pressures, especially the acoustic velocity, are poorly understood. Here we determined the ultrasonic sound velocity for the first time of a molten Hd and a molten Hd50Di50 at high pressure and temperature conditions up to 6

GPa and 2329 K, using high-pressure ultrasonic technique combined with synchrotron radiation in a multi-anvil apparatus. The results show that iron can significantly reduce the sound velocity while increase the density of silicate melts. The sound velocity does not mix linearly for melts in the Hd-Di join, but the density can be well-described by linear mixing for Hd-Di melts at high pressures. Our results, combined with melt geometry model, have significant implications for the stability and seismic signature of iron-rich melts in the upper mantle. For the low-velocity zone in mantle asthenosphere, though the seismic velocity reduction can be explained by partial melts, the melts even with high iron content are unlikely to be gravitationally stable. For the low-velocity layer above mantle transition zone, the presence of iron-rich melt is a highly plausible explanation.

96 Introduction

Iron is one of the most important elements in silicate melts that can strongly affect the properties of melts in planetary interiors. First, iron is the heaviest major element in silicate melts, thus exerting a strong influence on the melt density. Second, during partial melting of mantle rocks, iron prefers to concentrate in the melt phase (Andrault et al., 2012; Mibe et al., 2006), producing iron-rich melts observed in many terrestrial planets. In addition, iron can have different valence states in mantle rocks and silicate melts. Fe2+ and Fe3+ can form as a redox couple and their ratio is a sensitive indicator of the melt oxidation state

(Frost and McCammon, 2008; Wilke, 2005). Besides, various spectroscopic studies

(Jackson et al., 2005; Wilke et al., 2007; Zhang et al., 2016) have shown that iron can exist in different coordination states in silicate glasses and melts. Since melt density and compressibility is strongly dependent on the geometrical packing and the coordination of its network-forming ions, changes of iron coordination numbers can significantly affect the volumetric and elastic properties of iron-bearing melts. Last but not least, terrestrial and lunar magmas could contain iron content of ~10 wt% to above 20 wt% (Delano, 1986). In order to understand the solidification of terrestrial and lunar magma oceans, knowledge of the elastic properties of iron-rich melt is required.

Despite the importance of iron-rich melts in planetary magmatic history and dynamics, their elastic properties and compressional behaviors are still not well-constrained, partly due to the complex behavior of iron in silicate melts. Systematic room-pressure density and sound velocity studies on Fe-rich melts has been carried out in the CaO-FeO-SiO2

(CFS) system (Guo et al., 2013) and model basalt (An-Di-Hd) system (Guo et al., 2014).

These room-pressure studies show that the partial molar volume and compressibility of

97 FeO component in silicate melts is dependent on melt composition and Fe2+ coordination.

Thus, an ideal mixing model using oxide components for the molar volume and compressibility does not work well for iron-rich silicate melts. At high pressures, shock compression has been performed to derive the equation of state (EOS) of several iron-rich melts (e.g., fayalite, hedenbergite and iron-bearing model basalt) (Thomas et al., 2012;

Thomas and Asimow, 2013a), confirming that compositional variations in partial molar volume of FeO extend to high pressure and only iron-bearing liquid with FeO mole fraction less than 0.06 can be adequately described by the ideal mixing. Because of the iron-rich nature of lunar basaltic melts, density measurements has also been conducted on iron-rich lunar glasses at pressures of a few GPa using the sink-float technique (Vander Kaaden et al., 2015) and X-ray absorption method (Van Kan Parker et al., 2012). However, due to the limited density points obtained and limited pressure range investigated, it is still not well- constrained whether Fe-Ti rich lunar melts could be neutrally buoyant at lunar deep mantle conditions or not (Mallik et al., 2019), which are important to understand the possibility of lunar mantle overturn. Recently, X-ray diffraction has been used to study the structure and density of a fayalite melt (FeSi2O4) melt at high pressures (Sanloup et al., 2013), showing that Fe-rich melts may have a higher densification rate than their Mg counterparts at 0-10

GPa due to the increase of Fe-O coordination number. As a result, iron-rich melts are more likely to be trapped at depth.

Until now, no high-pressure acoustic velocity data are available for iron-rich melts.

This has significantly limited our understanding of the seismic features of these melts, and in turn the ability to use seismic observations to detect these melts at depth. Sound velocity of melts measured at high pressures can not only tightly constrain the EOS and

98 compressibility of melts, but also can be compared with seismic wave velocity to infer the presence of melts and the amount of melts needed to explain a given velocity reduction. In this study, we use the molten Di (CaMgSi2O6) – Hd (CaFeSi2O6) as a simplified system to investigate the compressional properties of iron-rich melt at high pressure and temperature conditions. We report the first high-pressure sound velocity data on iron-rich melts including the Hd melt and the Hd50Di50 melt up to ~6 GPa and 2329 K. Combined with our previous data on Di melt (Xu et al., 2018), the mixing behavior between these two Mg-Fe end-members are discussed. The elastic results obtained here are important to understand terrestrial and lunar magma ocean solidifications, and have significant implications for the stability and seismic signature of iron-rich melts in the mantle.

Materials and Methods

Starting materials

Appropriate amount of reagent-grade chemical powders of SiO2, FeO, MgO and

CaCO3 (Alfa Aesar, >99% purity) were fully mixed in an agate mortar with ethanol according to the composition of Hd (CaFeSi2O6) and Hd50Di50 (50 mol% CaFeSi2O6 + 50 mol% CaMgSi2O6). The mixtures were dried and decarbonated at 1173 K in a high- temperature box furnace for 24 hrs. Full release of CO2 from the carbonates were confirmed by checking the mixture weight before and after decarbonation. The mixtures were then loaded into a piston cylinder apparatus, with graphite as the sample capsule to prevent the oxidation of FeO to Fe2O3 by providing a relatively reducing sample environment. The sample mixtures in piston cylinder were melted at 1973 K and 1 GPa for about 10 mins and then quenched to a glass. The recovered glass is homogenous, transparent and bubble- free. The glass was then precisely machined to a cylindrical disk with desired diameter (1.8

99 mm). The top and bottom surfaces of the glass disk were polished to 1m with nearly perfect parallelism using diamond paste. After polishing, the disk with a height of 1 mm can be used as the starting materials for high-pressure experiments.

High-pressure ultrasonic measurements

High-pressure ultrasonic measurements were performed using a 10-MN multi-anvil press with a Kawai-type module (Wang et al., 2009) at the GSECARS Beamline 13-ID-D of the Advanced Photon Source, Argonne National Laboratory. The cell assembly used for silicate melts and the ultrasonic experimental setup has been described in detail in a previous study (Xu et al., 2018). Thus, only a brief description of the experiments is given here. Figure IV.1 shows the details of the cell assembly and experimental setup. Pressure of the experiments was determined by energy-dispersive X-ray diffraction of the pressure standard in the cell assembly, consisting of a mixture of MgO and h-BN in a proportion of

3:1 by weight. Temperature was estimated from the thermocouple readings with correction for thermal gradient based on the calibrations from Xu et al. (2018). Accuracy in pressure is believed to be within 10% of the determined values and temperature within ±50 K.

For the ultrasonic measurements, a 10° Y-cut LiNbO3 piezoelectric transducer attached at the corner of the bottom anvil was used to transform the electric signals programed in the waveform generator to elastic waves. The elastic waves travel through the cell assembly and are reflected at the boundaries of anvil-buffer rod (BR), BR-sample and sample-backing plate (BP). The reflected elastic waves from each boundary are then converted back to electric signals by the same transducer, which then are amplified and recorded by a digital oscilloscope at a sampling rate of 5  109 /s. The material used for

BR and BP is molybdenum which provides sufficient acoustic impedance contrast and X-

100 ray imaging contrast with the sample. Travel time through the sample can be obtained from the reflected signals at the boundaries of BR-sample and sample-BP using the pulse- overlap method (Jing et al., 2014; Kono et al., 2012). Sample length can be measured by

X-ray imaging of the sample (Figure IV.2a). Then, the sound velocity through the sample can be calculated from travel time and sample length, with an uncertainty estimated to be less than 1%.

Figure IV.1 Diagram showing the experimental setup and cell assembly for high-pressure ultrasonic measurements on silicate melts. For experiments on Hd melt, the experimental conditions are ~1.7-6.0 GPa and 1827-

2101 K and for Hd50Di50 melt, the experimental conditions are ~1.6-4.3 GPa and 1919-

2329 K. For each experiment, the sample was first compressed to the target load, and then the temperature was steadily increased to above the melting temperature of the sample

(Agee et al., 2010). We measured the sample pressure using an energy-dispersive diffraction setup, with a Ge solid state detector and a fixed two-theta angle at ~6° (Wang

101 et al., 2009). With increasing temperature, the ultrasonic signals change as the state of the sample transforms from solid to partial melting and then to fully molten liquid (Figure

IV.2b). During partial melting, two P-wave ultrasonic signals for the sample (signals reflected at the interface between sample and BP) can be seen: One is for the liquid part of the sample (denoted as LS in Figure IV.2b) and the other is for the remaining solid (denoted as SS in Figure IV.2b). S-wave signals for the sample totally disappear when the sample enters into partially molten state. Fully molten of the sample is indicated by: (1) disappearing of the solid sample P-wave signals; (2) increase in the amplitude of the sample

P-wave signals compared to the partially molten state; (3) shift of the liquid sample P-wave signals to the right on the time axis with increasing temperature until fully molten state is achieved (Figure IV.2b). All the data reported in this study were measured on the fully molten liquid sample. After experiment, the sample was quenched by turning off the heater power.

102 (a)

P-wave signals (20 MHz) S-wave signals (30 MHz)

(b) Anvil Anvil 1371 K Solid 1371 K Solid BR BP BR BP

Noise Noise SS SS

Anvil Anvil 1827 K Partial melting 1827 K Partial melting

) ) BR

V BR V

BP m

(

s Noise SS LS s Noise

Anvil 2010 K Liquid Anvil 2010 K Liquid BR BR BP

Noise LS Noise

Time (s) Time (s)

Figure IV.2 (a) A representative radiographic image of Hd50Di50 melt sample at ~3.6 GPa and 2010 K. (b) Ultrasonic signals for Hd50Di50 at a constant load of 200 tons with increasing temperature. BR-buffer rod, BP-backing plate, SS-solid sample, LS-liquid sample.

Results

Hd melt sound velocity

The sound velocity data for Hd melt are reported in Table IV.1 and Figure IV.3a. The sound velocity of Hd melt increases continuously with pressure from 3133 m/s at 1.72 GPa,

1827 K to 3603 m/s at 4.19 GPa, 1827 K, and decreases with increasing temperature.

103 Combined with the room-pressure density for Hd melt (2.913 g/cm3 at 1673 K) (Guo et al.,

2013), the pressure-temperature-velocity data can be fitted to the third-order Birch-

Murnaghan equation of state (EOS) using a Monte-Carlo approach (Appendix A). The fitted results for the room-pressure isothermal bulk modulus 퐾푇0, the pressure derivative

′ of the bulk modulus 퐾푇, and the Anderson-Grüneisen parameter 훿푇 are 19.3 ± 0.2 GPa, 6.5

± 0.3, and 4.3 ± 1.1 (1), respectively, at a reference temperature of 1673 K (Table IV.2).

The calculated velocity curve recovers the experimental data very well (Figure IV.3a), and the extrapolated room-pressure velocity is in excellent agreement with the room-pressure experimental result measured by Guo et al. (2013).

Hd50Di50 melt sound velocity

The sound velocity data for Hd50Di50 melt are reported in Table IV.1 and Figure IV.3b.

The sound velocity of Hd50Di50 melt increases continuously with pressure from 3501 m/s at 1.55 GPa to 4024 m/s at 4.34 GPa, and has a weak and negligible temperature

3 dependence. Combined with the room-pressure density for Hd50Di50 melt (2.821 g/cm at

1673 K) (Guo et al., 2014), the pressure-temperature-velocity data can be fitted to the third- order Birch-Murnaghan equation of state (EOS) using a Monte-Carlo approach (Appendix

A). The fitted results for the room-pressure isothermal bulk modulus 퐾푇0, the pressure

′ derivative of the bulk modulus 퐾푇, and the Anderson-Grüneisen parameter 훿푇 are 21.9 ±

0.3 GPa, 7.6 ± 0.6, and 2.0 ± 1.1 (1), respectively, at a reference temperature of 1673 K

(Table IV.2). The calculated velocity curve recovers the experimental data well (Figure

IV.3b), and the extrapolated room-pressure velocity is in excellent agreement with the room-pressure experimental result measured by Guo et al. (2014).

104 (a) 4200 (b) 4400

4000 4200 Hd melt Hd50Di50 melt 3800 4000

3600

) ) 3800

s s

/ /

m m

( 3400 (

y y

t t 3600

i i

c c

o 3200 o

l l

e e

V V 3400 3000

3200 2800

1673 K isotherm 3000 2600 1919 K isotherm 1673 K isotherm Room-pressure data Room-pressure data from Guo et al. (2013) 2101 K isotherm from Guo et al. (2014) 2101 K isotherm 2400 2800 01234567 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Pressure (GPa) Pressure (GPa)

Figure IV.3 Velocity as a function of pressure for (a) Hd melt and (b) Hd50Di50 melt. The temperature range for Hd melt data measured in this study is 1827-2101 K, and for Hd50Di50 melt data is 1919-2329 K. Room- pressure velocity data for Hd melt is from Guo et al. (2013) and is measured in the temperature range of 1571-1879 K, and room-pressure velocity data for Hd50Di50 melt is from Guo et al. (2014) and is measured in the temperature range of 1653-1847 K.

Table IV.1 Sound velocity data measured for Hd and Hd50Di50 melt.

Frequency Velocity c Average c Run# P (GPa) T (K) s.d. (m/s) (MHz) (m/s) (m/s) Hd T2367 1.72 1827 20 3149 3133 10 T2367 1.72 1827 25 3140 T2367 1.72 1827 30 3132 T2367 1.72 1827 40 3127 T2367 1.72 1827 50 3127 T2367 1.72 1827 60 3124 T2367 1.81 1919 20 3134 3116 10 T2367 1.81 1919 25 3120 T2367 1.81 1919 30 3113 T2367 1.81 1919 40 3110 T2367 1.81 1919 50 3110 T2367 1.81 1919 60 3109 T2367 3.76 1919 20 3514 3530 25 T2367 3.76 1919 25 3523 T2367 3.76 1919 30 3493 T2367 3.76 1919 40 3563 T2367 3.76 1919 50 3550 T2367 3.76 1919 60 3538 T2371 3.72 1919 20 3569 3547 19 T2371 3.72 1919 25 3556 T2371 3.72 1919 30 3553 T2371 3.72 1919 40 3546 T2371 3.72 1919 50 3512 T2371 3.72 1919 60 3547 T2371 3.72 2010 20 3526 3526 14 T2371 3.72 2010 25 3517 T2371 3.72 2010 30 3506

105 T2371 3.72 2010 40 3526 T2371 3.72 2010 50 3542 T2371 3.72 2010 60 3540 T2371 3.73 2101 20 3452 3519 38 T2371 3.73 2101 25 3501 T2371 3.73 2101 30 3524 T2371 3.73 2101 40 3560 T2371 3.73 2101 50 3543 T2371 3.73 2101 60 3533 T2482 4.19 1827 20 3618 3603 14 T2482 4.19 1827 25 3602 T2482 4.19 1827 30 3590 T2482 4.01 1919 20 3590 3576 10 T2482 4.01 1919 25 3584 T2482 4.01 1919 30 3576 T2482 4.01 1919 40 3573 T2482 4.01 1919 50 3571 T2482 4.01 1919 60 3560 T2482 5.95 2010 20 3843 3866 25 T2482 5.95 2010 25 3847 T2482 5.95 2010 30 3875 T2482 5.95 2010 40 3896

Hd50Di50 T2435 1.55 1919 20 3527 3501 31 T2435 1.55 1919 25 3514 T2435 1.55 1919 30 3500 T2435 1.55 1919 40 3471 T2435 1.55 1919 50 3457 T2435 1.55 1919 60 3537 T2435 1.66 2010 20 3503 3506 8 T2435 1.66 2010 25 3515 T2435 1.66 2010 30 3500 T2483 3.65 1919 20 3870 3870 3 T2483 3.65 1919 25 3867 T2483 3.65 1919 30 3873 T2483 3.57 2010 20 3844 3859 36 T2483 3.57 2010 25 3825 T2483 3.57 2010 30 3816 T2483 3.57 2010 40 3867 T2483 3.57 2010 50 3902 T2483 3.57 2010 60 3898 T2483 4.34 2238* 20 4074 4024 44 T2483 4.34 2238* 25 4008 T2483 4.34 2238* 30 3990 T2483 4.10 2329* 20 3920 3943 34 T2483 4.10 2329* 25 3899 T2483 4.10 2329* 30 3918 T2483 4.10 2329* 40 3971 T2483 4.10 2329* 50 3981 T2483 4.10 2329* 60 3969 *Temperature was estimated by the power-temperature relationships due to the failure of thermocouple.

106 Table IV.2 Fitting results for melts in the Hd-Di join.

Hd Di Hd50Di50

−3 𝜌0 (푔푐푚 ) 2.913 2.643 2.821

* * 퐾푇0 (퐺푃푎) 19.3 ± 0.2 (19.89) 23.0 ± 0.3 (24.57) 21.9 ± 0.3

′ * * 퐾푇0 6.5 ± 0.3 (6.22) 7.2 ± 0.5 (6.98) 7.6 ± 0.6

훿푇 4.3 ± 1.1 3.2 ± 0.9 2.0 ± 1.1

Note: Reference temperature 푇푟푒푓 for all three melts is 1673 K. Data for Di melt is from Xu et al. (2018).

Room-pressure densities for Di, Hd and Hd50Di50 melts are from Lange (1997), Guo et al. (2013) and Guo et al. (2014), respectively. *Numbers in parenthesis are the determined adiabatic values from shock-wave studies by Asimow and Ahrens (2010) for Di melt and Thomas and Asimow (2013) for Hd melt.

Discussions

Velocity and density comparison in the molten Hd-Di join and test of linear mixing

Comparisons of the sound velocity and density among the three melts in the Hd-Di join are shown in Figure IV.4. The most iron-rich melt, Hd melt, has the lowest sound velocity and the highest density. Obviously, iron can significantly reduce the sound velocity while increase the density of silicate melts. Hd melt could have a density crossover with mantle materials at ~4 GPa, and Hd50Di50 melt may become denser than surrounding mantle at ~10.5 GPa. While for iron-free Di melt, it is always buoyant under upper mantle conditions (Figure IV.4b). Our data provides a way to evaluate if the linear mixing model works for iron-rich melt at high pressures in the Hd-Di join. Linear mixing has been widely employed to interpolate melt properties (e.g., volume, compressibility, sound velocity) at ambient pressures (Ai and Lange, 2008; Bottinga et al., 1982; Lange, 1997; Lange and

Carmichael, 1987; Rivers and Carmichael, 1987). This is the simplest assumption that can be made for mixtures. The property of the mixture is just a linear combination of the partial molar property of end-members multiplied by their respective mole fractions. Previous

107 room-pressure study (Guo et al., 2014) has shown that the molar volume, isothermal compressibility and thermal expansion of melts in the model basalt system (An-Di-Hd) can be adequately described by the linear mixing model using oxides as components, but cannot be extended to the pure Hd end-member. The derived partial molar volume for FeO

3 component (VFeO) in An-Di-Hd melts is 12.86 cm /mol, significantly lower than the value derived for pure Hd melt (15.47 cm3/mol), which is believed to reflect different average

Fe2+ coordination numbers (5.7 vs. 4.6) in model basalt and pure Hd melts (Guo et al.,

2+ 2014), and a reverse linear relationship between room-pressure VFeO and Fe average coordination is also proposed (Guo et al., 2013). Our results suggest that linear mixing model cannot recover the sound velocity for molten Hd-Di, and the deviation from linear mixing behavior for the sound velocity increases with pressure (Figure IV.4a). As for the density, although non-linear mixing is observed for Hd50Di50 melt at pressures < ~5 GPa, with increasing pressure, the density of Hd50Di50 melt can be well-described by the linear mixing of end-member Di and Hd melt (Figure IV.4b). This implies that the non-linear behavior for molar volume observed at room pressure in the model basalt system (Guo et al., 2014) is gradually vanished with pressure, and that Fe2+ coordination in pure Hd melt may change toward similar values as that in the Hd-Di binary melts. Our results demonstrate that for melt compositions falling into the Hd-Di join, its high-pressure volume/density may be calculated using linear mixing of the oxide components, as long as the partial molar volume for FeO component (VFeO) used in the calculation is derived from

Hd melt. This is because that the partial molar volume VFeO derived for Hd melt is significantly different than the VFeO derived for other iron-rich melts such as fayalite melts

2+ (Fa, Fe2SiO4) due to different Fe coordination states in these melts. Thus, the high-

108 pressure linear mixing of density/volume tested here cannot be extended to other iron-rich melts and is only valid for Hd-Di melts. More data on iron-bearing melts with various Fe2+ coordinations are needed in order to better understand the mixing behaviors of iron-rich melts.

6000 4 (a) (b) 5500 3.5

5000 3

)

4500 c

(

t 2.5

s PREM l 4000

e Di

D Hd 2 Di Hd 3500 50 50 Lange (1997) Di room pressure Di Guo et al. (2013) Hd room pressure Hd 1.5 Guo et al. (2014) Di Hd room pressure 3000 50 50 Di Hd 50 50 Asimow & Ahrens (2010) Di shock wave linear mixing linear mixing 2500 1 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 Pressure (GPa) Pressure (GPa)

Figure IV.4 Comparison of sound velocity (a) and density (b) as a function of pressure among melts in the Hd-Di join and test of linear mixing. PREM model for density is from Dziewonski and Anderson (1981).

Implications for the upper mantle low-velocity zone (LVZ) and low-velocity layer (LVL)

Seismic observations have revealed several low-velocity regions within the Earth’s upper mantle, which are typically attributed to the presence of partial melts (Anderson and

Spetzler, 1970; Hirschmann, 2010a). If these velocity reductions were truly caused by partial melts, this means that the melts must be stable over there for an extended period of time so that they can be detected by seismology, and that the amount of melts present can satisfy the degree of velocity reduction constrained by seismology. Our sound velocity and

EOS results for silicate melts, combined with proper melt geometry model, provides a natural way to test if partial melts can satisfy both the density and velocity constraints to explain the seismic observations. Since FeO content in silicate melts plays a major role in affecting the density and velocity of the melts, the stability and seismic signature of iron- rich melts are our primary focus.

109 The first prominent low-velocity region in the upper mantle is at the depth of ~80-100 km, named the low-velocity zone (LVZ), roughly coinciding with the depth of asthenosphere where the rheology properties and temperature/velocity/viscosity/electrical conductivity gradients differ sharply with above plate-like lithosphere (Fischer et al., 2010).

The degree of S-wave velocity reduction (푑푙푛푉푠) compared to the average mantle is ~7-8% in the LVZ, and is commonly attributed to the presence of silicate melts (Chantel et al.,

2016; Kawakatsu et al., 2009; Schmerr, 2012). In order to test the viability in terms of buoyancy and seismic velocity of the presence of silicate melts in the LVZ, we have calculated the density change (푑푙푛𝜌) and S-wave velocity change (푑푙푛푉푠 ) at the P-T conditions of LVZ as a function of melt fraction for silicate melts in the Hd-Di join, using the theoretical melt geometry model for partially molten assemblages from Takei (2002).

The calculation details are in Appendix B. The results are compared with seismic constraints in Figure IV.5a. It can be seen from Figure IV.5a that the seismic velocity reduction for LVZ (shaded area) can be well-explained by the presence of ~3% partial melts if assuming the equilibrium melt geometry (Takei, 2002). However, even the presence of the most iron-rich Hd melt reduces the mantle density by ~0.1%. This means that even iron-rich Hd melt cannot be gravitationally stable at this depth, and hence silicate melts generated in the LVZ are most likely to be buoyant and tend to migrate upwards.

Therefore, if the LVZ was truly caused by partial melts, other mechanisms must be proposed to explain the extended period of existence of melts at the depth of LVZ. One possible mechanism is that the required melt fraction to explain the velocity reduction in

LVZ could be very small (e.g., <0.5% if assuming the melt film geometry) as argued by petrologic studies (Hirschmann, 2010a) and experimental results (Chantel et al., 2016). For

110 such a small melt fraction, even if the melt has a low dihedral angle and can be interconnected (Holness, 2006), the melt is likely to be retained in the mantle due to the low permeability of mantle rocks and surface tension of the melt network which may dominate over the buoyancy-driven draining at very small melt fractions (Holtzman, 2016).

This small, unextractable fraction of melts in LVZ (Selway and O’Donnell, 2019) may thus be stable for a long time and responsible for the velocity reductions. Another possible mechanism for the extended period of presence of melt in LVZ is that melt is likely accumulated dynamically due to a change in melt viscosity/composition (Sakamaki et al.,

2013). Experimental results (Sakamaki et al., 2013) have shown that the basaltic melt mobility, the ratio of the melt-solid density contrast to the melt viscosity, exhibits a maximum at depths of 120-150 km, up to one order of magnitude higher than melt at depths of 80-100 km. Thus, as melt ascends, the mobility contrast in the asthenosphere could lead to excessive melt ponded at depths of 80-100 km, which may be responsible for the LVZ

(Sakamaki et al., 2013).

Another prominent low-velocity region in the upper mantle is the so-called low- velocity layer (LVL) atop the mantle transition zone (MTZ) (Hier-majumder et al., 2014;

Hier-majumder and Courtier, 2011; Tauzin et al., 2010). This LVL could be a global feature at a depth of ~350 km, with an average S-wave velocity reduction (푑푙푛푉푠) of ~4%

(Freitas et al., 2017; Tauzin et al., 2010). The origin of LVL is also thought to be related to partial melting above the MTZ (Freitas et al., 2017; Hier-majumder et al., 2014; Tauzin et al., 2010). According to the MTZ water filter model (Bercovici and Karato, 2003), mantle upwelling across the 410 km discontinuity would result in hydrous melting due to the release of water from mantle minerals, as the water storage capacity of the upper mantle

111 olivine is significantly lower than that of the MTZ wadsleyite and ringwoodite. This hydrous melting has been experimentally simulated to be a plausible mechanism to account for the seismic observations of the LVL (Freitas et al., 2017). Here we have calculated the density change (푑푙푛𝜌) and S-wave velocity change (푑푙푛푉푠) at the P-T conditions of LVL

(Appendix B) to see if iron-rich partial melts could explain the seismic velocity reduction and be gravitationally stable in LVL. The calculation results are shown in Figure IV.5b. If assuming equilibrium melt geometry (Takei, 2002), the ~4% S-wave velocity reduction in

LVL can be explained by the presence of ~1-2% silicate melts. However, only iron-rich melts (Hd and Hd50Di50) can increase the density of melt-bearing mantle while iron-free melt (Di) decreases the mantle density. This means that only iron-rich melts can be gravitationally trapped in the LVL, since the densities of iron-rich melts (29 wt% FeO for

Hd melt and 15 wt% FeO for Hd50Di50) are higher than those of the ambient mantle in LVL, but still lower than those of the minerals below the 410 km discontinuity, as mantle minerals such as olivine transforms to high-density polymorphs, resulting in a density trap for melts just above the MTZ. Therefore, our results show that partial melt could be a viable origin for the LVL, as long as the partial melt is iron-rich (with total FeO content > ~10 wt%), consistent with the experimental results by Freitas et al. (2017).

112 (a) (b)

Figure IV.5 S-wave velocity reduction (푑푙푛푉푠) as a function of density change (푑푙푛𝜌) and melt fraction for Hd-Di melts-bearing mantle in the (a) LVZ at 2.5 GPa and (b) LVL at 12 GPa based on the theoretical model for partially model assemblages (Takei, 2002). The shaded area in (a) is based on seismic observations from Kawakatsu et al. (2009) and Schmerr (2012) for the velocity reductions in LVZ. The shaded area in (b) represents seismic velocity reduction reported in Tauzin et al. (2010) and buoyancy constraints for LVL. Colorbar represents the melt fraction.

Conclusions

1. The sound velocity increases continuously with pressure for molten Hd and

Hd50Di50. With increasing temperature, the velocity of Hd melt decreases, while the effect of temperature on the velocity of Hd50Di50 is negligible.

2. Iron content in silicate melts has a strong effect on the elastic properties of melts.

With more FeO in the melt, the melt will have a higher density and a lower sound velocity.

The sound velocity of melts in the Hd-Di join does not mix linearly, while the density at high pressures can be adequately described by the linear mixing model as a long as a proper partial molar volume for the FeO component is chosen.

3. Partial melts may explain the velocity reductions in LVZ, but cannot satisfy the buoyancy constraints. Other mechanisms such as unextractable melt fraction and change of melt mobility are likely responsible for presence of melts in LVZ for an extended period.

Iron-rich silicate melts (with FeO>10 wt%) may well explain the stability and seismic observations of the LVL.

113 Acknowledgements

This study was supported by the National Science Foundation (EAR-1619964). The ultrasonic measurements were performed at GSECARS beamline 13-ID-D, Advanced

Photon Source (APS), Argonne National Laboratory. GSECARS is supported by the

National Science Foundation - Earth Sciences (EAR-1634415) and Department of Energy

- GeoSciences (DE-FG02-94ER14466). This research used resources of the Advanced

Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract

No. DE-AC02-06CH11357.

Appendix A. Monte-Carlo fitting of the sound velocity data

The sound velocity data, combined with previous determined room-pressure density

(Guo et al., 2014, 2013), can tightly constrain the EOS for silicate melts. We fit our experimental data using the third-order isothermal Birch-Murnaghan EOS (e.g., Birch,

1952), which is given as

7 5 2 3퐾푇0 𝜌 3 𝜌 3 3 ′ 𝜌 3 푃 = [( ) − ( ) ] {1 + (퐾푇 − 4) [( ) − 1]} (A1) 2 𝜌0 𝜌0 4 𝜌0

′ where 푃 is pressure, 퐾푇0 the isothermal bulk modulus at room pressure, 퐾푇 the pressure derivative of the bulk modulus, 𝜌0 the room-pressure density, and 𝜌 the density at high pressures. Based on Eulerian finite strain theory, the high-pressure bulk modulus is given as (Anderson, 1995)

5 2 2 𝜌 3 1 𝜌 3 ′ 27 ′ 𝜌 3 퐾푇 = 퐾푇0 ( ) {1 + (1 − ( ) ) [5 − 3퐾푇 − (4 − 퐾푇) (1 − ( ) )]}. (A2) 𝜌0 2 𝜌0 4 𝜌0

The room-pressure density (𝜌0) at a temperature T is given as

114 𝜌0 = 𝜌0,푇푟푒푓 exp[−훼(푇 − 푇푟푒푓)], (A3) where 푇푟푒푓 is the reference temperature and is chosen to be 1673 K in this study, and 훼 is

3 -5 - the thermal expansion coefficient. 𝜌0 and 훼 for Hd melt are 2.913 g/cm and 5.91  10 K

1 at 1673 K, respectively, based on room-pressure experimental measurements by Guo et

3 -5 -1 al. (2013), and for Hd50Di50 melt are 2.821 g/cm and 7.67  10 K at 1673 K, respectively, based on Guo et al. (2014). These parameters are fixed during the fitting.

The room-pressure bulk modulus (퐾푇0 ) is also a function of temperature and can be expressed in terms of the Anderson-Grüneisen parameter 훿푇 (e.g., Stacey, 2005) as

−훿 𝜌0,푇푟푒푓 푇 퐾푇0 = 퐾푇0,푇푟푒푓 ( ) , (A4) 𝜌0

Inserting (4) into (3), we can get

퐾푇0 = 퐾푇0,푇푟푒푓푒푥푝[−훼훿푇(푇 − 푇푟푒푓)]. (A5)

The adiabatic bulk modulus is related to the isothermal bulk modulus through

퐾푆 = 퐾푇(1 + 훼훾푇), (A6) where 훾 is the Grüneisen parameter. The Grüneisen parameter for Hd melt has been determined by Thomas and Asimow (2013) to be 0.30 at room pressure. While the

Grüneisen parameter for Hd50Di50 melt has not been determined yet, we estimated a room- pressure Grüneisen parameter value of 0.40 for Hd50Di50 melt based on the shock-wave studies on melts in the Hd-Di-An model basalt (Asimow and Ahrens, 2010; Thomas and

Asimow, 2013a). Though the Grüneisen parameter increases with pressure for silicate melts, considering the limited pressure range in this study, the Grüneisen parameter can be treated as a constant for the fitting process. Changes in the Grüneisen parameter does not affect the fitting results significantly.

115 Sound velocity (푐) is related to adiabatic bulk modulus (퐾푆) and density (𝜌) through

푐 = √퐾푆/𝜌 (A7)

′ The fitting parameters in this study are 퐾푇0,푇푟푒푓 , 퐾푇 and 훿푇. A million sets of random numbers were generated in appropriate parameter spaces. For a given set of parameters, we calculated 𝜌0,푖 and 퐾푇0,푖 at experimental temperature 푇푖 using Eqns. (A3) and (A5), and then high-pressure density 𝜌푖 and isothermal bulk modulus 퐾푇,푖 can be calculated using

Eqns. (A1) and (A2), respectively, with our experimental pressure data 푃푖. The calculated

푚표푑푒푙 퐾푇,푖 was converted to 퐾푆,푖 using Eqn. (A6) and finally the modeled sound velocity 푐푖 can be calculated by 𝜌푖 and 퐾푆,푖 via Eqn. (A7). The same calculations were repeated for each experimental P, T conditions, and finally the best-fit values were found by minimizing the 2, which is calculated as

2 (푐푑푎푡푎−푐푚표푑푒푙) 2 ∑ 푖 푖 휒 = 푖 [ 푐 2 ] (A8) (𝜎푖 )

푑푎푡푎 푐 where 푐푖 is the measured sound velocity for experiment 푖, 𝜎푖 is the total uncertainty in the sound velocity which is the sum of the uncertainty in the sound velocity measurements and the propagated equivalent uncertainty in sound velocity due to uncertainty in pressure.

Appendix B. Calculation of S-wave velocity change (풅풍풏푽풔) and density change (풅풍풏흆) for partially molten assemblages

The S-wave velocity change as a function of melt fraction (F) is given as (Clark and

Lesher, 2017; Takei, 2002)

푑푉푠 푉푠−푉푠0 𝜌푙 퐹 푑푙푛푉푠 = = = [Λ퐺 − (1 − ( ))] , (A9) 푉푠0 푉푠0 𝜌푠 2

116 and the density change for the melt-bearing assemblage as a function of melt fraction (F) is calculated assuming a linear mixing of the density between melt and solid mantle:

푑푙푛𝜌 = {[(1 − 퐹) × 𝜌푠 + 퐹 × 𝜌푙] − 𝜌푠}/𝜌푠 , (A10) where 푉푠0 represents the S-wave velocity of the solid mantle, and 푑푉푠 is the reduction in the velocity. 𝜌푙 and 𝜌푠 are density of the melt phase and solid mantle, respectively. Λ퐺 is a function of melt geometry and can be approximated by (Takei, 2002)

( ) 푁 퐹,훼 = 1 − 퐹Λ (훼) (A11) 퐺 퐺 where 퐺 is the shear modulus of the solid mantle, and 푁 is the shear modulus of the solid skeleton, which was calculated at a given melt fraction 퐹 by replacing the regions containing liquid with empty pore spaces and the pore shape is described by the equivalent aspect ratio 훼 (Takei, 2002). All the melt geometrical parameters (e.g., oblate spheroid model, equilibrium model, tube and crack model) can be converted to the equivalent aspect ratio. Λ , which is a function of 훼, represents the slope of the normalized shear modulus 푁 퐺 퐺 as a function of melt fraction 퐹. It can be approximated as a liner function when 퐹 is relatively small (< ~10%). The slope Λ퐺 for different melt geometries can be obtained from the Figs. 2 and 3 in Takei (2002). We used the elastic properties of San Carlos olivine (Liu et al., 2005) for the properties of solid mantle, and our experimental results on Hd-Di melts for the liquid phase. For the LVZ, calculations were performed at a constant pressure of

2.5 GPa, and for the LVL, calculations were performed at a constant pressure of 12 GPa.

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124 Chapter V

Density of NaAlSi2O6 melt at high pressure and temperature measured

by in-situ X-ray microtomography

(Published in Minerals)

Abstract

The volumetric compression of jadeite (NaAlSi2O6) melt at high pressures was determined by three-dimensional volume imaging using the synchrotron-based X-ray microtomography technique in a rotation-anvil device. Combined with the sample mass measured using a high-precision analytical balance prior to the high-pressure experiment, the density of jadeite melt was obtained at high pressures and high temperatures up to 4.8

GPa and 1955 K. The density data were fitted to a third-order Birch-Murnaghan equation

+1.9 of state, resulting in a best-fit isothermal bulk modulus 퐾푇0 of 10.8−5.3 GPa and its

′ +6.6 pressure derivative 퐾푇0 of 3.4−0.4 . Comparison with data for silicate melts of various compositions from the literature shows that alkali-rich, polymerized melts are generally more compressible than alkali-poor, depolymerized ones. The high compressibility of jadeite melt at high pressures implies that polymerized sodium aluminosilicate melts, if generated by low-degree partial melting of mantle peridotite at ~250-400 km depth in the deep upper mantle, are likely denser than surrounding mantle materials and thus gravitationally stable.

Introduction

Silicate melts are major agents for transferring heat and chemical species in the interior of Earth and other terrestrial planets, playing a critical role in planetary differentiation. The

125 density of silicate melts is a key factor controlling the direction of magma migration during the differentiation process: Depending on the density contrast between silicate melts and the ambient mantle, melts can either migrate upwards or sink into the deep interior, resulting in quite different geodynamical scenarios (Agee, 1998; Sanloup, 2016; Stolper et al., 1981). For magmas that erupt to the surface, knowing their density as a function of pressure is essential to model their rates of segregation from source regions and the subsequent migration to the surface (Faul, 2001). For deep melts, which have been suggested by geophysical observations, e.g., at the lithosphere-asthenosphere boundary

(Naif et al., 2013; Schmerr, 2012), atop the 410 km (Tauzin et al., 2010) and 660 km

(Schmandt et al., 2014) discontinuities, and in the ultra-low velocity zone above the core- mantle boundary (Williams and Garnero, 1996), knowledge of the density of silicate melts at high pressures is essential to evaluate their gravitational stability in the mantle. In addition, the early history of the Earth and the Moon is believed to be characterized by at least one stage of large-scale melting of the mantle, resulting in a magma ocean, formed in the aftermath of the Moon-forming giant impact event (Hosono et al., 2019; Nakajima and

Stevenson, 2015). In order to model the solidification of the early magma ocean, we need to know the high-pressure density of the magmas.

Alkalis (Na2O and K2O) are important components of silicate melts and their presence in mantle rocks can significantly lower the solidus of the mantle peridotite (Hirschmann,

2000). Due to their incompatible nature, alkalis are relatively concentrated in silicate melts

(up to 6-13 wt% alkalis (Baker et al., 1995; Schiano and Clocchiatti, 1994)), when a small degree of partial melting of peridotite is produced. The jadeite composition, NaAlSi2O6

(15.3 wt% Na2O content), is relevant to alkali-rich silicate melts in the mantle, especially

126 those low-degree partial melts (Falloon et al., 2008, 1997; Pommier and Garnero, 2014).

Its melting behavior and transport properties (e.g., viscosity, diffusivity) have been experimentally studied up to 16.5 and 5.5 GPa, respectively (Kushiro, 1976; Litvin and

Gasparik, 1993; Shimizu and Kushiro, 1984; Suzuki et al., 2011). The phase transition, structure, and compressibility of the crystalline jadeite has also been extensively studied due to its importance in high-pressure metamorphic rocks and as a major clinopyroxene group mineral in the mantle (Liu, 1978; Nestola et al., 2006; Wu et al., 2013; Zhao et al.,

1997). However, the density of jadeite melt, as well as the effect of alkali components on the density of silicate melts at high pressures more generally, is poorly determined due to experimental difficulties. The high viscosity, high reactivity, and low density of alkali-rich melts hinder the application of some of the most widely used melt density measuring techniques, such as the sink-float (Agee, 1998; Agee and Walker, 1993; Ghosh et al., 2007;

Jing and Karato, 2012; Matsukage et al., 2005) and shock-wave (Asimow and Ahrens,

2010; Rigden et al., 1989; Thomas and Asimow, 2013a) techniques. Until now, the only experimental data on the density of jadeite melt at high pressures were obtained by

Sakamaki (Sakamaki, 2017) using the X-ray absorption method (Malfait et al., 2014;

Petitgirard et al., 2015; Sato and Funamori, 2008; Seifert et al., 2013), in which the density was calculated from the X-ray absorption contrast between the sample and diamond lid using the Beer-Lambert law and the mass absorption coefficients, but his results are not in agreement with a recent first-principles molecular dynamics (FPMD) study on jadeite melt

(Bajgain et al., 2019).

Other than the aforementioned techniques, the X-ray microtomography technique has the capability to directly measure the 3D volume of samples in any states including

127 amorphous phases at high pressures (Clark et al., 2016; Lesher et al., 2009; Li et al., 2014;

R. Li et al., 2017). However, application of this technique has so far been limited to silicate glasses (Clark et al., 2016; Kono et al., 2011; Lesher et al., 2009) and low melting temperature liquids such as gallium liquid (Li et al., 2014; R. Li et al., 2017). Because of the relatively low X-ray absorption of silicate melts, a long duration (up to a few hours) would be required in traditional tomography setup employing a monochromatic X-ray beam and light sample capsuling materials. Such long durations thus prevent reliable measurements on the highly mobile and reactive silicate melts at very high temperatures

(likely higher than 1500 K).

In this study, we have made new technical developments using a modified Paris-

Edinburgh (PE) cell assembly in a tomographic apparatus to enable volume measurements on jadeite melt up to 4.8 GPa and 1955 K. We employed a pink X-ray beam (Rivers, 2016) to image the molten sample, providing much faster data collection than previous studies

(Clark et al., 2016; Lesher et al., 2009) using a monochromatic beam. This is critical to reducing possible chemical reactions of silicate melts with surrounding materials at very high temperatures. In order to obtain sufficient spatial resolution given the short imaging duration, we used a relatively strongly absorbing material (molybdenum) to encapsulate the melt sample and to provide sharp X-ray absorption contrast with the low-absorbing jadeite melt. Combined with the sample mass measured at room pressure before loading to the cell, new density data of jadeite melt at high pressures and temperatures were obtained.

Our results can help resolve the discrepancy in density estimates for jadeite melt, and to place constraints on the density of sodium-rich silicate melts at upper mantle conditions.

Besides, the experimental technique developed in this study for melt density measurements

128 may be readily extended to other melt compositions such as volatile-bearing melts and carbonatite melts, expanding the composition space for melt density measurements significantly, which is essential for developing a unified model for the equation of state

(EOS) of mantle melts at high pressures (Jing and Karato, 2011).

Materials and Methods

Starting materials

Reagent-grade powders of Na2CO3, Al2O3 and SiO2 were mixed in appropriate proportions according to the jadeite composition and ground in ethanol for ~2 hrs. The mixture was dried and decarbonated at 1173 K in a high-temperature box furnace for ~24 hrs using a platinum crucible. The full release of CO2 was confirmed by checking the mixture weight before and after decarbonation. The decarbonated mixture was then fused at 1873 K for ~4 hrs, and finally quenched to a glass. The fusion process was repeated twice to ensure homogeneity of the glass. The sodium loss during the fusion process is insignificant as shown by the composition of the quenched experimental product

(Supplementary Table 1). The resulting glass was transparent, bubble-free, and homogeneous. A perfect cylindrical glass disk with the desired outer diameter (1.6 mm) and thickness (1.0 mm) was machined from the quenched glass by using a CNC-milling machine and was used as the starting material for the experiment. The weight of the glass disk was measured by a high-precision analytical balance with a resolution of 0.01 mg

(Scientech SM50). The measured weight is 4.385 ± 0.024 mg by repeating the measurements five times.

129 High-pressure experiments

The high-pressure X-ray microtomography (HPXMT) experiments were carried out in a 250-ton hydraulic press with a tomography module installed at the GSECARS

Beamline 13-BM-D of the Advanced Photon Source, Argonne National Laboratory (Wang et al., 2005; Yu et al., 2016). Pressure was generated by two opposing PE anvils inserted in the HPXMT module. The HPXMT module allows for a full 360° rotation of the PE cell while under loads up to 50 tons thanks to supports from the thrust bearings (Wang et al.,

2005). The detailed PE cell assembly is shown in Figure V.1. Boron epoxy, which is nearly transparent to the X-ray employed in the experiments, was used as the pressure medium.

A Lexan ring was placed outside the boron epoxy to prevent the extrusion of the cell materials under the axial load. A graphite sleeve was used as the heater, together with zirconia as the thermal insulator and tantalum as the electrodes. Molybdenum was chosen as the capsule material for the sample melt due to its low reactivity with silicate melts at high P-T conditions, as demonstrated by the use of molybdenum capsules in various experiments including sink-float density measurements (Agee and Walker, 1993), shock- wave experiments (Asimow and Ahrens, 2010), and ultrasonic measurements (Xu et al.,

2018). Another advantage of using a molybdenum capsule is that it has relatively strong

X-ray absorption to show clear contrast to silicate melts, which is critical for X-ray imaging of the sample, but not too strong absorption to allow sufficient X-ray photons passing through the sample to image sample details. No welding of the capsule was applied to prevent chemical reactions and mass loss of the sample at high welding temperatures. The capsule would simply be pressure-sealed upon compression and this provides sufficient

130 confining of melt during the tomographic measurements as confirmed by X-ray imaging and the quenched product analysis (see later part of this section).

Figure V.1 Cross section of the PE cell assembly used for X-ray microtomography experiments on silicate melts. Since tomographic measurements require a 180° rotation of the cell assembly, it is not possible to insert a thermocouple in the cell for temperature measurements during the experiments. Instead, the temperature of experiments was estimated based on the temperature-power relationships (Supplementary Figure V.7) calibrated in a separate experimental run without rotating the sample, using exactly the same cell assembly as in the tomographic experiments but with a thermocouple placed in the middle of the sample.

The uncertainties in the estimated temperatures are within ±100 K. The pressure of the experiments was obtained by energy-dispersive X-ray diffraction measurements of the cell parameters of the MgO pressure standard, either the MgO disk atop of the sample or the

MgO ring outside the heater (the differences between the two are within 0.5 GPa), using the thermal equation of state of MgO (Tange et al., 2009). The uncertainty in pressure

131 mainly comes from the uncertainty in temperature measurements, and is estimated to be about ±0.5 GPa.

The high-pressure tomographic measurements on the jadeite melt were carried out at three different hydraulic ram loads, corresponding to pressures from ~1.3 to 4.8 GPa, depending on temperature. The pressure was first increased to the target load during the experiment. After the target load was reached, the sample was steadily heated up to a temperature above the melting temperature of jadeite (Litvin and Gasparik, 1993) by ramping up the heating power output. After the experiment, the sample was quenched from high temperature by turning off the heater power. The quenched sample was analyzed by a field-emission scanning electron microscope (FE-SEM) at the Swagelok Center for

Surface Analysis of Materials (SCSAM) of Case Western Reserve University (CWRU)

(FEI Nova 200 Nanolab SEM). The acceleration voltage and probe current were set at 10 kV and 15 nA, respectively. No sign of leakage of the molten sample under high P-T conditions was observed based on the secondary electron (SE) and backscattered electron

(BSE) images of the quenched product (Supplementary Figure V.8a), and no sign of molybdenum contamination of the sample was found based on the elemental mapping using the energy-dispersive spectroscopy (EDS) (Oxford EDS X-Max 50 sq. mm) with internal standards (Supplementary Figure V.8b and Supplementary Table V.3).

X-ray microtomography measurements

We followed the experimental setup for the in-situ X-ray microtomography technique that was described in Yu et al. (Yu et al., 2016). In this technique, the three-dimensional

(3D) tomographic image of the sample can be reconstructed from a series of X-ray radiographic images taken while rotating the cell (hereafter referred to as a tomography

132 scan). A pink beam (energy ~25-65 keV, mirror pitch angle ~1.2 mrad for imaging, with a

1 mm-thick Ti filter applied) was used for taking radiographic images of the sample, including its capsule. This enables significantly faster data collection than using a monochromatic beam (Rivers, 2016) and helps reduce the time that the sample spends at high temperatures. The transmitted X-ray from the cell assembly was converted to visible light by a LuAG scintillator, reflected by a mirror, zoomed in by an objective lens, and finally detected by a CCD (charge-coupled device) camera and recorded as a 2-D image.

Before each tomography scan, the dark current - the image intensity signal recorded in absence of X-rays - was first measured in order to properly account for the background noise from the scintillator and the CCD detector. During each scan, the high-pressure cell inside the tomography module was rotated from 0° to 180° continuously, with the rotation axis perpendicular to the incident beam. The rotation rate was set to about 0.1 rpm

(revolutions per minute), which is sufficiently slow to limit the blurring of images to less than 1 pixel for the exposure time of 0.045 s used in this study. Three flat field images of a dummy cell with an empty sample chamber were taken both before and after each tomography scan. The averaged flat field is then used as the intensity background to account for non-uniformities in the X-ray beams. Each tomography scan at one P-T condition takes approximately 20 mins. The raw data collected for each scan are 360 frames of 16-bit images with 1920  1440 pixels for each image. The pixel length was calibrated to be 1.687 m/pixel for both horizontal and vertical directions.

Tomographic reconstruction and 3D volume rendering

Tomography reconstruction was performed using the tomoRecon multi-threaded code available at GSECARS (Rivers, 2012). This code uses the high-speed Gridrec FFT

133 algorithm and can reconstruct the slices in parallel on multiple CPU threads. Figure V.2 shows the steps to transform raw images from the tomographic scans to a 3D volume rendering of the sample. First, the raw radiographic images (Figure V.2a) were corrected by subtracting background dark current and flat field intensities. Then, the corrected images were combined to produce a series of sinograms for each slice of the 3D rendering, after correcting rotation center and minimizing ring artifacts. The sinogram represents line integral of pixel intensities for a given pixel row height in each radiograph (Figure V.2b).

Each slice of the final 3D volume representing a 2D map of linear attenuation coefficient

(Figure V.2c) was then reconstructed from the sinograms using tomoRecon (Rivers, 2012).

Figure V.2c shows the reconstructed horizontal slice (viewed from the top), and the inset is a corresponding reconstructed vertical slice (viewed from the side). The sample can be clearly distinguished from the molybdenum capsule in these reconstructed slices. All these processing steps were accomplished using the IDL GUI program of the tomoRecon code

(TOMO_DISPLAY) (Rivers and Wang, 2006). Finally, the reconstructed horizontal slices

(Figure V.2c) were imported into ImageJ (https://imagej.nih.gov/ij/) for additional filtering, and then the Blob3D software ((Ketcham, 2005); http://www.ctlab.geo.utexas.edu/software/blob3d/) was used to separate the sample and capsule, and to get the volume rendering of the sample (Figure V.2d).

134 (a) Mo capsule (b)

Sample

Mo capsule

Sample

Figure V.2 Steps for tomographic reconstruction. (a) A representative raw radiographic image obtained for the sample at 3.7 GPa and 1934 K. The inset is the same image after adjusting brightness and contrast. (b) Sinogram showing the stack of line integrals of the pixel values at a given row height within the sample. (c) Reconstructed horizontal slice (viewed from the top) using the TOMO_DISPLAY program. The inset shows the reconstructed vertical slice (viewed from the side). The rectangular area is zoomed in Figure V.3 showing the filtering and separation processes. (d) 3D volume rendering of the sample using Blob3D. The Mo capsule was removed for clarity in this view. Figure V.3 shows the processed images after various stages of filtering and thresholding procedures. Using ImageJ, the reconstructed horizontal slices were first cropped to reduce image size without affecting the pixels of the sample and capsule, and then were adjusted for brightness and contrast to maximize the contrast between the Mo capsule and the jadeite melt sample without saturating the image (Figure V.3a). A mean filter with a radius of two pixels was applied to each slice to smooth out the noisy pixels and enhance the contrast between the sample and surrounding materials (Figure V.3b).

Lesher et al. (2009) showed that the volume obtained by using the mean filter is within 1%

135 of the true volume. The filtered images were then imported into Blob3D for sample segmentation, separation and volume extraction (Ketcham and Carlson, 2001). The pixel size and slice distances were input into Blob3D, forming an effective voxel size of 4.801

m3. The pixel intensity of each imported slice was rescaled to 0-255 in Blob3D, and the voxel intensity ranges of the sample and capsule were examined carefully. The sample volume was first segmented from the capsule using the general thresholding range (GTR) based on the voxel intensity range of the sample, and subsequently modified by the Seed

Range (SR) in Blob3D. This removes the voxels selected by GTR values that are not connected to the sample volume. After these thresholding processes, the sample can be segmented from the capsule and surrounding materials (Figure V.3c). Two additional filters, the Remove Islands/Holes filter (removing small areas of voxels forming as islands or holes in the sample) and the Majority filter (facilitating segmentation based on homogeneity rather than just grayscale to smooth the boundary between sample and capsule), were then applied to the segmented images to refine the segmentation (Figure

V.3d). After segmentation, the sample can be easily separated from the surrounding voxel volumes in Blob3D, and its real volume was then extracted from the total sample voxel volumes.

136 (a) (b) (c) (d)

Figure V.3 Images showing the filtering and separation processes of the sample and capsule. The images are zoomed in corresponding to the rectangular area in Figure V.2c to better show the effects of different processes. (a) Reconstructed slice after adjusting contrast and brightness. (b) Slice after applying the mean filter. (c) Slice showing the separated sample based on specifying the GTR and SR. (d) Slice showing the separated sample after applying the Remove Islands/Holes filter and the Majority filter. The typical sample volume in this study is on the order of ~1-2 mm3, which is more than eight orders of magnitude larger than the volume of a voxel (4.80110-9 mm3). This high spatial resolution in voxels greatly helps reduce the uncertainty in the measured volumes. The tomographic technique at the same beamline has been benchmarked against a sapphire sphere with known volume embedded in FeS by Lesher et al. (2009), showing that the measured volume can be accurate to within 1% of the true volume. The uncertainty in the reconstructed sample volume mainly comes from the thresholding process. By adjusting the threshold value, an optimal range of threshold values can be found in which the resulted sample volume is relatively insensitive to the threshold value (Lesher et al.,

2009). The variation of the reconstructed volume in this threshold range is ~0.015 mm3, which gives a relative uncertainty of ~1%. The density of jadeite melt was then obtained by dividing the mass of the glass sample measured before the experiment by the reconstructed sample volume. Uncertainty in the mass was estimated by the deviation of

137 repeated measurements and is estimated to be ~0.6%. Therefore, the propagated uncertainty in the density is about 1.2%.

Results and discussions

Density of jadeite melt at high pressures

The P-T conditions, reconstructed volumes, and calculated densities for the jadeite melt are listed in Table V.1. Since most of the data were measured at around 1900 K, the densities obtained at different temperatures were corrected to the 1900 K isotherm, using a fixed thermal expansion coefficient of 4.4  10-5 K-1 for jadeite melt calculated from the partial molar volumes and the temperature dependence of partial molar volumes of the oxide components (Na2O, Al2O3, and SiO2) given in (Lange, 1997). The density of jadeite melt increases with pressure monotonically from 2.56 g/cm3 at 1.4 GPa to 3.05 g/cm3 at

4.8 GPa. The high-pressure densities determined in this study are consistent with the room- pressure density calculated from the ideal mixing model using partial molar volumes of the oxide components (Lange, 1997). Figure V.4 compares our results with previous studies on jadeite melt including X-ray absorption measurements from Sakamaki (2017), FPMD simulations from Bajgain et al. (2019), and classical molecular dynamics (MD) simulations from Suzuki et al. (2011). After correcting for thermal effects, our data are mostly consistent with the results from the FPMD (Bajgain et al., 2019) over the entire pressure range of our experiments. Although our results also agree with those of classical MD simulations (Suzuki et al., 2011) between ~1-3 GPa, a deviation in the pressure effects on density can be observed. Such a deviation could be partly resulted from the particular choice of the pairwise interatomic potentials used in (Suzuki et al., 2011). However, because the study of Suzuki et al. (2011) is mainly devoted to viscosity measurements and

138 only a small fraction of the paper describes the MD simulations of density for jadeite melt, not sufficient details are given to resolve the deviation in pressure effects. The densities measured by the X-ray absorption method in the study of (Sakamaki, 2017), on the other hand, are significantly lower than our results and both simulation results. The reason for this discrepancy is not unclear. However, in the study of Sakamaki (2017), the sample was scanned by moving the incident slits instead of moving the sample directly as in most other

X-ray absorption measurements (e.g., (Malfait et al., 2014b; Seifert et al., 2013)). This difference in scanning techniques to obtain the X-ray absorption profiles would result in an unwanted variation of the incident X-ray beam intensity due to the inhomogeneity of the defocused X-ray beam at 13-BM-D of APS. In addition, the divergence of the beam

(change of beam direction) caused by moving the incident slits (relative to the front slits of the hutch) would also result in an inconsistency of slit position and the actual sample location shone by the X-ray beam. This would result in a deviation in the estimated X-ray travel lengths in the sample and hence the absolute density at a given mass absorption coefficient.

Table V.1 Experimental P-T conditions and measured densities for jadeite melt.

3 3 3 Load (tons) P (GPa) T (K) V (mm ) V1900 K (mm )  (g/cm )

10 1.4 1741 1.704 1.716 2.556

10 2.2 1955 1.629 1.625 2.698

20 3.7 1934 1.508 1.506 2.912

30 4.8 1921 1.437 1.436 3.054

Note: Uncertainty in pressure is about 0.5 GPa, uncertainty in temperature is about 100 K and uncertainties in reconstructed volume and density are about 1% and 1.2%, respectively.

139

Figure V.4 Density of jadeite melt as a function of pressure measured in this study and its comparison with previous studies. The shaded area is the uncertainty of the compression curve based on the BM-EOS fitting results. The solid black line for BM-EOS overlaps with the dashed black line for M-EOS. L97-Lange (1997), B19-Bajgain et al. (2019), Sa17-Sakamaki (2017) and Su11-Suzuki et al. (2011). The density data in this study were fit to the third-order Birch-Murnaghan equation of

state (BM-EOS) (Birch, 1952) using a Monte-Carlo approach to estimate the uncertainties

in the fit parameters (Xu et al., 2018). The third-order Birch-Murnaghan EOS is given as

7 5 2 3퐾푇0 𝜌 3 𝜌 3 3 ′ 𝜌 3 푃 = [( ) − ( ) ] {1 + (퐾푇 − 4) [( ) − 1]} (1) 2 𝜌0 𝜌0 4 𝜌0

′ where 푃 is pressure, 퐾푇0 the isothermal bulk modulus at room pressure, 퐾푇 the pressure

derivative of bulk modulus, 𝜌0 the room-pressure density, and 𝜌 the density at high

3 pressures. 𝜌0 was fixed to 2.30 g/cm at 1900 K, based on the ideal-mixing model of

′ (Lange, 1997), during the fitting procedure. The best-fit values for 퐾푇0 and 퐾푇 were

searched by minimizing 휒2, which is defined as

140 2 (𝜌푑푎푡푎−𝜌푚표푑푒푙) 2 푖 푖 휒 = ∑푖 휌 2 (2) (𝜎푖 )

푑푎푡푎 푚표푑푒푙 where 𝜌푖 is the i-th density data point at high pressures, 𝜌푖 is the modeled density

′ 𝜌 from BM-EOS using randomly generated values of 퐾푇0 and 퐾푇, and 𝜎푖 is the uncertainty in measured density including both the uncertainty from density measurements and the propagated equivalent uncertainty in density from the uncertainty in pressure

′ measurements. We explored the parameter range of 5-25 GPa for 퐾푇0 and 3-13 for 퐾푇,

′ with the lower bound on 퐾푇 being constrained by the use of the 3rd order BM-EOS, which

′ does not give reasonable solutions for 퐾푇 < 3.

′ +1.9 +6.6 The best-fit values for 퐾푇0 and 퐾푇 are 10.8−5.3 GPa and 3.4−0.4 , respectively. As shown by the large uncertainties associated with the fitting, there exists a strong correlation

′ between 퐾푇0 and 퐾푇 due to the limited pressure range in this study (Supplementary Figure

′ V.9a) and as a result, 퐾푇0 and 퐾푇 cannot be uniquely constrained from current density data.

′ A large number of 퐾푇0 and 퐾푇 pairs can recover the experimental data equally well. If we

′ +1.2 fix the 퐾푇 to 4 and fit only 퐾푇0, the fitted 퐾푇0 in this case is 9.9−1.1 GPa. It should be noted

′ that although a very small 퐾푇 (< 3) is not compatible with the BM-EOS and gives no reasonable solutions, the compression curve calculated from the BM-EOS using a very

′ small 퐾푇 (e.g., 1.3) can pass through the data (the thin black dash-dotted line in Figure V.4).

′ In order to examine the possibility of a very small 퐾푇, we also fit the data to the Murnaghan equation of state (M-EOS) (Murnaghan, 1967) in the parameter space of 5 to 25 GPa for

′ 퐾푇0 and -1 to 15 for 퐾푇, respectively, using the same approach as that in fitting the BM-

EOS. The M-EOS is given as

′ ′ 1/퐾푇 퐾푇 𝜌 = 𝜌0 (1 + 푃) (3) 퐾푇0

141 and the parameters are same as those in BM-EOS. The best-fit values using the M-EOS for

′ +6.5 +3.7 퐾푇0 and 퐾푇 are 11.0−4.6 GPa and 3.0−3.7, respectively, and their correlations are shown in

Supplementary Figure V.9b. The fitting results are generally consistent with those using

′ BM-EOS, with the 퐾푇0 and 퐾푇 in M-EOS having slightly larger and smaller values, respectively than those in BM-EOS.

The calculated compression curve using the BM-EOS and its uncertainty range as well as the compression curve using M-EOS are shown in Figure V.4. The compression curves for jadeite melt obtained from both the EOS models nearly overlap with each other and recover the experimental densities well. Table V.2 shows the comparison of the fitting results with previous studies. Kress et al. (1988) measured the ultrasonic velocity in the

Na2O-Al2O3-SiO2 liquid ternary at room pressure and developed a linear compressibility model for this ternary. The isothermal bulk modulus of jadeite melt calculated from their model is 19.1 GPa and significantly higher than the values determined in our study and from molecular simulations. This may be because that the model developed in Kress et al.

(1988) was based on melt compositions that are significantly different from the jadeite composition, which has equal molar amounts of Na2O and Al2O3. The starting compositions for which Kress et al. (1988) were able to obtain relaxed sound velocities, on the contrary, all have an excess in Na2O content relative to Al2O3 content and hence are more depolymerized than the jadeite melt. As a result, without experimental constraints on the Al2O3-rich side, it may not be appropriate to directly extrapolate of results of Kress et al. (1988) to obtain the room-pressure bulk modulus for jadeite melt. The derived 퐾푇0 and

′ 퐾푇 in this study are also generally in agreement with the simulation results. Although the simulations in Bajgain et al. (2019) were performed in a larger pressure range (up to 30

142 GPa) than the present study, no abrupt change or discontinuity is observed in the density data with pressure and the data can be fitted using a single 3rd-order EOS up to ~30 GPa

(Bajgain et al., 2019), indicating that if there is any change in compression mechanisms of jadeite melt at low to moderate pressures (Sanloup, 2016), such a change does not affect the EOS behavior of jadeite melt significantly. Only at very high pressures as in the study of Ni and de Koker (2011) (up to 144 GPa), the structural change can be evident from the

EOS as a 4th-order formula is needed for the fitting. The X-ray absorption study by

′ Sakamaki (2017), however, shows a quite different compression curve and distinct 퐾푇0-퐾푇 values from this study and the simulations.

Table V.2 Fitting results on bulk modulus and its pressure derivative and comparison with previous studies.

′ References 푲ퟎ (GPa) 푲 T (K) Method

+1.9 +6.6 10.8−5.3 3.4−0.4 1900 This study (BM-EOS) +1.2 9.9−1.1 4 (fixed) 1900 HPXTM

+6.5 +3.7 This study (M-EOS) 11.0−4.6 3.0−3.7 1900

Bajgain et al. (2019) 9.70 ± 3.88 5.42 ± 1.35 2500 FPMD

Ni and de Koker (2011)* 15.0 3.56 3000 FPMD

Sakamaki (2017) 21.5 ± 0.8 8.9 ± 1.2 1473 X-ray absorption

Kress et al. (1988)# 19.1 1773 Room-pressure ultrasonics

Note: All reported values are isothermal ones. * This study does not report density values and the fitting was performed using a fourth order finite strain expansion with a 퐾′′ of about -0.11. # The value was calculated using the linear compressibility model developed in this study for Na2O-Al2O3-SiO2 ternary with mole fractions of Na2O>Al2O3, which may not be applicable to jadeite melt. See discussion in the text.

Comparison of the compressibility with other silicate melts and geological implications

The relatively small 퐾0 and 퐾′ determined for jadeite melt in this study imply that it may be more compressible at high pressures than previously thought. Figure V.5 compares

143 the isothermal compressibility for silicate melts with different alkali concentration and degree of polymerization at high pressures, including the jadeite melt (~16.7 mol% alkalis,

NBO/T=0) from this study, peridotite melt (no alkalis, NBO/T=2.45) from Sakamaki et al.

(2010), MORB melt (~3.2 mol% alkalis, NBO/T=0.76) from Agee (1998), diopside melt

(no alkalis, NBO/T=2.01) from Ai and Lange (2008), rhyolitic melt (~7.9 mol% alkalis,

NBO/T=0.01) from Malfait et al. (2014b) and phonolitic melt (~12.7 mol% alkalis,

NBO/T=0.13) from Seifert et al. (2013), where the NBO/T is the ratio of non-bridging oxygen (NBO) to tetrahedrally coordinated cations (T) (Mysen et al., 1985). It can be seen from Figure V.5 that alkali-rich and polymerized melts are in general more compressible than alkali-poor and depolymerized melts under upper mantle conditions, and jadeite melt has the highest compressibility among these melts over the entire pressure range shown here. It is likely that both the alkali content and the degree of polymerization can significantly affect the compressibility of silicate melts. However, it is difficult to assess the relative roles of alkali and polymerization in affecting the melt compressibility based on currently available data, as melts containing more alkalis are often more polymerized at the same time.

144 0.1 Jd (alkalis=16.7 mol%, SiO =66.7 mol%, NBO/T=0) 2 MORB (alkalis=3.2 mol%,SiO =52.9 mol%, NBO/T=0.76) 0.09 2 Rhyolite (alkalis=7.9 mol%, SiO =84.6 mol%, NBO/T=0.01) 2 Phonolite (alkalis=12.7 mol%, SiO =63.1 mol%, NBO/T=0.13) 2 0.08 Di (no alkalis, SiO =49.8 mol%, NBO/T=2.01) 2

) Peridotite (no alkalis, SiO =40.8 mol%, NBO/T=2.45)

1 2

a 0.07

(

y 0.06

s 0.05

m 0.04

C 0.03

0.02

0.01 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Pressure (GPa)

Figure V.5 Comparison of the isothermal compressibility (at 1473 K) for various anhydrous silicate melts at high pressures. Data for MORB, rhyolite, phonolite, diopside (Di) and peridotite melts are from Agee (1998), Malfait et al. (2014b), Seifert et al. (2013), Ai and Lange (2008) and Sakamaki et al. (2010), respectively. The compressibility curve for jadeite melt was calculated using the best-fit values from BM-EOS. Blue curves are for polymerized melts based on the NBO/T ratios, and red curves are for depolymerized melts. Sodium-rich melts have been observed in the experimental products of low-degree partial melting of mantle rocks (Falloon et al., 2008, 1997; Hirose and Kushiro, 1993;

Robinson et al., 1998). For example, the liquid composition of low-degree partial melting of a fertile peridotite near the solidus temperature at 1.5 GPa in the experimental study of

Robinson et al. (1998) has Na2O content up to ~8 wt%. The experimental results of Falloon et al. (1997) show that the first melt in equilibrium with a harzburgite residue at 1493 K could contain ~12 wt% Na2O. The melt compositions calculated for partial melting of both fertile and depleted peridotite by using the pMELTS package (Ghiorso et al., 2002) also show high sodium content (Pommier and Garnero, 2014). It is important to evaluate the

145 density and gravitational stability of sodium-rich melts at upper mantle conditions, in order to understand the migration behavior of early partial melts in the mantle. Jadeite melt may be used as a representative and simplified sodium-rich melt composition in the upper mantle. Our experimental results show that jadeite melt is very compressible and that its density increases rapidly with pressure. The calculated density profile for jadeite melt is compared with the density of jadeite solid (Zhao et al., 1997), the PREM density model

(Dziewonski and Anderson, 1981) and the density of diopside, anorthite, and model basalt

(Di64An36) melts from shock-wave studies by Asimow and Ahrens (Asimow and Ahrens,

2010) in Figure V.6. The density of jadeite melt is the lowest among these silicate melts at room pressure, while at around 4-6 GPa the density of jadeite melt exceeds those of Ca-

Mg rich melts. At around 8-13 GPa, there could be a density crossover between the jadeite melt and mantle minerals (Figure V.6) if our equation of state can be extrapolated to higher pressures. This implies that sodium-rich melts generated by low-degree partial melting of mantle peridotite may become gravitationally stable at ~250-400 km depth in the upper mantle, which could be a possible explanation for the seismically observed anomalies at around these depths in the upper mantle (Ritsema and Van Heijst, 2000; Tauzin et al., 2010).

In addition to the Na2O component, FeO, the heaviest major component in silicate melts, also prefers the melt phase during partial melting (Mibe et al., 2006). Thus, the presence of iron in these early melts would make the density-crossover happen more easily (Jing and Karato, 2009, 2011).

146

Figure V.6 Comparison of the density profile of jadeite melt obtained in this study with that of jadeite solid (Zhao et al., 1997), PREM model (Dziewonski and Anderson, 1981) and Di, An, model basalt (Di64An36) melts (Asimow and Ahrens, 2010). The Jd melt and solid are compared at 1673 K isotherm, while the Di, An and model basalt liquids from shock-wave studies are along their respective adiabats with a potential temperature of 1673 K. The shaded area represents the uncertainty in the compression curve for jadeite melt.

Conclusions

We have successfully measured the density of a jadeite melt up to 4.8 GPa and 1955

K using the high-pressure X-ray microtomography technique in a Paris-Edinburgh cell assembly. The microtomographic technique can accurately recover the density for silicate melts with low X-ray absorption by using a pink X-ray beam and a relatively strongly absorbing material to encapsulate the liquid sample. The densities obtained are higher than previous experimental results using X-ray absorption method but are generally consistent with previous molecular dynamics simulation results, especially the first-principles molecular dynamics results. By comparing the compressibility of various silicate melts, we

147 show that alkali-rich, polymerized melt are more compressible than alkali-poor, depolymerized melt under upper mantle conditions. The high compressibility of jadeite melt implies that low-degree sodium-rich silicate melts in the deep upper mantle may become denser than surrounding mantle materials.

Acknowledgments

This research was partly supported by the National Science Foundation (EAR-

1619964 and 1620548) and the National Natural Science Foundation of China (41974098).

The high pressure microtomographic experiments were performed at GSECARS beamline

13-BM-D, Advanced Photon Source (APS), Argonne National Laboratory. GSECARS is supported by the National Science Foundation - Earth Sciences (EAR-1634415) and

Department of Energy - GeoSciences (DE-FG02-94ER14466). This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of

Science User Facility operated for the DOE Office of Science by Argonne National

Laboratory under Contract No. DE-AC02-06CH11357. We thank Nanthawan Avishai for her assistance on the SEM analysis of the quenched sample at the Swagelok Center for

Surface Analysis of Materials (SCSAM) of CWRU.

148 Supplementary Materials

2500 10 tons 20 tons 30 tons 2000 Poly. (10 tons) Poly. (20 tons) Poly. (30 tons)

)

K 1500

(

e 2 p y = 0.0027x + 3.5064x + 342.6

e 1000 R² = 0.9979

y = 0.002x2 + 3.5402x + 300.28 R² = 0.9999 500 y = 0.0022x2 + 3.1433x + 311.85 R² = 0.9999

0 0 100 200 300 400 500 Power (W)

Supplementary Figure V.7 Temperature-power relationships calibrated at different loads for the PE cell assembly used for tomographic measurements on silicate melts.

149

Supplementary Figure V.8 (a) Secondary electron (SE) image (left) and backscattered electron (BSE) image (right) of the quenched sample. (b) Composition mapping of the quenched sample.

150

Supplementary Figure V.9 (a) Correlations between fitted K0 and K’ using Birch-Murnaghan equation of state (EOS) in the parameter space of 5 to 25 GPa for K0 and 3 to 13 for K’. Birch-Murnaghan EOS fails at K’<3. See discussions in the main text. (b) Correlations between fitted K0 and K’ using Murnaghan EOS in the parameter spaces of 5 to 25 GPa for K0 and -1 to 15 for K’. Red circles indicate the best-fit values.

Supplementary Table V.3 Compositions of the quenched sample measured by EDS (atomic %).

At%

Si 19.31

Na 9.67

Al 10.41

O 60.61

Mo 0

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160 Chapter VI

High-pressure elastic properties of dolomite melt supporting carbonate-

induced melting in deep upper mantle

(In preparation for submission)

Abstract

Deep subducted carbonates likely cause low-degree melting of the upper mantle and thus play an important role in deep carbon cycles. However, direct seismic detection of carbonate-induced partial melts in the Earth’s interior is hindered by our poor knowledge on the elastic properties of carbonate melts. Here we report the first experimentally determined sound velocity and density data on dolomite melt up to 5.9 GPa and 2046 K by in-situ ultrasonic and sink-float techniques, respectively, as well as first-principles molecular dynamics simulations of dolomite melt up to 16 GPa and 3000 K. Using our new elastic data, the calculated VP/VS ratio of the deep upper mantle (~180 to 330 km) with a small amount of carbonate-rich melt provides a natural explanation for the elevated VP/VS ratio of the upper mantle from global seismic observations, supporting the pervasive presence of a low-degree carbonate-rich partial melt (~0.05%) as argued by petrologic studies. This carbonate-rich partial melt layer, probably corresponding to the base of volatile-induced or redox-regulated initial melting in the upper mantle, helps estimate the global average carbon concentration to be 80-140 p.p.m. in the deep upper mantle source, consistent with mantle carbon content determined from geochemical studies.

161 Introduction

Carbon, one of the most important chemical elements for life, energy, and climate, is widely distributed in the Earth’s upper mantle, through deep carbon cycles (Dasgupta and

Hirschmann, 2010). Due to the limited solubility of carbon in mantle minerals (Keppler et al., 2003) and the relatively oxidized environment in shallower part of the upper mantle

(<~250 km) (Frost and McCammon, 2008), carbon is mostly stored in forms of carbonate minerals as accessory phases in mantle rocks. Petrologic studies suggest that the presence of carbonates can dramatically lower the solidus of mantle rocks (Dasgupta et al., 2013;

Dasgupta and Hirschmann, 2006; Litasov and Ohtani, 2010), thereby producing incipient carbonate-rich melts (carbonatite melts) in the deep upper mantle through either partial melting of carbonated lithologies (Dasgupta et al., 2013; Dasgupta and Hirschmann, 2006) or redox melting of upwelling reduced carbon domains (Rohrbach and Schmidt, 2011).

These carbonate-rich melts are efficient agents for mantle metasomatism due to their high mobility (Kono et al., 2014) and enrichment in various incompatible elements (Blundy and

Dalton, 2000). The presence of carbonate melts in the upper mantle has been argued by a range of petrological and geochemical studies including the discovery of carbonate melt inclusions in gem-quality diamond (Logvinova et al., 2019), observations of CO2-rich petit-spot volcanos (Machida et al., 2017), and the investigation of Mg isotope anomaly of mantle-derived melts (Li et al., 2017), and has been suggested to be the cause for high electrical conductivity anomalies (Gaillard et al., 2008; Sifré et al., 2014) in the mantle.

However, direct seismic detection of the existence and distribution of carbonate-rich partial melts has been hindered by our poor understanding of the elastic properties such as sound velocity and density of carbonate melts at high pressures.

162 Experimental measurements on the sound velocity and density of carbonate melts most relevant to Earth’s upper mantle (Dasgupta and Hirschmann, 2010), including CaCO3

(calcite), MgCO3 (magnesite), and CaMg(CO3)2 (dolomite) melts, are essentially nonexistent due to experimental challenges. At room pressure, these melt properties cannot be measured directly because carbonates in the CaCO3-MgCO3 system undergo decarbonation reactions prior to melting. As a result, room-pressure sound velocity and density measurements are only limited to CaCO3-bearing alkali carbonate melts (Hurt and

Lange, 2019; Liu and Lange, 2003; O’Leary et al., 2015) (with a CaCO3 mole fraction less than 0.5). At high pressures, only the density of CaCO3 melt was studied using X-ray diffraction measurements (Hudspeth et al., 2018), but this method suffers from complex data analysis procedures for background correction. So far, most our knowledge on the compressibility and equation of state (EOS) of CaCO3-MgCO3 melts comes from molecular dynamics (MD) simulations. For example, CaCO3 melt has been studied by both classical MD simulations (Genge et al., 1995; Hurt and Wolf, 2018) and first-principles molecular dynamics (FPMD) simulations (Vuilleumier et al., 2014; Zhang and Liu, 2015).

However, the estimated pressure derivative of compressibility for CaCO3 melt differs by more than 30% among these simulations, highlighting the need for direct high-pressure experiments to validate the results from theoretical calculations. As for MgCO3 and

CaMg(CO3)2 melts, most of the results were obtained recently from classical MD simulations (Desmaele et al., 2019; Hurt, 2018) using empirical atomic potentials, with only two FPMD simulated density results reported in Desmaele et al. (2019). However, large discrepancies also exist between these studies. For example, Hurt (2018) reported an

163 anomalous compression behavior for MgCO3 melt, resulting in about 12% lower densities than those from Desmaele et al. (2019).

Here we report the first high-pressure experimental study on the density and sound velocity of a carbonate melt (dolomite composition, CaMg(CO3)2), as well as new FPMD simulation results on dolomite melt. Of all the carbonate melt compositions, the dolomite composition is of primary interest to the upper mantle because it is close to the primary near-solidus carbonatite melt compositions at upper mantle conditions by melting of carbonated mantle lithologies (Dasgupta and Hirschmann, 2010, 2006; Wallace and Green,

1988). Using our sound velocity and EOS results for dolomite melt and the results for diopside melt from Xu et al. (2018), we calculate the compressional wave velocity (VP) to shear wave velocity (VS) ratio for melt-bearing mantle as a function of melt fraction and depth. Comparison of our calculated VP/VS ratio with that of the global seismic models

(Dziewonski and Anderson, 1981; Kennett et al., 1995; Kennett and Engdahl, 1991) provides new insights into the possible distribution, composition and amount of partial melts in the deep upper mantle.

Results

Sound velocity of dolomite melt

High-pressure ultrasonic measurements were conducted in a Kawai-type multi-anvil apparatus (Methods) with a 14/8 cell assembly (Supplementary Figure VI.4). The length of the melt sample can be obtained from in-situ X-ray radiographic imaging (Figure VI.1a), and the travel time through the sample can be determined by the pulse-overlap method

(Jing et al., 2014; Kono et al., 2012) using the reflected signals from buffer rod (BR)- sample and sample-backing plate (BP) interfaces (Figure VI.1b). With increasing

164 temperature, the pattern of ultrasonic signals changes as the sample transforms from solid to partially molten and then to fully molten liquid (Supplementary Text S1 and

Supplementary Figure VI.5). The sound velocity data for dolomite melt are reported in

Figure VI.2a and tabulated in Supplementary Table VI.3. The uncertainty in measured sound velocities are less than 1%, coming mostly from the uncertainties in sample length determinations. The sound velocity is nearly independent of frequency from 20 to 60 MHz

(Supplementary Table VI.3) and no S-wave signals were observed for the melt

(Supplementary Figure VI.5), indicating that the measured sound velocity for dolomite melt is fully relaxed (Rivers and Carmichael, 1987) and can be directly compared with seismic wave velocity. At 1837 K, the sound velocity for dolomite melt increases with pressure from 3757 m/s at 1.9 GPa to 4905 m/s at 5.9 GPa. At pressures below ~4 GPa, the sound velocity decreases slightly with temperature, and the effect of temperature on the sound velocity becomes negligible with increasing pressure.

165 (a)

Backing plate

Sample Pt capsule length

Buffer rod

(b) Anvil BR

) Noise BP

(

n Sample

Time (s)

Figure VI.1 (a) A representative radiographic image of the liquid sample at 4.1 GPa and 1733 K. Red lines indicate the positions of the buffer rod (BR)-sample and sample-backing plate (BP) boundaries. (b) Corresponding P-wave ultrasonic signals obtained for the dolomite melt sample.

Density and EOS for dolomite melt

The density of dolomite melt at high pressures was determined using the sink-float technique (Agee, 1998; Knoche and Luth, 1996) with boron carbide (B4C) as the solid density marker in a Walker-type multi-anvil press (Methods). We have successfully observed neutral and float cases at 3 and 5 GPa, respectively, whereas sinking of the solid markers, which is expected at lower pressures, was not observed due to the decomposition of dolomite at low pressures (<2.5 GPa) (Buob et al., 2006; Irving and Wyllie, 1975)

166 (Supplementary Figure VI.6). The neutral buoyancy of B4C spheres in dolomite melt allows us to estimate the density of dolomite melt to be 2.54 g/cm3 at 3 GPa and 1773 K, using the EOS parameters for B4C from Dodd et al. (2002). The uncertainty in the density is determined to be ~1% and the uncertainty in pressure is ~0.5 GPa. The flotation of B4C spheres in dolomite melt indicates that the melt density is higher than 2.56 g/cm3 at 5 GPa and 1873 K.

The sound velocity data, combined with the measured high-pressure density, can tightly constrain the EOS for dolomite melt. We fit our experimental data with the third- order isothermal Birch-Murnaghan EOS using a Monte-Carlo approach (Supplementary

Text S2). The fitting results are shown in Table VI.1. Our best-fit values for the room- pressure density 𝜌0 , the room-pressure isothermal bulk modulus 퐾푇0 , the pressure

′ derivative of the bulk modulus 퐾푇, and the Anderson-Grüneisen parameter 훿푇 are 2.33 ±

0.02 g/cm3, 16.1 ± 1.9 GPa, 9.0 ± 1.5, and 3.5 ± 1.3 (1), respectively, at a reference temperature of 1573 K. The negative correlation between the fitted bulk modulus (퐾푇0)

′ and its pressure derivative (퐾푇) is shown in Supplementary Figure VI.8. The calculated velocity and density profiles for dolomite melt recover the experimental data very well

(Figure VI.2). Compared to the velocity of diopside melt (CaMgSi2O6) (Xu et al., 2018), the velocity of dolomite melt is significantly higher than that of diopside melt at upper mantle conditions and the velocity differences between the two melts increase with pressure. This implies that carbonate melt may be less efficient than silicate melt in reducing the seismic velocity in the upper mantle of the Earth.

167 FPMD simulation results and comparison with experimental results and previous studies

We also performed first-principles molecular dynamics (FPMD) simulations to determine the density and compressibility of dolomite melt at high pressures using the canonical (NVT) ensemble as implemented in the Vienna ab initio simulation package

(VASP) (Kresse and Furthmüller, 1996a, 1996b; Kresse and Hafner, 1993) (Methods).

Both the local density approximation (LDA) and the generalized gradient approximation

(GGA-PBE) (Ceperley and Alder, 1980; Perdew et al., 1996) were used for the estimation of electronic exchange-correlation energy. The full simulation data on dolomite melt are reported in Supplementary Table VI.4 and Supplementary Figure VI.9. We use the Mie-

Grüneisen thermal equation of state to describe the pressure, temperature and volume data obtained for dolomite melt from the simulations (Supplementary Text S2). The calculated velocity profile for dolomite melt by the LDA method agrees very well with the experimentally measured sound velocity (Figure VI.2a) at pressures from ~2 to 5 GPa, despite a small deviation at pressures less than about 1.5 GPa where dolomite melt is not stable. The pressure dependence of sound velocity is similar in both the experiments and the simulations, although the velocity calculated by the GGA method is systematically lower than that from the LDA and experiments. The experimentally determined density profile for dolomite melt lies between the two curves issued from LDA and GGA, respectively (Figure VI.2b). This is reasonable as it is well-known that LDA often overestimates the density while GGA underestimates it (Oganov and Ono, 2004; Wu et al.,

2004). The density calculated using GGA from Desmaele et al. (2019) is consistent with our GGA results, and their density data obtained by classical MD simulations are also in agreement with our experimental results (Figure VI.2b). The fitting results for bulk

168 ′ modulus (퐾푇0) and its pressure derivative (퐾푇0) also agree with each other within the uncertainties (Table VI.1). The classical MD simulations from Hurt (2018), however, report a lower density for dolomite melt and a slightly different pressure dependence than our results and the results from Desmaele et al. (2019). This may be because that the empirical potentials employed in Hurt (2018) do not fully describe the behavior of dolomite melt. Using the empirical potentials developed by Hurt and Wolf (2018), Hurt (2018) reported an anomalous compression behavior for MgCO3 melt with a surprisingly low density and high compressibility at low pressures compared to other carbonate melts.

However, the anomalous behavior is not confirmed by our experimental measurements, at least not for MgCO3-bearing dolomite melt.

(a) 5500 (b) 3 1773 K fitting 2000 K fitting 5000 LDA 2000 K fitting 2.8 GGA 2000 K fitting

4500 2.6

)

4000 c

(

t 2.4

s l 3500

V D 2.2 Neutral 1773 K 3000 Floatation 1873 K dolomite 1629 K LDA 2000 K dolomite 1837 K 2 GGA 2000 K 2500 LDA 2000 K Desmaele et al. (2019) MD 2073 K GGA 2000 K Desmaele et al. (2019) FPMD 1773 K diopside 1673 K Hurt (2018) MD 1100 K 2000 1.8 01234567 01234567 Pressure (GPa) Pressure (GPa)

Figure VI.2 (a) Sound velocity as a function of pressure for dolomite melt. Different markers correspond to different experimental runs: square-T2207, circle-T2208, upward-pointing triangle-T2261, downward- pointing triangle-T2262, diamond-T2439. Different marker colors correspond to different temperatures: blue-1629 K, green-1733 K, orange-1837 K, magenta-1942 K, red-2046 K. The blue and orange curves are fitted velocity results of dolomite melt along the 1629 K and 1837 K isotherms, respectively. The dashed and dash-dot curves are our FPMD results for dolomite melt along the 2000 K isotherm based on LDA and GGA, respectively. The thick black curve is the velocity profile for diopside melt from Xu et al. (2018) for comparison. The diopside melt velocity is calculated along its adiabat with a potential temperature of 1673 K, but the temperature effect on the velocity of diopside melt at high pressures is negligible (Xu et al., 2018). (b) Density as a function of pressure for dolomite melt obtained from experiments and FPMD simulations in this study, and comparison with previous studies. Blue asterisk-neutral point, blue upward-pointing triangle- floatation point, blue solid line-EOS fitting based on experimental data at 1773 K, blue dotted line-EOS fitting at 2000 K, red circle-density data obtained by LDA, red square-density data obtained by GGA, red dashed line-EOS fitting at 2000 K for LDA, red dash-dot line-EOS fitting at 2000 K for GGA, green diamond- classical MD simulations data at 2073 K from Desmaele et al. (2019), dark green diamond-GGA simulation

169 data at 1773 K from Desmaele et al. (2019), cyan cross-classical MD simulations data at 1100 K from Hurt (2018).

Table VI.1 Fitting results for the EOS of dolomite melt

Experiments GGA LDA Desmaele et al. (2019) 푇푟푒푓 (퐾) 1573 2000 2000 1653 푃 (퐺푃푎) 1.4-5.9 0-15 0-16 0-15 푇 (퐾) 1629-2046 2000-3000 2000-3000 1653-2073 −3 𝜌0 (푔푐푚 ) 2.33 ± 0.02 1.92 ± 0.02 2.41 ± 0.01 2.26 퐾푇0 (퐺푃푎) 16.1 ± 1.9 9.04 ± 1.56 19.87 ± 1.71 12.13 ′ 퐾푇0 9.0 ± 1.5 6.45 ± 0.80 6.94 ± 0.45 8.5 훿푇 3.5 ± 1.3 −6.8 푢 (푑푃/푑푇)푉 (푀푃푎/퐾) 1.4 + 283.1푒 7.5 − 5.8푢 훾 2.8 − 2.0푢 3.3 − 2.6푢 *푢 = 푉⁄푉푟푒푓 표푟 𝜌푟푒푓⁄𝜌

Discussion

Petrologic studies on melting of carbonated upper mantle have shown that the

initiation of partial melting beneath mid-ocean ridges can occur as deep as ~220-330 km

(Dasgupta et al., 2013; Dasgupta and Hirschmann, 2006). For typical mantle carbon

concentration of tens to hundreds of ppm, the determined carbonated mantle solidus is

expected to be always lower than the upper mantle adiabat (Dasgupta, 2018), implying a

pervasive volatile-induced partial melting in the deep upper mantle. The small amount

(<0.1%) of melt produced by melting of carbonated peridotite (Dasgupta and Hirschmann,

2010), or by redox melting of upwelling reduced carbon-enriched mantle (Rohrbach and

Schmidt, 2011) is likely to be carbonatite (with ~40 wt% CO2) at >~300 km depth or

carbonate-rich silicate melt ( 25 wt% CO2 and 25 wt% SiO2) at shallower depth.

Geodynamic modeling on the rates and distribution of carbonate melting using mantle

upwelling patterns also shows that low-degree carbonate-induced melting occurs

pervasively throughout the oceanic upper mantle at depths greater than ~150 km (Clerc et

al., 2018). The presence of such carbonate-rich melt at greater depths (~150-330 km) than

170 typical silicate melting (<~85 km) may well explain the observed deeper seismological and magnetotelluric anomalies in the upper mantle (Bagley and Revenaugh, 2008; Gu et al.,

2005; Lizarralde et al., 1995; The MELT Seismic Team, 1998), implying that carbonated incipient melting may extend to as deep as ~330 km. However, no direct constraint from seismic velocity has ever been placed on the extent of this deep melting, due to the lack of available elastic data on melts at high pressures. Here we employ the theoretical model for partially molten assemblages from Takei (2002) and use our relaxed elastic data on dolomite melt (CaMg(CO3)2) and previous results on diopside melt (CaMgSi2O6) (Xu et al., 2018) to evaluate the effect of deep partial melting on the seismic structure of the upper mantle.

The calculation details are shown in Supplementary Text S3. The calculated VP/VS ratios for partially molten mantle (olivine + various amount of carbonate or silicate melt) as a function of depth are compared with global radial seismic profiles (PREM, Dziewonski and Anderson (1981); IASP91, Kennett and Engdahl (1991); AK135, Kennett et al. (1995)) in Figure VI.3. In the deep upper mantle from ~180 to 330 km depth, most of the global seismic profiles show a relatively higher VP/VS ratio than that of the dry mantle and require the presence of a very small fraction (~0.05%) of either carbonate or silicate melt (Figure

VI.3). This implies that the initial melting in the upper mantle is indeed likely to extend as deep as ~330 km, consistent with previous petrologic studies on mantle melting (Dasgupta et al., 2013; Dasgupta and Hirschmann, 2010, 2006). Although carbonate melt has significantly higher acoustic velocities than silicate melt at high pressures (Figure VI.2a), our modeling results show that for such a small melt fraction, seismology is unlikely to be able to distinguish the melt composition (carbonate vs. silicate) based on the observed

171 velocity anomalies. However, according to the melt compositions determined from petrologic studies, the melt is most likely to be carbonatite melt (Dasgupta and Hirschmann,

2006) or carbonate-rich silicate melt (Dasgupta et al., 2013). Our results thus suggest that a small fraction of carbonate-rich melt corresponding to the volatile-induced mantle incipient melting may be globally present in the deep upper mantle.

This is potentially at odds with the redox state suggested for the upper mantle below

~250 km where the fO2 is inferred to be too low for oxidized carbonate to be stable (Frost and McCammon, 2008; Rohrbach and Schmidt, 2011). However, as pointed out by

Dasgupta (2018), although the average fO2 in the mantle is expected to decrease with depth, the variation of fO2 at a given depth can be as much as 2 to 4 orders of magnitude (Yaxley et al., 2017). This means that the upper mantle at ~250-330 km depth could have significant heterogeneity, containing both reduced diamond/graphite and oxidized carbonate domains.

A recent study (Eguchi and Dasgupta, 2018) on mantle redox state using CO2-trace element systematics of oceanic basalt showed that the convecting upper mantle is likely to be more oxidized than the fO2 recorded in mantle xenoliths. In addition, the melt present at these depths is likely to be a carbonate-silicate mixture rather than a pure carbonate melt. The lower CO2 content of these melts increases their thermodynamic stability at depths below the pure carbonate redox front (Stagno et al., 2013). Hence, a pervasive presence of carbonate-rich melt in the deep upper mantle seems plausible, and this carbonate-rich melt layer itself may be also a reflection of the redox-regulated incipient melting in the deep upper mantle. Further studies on the stability of carbonated melt as a function of fO2 and pressure are needed to verify this.

172 Due to the low wetting angle (Minarik and Watson, 1995) and high enrichment of incompatible elements in carbonate melt (Blundy and Dalton, 2000), the presence of even a very small amount of such melt will have a significant influence on the physical and chemical properties of the upper mantle. Even with fully connected melt networks, as is the case for carbonate melt (Minarik and Watson, 1995), the very small fraction of melt is likely to be retained in the deep upper mantle due to a combination of low permeability and surface tension forces (Holtzman, 2016; Selway and O’Donnell, 2019), thus resulting in the high VP/VS ratio observed in the global seismic structures. Alternatively, carbonate- rich melt in deeper regions may migrate upwards, with gradual transition in composition to more silicate-rich melt (Dasgupta and Hirschmann, 2010), which could result in possible accumulations of melt at deep depth due to an increase in melt viscosity and/or a change in melt topology (Kono et al., 2014).

The pervasive presence of ~0.05% carbonate-rich melt provides a new way to estimate the global average carbon concentration in the deep upper mantle, a critical parameter for understanding the deep carbon reservoir. Although it is well-known that carbon distribution in the upper mantle is highly heterogeneous (Le Voyer et al., 2017), a global average value for carbon content is still useful for planetary scale geochemical and geophysical modeling.

Assuming the melt is carbonatitic with ~40 wt% CO2 (Dasgupta and Hirschmann, 2006), which should provide the upper bound for the carbon content as the melt may evolve to more silicate-rich at shallower depth, and employing the carbon partitioning coefficient between mantle melt and solid (0.00055 ± 0.00025) determined experimentally (Rosenthal et al., 2015) and the batch melting model, the estimated average carbon concentration in the deep upper mantle is about 80-140 p.p.m., lying between the carbon content for a

173 depleted mantle source (~10-30 p.p.m.) and an enriched mantle source (~50-500 p.p.m.)

(Dasgupta and Hirschmann, 2010) estimated by geochemical measurements on erupted basalts, associated melt inclusions and CO2/incompatible elements systematics. This further implies that global presence of carbonate-rich partial melts in the deep upper mantle, probably corresponding to the effective base of volatile-induced/redox regulated incipient melting (Le Voyer et al., 2017), is highly possible. In order for seismology to be able to detect these partial melts, their amounts and possible transitions in the melt composition, a comprehensive knowledge of the melt stability and elastic properties as a function of composition, pressure, temperature and oxygen fugacity is needed. Our study provides the first comprehensive datasets for the elastic properties of carbonate melt at high pressures, which are essential for thermodynamic modeling of carbonated mantle melting and understanding the deep carbon cycle.

174 Vp/Vs 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2 0 PREM 50 IASP91 AK135

100

150

)

k 200

(

p 250

D 300

350 Melt fraction 0% Melt fraction 0.05% Melt fraction 0.1% 400 Melt fraction 0.2% Melt fraction 0.5% 450

Figure VI.3 VP/VS ratio calculated for a partially molten mantle analog as a function of depth and melt fraction, and its comparison with global seismic profiles. Colored solid lines-SC olivine + dolomite melt and colored dashed lines-SC olivine + diopside melt. The elastic properties for diopside melt is from Xu et al. (2018). PREM model is from Dziewonski and Anderson (1981), IASP91 model from Kennett and Engdahl (1991) and AK135 model from Kennett et al. (1995). All the calculations were performed along a plausible mantle adiabatic temperature profile (Katsura et al., 2010).

Materials and Methods

Starting materials

The samples used in both ultrasonic and sink-float experiments were synthetic dolomite cores provided by Dr. Caleb W. Holyoke III from the University of Akron. The dolomite was synthesized by the hot isostatic pressing method described in detail in previous studies (Davis et al., 2008; Holyoke et al., 2013). The synthetic dolomite is fine- grained (2.5 ± 1.5 m), has a uniform texture and a nearly perfect stoichiometric composition (Davis et al., 2008). For ultrasonic experiments, cylindrical disks with the

175 desired diameter were machined from the synthetic dolomite chunk by using a CNC- milling machine. The top and bottom of the disks were then polished to mirror reflection

(<1 m) with nearly perfect parallelism. The polished disks were used as the starting materials for the ultrasonic experiments. For sink-float experiments, the dolomite chunk was crushed and ground to powders and stored in a vacuum oven before each experiment.

High-pressure ultrasonic measurements

The high-pressure ultrasonic measurements were performed at the GSECARS

Beamline 13-ID-D of the Advanced Photon Source, Argonne National Laboratory, using a

10-MN multi-anvil press with a double-stage Kawai-type module (Wang et al., 2009).

Tungsten carbide anvils with a truncation edge length of 8 mm were used as the second- stage anvils. The detailed cell assembly is shown in Supplementary Figure VI.4a. Pressure of the experiments was determined by energy-dispersive X-ray diffraction of the pressure marker consisting of a mixture of MgO and h-BN (MgO:BN=3:1 by weight) in the cell assembly, using the EOS of MgO (Tange et al., 2009). The uncertainty in pressure is about

10%. Temperature of the experiments was estimated by a W5Re-W26Re thermocouple, with corrections for the thermal gradient which has been calibrated on a similar cell assembly by Chantel et al. (2018). The uncertainty in temperature is about 50 K.

The setup for ultrasonic measurements has been described in detail by Jing et al. (2014) and Xu et al. (2018). Elastic waves, converted from electrical signals in the frequency range of 20-60 MHz by a 10° Y-cut LiNbO3 piezoelectric transducer attached to the corner of the bottom WC anvil, travel through the cell assembly, and are reflected at various interfaces including the anvil-buffer rod (BR), buffer rod-sample and sample-backing plate (BP) interfaces (see Supplementary Figure VI.4a for positions of these interfaces). The reflected

176 elastic waves are then converted back by the same transducer to electrical signals which are recorded by a digital oscilloscope at a sampling rate of 5  109 /s. Travel time through the sample was determined by the pulse-overlap method (Jing et al., 2014; Kono et al.,

2012) using the reflected signals from BR-sample and sample-BP interfaces (Figure VI.2b).

Uncertainty in travel time is within ±0.2 ns, corresponding to a relative uncertainty of 0.2%.

Sample length was determined by X-ray radiographic imaging (Figure VI.2a), with an uncertainty within ±1.774 m (1 pixel), corresponding to a relative uncertainty of 0.5%.

Then, the sound velocity of the sample was calculated from travel time and sample length, with a total propagated uncertainty of less than ~1%. In this study, platinum was used as the sample capsule and densified Al2O3 rod as BR and BP, which have also been successfully used in room-pressure ultrasonic measurements on carbonate melts (O’Leary et al., 2015).

For each experiment, the ultrasonic measurements were carried out at one to four fixed hydraulic ram loads, corresponding to pressures from ~1.4 to 5.9 GPa and at temperatures from 1629 to 2046 K. After reaching the target load, the temperature was increased steadily to above the melting temperature of dolomite (Buob et al., 2006). With increasing temperature, the ultrasonic signals change as the state of the sample changes from solid to partial melting and then to fully molten liquid (Supplementary Figure VI.5). For each experiment, two to four heating cycles were performed and finally the sample was quenched by turning the heater power off.

Sink-float density measurements

The sink-float technique has been widely used to determine the density of silicate melts at high pressures (Agee, 1998; Knoche and Luth, 1996). In this technique, the density

177 of a melt is bracketed by the sinking and floatation of preloaded solid markers, with known density, in the melt. However, this technique has never been applied to carbonate melts due to the difficulty of finding a suitable solid marker for carbonate melts. In this study, we have tested a range of materials and found that boron carbide (B4C), which is a super-hard material and has a low room-pressure density (~2.52 g/cm3) and high melting temperature

(~3036 K), is an effective density marker for carbonate melts.

The experiments were performed in a Walker-type multi-anvil press at Case Western

Reserve University using the COMPRES 14/8 cell assembly (Leinenweber et al., 2012).

The detailed cell assembly is shown in Supplementary Figure VI.4b. A stepped heater was used to reduce the thermal gradient in the assembly and graphite, which has been widely used in various experiments for carbonate melts (Hudspeth et al., 2018; Kono et al., 2014), was used as the sample capsule. The powdered dolomite sample together with several B4C spheres (Sigma-Aldrich, 98% purity, ~50-70 m size) was packed and loaded into the graphite capsule. Then, the graphite capsule was inserted into the assembly and separated from the heater by an MgO sleeve. The high-pressure density of the solid markers was calculated using the experimentally determined EOS of B4C (Dodd et al., 2002). The pressure of the experiments was estimated based on the pressure-load relationship calibrated by the phase transitions of bismuth and SiO2, and the uncertainty in pressure was estimated to be ~0.5 GPa. The temperature of the experiments was estimated based on the

W5Re-W26Re thermocouple readings, believed to be accurate within ±20 K.

In each experiment, the sample was first compressed to the target load at room temperature and then heated to 1073 K at a rate of about 50 K/min. After that, the temperature was quickly raised to the target temperature (in less than 1 min) to minimize

178 possible reactions between the sample and solid markers. The experiment was then kept at the target temperature, which is higher than dolomite melting temperature (Buob et al.,

2006) for about 2 mins to allow the settling of the solid markers. The ultra-low viscosity of dolomite melt, estimated to be in the range of 0.007-0.010 Pa s at about 3-5 GPa and

1633-1783 K (Kono et al., 2014), ensures fast settling of the solid markers within the experimental duration. After the experiment, the sample was quenched by turning off the heater power. The quenched sample was then mounted in epoxy and polished for inspection under the microscope.

SEM analysis of quenched samples

The quenched samples from ultrasonic experiments were analyzed by a field-emission scanning electron microscope (SEM) at the Swagelok Center for Surface Analysis of

Materials of Case Western Reserve University. The acceleration voltage and probe current were set at 10 kV and 3.7 nA, respectively. Back scattered electron (BSE) images of the samples show the typical quench texture for carbonate melt (Supplementary Figure VI.7), indicating that the samples are fully molten. For experiments at pressures lower than ~2.5

GPa, a small amount of bubbles and MgO blobs were found from the BSE images and EDS elemental mapping (Supplementary Figure VI.7). This is consistent with previous melting experiments on dolomite (Buob et al., 2006; Irving and Wyllie, 1975) showing that dolomite melts incongruently at pressures below ~2.5 GPa, which produces a liquid phase plus a vapor phase and periclase (MgO). The MgO blobs sank to the bottom of sample and partly reacted with the top of Al2O3 buffer rod to form spinel (Supplementary Figure VI.7).

Due to this incongruent melting at low pressures, the quenched melt composition is slightly more calcium-rich than the stoichiometric dolomite composition (Supplementary Table

179 VI.2). The MgO blobs and bubbles are unlikely to significantly affect the velocity results, because they are present in low abundance.

First-principles molecular dynamics simulations

FPMD simulation on dolomite melt was performed in canonical (NVT) ensemble as implemented in the Vienna ab initio simulation package (VASP) (Kresse and Furthmüller,

1996a, 1996b; Kresse and Hafner, 1993). In FPMD simulations, the calculation of forces and energies are based on density functional theory (DFT) with the projector augmented- wave (PAW) method (Kresse and Joubert, 1999). For the estimation of electronic exchange-correlation energy, we used both the local density approximation (LDA) and the generalized gradient approximation (GGA-PBE) (Ceperley and Alder, 1980; Perdew et al.,

1996). We used -point sampling to integrate the Brillouin-zone with a time step of 1 fs

(where, 1 fs= 10-15 s). The Nosé thermostat algorithm provides a constant temperature in our MD simulations with a finite size of the plane wave basis set by energy cutoff of 450 eV (Nosé, 1984). A volume dependent Pulay correction is added to the pressure to account for the use of limited cutoff energy, i.e., 450 eV (Francis and Payne, 1990).

푃 = 푃푀퐷 + 푃푃푢푙푎푦 , where 푃푃푢푙푎푦 = 푃퐸푐푢푡=950푒푉 − 푃퐸푐푢푡=450푒푉

Pulay corrections for the explored range of pressure, 0-20 GPa, ranges from 0.6 to 1.0 GPa.

We used the trigonal crystal structure of dolomite as a starting point and homogeneously strained the lattice to cubic cell and melted at 4000 K. Straining of the lower symmetry unit cells of crystalline matter to a cubic cell has been used in previous

FPMD studies (Bajgain et al., 2019; Stixrude and Karki, 2005). We used a cubic unit cell

3 with a reference volume (Vref =1157.62 Å ) with eight formula units of CaMg(CO3)2. Vref was chosen based on the ambient-pressure volume of carbonate melt (Desmaele et al.,

180 3 2019). The density of CaMg(CO3)2 melt at the reference volume is 2.12 g/cm . After equilibrating the melt structure at 4000 K, the temperature was lowered to 3000 K. At 3000

K, simulations were performed along many constant volumes that correspond to pressures between 0 and 15 GPa. The dolomite melt was then cooled along an isochore to lower temperatures of 2600 K, 2500 K, 2300 K and 2000 K. Using a similar procedure, we also performed simulations using the GGA pseudopotential along 3000 K, 2500 K, and 2000 K isotherms.

Acknowledgments

This study was partly supported by the National Science Foundation (EAR-1619964 and 1620548) and the National Natural Science Foundation of China (41974098). The ultrasonic measurements were performed at GSECARS beamline 13-ID-D, Advanced

Photon Source (APS), Argonne National Laboratory. GSECARS is supported by the

National Science Foundation - Earth Sciences (EAR-1634415) and Department of Energy

- GeoSciences (DE-FG02-94ER14466). This research used resources of the Advanced

Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract

No. DE-AC02-06CH11357. We thank Dr. Caleb W. Holyoke III for providing us the dolomite sample for the experiments. Nanthawan Avishai is thanked for her assistance on the SEM analysis of the quenched samples at the Swagelok Center for Surface Analysis of

Materials (SCSAM) of CWRU.

Supplementary Information

This supplementary file includes:

 Text S1. Criteria for detecting melting using ultrasonic signals.

181  Text S2. Data fitting procedure.

 Text S3. Calculation of velocity reductions for partially molten assemblages.

 Supplementary Figure VI.4. Cell assemblies for the experiments.

 Supplementary Figure VI.5. Ultrasonic signals for the sample with increasing

temperatures.

 Supplementary Figure VI.6. Experimental images for the sink-float

experiments.

 Supplementary Figure VI.7. SEM results for the sample quenched from

ultrasonic experiments.

 Supplementary Figure VI.8. Correlations between fitted K and K’ using

experimental data.

 Supplementary Figure VI.9. FPMD simulation results for the density of

dolomite melt.

 Supplementary Figure VI.10. Constraint on melt geometry applicable to upper

mantle

 Supplementary Table VI.2. Composition of the quenched samples measured by

EDS.

 Supplementary Table VI.3. Experimentally measured sound velocity data for

dolomite melt.

 Supplementary Table VI.4. FPMD simulation data for dolomite melt.

Text S1. Criteria for detecting melting using ultrasonic signals

With increasing temperature, the pattern of ultrasonic signals changes as the sample transforms from solid to partially molten and then to fully molten liquid (Supplementary

182 Figure VI.5). In the solid state, both P-wave and S-wave signals for the sample (signals reflected at the sample-BP interface) can be clearly observed; whereas in the partially molten state, the S-wave signal completely disappears and the P-wave signal becomes very weak (Supplementary Figure VI.5). Complete melting of the sample is indicated by: (1) reappearance of a clear P-wave signal for the sample; (2) increase in the P-wave signal amplitude compared to the partially molten state; (3) shift of the liquid sample P-wave signal to the right on the time axis compared to the solid sample signal (Supplementary

Figure VI.5). After the sample is fully molten, the amplitude of the signals becomes smaller with increasing temperature. All the data reported in this study were measured on the liquid phase when the fully molten state had been achieved. The quenched samples show typical quench textures for carbonate melts (Supplementary Figure VI.7), confirming that samples were fully molten during the experiments.

Text S2. EOS fitting procedure

We fit our experimental data using the third-order isothermal Birch-Murnaghan EOS

(Birch, 1952), which is given as

7 5 2 3퐾푇0 𝜌 3 𝜌 3 3 ′ 𝜌 3 푃 = [( ) − ( ) ] {1 + (퐾푇 − 4) [( ) − 1]} (1) 2 𝜌0 𝜌0 4 𝜌0

′ where 푃 is pressure, 퐾푇0 the isothermal bulk modulus at room pressure, 퐾푇 the pressure derivative of the bulk modulus, 𝜌0 the room-pressure density, and 𝜌 is the high-pressure density. Based on Eulerian finite strain theory, the high-pressure bulk modulus is given as

(Anderson, 1995)

5 2 2 𝜌 3 1 𝜌 3 ′ 27 ′ 𝜌 3 퐾푇 = 퐾푇0 ( ) {1 + (1 − ( ) ) [5 − 3퐾푇 − (4 − 퐾푇) (1 − ( ) )]}. (2) 𝜌0 2 𝜌0 4 𝜌0

The room-pressure density (𝜌0) at a temperature T is given as

183 𝜌0 = 𝜌0,푇푟푒푓 exp[−훼(푇 − 푇푟푒푓)], (3) where 푇푟푒푓 is the reference temperature and is chosen to be 1573 K in this study, and 훼 is the thermal expansion coefficient for dolomite melt. Although the thermal expansion coefficient for dolomite melt has not been directly measured yet, a recent room-pressure experimental study by Hurt and Lange (2019) showed that all alkaline-earth carbonate melts have nearly identical thermal expansion coefficient which is 1.64  10-4 K-1, and we use this value as a fixed parameter for dolomite melt in this study. The room-pressure bulk modulus (퐾푇0) is also a function of temperature and can be expressed in terms of the

Anderson-Grüneisen parameter 훿푇 (Stacey, 2005) as

−훿 𝜌0,푇푟푒푓 푇 퐾푇0 = 퐾푇0,푇푟푒푓 ( ) , (4) 𝜌0

Inserting (4) into (3), we get

퐾푇0 = 퐾푇0,푇푟푒푓푒푥푝[−훼훿푇(푇 − 푇푟푒푓)]. (5)

The adiabatic bulk modulus is related to the isothermal bulk modulus through

퐾푆 = 퐾푇(1 + 훼훾푇), (6) where 훾 is the Grüneisen parameter. The Grüneisen parameter for dolomite melt can be estimated from our FPMD simulations, and is 0.8 and 0.7 at room pressure based on GGA and LDA, respectively (Table VI.1). Although the simulation results show that the

Grüneisen parameter increases slightly with pressure for dolomite melt, similar to what has been observed in silicate melts (Asimow and Ahrens, 2010; Stixrude et al., 2009), the

Grüneisen parameter can be treated as a constant for fitting our experimental data, considering the limited pressure range (<6 GPa). We take the average of the results from

GGA and LDA simulations and use 0.75 for the Grüneisen parameter for dolomite melt. A

184 slight change of the Grüneisen parameter does not affect the fitting results significantly.

Sound velocity (푐) is related to adiabatic bulk modulus (퐾푆) and density (𝜌) through

푐 = √퐾푆/𝜌 (7)

We fit our data using a Monte-Carlo approach which can help us better estimate the fitting uncertainties (Xu et al., 2018). The fitting parameters in this study are 𝜌0,푇푟푒푓 ,

′ 퐾푇0,푇푟푒푓, 퐾푇 and 훿푇. A million sets of parameter values were generated from a random

3 distribution in the parameter space of 2.19-2.42 g/cm for 𝜌0,1573 퐾, 5-25 GPa for 퐾푇0,1573 퐾,

′ 3-13 for 퐾푇 and 1-5 for 훿푇 based on a previous simulation study on dolomite melt

(Desmaele et al., 2019). For a given set of parameters, we calculated 𝜌0,푖 and 퐾푇0,푖 at experimental temperature 푇푖 using Eqns. (3) and (5), and high-pressure density 𝜌푖 and isothermal bulk modulus 퐾푇,푖 can be calculated using Eqns. (1) and (2), respectively, with our experimental pressure data 푃푖. The calculated 퐾푇,푖 was converted to 퐾푆,푖 using Eqn. (6)

푚표푑푒푙 and finally the modeled sound velocity 푐푖 was calculated via Eqn. (7). The same calculations were repeated for each experimental P, T condition. As for the high-pressure density, we used the neutral point as an anchor for the EOS curve. The same randomly generated parameter sets as those in velocity data fitting were used to calculate the modeled high-pressure density 𝜌푚표푑푒푙 at experimental P and T according to Eqns. (3), (5) and (1).

The fitting was performed simultaneously on both the velocity data and the density data, by minimizing the combined 2, which was calculated as

2 푑푎푡푎 푚표푑푒푙 2 (푐 −푐 ) (𝜌푑푎푡푎−𝜌푚표푑푒푙) 휒2 = ∑ [ 푖 푖 + ] (8) 푖 푐 2 (𝜎휌)2 (𝜎푖 )

185 and the propagated equivalent uncertainty in sound velocity due to the uncertainty in pressure, 𝜌푑푎푡푎 is the measured high-pressure density for the neutral point and 𝜎𝜌 is the uncertainty in density measurements including both the uncertainty in density and propagated equivalent uncertainty from pressure. The 2 calculations were performed for

′ all of the one million randomly generated parameter sets for (𝜌0, 퐾푇0, 퐾푇, 훿푇). The best-fit values for the parameters were those that generated the minimum 2.

For the FPMD simulation results, we use the Mie-Grüneisen thermal equation of state to describe the pressure, temperature and volume data obtained for dolomite melt:

푑푃 푃 (푉, 푇) = 푃 (푉, 푇푟푒푓) + ( ) (푇 − 푇푟푒푓) (9) 푑푇 푉 where (푑푃) is the temperature derivative of pressure at constant density or volume. In 푑푇 푉

Eqn. (9), 푃 (푉, 푇푟푒푓) is the pressure at reference isotherm (푇푟푒푓 = 2000 퐾). The pressure- volume relationship at reference temperature is defined by the third-order Birch-

Murnaghan equation of state (Eqn. 1). Other thermodynamic quantities such as the

Grüneisen parameter (γ), and the isothermal bulk modulus (퐾푇) are calculated using the following relations:

훾 = 푉 (푑푃) (10) 퐶푉 푑푇 푉

푑푃 퐾푇 = −푉 ( ) (11) 푑푉 푇 where (푑푃) and 훾 can be expressed as a function of volume or density (Table VI.1). 푑푇 푉

Text S3. Calculation of velocity reductions for partially molten assemblages

The velocity reductions in P- and S-wave velocities as a function of melt fraction (F) is given as (Clark and Lesher, 2017; Takei, 2002)

186 (훽−1)Λ퐾 4 + 훾Λ퐺 푑푉푝 푉푝0−푉푝 Λ퐾+(훽−1) 3 𝜌푙 퐹 푑푙푛푉푝 = = = [ 4 − (1 − )] (12) 푉 푉 1+ 훾 𝜌 2 푝0 푝0 3 푠

푑푉푠 푉푠0−푉푠 𝜌푙 퐹 푑푙푛푉푠 = = = [Λ퐺 − (1 − ( ))] (13) 푉푠0 푉푠0 𝜌푠 2 where 푉푝0 and 푉푠0 represent the P- and S-wave velocity of the solid mantle, respectively, and 푑푉 is the reduction in the velocity, 훽 is the ratio of the adiabatic bulk modulus (퐾푆) of the solid to the liquid, 훾 is the ratio of the shear modulus 퐺 to 퐾푆 for the solid mantle, and

𝜌푙 and 𝜌푠 are density of the melt phase and solid mantle, respectively. Λ퐾 and Λ퐺 are functions of melt geometry and can be approximated by (Takei, 2002)

퐾푏(퐹,훼) = 1 − 퐹Λ퐾 (훼) (14) 퐾푆

( ) 푁 퐹,훼 = 1 − 퐹Λ (훼) (15) 퐺 퐺 where 퐾푏 and 푁 are the bulk and shear modulus, respectively, of the solid skeleton, which are calculated at a given melt fraction 퐹 by replacing the regions containing liquid with empty pore spaces and the pore shape is described by the equivalent aspect ratio 훼 (Takei,

2002). All the melt geometrical parameters (e.g., oblate spheroid model, equilibrium model, tube and crack model) can be converted to the equivalent aspect ratio. Λ퐾 and Λ퐺 , which are functions of 훼, are slopes of the normalized moduli 퐾푏 and 푁 as a function of melt 퐾푆 퐺 fraction 퐹, respectively. They can be approximated as a liner function when 퐹 is relatively small (< ~10%). The slopes Λ퐾 and Λ퐺 for different melt geometries can be obtained from the Figs. 2 and 3 in Takei (2002).

In order to assess which melt geometry is most applicable to realistic melts in the upper mantle, we have calculated the P-wave velocity reductions (푑푙푛푉푝) and S-wave velocity reductions (푑푙푛푉푠) for a partially molten assemblage consisting of San Carlos (SC) olivine

187 (elastic data from Liu et al. (2005)) plus various amount of dolomite or diopside melt as a function of the equivalent aspect ratio  (Supplementary Figure VI.10). The results were then compared with (1) experimentally determined relationship between velocity reduction and melt fraction by Chantel et al. (2016) in a similar partially molten system (SC olivine

+ basaltic melt) at about 2.5 GPa, (2) well-constrained seismic velocity reductions for the upper mantle low-velocity zone (Fischer et al., 2010; Kawakatsu et al., 2009; Rychert and

Shearer, 2009), and (3) melt fractions in the low-velocity zone estimated from petrologic studies (Hirschmann, 2010b; Presnall and Gudfinnsson, 2005) and space-time distribution of seamounts (Conrad et al., 2017). For low-degree partial melts, the experimental results, seismic observations and petrologic melt fraction constraints can all be satisfied only when the melt aspect ratio () is about 0.01 (Supplementary Figure VI.10), which corresponds to the melt film geometry (Takei, 2002). In addition, carbonate melt has high wetting properties (Minarik and Watson, 1995) and tends to form grain boundary thin films in olivine-carbonatite system (Yoshino et al., 2010). Thus, the melt film geometry with  =

0.01 is adopted in our following calculations for the velocities of melt-bearing mantle.

All the calculations were performed along a plausible mantle adiabatic temperature profile (Katsura et al., 2010). We use the SC olivine data (Liu et al., 2005) as a representative for the solid mantle, since the elastic data for natural peridotite at simultaneous high pressure and high temperature conditions are not available. Most of the elastic data on peridotite are measured at high pressure but at room temperature (Wang et al., 2015), and their extrapolation to high temperature has significant uncertainty. Although the sound velocity of olivine is intrinsically different from peridotite, the relative changes in seismic properties due to the presence of melt should be comparable in both olivine and

188 peridotite. The combination of VP and VS into the VP/VS ratio can be more sensitive to mantle physical state than the absolute VP or VS value alone (Chantel et al., 2016). In addition, the major minerals in upper mantle show a relatively small range of VP/VS ratios

(Takei, 2002) and the determined VP/VS ratio for natural peridotite at high pressures resembles that of olivine (Wang et al., 2015). We thus choose to use the VP/VS ratios calculated for the partially molten mantle analog (olivine + various amount of carbonate or silicate melt) as a function of depth for comparison with global radial seismic profiles in

Figure VI.3.

189 plate. (b) Cell assembly for sink-float density measurements and schematic drawings of sample capsules showing the sink, neutral, and float scenarios, respectively.

190 temperature from the solid state (top), to the partially molten state (middle), and then to the fully molten state (bottom).

191

192 is a bulk property of a material, and most of the blobs are at the bottom of the sample, it is unlikely that they can affect the velocity results of the melt significantly.

' 8

3 5 10152025 K (GPa)

Supplementary Figure VI.8 Correlations between fitted K and K’ for Birch-Murnaghan equation of state using the experimental velocity and density data.

(a) (b) 3 3.4

LDA 2.8 GGA 3.2

2.6 3

) )

3 3

m m

c 2.4 c 2.8

/ /

g g

( (

y y

t t

i i s 2.2 s 2.6

n n

e e

D D

2 2.4

2000 K 2000 K 1.8 2.2 2500 K 2500 K 3000 K 3000 K 1.6 2 0 2 4 6 8 10 12 14 16 -2 0 2 4 6 8 10 12 14 16 18 Pressure (GPa) Pressure (GPa)

Supplementary Figure VI.9 FPMD simulation results for the density of dolomite melt based on (a) GGA and (b) LDA, respectively.

193 (a) (b)

Supplementary Figure VI.10 . (a) P-wave velocity reduction (dlnVp) and (b) S-wave velocity reduction (dlVs) as a function of melt fraction and equivalent aspect ratio  based on the model of Takei (2002). Solid black lines-SC olivine + dolomite melt, dashed black lines-SC olivine + diopside melt and the numbers labelled are corresponding aspect ratio . The data used for SC olivine is from Liu et al. (2005). Red squares- experimental data from Chantel et al. (2016) for SC olivine + basaltic melt and thin red lines-modeled results by correcting the anelastic effects expected for seismic waves using a range of values for the anelastic factor (See details in Chantel et al. (2016)). Purple shaded areas-seismic velocity reductions observed for the low- velocity zone (Fischer et al., 2010; Kawakatsu et al., 2009; Rychert and Shearer, 2009). Pink shaded areas- melt fractions for the low-velocity zone constrained from petrologic studies (Hirschmann, 2010a; Presnall and Gudfinnsson, 2005) and space-time distribution of seamounts (Conrad et al., 2017). For low-degree partial melts, the experimental results, seismic observations and petrologic constraints can only be satisfied when the melt aspect ratio  is ~0.01, corresponding to the melt film geometry.

Supplementary Table VI.2 Composition of the quenched samples measured by EDS (atomic %).

T2207 T2208 T2261 T2262 C 22.33 19.51 19.37 20.65 O 57.42 58.62 61.16 59.52 Mg 7.48 9.59 8.81 9.17 Ca 12.52 11.91 10.50 10.43 Al 0.25 0.38 0.16 0.23 Pt 0 0 0 0

Supplementary Table VI.3 Sound velocity data measured for dolomite melt.

Frequency Velocity c Average c Run# P (GPa) T (K) s.d. (m/s) (MHz) (m/s) (m/s) T2207 2.14 1629 20 3871 3880 7 T2207 2.14 1629 25 3874 T2207 2.14 1629 30 3878 T2207 2.14 1629 40 3881 T2207 2.14 1629 50 3884 T2207 2.14 1629 60 3890 T2207 1.96 1733 20 3836 3817 14 T2207 1.96 1733 25 3827 T2207 1.96 1733 30 3824 T2207 1.96 1733 40 3811 T2207 1.96 1733 50 3805 T2207 1.96 1733 60 3802

194 T2207 1.91 1837 20 3786 3757 20 T2207 1.91 1837 25 3774 T2207 1.91 1837 30 3761 T2207 1.91 1837 40 3743 T2207 1.91 1837 50 3740 T2207 1.91 1837 60 3737 T2207 1.82 1942 20 3653 3672 15 T2207 1.82 1942 25 3674 T2207 1.82 1942 30 3686 T2207 1.82 1942 40 3683 T2207 1.82 1942 50 3653 T2207 1.82 1942 60 3680 T2208 1.39 1629 20 3732 3724 6 T2208 1.39 1629 25 3726 T2208 1.39 1629 30 3721 T2208 1.39 1629 40 3718 T2208 1.39 1629 50 3723 T2208 1.44 1733 20 3649 3643 6 T2208 1.44 1733 25 3646 T2208 1.44 1733 30 3643 T2208 1.44 1733 40 3643 T2208 1.44 1733 50 3641 T2208 1.44 1733 60 3633 T2208 3.40 1629 20 4219 4226 8 T2208 3.40 1629 25 4227 T2208 3.40 1629 30 4235 T2208 3.40 1629 40 4231 T2208 3.40 1629 50 4219 T2261 2.43 1629 20 3904 3907 3 T2261 2.43 1629 25 3904 T2261 2.43 1629 30 3904 T2261 2.43 1629 40 3909 T2261 2.43 1629 50 3909 T2261 2.43 1629 60 3909 T2261 2.05 1733 20 3888 3878 8 T2261 2.05 1733 25 3882 T2261 2.05 1733 30 3883 T2261 2.05 1733 40 3877 T2261 2.05 1733 50 3872 T2261 2.05 1733 60 3866 T2261 1.96 1837 20 3865 3869 9 T2261 1.96 1837 25 3869 T2261 1.96 1837 30 3869 T2261 1.96 1837 40 3854 T2261 1.96 1837 50 3872 T2261 1.96 1837 60 3882 T2262 3.23 1837 20 4121 4112 20 T2262 3.23 1837 25 4128 T2262 3.23 1837 30 4130 T2262 3.23 1837 40 4115 T2262 3.23 1837 50 4099 T2262 3.23 1837 60 4079 T2262 4.46 1837 20 4517 4528 16 T2262 4.46 1837 25 4535 T2262 4.46 1837 30 4552 T2262 4.46 1837 40 4538

195 T2262 4.46 1837 50 4517 T2262 4.46 1837 60 4510 T2439 2.08 1629 20 3825 3814 6 T2439 2.08 1629 25 3814 T2439 2.08 1629 30 3809 T2439 2.08 1629 40 3808 T2439 2.08 1629 50 3813 T2439 2.08 1629 60 3817 T2439 1.64 1733 20 3749 3728 18 T2439 1.64 1733 25 3742 T2439 1.64 1733 30 3734 T2439 1.64 1733 40 3731 T2439 1.64 1733 50 3701 T2439 1.64 1733 60 3711 T2439 2.97 1733 20 4278 4268 5 T2439 2.97 1733 25 4267 T2439 2.97 1733 30 4267 T2439 2.97 1733 40 4263 T2439 2.97 1733 50 4265 T2439 2.97 1733 60 4265 T2439 2.36 1837 20 4033 4023 6 T2439 2.36 1837 25 4025 T2439 2.36 1837 30 4019 T2439 2.36 1837 40 4017 T2439 2.36 1837 50 4021 T2439 2.36 1837 60 4027 T2439 4.11 1733 20 4611 4645 21 T2439 4.11 1733 25 4641 T2439 4.11 1733 30 4639 T2439 4.11 1733 40 4647 T2439 4.11 1733 50 4664 T2439 4.11 1733 60 4670 T2439 4.19 1837 20 4632 4648 13 T2439 4.19 1837 25 4643 T2439 4.19 1837 30 4641 T2439 4.19 1837 40 4643 T2439 4.19 1837 50 4660 T2439 4.19 1837 60 4666 T2439 4.52 1942 20 4557 4554 9 T2439 4.52 1942 25 4557 T2439 4.52 1942 30 4562 T2439 4.52 1942 40 4540 T2439 5.88 1837 20 4928 4905 32 T2439 5.88 1837 25 4905 T2439 5.88 1837 30 4888 T2439 5.88 1837 40 4862 T2439 5.88 1837 50 4942 T2439 5.06 1942 20 4865 4856 18 T2439 5.06 1942 25 4868 T2439 5.06 1942 30 4861 T2439 5.06 1942 40 4830 T2439 5.27 2046 20 4706 4701 7 T2439 5.27 2046 25 4697

196 Supplementary Table VI.4 FPMD simulation results for dolomite melt. Time refers to the simulation time.

V/Vx Time (ps) V (Å3)  (g/cm3) T (K) E (eV) E, eV P (GPa) P, GPa GGA Vx = 1157.62 Å3 1.1 27.33 1273.38 1.92 2000 -552.98 0.19 0.04 0.18 1.05 48.32 1215.50 2.02 2000 -553.01 0.21 0.66 0.11 1 56.34 1157.62 2.12 2000 -553.98 0.14 1.30 0.19 0.95 46.88 1099.74 2.23 2000 -554.22 0.13 2.07 0.12 0.9 55.16 1041.86 2.35 2000 -554.39 0.16 3.38 0.28 0.85 51.52 983.98 2.49 2000 -554.95 0.08 5.21 0.24 0.8 50.62 926.10 2.65 2000 -554.58 0.10 7.60 0.22 0.775 55.35 897.16 2.73 2000 -554.38 0.07 9.67 0.13 0.75 62.07 868.22 2.82 2000 -553.76 0.14 11.49 0.20 0.725 54.43 839.27 2.92 2000 -552.63 0.25 14.17 0.22 1.1 55.66 1273.38 1.92 2500 -544.39 0.24 0.83 0.11 1 55.97 1157.62 2.12 2500 -545.00 0.21 2.45 0.11 0.95 56.07 1099.74 2.23 2500 -547.15 0.29 3.12 0.17 0.9 55.22 1041.86 2.35 2500 -547.69 0.32 4.56 0.16 0.85 54.71 983.98 2.49 2500 -548.31 0.09 6.29 0.15 0.8 63.17 926.10 2.65 2500 -547.73 0.17 9.29 0.19 0.75 64.77 868.22 2.82 2500 -546.97 0.15 13.48 0.17 1.1 79.64 1273.38 1.92 3000 -534.57 0.27 1.75 0.14 1 85.25 1157.62 2.12 3000 -538.31 0.33 3.03 0.09 0.95 69.51 1099.74 2.23 3000 -539.19 0.32 4.12 0.14 0.9 84.13 1041.86 2.35 3000 -540.56 0.59 5.87 0.18 0.85 83.50 983.98 2.49 3000 -541.01 0.31 7.77 0.16 0.8 82.60 926.10 2.65 3000 -540.53 0.44 10.81 0.16 0.75 87.77 868.22 2.82 3000 -538.89 0.43 15.31 0.26

LDA Vx = 1157.62 Å3 0.9 52.57 1041.86 2.35 2000 -612.62 0.07 -0.38 0.14 0.85 59.40 983.98 2.49 2000 -613.76 0.10 0.61 0.15 0.8 58.57 926.10 2.65 2000 -615.04 0.08 2.19 0.16 0.775 48.92 897.16 2.73 2000 -615.31 0.09 3.81 0.12 0.75 31.00 868.22 2.82 2000 -615.55 0.16 5.39 0.19 0.725 58.49 839.27 2.92 2000 -615.70 0.17 7.13 0.89 0.7 68.33 810.33 3.02 2000 -615.52 0.14 9.67 0.23 0.675 65.09 781.39 3.13 2000 -615.25 0.18 12.16 0.24 0.65 64.87 752.45 3.26 2000 -614.30 0.16 16.19 0.21 0.9 51.52 1041.86 2.35 2300 -608.38 0.26 0.21 0.15 0.85 50.62 983.98 2.49 2300 -609.81 0.14 1.42 0.13 0.8 62.07 926.10 2.65 2300 -610.85 0.12 3.30 0.14 0.75 55.66 868.22 2.82 2300 -611.64 0.11 6.19 0.19 0.7 55.97 810.33 3.02 2300 -611.53 0.11 10.85 0.16 1 60.65 1157.62 2.12 2500 -602.93 0.32 -0.60 0.16 0.9 58.27 1041.86 2.35 2500 -606.34 0.14 0.61 0.14 0.85 50.72 983.98 2.49 2500 -607.53 0.08 1.69 0.08 0.8 56.56 926.10 2.65 2500 -608.58 0.12 3.77 0.16 0.75 60.06 868.22 2.82 2500 -609.37 0.13 6.70 0.12 0.7 66.16 810.33 3.02 2500 -608.94 0.09 11.52 0.15 1 56.07 1157.62 2.12 2600 -602.30 0.20 -0.50 0.15 0.9 55.22 1041.86 2.35 2600 -603.11 0.28 1.03 0.18 0.85 54.71 983.98 2.49 2600 -605.43 0.36 2.17 0.21 0.8 63.17 926.10 2.65 2600 -607.24 0.14 4.05 0.28 0.75 64.77 868.22 2.82 2600 -607.98 0.34 7.22 0.26 0.7 79.64 810.33 3.02 2600 -607.82 0.11 11.86 0.24

197 1 85.25 1157.62 2.12 3000 -592.89 0.53 0.02 0.21 0.9 69.51 1041.86 2.35 3000 -598.21 0.81 1.56 0.15 0.85 84.13 983.98 2.49 3000 -600.90 0.19 2.89 0.27 0.8 83.50 926.10 2.65 3000 -601.23 0.43 5.18 0.16 0.75 82.60 868.22 2.82 3000 -602.94 0.32 8.41 0.21 0.7 87.77 810.33 3.02 3000 -601.99 0.42 13.44 0.22

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