INSIGHTS INTO THE KINETICS OF SOLID GYPSUM DEHYDRATION FROM WIDE- AND SMALL-ANGLE SYNCHROTRON X-RAY SCATTERING

Katherine C. M. Gioseffi B. Sc. (Earth Science), Queensland University of Technology, Brisbane, 2015 Grad. Dip. (Psychology), Queensland University of Technology, Brisbane, 2009 B. A. Sc. (Biotechnology), Queensland University of Technology, Brisbane, 2009

Thesis submitted in fulfilment of the requirements for the degree of Masters of Applied Science

School of Earth, Environmental and Biological Sciences Science and Engineering Faculty Queensland University of Technology 2019

Keywords

Dehydration kinetics, dissolution-precipitation, gypsum, microstructure, polycrystalline, pre-stress, pseudomorphs, SAXS/WAXS, solid-state kinetics, synchrotron.

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Abstract

Fluids liberated through the dehydration of hydrous minerals play a major role in the occurrence of earthquakes, metasomatism, and metamorphism in the lithosphere. Dehydration reactions often create porosity because the anhydrous solid product is generally denser than its hydrous counterpart. The liberated fluids then drain through the newly established pore network. Pore pressure can build up when fluid release rate outpaces drainage. Subsequent over-pressure can result in hydraulic fracturing, weakening the solid phase. Gypsum is an ideal experimental analogue for hydrous minerals found in fault zones and subducting slabs due to its relatively low dehydration temperatures (~100°C). Previous studies on gypsum dehydration have predominantly used ‘black-box’ experimental set-ups where reaction progression is assessed using proxy measurements. Furthermore, in-situ gypsum dehydration kinetics have only been obtained using powdered starting materials. This thesis presents a unique set of novel in-situ dehydration experiments performed on polycrystalline gypsum discs (Volterra alabaster) using X-ray scattering techniques at the Australian Synchrotron. The dehydration reaction is tracked in-situ in real-time using: [1] Wide-angle X-ray Scattering (WAXS) and [2] Small-angle X-ray Scattering (SAXS), which monitor in-situ changes in mineral phase and nano-porosity, respectively. The primary focus is on the kinetics of polycrystalline gypsum dehydration. Results are reported for five different dehydration temperatures (120/128/141/151/170˚C) recorded at two different constant axial pre-stress states under radially drained conditions. These data show that [1] solid polycrystalline gypsum dehydrates slower than finer-grained powder, and [2] an increase in axial pre-stress enhances reaction rate. Activation energies of 73.8 kJ/mol (R2: 0.97) and 50.4 kJ/mol (R2: 0.98) were calculated for low- and high-pre-stressed states of gypsum, respectively (T: 128°C - 173°C). Three distinct bassanite morphologies were observed from post-mortem microstructural analysis: single-crystal pseudomorphs, multi-crystal pseudomorphs, and idiomorphic prismatic bassanite. Dehydration microstructures were highly sensitive to the sample chamber’s water vapour pressure. Morphologies are hypothesised to form along a spectrum of rate-coupled dissolution-precipitation mechanisms, where the dominant microstructure is related to the phase of water in the system. These results provide key insights into the complexity of polycrystalline gypsum dehydration. This has important implications when upscaling dehydration kinetics to understand the reaction-induced embrittlement and weakening of hydrous mineral host rock, and the migration pathways of fluids in the Earth’s crust.

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Table of Contents

Keywords ...... i Abstract ...... ii Table of Contents ...... iii List of Figures ...... v List of Tables ...... xi List of Abbreviations ...... xiii List of Symbols ...... xiv Statement of Original Authorship ...... xv Acknowledgements ...... xvi Chapter 1: Introduction ...... 1 1.1 Context, purpose and significance ...... 2 Chapter 2: Literature Review ...... 4 2.1 Gypsum Dehydration ...... 4 2.2 Kinetics ...... 32 2.3 X-ray Scattering ...... 42 Chapter 3: Methodology ...... 47 3.1 Starting materials ...... 49 3.2 The Blach cell ...... 49 3.3 Stage 1: Preliminary microstructural and chemical characterisation...... 51 3.4 Stage 2: In-situ time-resolved dehydration experiments using X-ray scattering ...... 52 3.5 Stage 3: Post-Synchrotron microstructural and chemical characterisation...... 62 3.6 Stage 4: Ex-situ dehydration experiments ...... 65 3.7 Stage 5: Temperature calibrations of the Blach cell ...... 66 3.8 Ethics and Limitations ...... 67 Chapter 4: Results ...... 68 4.1 Starting material volterra alabaster: Microstructure and composition ...... 68 4.2 Cell loading conditions: calibration of temperature and axial pre-stress ...... 70 4.3 In-situ time-resolved dehydration experiments using X-ray scattering ...... 73 4.4 Post-experimental characterisation ...... 79 Chapter 5: Discussion ...... 101 5.1 Bassanite microstructures ...... 101 5.2 The effect of pre-stress on polycrystalline gypsum dehydration kinetics ...... 114 5.3 The effect of microstructure on mineral dehydration ...... 120 5.4 Limitations ...... 125

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Chapter 6: Conclusions ...... 128 Bibliography ...... 131 Appendices ...... 146 Appendix A: Dehydration contour plots ...... 146 Appendix B: WAXS 1D Scattering profiles: Final vs. Initial ...... 152 Appendix C: Calculated Q Values For Bassanite ...... 158 Appendix D: Calculated Q Values For Gamma-Anhydrite ...... 162

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List of Figures

Figure 2-1: The crystallographic structures of the monoclinic gypsum (a) and bassanite (b), and the orthorhombic insoluble anhydrite (c), viewed along their c-axes. Image made using Vesta (Momma and Izumi, 2011)...... 8 Figure 2-2: Post-dehydration SEM micrographs (a, b) and reaction curves for a drained gypsum dehydration experiment under constant pore pressure (128°C, Pc = 150MPa, Pp = 10 MPa); where (c): Volume of fluid expelled (ΔV/V0 versus time), and (d) the first derivative of (ΔV/V0). The 3 stages show the initial slow increase of fluid expelled (linked to isolated porosity pockets, (a)), followed by a period of rapid increase where the majority of fluid is expelled (linked to coalescence of pore network (b); followed by a final stage of fluid expulsion decrease indicating reaction cessation. Figures from Ko et al. (1997)...... 15 Figure 2-3: Photomicrographs from partially dehydrated polycrystalline gypsum identifying a sharp boundary between undehydrated gypsum and dehydrated bassanite. Modified from Stretton (1996) (left image, taken under plane- polarised light) and Hildyard et al. (2011) (right image, taken under cross- polarised light)...... 16 Figure 2-4: SEM micrographs (a-c) were taken in secondary electron mode by Brantut et al. (2012) during in-situ dehydration of Volterra gypsum discs under low vacuum (360 Pa). Initiation of intragranular microcracks is indicated with arrows, seen at 120°C (b), followed by grain boundary widening at 143°C (c). FE-SEM micrographs (d-f) were taken after dehydration showing a preferred orientation of microcracks, carbon-coated samples were imaged with a 10 kV accelerating voltage...... 19 Figure 2-5: The pressure-temperature stability diagram for bassanite and gypsum within the range of 0 – 800 MPa, and 90°C – 170°C. Equilibrium lines were plotted based on experimental parameters and thermodynamic data provided in McConnell et al. (1987) and Llana-Fúnez et al. (2012)...... 24 Figure 2-6: Isothermal α versus time (min) curves for solid-state reaction models simulated with a rate constant (k) of 0.049 min-1 (after Khawam and Flanagan, 2006). a) zero-order (constant), b) first- to third-order (deceleratory), c) power law (acceleratory), d) Avrami-Erofeyev (JMAEK; sigmoidal), e) geometrical contraction (deceleratory), and f) diffusion (deceleratory)...... 34 Figure 2-7: Schematic of an X-ray scattering experimental set-up. The incoming, incident X-ray (ki) beam (green) penetrates and interacts with the sample and scatters at a value of 2θ to the incident beam. Scattered X-rays (kf) are collected on a 2D detector where a beamstop protects the detector from any transmitted incident X-rays...... 44 Figure 3-1: a) Opened Blach cell exposing the sample chamber. b) Schematic of the Blach cell and the components removed to open the sample chamber. c) Schematic of the X-ray path through the Blach cell sample chamber...... 50

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Figure 3-2: Schematic of the beamline optical layout for the SAXS/WAXS beamline at the Australian Synchrotron (after Kirby et al., 2013)...... 53 Figure 3-3: The Australian Synchrotron SAXS/WAXS set-up for dehydration experiments at short-camera length...... 54 Figure 3-4: Schematic of the points measured during the dehydration experiment...56 Figure 3-5: False-colour visualisation of the raw 2D scattering patterns collected during gypsum dehydration by the SAXS (left) and WAXS (right) detectors. The key elements shown are the beamstop, Scattering Vector (Q) (green arrow) and Scattered X-ray intensity (scattering patterns). The SAXS Pilatus 1M detector contains 10 modules set up in a 2 x 5 array (7 x 17-pixel gap between modules). The WAXS Pilatus 200K detector contains 2 modules in a 2 x 1 array (7-pixel gap)...... 58 Figure 3-6: Stacked 1D WAXS scattering profiles are depicting the time evolution of gypsum disc G16, dehydrated at 151°C with high axial pre-stress for 69 minutes. WAXS measures crystal lattice diffractions (from 2θ = 13.02° - 46.33°)...... 59 Figure 3-7: Stacked 1D SAXS scattering profiles are depicting the time evolution of gypsum disc G16, dehydrated at 151°C with high axial pre-stress for 69 minutes. High-Q SAXS (right) measures crystal lattice diffractions (from 2θ = 0.25° - 16.78°), and medium/low-Q SAXS (left) measures scattering from pores...... 59 Figure 3-8: Examples of the method used to measure the approximate grain size for each post-dehydrated mineral habit from SEM micrographs using ImageJ. Either the width (a, d) or the cross-section (b, c) was measured. Grains orientated highly oblique to the sample surface, or perpendicular to the c-axis (platy habits) were not measured...... 64 Figure 4-1: SEM micrographs of Volterra gypsum microstructure highlighting a) weak- moderate localised preferred orientation of gypsum, b) the sheet-like structure of tabular grains, c) the texture of partially exposed crystallographic planes.69 Figure 4-2: Curves of temperature over time measured in the cell interior for six different external heater unit settings...... 70 Figure 4-3: Regression analysis of the equilibrium temperature within the cell as a function of temperature at the external heater unit...... 70 Figure 4-4: The data from calibration measurements on the Blach cell filled with distilled water, applying incrementally increased torque, via a torque wrench, whilst using a Rosemount Pressure transducer to measure stress. The stress was converted to a force measurement and plotted against the applied torque. Data were fit with a logistic function: 퐹 = 퐹0 + 푎1 + 푇푇0푏 .Where: F is Force (Newtons); F0 = Function fit force offset (the force present when no torque is applied) (Newtons); a & b = Function fit constants; T = Torque applied (ft-pd force); T0 = Function fit torque where the slope reaches zero.72 Figure 4-5: A labelled sigmoidal dehydration curve produced as a Relative Intensity versus Time plot. The three unique bassanite peaks (100, 020 and 220 reflections) are tracked over the duration of the experiment. The sigmoidal

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shape of the curve can be separated into three sections: [1] the induction period; [2] the transient slope region (reflecting active dehydration); [3] the plateau region (indicating complete dehydration)...... 74 Figure 4-6: A comparison of the reaction rates and Avrami fit of low (purple, G28) and high (green, G18) axially pre-stressed samples, both dehydrated at 128°C. Reaction rate data tracks the growth of the bassanite peaks (110), (020), and (220) from the centre point sampled on each disc...... 76 Figure 4-7: A comparison of the reaction rates and Avrami fit of low (purple, G29) and high (green, G31) axially pre-stressed samples, both dehydrated at 141°C. Reaction rate data tracks the growth of the bassanite peaks (110), (020), and (220) from the centre point sampled on each disc...... 76 Figure 4-8: A comparison of the reaction rates and Avrami fit of low (purple, G77) and high (green, G16) axially pre-stressed samples, both dehydrated at 151°C. Reaction rate data tracks the growth of the bassanite peaks (110), (020), and (220) from the centre point sampled on each disc...... 77 Figure 4-9: A comparison of the reaction rates and Avrami fit of low (purple, G17) and high (green, G23) axially pre-stressed samples, both dehydrated at 173°C. Reaction rate data tracks the growth of the bassanite peaks (110), (020), and (220) from the centre point sampled on each disc...... 78 Figure 4-10: Compilation of the kinetic results for the samples dehydrated under low and high applied axial pre-stress (centre point). The vertical axis displays the inverse of the reaction constant obtained through the Avrami fit (Table 4.3). It corresponds to the time when 63% of bassanite has been produced in the sample. As seen in Figure 4.6 - 4.9, the Avrami model does not fit the low conversion percentages of ‘stepped’ reaction curves well, however, describes conversions > 50% excellently. The results demonstrate that high-pre-stress samples dehydration faster than low-pre-stressed samples at T < 160°C. ...79 Figure 4-11: Adapted surface plot of the three-step gypsum dehydration process from Jacques et al. (2009), using in-situ Synchrotron angle dispersive XRD. The plot displays two distinct crystallographic peak changes during the gypsum  hemihydrate and γ-anhydrite  anhydrite transitions. The transformation of hemihydrate  γ-anhydrite is identified only by a slight shift in the peak 2θ position...... 80 Figure 4-12: SEM micrographs are comparing the original Volterra gypsum tabular habits (left), with the columnar and swallow-tail contact twin gypsum habits observed in dehydrated discs that have back-reacted...... 83 Figure 4-13: SEM micrographs of acicular (a) and tabular single-crystal pseudomorph (b) bassanite habits. Saw marks remain in some samples from cutting the gypsum sub-cores into experimental discs...... 84 Figure 4-14: SEM micrographs of acicular and prismatic habits in cross-section (a) and prismatic (b) bassanite habits. Bassanite channels can be seen in cross-sections (a)...... 84 Figure 4-15: SEM micrographs of fibrous multi-crystal pseudomorph bassanite habits, where the relict gypsum grain boundaries are preserved...... 85

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Figure 4-16: SEM micrographs of prismatic multi-crystal pseudomorphs (b), and combination fibrous/prismatic multi-crystal pseudomorphs (a, c, d), where the relict gypsum grain boundaries are preserved. Crystals within combination pseudomorphs either have parallel (a, c) or diverging orientations (d)...... 86 Figure 4-17: Post-dehydration SEM micrographs of discs dehydrated at 128°C, under low axial pre-stress (left), and high axial pre-stress (right)...... 87 Figure 4-18: SEM micrographs of prismatic bassanite (light grey grains), and relict partially absorbed gypsum grains (darker grey grains); gypsum dissolution textures are indicated in red...... 88 Figure 4-19: Post-dehydration SEM micrographs of discs dehydrated at 141°C, under low axial pre-stress. G13 was imaged twice; first over the disc surface, and then a cross-section of the internal disc microstructure along a freshly broken surface...... 90 Figure 4-20: Dehydration fractures observed in tabular bassanite pseudomorphs. ...90 Figure 4-21: Dehydration fractures observed in tabular pseudomorphs. Grains are partially dehydrated, and intra-granular fractures are isolated within the light grey bassanite domains. Relict gypsum is observed as the smooth, un- fractured, darker grey domains of the grain...... 91 Figure 4-22: G13 micrographs of the disc surface (left) and internal cross-section (right), highlighting the difference in microfabric. Internally aggregates of fibrous bassanite dominate. High magnification of surface tabular pseudomorphs (left), indicate a fibrous multi-crystal nature...... 92 Figure 4-23: SEM micrographs of G45 dehydrated at 141°C, low pre-stress. The area under the red line indicates the exact same grains imaged pre- and post- dehydration. The boxed areas show enlarged sections of the initial gypsum microstructure (left), and dehydrated bassanite microstructure (right)...... 93 Figure 4-24: Post-dehydration SEM micrographs of discs dehydrated at 141°C, under high axial pre-stress. Acicular bassanite was observed surrounding pervasive relict saw marks, which dominate the surface of the disc (right)...... 94 Figure 4-25: Post-dehydration SEM micrographs of G16, dehydrated at 151°C under high axial pre-stress. The surface microstructure was largely obscured by pervasive relict saw marks (left)...... 96 Figure 4-26: Post-dehydration SEM micrographs of discs dehydrated at 173°C under low axial pre-stress (G34) and high axial pre-stress (G23, G33)...... 98 Figure 4-27: Sub-parallel crystallographically controlled (left) and radiating (right) dehydration fractures in G34...... 99 Figure 4-28: Curved and linear dehydration fractures in G33...... 99 Figure 5-1: Main bassanite morphologies observed in SEM micrographs post- dehydration: (a) prismatic bassanite grains, (b, c) multi-crystal pseudomorphs, and (d) single-crystal pseudomorphs...... 102 Figure 5-2: Schematic of (a) tightly-coupled dissolution-precipitation processes which form single-crystal bassanite pseudomorphs preserving gypsum grain boundaries and crystallography. (b) Moderately-couple dissolution-

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precipitation which form multi-crystal bassanite pseudomorphs preserving gypsum grain boundaries, bassanite fibres have a preferred orientation along the relict gypsum c-axis. (c) Uncoupled dissolution-precipitation where bassanite forms euhedral, prismatic habits with no retention of gypsum microstructure...... 106 Figure 5-3: SEM micrographs of partially dehydrated gypsum. Relict gypsum is darker grey (Gyp) compared to lighter grey bassanite (Bas). Bassanite morphologies are either single-crystal pseudomorphs (SCP) with intra-granular fracturing (a, b), multi-crystal pseudomorphs with intra-granular porosity (MCP) (c, d), or prismatic with inter- and intra-granular porosity (e, f)...... 107 Figure 5-4: SEM micrographs of intra-granular fractures observed in bassanite single- crystal pseudomorphs. Fractures are either non-crystallographically-controlled radiating, hydraulic fractures (a), or exfoliation fractures along the (010) plane (b)...... 109 Figure 5-5: Normalised dehydration curves of bassanite proportion ((110) peak) over time (sec) highlighting the lack of spatial dependence of reaction rates between the centre (circles), mid- (crosses) and margin point (diamonds) sampled. Kinetics of samples dehydrated at 128°C (purple), 141°C (green), 151°C (blue) and 173°C (red) are shown...... 110 Figure 5-6: Raw dehydration curves of the peak intensity of (110) over time (sec) highlighting the lack of spatial dependence of reaction rates for gypsum dehydrated at 120°C under high pre-stress (G80), and the spatial dependence of rates at 120°C, low pre-stress (G65). The centre (purple), mid- (blue) and margin points (red) sampled are shown...... 111 Figure 5-7: Sample pressure-temperature readings from dehydration experiments, prior to quenching, are plotted with the vapour pressure curves for pure water, calculated using the Antoine equation (Eq. 20). Shaded samples indicate the dominant bassanite morphology observed in SEM micrographs, where: green = single-crystal pseudomorphs, blue = multi-crystal pseudomorphs (MCP), and orange = prismatic habits. SEM analysis was not performed on non- shaded samples...... 112 Figure 5-8: Dehydration reaction curves highlight that powdered gypsum (solid lines) dehydrates faster than polycrystalline gypsum (solid lines) under similar conditions. Note that the activation energy calculated for polycrystalline gypsum (Figure 4.32), does not include 120°C reaction, as the sample was not fully dehydrated. *Kinetic data for powdered gypsum was taken from Ballirano and Melis (2009)...... 121 Figure 5-9: The non-isothermal conditions of the kinetically analysed low (solid lines) and high pre-stress (dashed lines) dehydration experiments are plotted using uncalibrated temperature measurements. The plateau region indicates the stabilisation of target temperature. The black linear line depicts the bassanite – gypsum transition temperature at 97°C (Section 3.4.6; Ballirano and Melis, 2009). Coloured symbols indicate the time at which 63% of the reaction has taken place (circles: low pre-stress, squares: high pre-stress). Note: G65 and G80 were still unreacted when quenched...... 125

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Figure A- 1: WAXS 1D scattering profile contour plots for samples dehydrated at 128°C with low axial pre-stress (G28 - top), and high axial pre-stress (G18 - bottom). The labelled peaks 020 and 220 were tracked for kinetic analysis. The red stars indicate the time bassanite peaks first appear. The high-Q peaks with a constant intensity result from Be cell window scattering...... 147 Figure A- 2: WAXS 1D scattering profile contour plots for samples dehydrated at 128°C with low axial pre-stress (G28 - top), and high axial pre-stress (G18 - bottom). The labelled peaks 020 and 220 were tracked for kinetic analysis. The red stars indicate the time bassanite peaks first appear. The high-Q peaks with a constant intensity result from Be cell window scattering...... 148 Figure A- 3: WAXS 1D scattering profile contour plots for samples dehydrated at 141°C with low axial pre-stress (G29 - top), and high axial pre-stress (G31 - bottom). The labelled peaks 020 and 220 were tracked for kinetic analysis. The red stars indicate the time bassanite peaks first appear. The high-Q peaks with a constant intensity result from Be cell window scattering...... 149 Figure A- 4: WAXS 1D scattering profile contour plots for samples dehydrated at 151°C with low axial pre-stress (G77 - top), and high axial pre-stress (G16 - bottom). The labelled peaks 020 and 220 were tracked for kinetic analysis. The red stars indicate the time bassanite peaks first appear. The high-Q peaks with a constant intensity result from Be cell window scattering...... 150 Figure A- 5: WAXS 1D scattering profile contour plots for samples dehydrated at 173°C with low axial pre-stress (G17 - top), and high axial pre-stress (G23 - bottom). The labelled peaks 020 and 220 were tracked for kinetic analysis. The red stars indicate the time bassanite peaks first appear. The high-Q peaks with a constant intensity result from Be cell window scattering...... 151 Figure B- 1: The initial (blue) and final (orange) 1D WAXS scattering profiles are overlain from the dehydration experiments at ~120°C with low axial pre-stress (G65 - top), and high axial pre-stress (G80 - bottom). Both are only partially dehydrated where the final profiles for both contain gypsum and bassanite. The bassanite crystal planes (020) and (220) are labelled in both graphs. 153 Figure B- 2: The initial (blue) and final (orange) WAXS 1D scattering profiles are overlain from dehydration experiments at 128°C with low axial pre-stress (G28 - top), and high axial pre-stress (G18 - bottom). The bassanite crystal planes (020) and (220) are labelled in both graphs...... 154 Figure B- 3: The initial (blue) and final (orange) WAXS 1D scattering profiles are overlain from dehydration experiments at 141°C with low axial pre-stress (G29 - top), and high axial pre-stress (G31 - bottom). The bassanite crystal planes (020) and (220) are labelled in both graphs...... 155 Figure B- 4: The initial (blue) and final (orange) WAXS 1D scattering profiles are overlain from dehydration experiments at 151°C with low axial pre-stress (G77 - top), and high axial pre-stress (G16 - bottom). The bassanite crystal planes (020) and (220) are labelled in both graphs...... 156 Figure B- 5: The initial (blue) and final (orange) WAXS 1D scattering profiles are overlain from dehydration experiments at 173°C with low axial pre-stress (G17 - top), and high axial pre-stress (G23 - bottom). The bassanite crystal planes (020) and (220) are labelled in both graphs...... 157

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List of Tables

Table 2-1: Literature summary of the determined crystallography of the calcium sulfate minerals...... 6 Table 2-2: Literature summary of gypsum dehydration following a one-step dehydration pathway, ordered in ascending dehydration temperature. Abbreviations: G (gypsum), B (bassanite), A (anhydrite), s (seconds), min (minutes), hr (hours), atm. (atmospheric), DTA (differential thermal analysis), TGA (thermogravimetric analysis), D (diameter), H (height), VNIR (visible to near infrared), IR (infrared), SR-PXD (synchrotron radiation powder XRD), PH2O (water vapour pressure), Pc (confining pressure), Pf (pore fluid pressure)...... 12 Table 2-3: Literature summary of gypsum dehydration following a two- and three-step dehydration pathway, ordered in ascending dehydration temperature. Abbreviations: G (gypsum), B (bassanite), A (anhydrite), s (seconds), min (minutes), hr (hours), atm. (atmospheric), DTA (differential thermal analysis), TGA (thermogravimetric analysis), D (diameter), H (height), VNIR (visible to near infrared), IR (infrared), SR-PXD (synchrotron radiation powder XRD), PH2O (water vapour pressure), Pc (confining pressure), Pf (pore fluid pressure)...... 14 Table 2-4: Literature comparison of the experimental parameters when gypsum dehydration proceeded via an inter-granular reaction front or through isolated bassanite nuclei. Abbreviations: Pc (confining pressure), Pe (effective pressure), Pf (pore fluid pressure), Pdiff (differential pressure)...... 18 Table 2-5: Literature summary of empirical activation energies for gypsum dehydration ordered firstly by increasing dehydration temperatures and then by increasing water vapour pressure (PH2O)...... 39 Table 3-1: PANalytical XRD optics configuration...... 51 Table 3-2: SAXS/WAXS instrument configuration, detector resolution and angular resolution across the three Synchrotron proposal rounds...... 54 Table 3-3: Experimental parameters for in-situ Synchrotron dehydration experiments...... 55 Table 3-4: Indexing of the measured scattering vector (Q) position of the three unique crystallographic peaks identified in SAXS/WAXS datasets, compared to the theoretical Q position calculated for bassanite reference pattern (Ballirano and Melis, 2001)...... 60 Table 4-1: Calibrated Blach cell temperatures and the corresponding heater unit temperature setting for in-situ synchrotron dehydration experiments...... 71 Table 4-2: Total estimated applied stress on the gypsum discs during synchrotron dehydration experiments, calculated by combining the calculated thermal- elastic stress at each dehydration temperature, and the applied external stress from confining the sample axially in the Blach cell...... 73

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Table 4-3: Avrami fit (JMAEK model) results for the eight fully dehydration samples...... 75 Table 4-4: The 100 vs 110 peak ratios calculated for eleven dehydration experiments. The experimental conditions and crystallographic peaks are listed for each sample...... 81 Table 4-5: The crystallographic details for -bassanite (Ballirano and Melis, 2001) and -anhydrite (Bezou et al., 1995) and their calculated scattering vectors (Q) for the three unique peaks identified in the dehydrated product phase...... 82 Table 4-6: A microstructural summary of two discs dehydrated at 128°C, imaged by SEM. Crystallographic information is reported as a normalised percentage for bassanite and gypsum; grain size is semi-quantitative (minimum of 50 grains per habit, per sample measured); and bassanite habits are listed in order of dominance...... 88 Table 4-7: A microstructural summary of four discs dehydrated at 141°C, imaged by SEM. Crystallographic information is reported as a normalised percentage for bassanite and gypsum; grain size is semi-quantitative (minimum of 50 grains per habit, per sample measured); and bassanite habits are listed in order of dominance...... 95 Table 4-8: A microstructural summary of one disc dehydrated at 151°C, imaged by SEM. Crystallographic information is reported as a normalised percentage for bassanite and gypsum; grain size is semi-quantitative (minimum of 50 grains per habit, per sample measured); and bassanite habits are listed in order of dominance...... 97 Table 4-9: A microstructural summary of three discs dehydrated at 173°C, imaged by SEM. Crystallographic information is reported as a normalised percentage for bassanite and gypsum; grain size is semi-quantitative (minimum of 50 grains per habit, per sample measured); and bassanite habits are listed in order of dominance...... 100 Table C-1: 2θ and calculated bassanite Q values for Synchrotron λ: 0.77490 Å and 0.619921 Å...... 159 Table D-1: 2θ and calculated γ-anhydrite Q values for Synchrotron λ: 0.77490 Å and 0.619921 Å...... 163

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List of Abbreviations

Be – Beryllium BSE – Backscatter Electron mode CARF – Central Analytical Research Facility DSC – Differential scanning calorimetry DTA – Differential thermal analysis FEG-SEM – Field Emission Scanning Electron Microscopy LEC – Linear expansion coefficient QUT – Queensland University of Technology SAXS – Small-angle X-ray Scattering SE – Secondary Electron mode SEM – Scanning Electron Microscopy TGA – Thermogravimetric analysis VEC – Volumetric expansion coefficient WAXS – Wide-angle X-ray Scattering XRD – X-ray Diffraction

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List of Symbols

2θ – Diffraction angle kα – X-ray produced when electrons move Δ – Change of quantity from the M to K electron shell

λ – Incident X-ray wavelength kß – X-ray produced when electrons move π – Pi from the L to K electron shell > – Greater than N – Newton Å – Angstrom n – Positive integer (in Braggs Law) -1 퐴푒 – Activation energy (kJ mol ) n – Avrami exponent A – Pre-exponential factor Nm – Newton-metre α – the volume fraction of transformed m – Metre material over time mA – Milliamperes

푎퐵푒 – Linear expansion coefficient of MPa – Megapascal beryllium (°C-1) L – Litre

푎퐺 – Linear expansion coefficient of P – Pressure (Pa) gypsum (°C-1) Pa – Pascal’s a & b – Function fit constants Pc: Confining pressure

C – Celsius Pdiff: Differential pressure

Co – Cobalt Pe: Effective pressure

Cu – Copper Pf: Pore fluid pressure d – Inter-planar crystallographic spacing PH2O - Water vapour pressure

EG – Young’s modulus of gypsum (Pa) Q – Scattering Vector F – Force (N) R – Universal gas constant (J K-1 mol-1)

F0 – Function fit force offset s – seconds ft-pd – Foot-pound force t – Time (seconds) hkl – Crystallographic planes T – Torque applied (ft-pd force) (Torque I – Scattering Intensity calibration equation) k – Rate coefficient (kinetic parameter T – Temperature (Kelvin) dependent on temperature) 푇0 – Initial temperature (°C)

K – Kelvin 푇1 – Target temperature (°C) keV – Kiloelectron volt TF – Function fit torque kV – Kilovolt x̄ – Average

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Statement of Original Authorship

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering xv

Acknowledgements

This research was undertaken on the SAXS/WAXS beamline at the Australian Synchrotron, part of ANSTO. I would like to thank the beamline scientists, Dr Nigel Kirby and Dr Stephen Mudie, for their support before, during and after our experimental time at the synchrotron. I gratefully acknowledge the Australian Institute of Geoscientists (AIG) and Petroleum Exploration Society of Australia (PESA) for the funding awarded by their Postgraduate Bursary and Queensland Postgraduate Scholarship, respectively. Thanks go to Dr Henry Spratt, Dr Tri Nguyen, Dr David Steele and Dr Tony Raftery of the X-ray and Particles laboratory, CARF, Queensland University of Technology (QUT) for their assistance with XRD analysis. Thanks to Dr Chris East of the Optical and Electron Microscopy laboratory, CARF, QUT for his assistance and training on the Tescan Mira 3 VP FE-SEM. I thank Donald McAuley at IFE, QUT for his help with sample preparation. Thanks as well to Dr Harald Milsch of the GFZ German Research Centre for Geosciences for supplying the Volterra gypsum samples. Many thanks to Dr Tomas Blach not only for the use of his experimental cell, but for his support, experimental wisdom, and being an entertaining road-trip partner. I can’t thank my supervisory team, Dr Christoph Schrank and Dr Oliver Gaede, enough. Their ongoing support and mentorship over the last few years have shaped me into the scientist I am today. Thank you for always making the time to answer my (many) questions, and helping me navigate through the ups and downs and sideways turns of research. With special thanks to the sage Dr David Gust for the care, he bestows on his students (which even retirement has not stopped), who has always been an anchor of guidance and support. Lastly, I would like to thank my friends and family for their endless support, but most of all for keeping me sane.

xvi Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Chapter 1: Introduction

Prograde metamorphism within the Earth’s crust can lead to the destabilisation of hydrous minerals which release crystal-bound water upon dehydration to more stable anhydrous phases. Dehydration reactions produce a negative solid volume change because the anhydrous product is generally denser than its hydrous counterpart. The associated compaction of the solid phase creates porosity, while the reaction itself produces fluids that drain through the newly established void network. The pore-pressure evolution within the material is therefore highly dynamic and controlled by the fluid release rate, internal stresses, the boundary conditions, and the drainage rate, which in turn is limited by the permeability of the reaction-generated porosity network (Olgaard et al., 1995; Bedford et al., 2017). Pore pressure builds up when fluids are released faster than drainage occurs. This over-pressure can result in hydraulic fracturing, weakening the host rock (Olgaard et al., 1995). These coupled- dehydration processes are linked to observed seismicity at subduction and active fault zones (Ko et al. 1997; Brantut et al., 2011; Veveakis et al., 2014). Therefore, the kinetic behaviour of dehydration reactions is of great importance to understand the weakening of crustal rocks and the migration pathways of fluids in the lithosphere.

The hydrous mineral gypsum is the most common sulfate mineral in the crust, predominantly occurring in evaporitic sedimentary deposits in conjunction with halite and limestone (Deer, Howie and Zussman, 1962). Gypsum (CaSO4·2H2O) dehydrates into a meta-stable hemihydrate phase, bassanite (CaSO4·0.5H2O), then to anhydrite (CaSO4). Experimentally, gypsum is an ideal mineral to study dehydration reactions for the following reasons:

1. The dehydration of gypsum has tectonic importance where it, and its anhydrous counterpart anhydrite, have been:

a. Commonly observed at the sole of thrust faults (e.g. Jura thrust zone, Heard and Rubey, 1966).

b. Known to act as detachment horizons, particularly in fold-and- thrust belts (e.g. Northern Apennines, De Paola, 2008).

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 1

c. Found in seismically active fault zones (E.g. Northern Apennines, De Paola, 2008).

2. Gypsum is an ideal experimental analogue for hydrous minerals found in fault zones and subducting slabs, such as serpentinite, due it is relatively low dehydration temperatures (~100°C) and relatively short reaction timescales (hours) (Llana-Fúnez et al., 2012; Leclère et al., 2016; Bedford et al., 2017).

3. The dehydration of calcium sulfate mineral species involves relatively

simple mineral transitions (all contain Ca2SO4 ± water), compared to the more complicated solid-solution dehydration series often found with silicate-bearing rocks and minerals, such as serpentinite and clays (Powers, 1967; Yamamoto and Kennedy, 1969; Bedford et al., 2017).

4. Enhancing the understanding of the poromechanical behaviour of evaporites during salt tectonics.

5. As an evaporitic mineral, the low-permeable and low-porosity nature of gypsum rock make it an ideal analogue for the fluid pathway evolution of other low-porosity strata undergoing deformation and metamorphism (Llana-Fúnez et al., 2009). This has practical implications for the oil and gas industry, where gypsum and clays can act as reservoir seals.

1.1 CONTEXT, PURPOSE AND SIGNIFICANCE

The work in this thesis is part of a larger collaborative research project using novel, in-situ synchrotron X-ray scattering techniques that allow for real-time penetrative observations of both microstructure and mineralogical phase evolution during dehydration. These techniques are: [1] Wide-angle X-ray scattering (WAXS), monitoring in-situ changes in mineral phase, and [2] Small-angle X-ray Scattering (SAXS) monitoring in-situ the evolution of nano-porosity. Volterra gypsum samples, a natural alabaster gypsum rock, are dehydrated at the Australian Synchrotron using a unique experimental cell, designed explicitly for in-situ X-ray experimental techniques. Radially unconfined gypsum samples are dehydrated at five dehydration temperatures (120°C – 170°C) at two constant uniaxial pre-stressed states. The aim of this thesis is to analyse the kinetics of polycrystalline gypsum dehydration.

2 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

The primary research questions to be addressed in this thesis are:

[1] What effect does microstructure have on mineral dehydration?

Objective: To compare the dehydration rates of the polycrystalline gypsum, analysed in this study, with reaction rates of powdered gypsum reported in the literature.

[2] Does application of a constant pre-stress have an effect on the dehydration rate of polycrystalline gypsum?

Objective: To compare the kinetics of synchrotron datasets, collected during this study, between low- and high-pre-stressed dehydrated samples.

There is a complete lack, to the author’s knowledge, of experiments that have observed the chemical transformation of whole-rock gypsum during dehydration in- situ. Gypsum dehydration studies reported in the literature have mainly focused on the kinetics of powdered gypsum. Powder kinetics are sensitive to the grain size of the starting material. Therefore, comparability to cohesive gypsum rock is limited. The few in-situ polycrystalline gypsum dehydration studies used 3D computed micro-tomography which only allows the direct observation of micron-scale pores and fractures (Fusseis et al., 2012; Bedford et al., 2017). Therefore, reaction progress was inferred indirectly. Moreover, none of these studies conducted enough experiments for a kinetic study. The lack of in-situ whole-rock data proves problematic when applying gypsum dehydration kinetics to Earth’s crustal conditions. Extrapolation of established powder-based kinetics is questionable due to the inconsistencies between activations energies, transition temperatures and reaction pathways revealed by the literature. These gaps are addressed by the use of novel in- situ techniques during this project which allows real-time tracking of mineralogical phases as whole-rock dehydration takes place. This work will aim to further address the secondary set of ‘small’ research questions: How do these reactions work in a polycrystalline material? What is the rate of dehydration?

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 3

Chapter 2: Literature Review

2.1 GYPSUM DEHYDRATION

Dehydration is a chemical reaction which produces a compositional and structural change in a mineral (or rock) by the removal of water from its crystal lattice (Hefferan and O’Brien, 2010). Dehydration reactions occur in the Earth’s crust during prograde metamorphism where increases in pressure and temperature destabilize hydrous minerals, liberating crystal bound water as the mineral transitions to a more stable anhydrous phase (Etheridge et al., 1983). This transition is often reversible, where the interaction of an anhydrous mineral with aqueous solutions can result in hydration (the addition of water in the crystal lattice).

2.1.1 Mineral description

Gypsum (CaSO4·2H2O) has two dehydration phases, a hemihydrate phase, bassanite (CaSO4·0.5H2O), and an anhydrous phase, anhydrite (CaSO4). An ongoing debate regarding the amount of water in the bassanite lattice is summarised in the following section. Gypsum itself is the most common sulfate mineral in the crust. It forms predominantly in evaporitic sedimentary deposits in conjunction with halite and limestone (Deer, Howie and Zussman, 1962). It has three natural varieties: a clear crystalline form (selenite); a massive, fine-grained form (alabaster); and a fibrous form (satin spar) (Deer, Howie and Zussman, 1962; Christensen et al., 2008). 2+ 2- Anhydrite can precipitate from super-saturated Ca and SO4 brines in evaporating sea/lake beds or form as a secondary mineral through gypsum dehydration (Hardie, 1971; Billo, 1987; Azam, 2007).

Bassanite is the transitional phase in the reversible dehydration-hydration process between gypsum and anhydrite (Bundy, 1956; Worku and Parker, 1992). It is metastable at atmospheric conditions and thus rarely found in nature. However, has been reported in salt beds (Bundy, 1956), arthropod fossils (Palmer, 1959), dry lake beds (Allen and Kramer, 1953; Gunatilaka et al., 1985), and volcanic settings such as fumeroles and leucitic tephra (Zambonini, 1910; Palache, Berman and Frondel, 1951; Holland, 2002). Gypsum and bassanite both have commercial importance, where the former is used in construction (gypsum wallboard and cement additive) and the latter in industry and medicine where it is commonly known as ‘Plaster of Paris’.

4 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

2.1.2 Crystallography of the calcium-sulfate mineral series There are five calcium sulfate species, three hydrous and two anhydrous ones

(Christensen et al., 2008): gypsum (CaSO4.2H2O), α-bassanite (CaSO4.0.5H2O), β- bassanite (CaSO4.0.5H2O), soluble γ-anhydrite (AIII; CaSO4), and insoluble anhydrite (AII; CaSO4). Early on, it was argued that postulated forms of CaSO4. nH20, with n = [0; 1], exist as a function of varying amounts of zeolitic water without structural crystallographic change (Kelly, Southard and Anderson, 1941; Ball and Norwood, 1969). However, dehydration and rehydration of gypsum studied with proton magnetic resonance (Saito, 1961) and infrared absorption spectra (Razouk, Salem and Mikhail, 1960) confirm the presence of crystalline water, suggesting there is a distinct crystallographic hemihydrate form with n = 0.5, termed bassanite. However, several other intermediate hemihydrate phases were reported (n = 0.48, 0.52, 0.6, 0.65, 0.65, 0.67, and 0.8), but have never been widely accepted (Frik and Kuzel, 1982; Bushev and Borisov, 1982; Abriel, 1983; Bezou et al., 1995; Schmidt et al., 2011; Table 2.1). The existence of bassanite is further supported by a double endothermic peak recorded between 100°C and 200°C in the differential thermal analysis of gypsum dehydration (Deer, Howie and Zussman, 1962). The first peak is interpreted as the initial loss of 1.5 water molecules. The second peak represents the removal of the remaining 0.5 water molecules to produce the anhydrous phase.

The reported crystallography (crystal system and space group) of bassanite varies widely in the literature, much more so than that of gypsum and anhydrite (Table 2.1). Bassanite structure has been classified with four different crystal systems and nine space groups. Older references favour the trigonal system, while recent studies use the monoclinic system (Table 2.1).

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 5

Table 2-1: Literature summary of the determined crystallography of the calcium sulfate minerals.

Unit cell (Å) Space Mineral β (°) Cyrstal System Reference a b c group Gypsum:

CaSO4.2H2O 6.2845 15.2079 5.6776 114.09 Monoclinic C2/c Natl. Bur. Stand. (1980) 6.284 15.2 5.6771 114.13 Monoclinic C12/c1 Ichharam & Boeyens (2002) 6.286 15.213 5.678 114.1 Monoclinic C2/c De La Torre et al. (2004) 6.277 15.181 5.372 114.11 Monoclinic C2/c Comodi et al. (2008) 5.679 15.202 6.522 118.43 Monoclinic I2/a Pedersen & Semmingsen (1982) 5.679 15.202 6.522 118.43 Monoclinic I2/a Schofield, Knight & Stretton (1996) Hemihydrate:

CaSO4.0.48H2O 12.06 6.933 12.6 90 Orthorhombic Frik & Kuzel (1982)

CaSO4.0.5H2O 11.5 6.8 12.7 90.66 Orthorhombic Florke (1952) 11.88 6.85 12.6 90 Monoclinic I Gay (1965) 12.062 12.66 6.93 ~ 90 Monoclinic I2 Lager et al. (1984) 12.028 6.931 12.692 90.18 Monoclinic I2 Kuzel & Hauner (1987) 12.027 6.937 12.69 90.18 Monoclinic I2 Abriel & Nesper (1993) 12.035 6.929 12.67 90.26 Monoclinic I2 Ballirano et al. (2001) 12.019 6.93 12.669 90.235 Monoclinic I121 Bezou et al. (1995) 11.94 6.83 12.7 90.66 Monoclinic C121 Gallitelli (1933) 12.028 6.927 12.674 90.21 Monoclinic C121 Bushuev (1982) 11.999 6.925 6.377 90 Monoclinic C121 Nonat et al. (1991) 11.94 6.82 6.24 90.66 Trigonal P3m1 Caspari (1936)

6.86 6.86 12.7 90 Trigonal P3221 Gallitelli (1933)

11.5 6.8 12.7 90.66 Trigonal P321 Florke (1952)

12.028 9.977 12.617 90.21 Trigonal P3121 Bushuev & Borisov (1982)

12.028 6.968 6.41 90.21 Trigonal P3121 Abriel (1983)

12.062 6.937 6.345 90 Trigonal P3121 Abriel & Nesper (1993)

6.9268 6.9268 12.7565 120 Hexagonal P31 Christensen, Jensen & Nonat (2010)

CaSO4.0.52H2O 12.06 13.865 12.67 90 Hexagonal Frik & Kuzel (1982)

CaSO4.0.6H2O 11.999 6.925 6.376 90 Monoclinic I 121 Bezou et al. (1995)

CaSO4.0.65H2O 17.518 6.929 12.034 133.65 Monoclinic C2 Schmidt et al. (2011)

13.869 13.869 12.718 90 Trigonal P3221 Schmidt et al. (2011)* at 75% humidity

CaSO4.0.67H2O 12.028 6.9727 12.672 90.21 Monoclinic I2 Bushuev & Borisov (1982)

CaSO4.0.8H2O 6.968 6.968 6.41 90 Trigonal P3121 Abriel (1983)

Soluble anhydrite:

γ-CaSO4 6.82 6.24 Trigonal Caspari (1936)

6.982 6.982 6.34 90 Hexagonal P6222 Florke (1952)

12.015 6.969 6.303 ~ 90 Hexagonal P6222 Lager et al. (1984)

6.968 9.968 6.3304 120 Hexagonal P6222 Christensen et al. (2008) 12.077 6.972 6.304 90 Orthorhombic C222 Bezou et al. (1995) Insoluble anhydrite:

CaSO4 6.23 6.98 6.97 90 Bbmm Hohne (1962) 6.991 6.996 6.238 90 Orthorhombic Amma Cheng & Zussman (1963) 6.993 6.995 6.245 90 Orthorhombic Amma Hawthorne & Ferguson (1975) 7.006 6.998 6.245 90 Orthorhombic Amma Kirfel & Will (1980) The existence of the two bassanite modifications, α- and β-bassanite, has also been disputed. The ambiguity arose because their similar crystal structure makes differentiation by X-ray Diffraction (XRD) difficult. However, slight differences in peak reflections (Morris, 1963a) were attributed to differences in stacking order of

6 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

the crystal lattice, which leads to changes in water distribution, density, thermodynamic properties, solubility, the heat of solution and formation activation energies (Kelly, Southard and Anderson, 1941, McAdie, 1965). These results were corroborated with differences in infrared spectra between the two, confirming two distinct phases (Morris, 1963b; Bartram, 1969; Fowler et al., 1968; Clifton, 1971). The two bassanite modifications are reportedly formed through different dehydration processes. α-bassanite is formed by the dehydration of gypsum in acidic or brine solutions, or in a saturated water vapour pressure environment. β-bassanite is formed by dehydrating gypsum under dry to low water vapour pressures or in vacuo (Kelly, Southard and Anderson, 1941; Ball and Norwood, 1970, Singh and Middendorf, 2007). α-bassanite forms idioblastic hexagonal prismatic grains with distinct boundaries, and β-bassanite forms small flaky particles (Freyer and Voigt, 2003; Singh and Middendorf, 2007). However, the experimental conditions of either hemihydrate formation are not clear (Singh and Middendorf, 2007). In-situ Raman spectroscopy indicates the thermal stability of bassanite is influenced by morphology, where fibres/prismatic crystals dehydrate at higher temperatures (100°C - 160°C) compared to disc-like grains (90°C - 125°C) (Freyer and Voigt, 2003).

2.1.3 Crystal structures Monoclinic gypsum has a layered crystal structure where stacked chains of 2+ 2- calcium ions (Ca ) and sulfate tetrahedra (SO4 ) alternate with layers of water molecules (Fowler et al., 1968; Freyer and Voigt, 2003). The layered sheets of Ca-

SO4 chains and lattice-bound water make-up the (010) crystallographic plane, which runs parallel to the c-axis (Figure 2.1a). The weaker bond strengths of the water molecule layer relative to the Ca-SO4 chains produce a perfect cleavage parallel to (010) (Fowler et al., 1968; Freyer and Voigt, 2003; Aquilano et al., 2016).

The monoclinic bassanite structure is markedly different. The layer structure of gypsum is replaced by a channel structure, where chains of Ca-SO4 and water molecules are running along the c-axis (Figure 2.1b) (Freyer and Voigt, 2003; Christensen et al., 2008). The water channels are approximately 3 - 4 Å in diameter (McAdie, 1964; Freyer and Voigt, 2003). Christensen et al. (2010) used powder neutron diffraction to show that β-bassanite is hexagonal, in contrast to monoclinic α-bassanite. They report that a difference in the packing of crystal-bound water in the

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 7

lattice channels changes the unit cell symmetry, from a 3-fold symmetry (β-) to pseudo-hexagonal (α-).

The anhydrous, orthorhombic structure of anhydrite (AII) consists of ordered, tightly packed Ca-SO4 chains oriented parallel to the c-axis (Figure 2.1c) (Freyer and Voigt, 2003; Christensen et al., 2008).

Figure 2-1: The crystallographic structures of the monoclinic gypsum (a) and bassanite (b), and the orthorhombic insoluble anhydrite (c), viewed along their c-axes. Image made using Vesta (Momma and Izumi, 2011).

2.1.4 Mass balance of dehydration and the interplay between fluid release rate, fluid drainage, and hydromechanical loading conditions Gypsum dehydration most commonly progresses via a two-step process (other reaction pathways are discussed in Section 2.1.5):

CaSO4·2H2O (gypsum)  CaSO4·0.5H2O (bassanite) + 1.5 H2O (1)

CaSO4·0.5H2O (bassanite)  CaSO4 (anhydrite) + 0.5 H2O (2)

Each dehydration step results in a negative solid volume change because of the decreasing molar volume of the denser product minerals: 74.53 cm3/mol for gypsum, 53.17 cm3/mol for bassanite, and 45.68 cm3/mol for anhydrite (Deer, Howie and Zussman, 1992). Unless the sample undergoes deformation, the volume decrease creates porosity in the rock matrix. Full dehydration of gypsum  bassanite or gypsum  anhydrite would produce 29.3% and 39% porosity respectively (Ko et al., 1995; Milsch, Priegnitz and Blöcher, 2011). Because free water has a larger molar volume (18.4 cm3/mol) than crystal-bound water, the dehydration of gypsum to bassanite releases 37.1% water. Therefore, under the assumption of a fully-saturated

8 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

pore network (29.3% porosity), there is a total product volume increase of 7.8% (Ko et al., 1995). Thus, a permeable interconnected pore network connected to a permeable sample boundary is required to allow fluid drainage driven by rising pore pressures due to the excess fluid volume.

The reaction-dependent porosity creation is coupled with the reaction- controlled liberation of crystal-bound fluids (Olgaard et al., 1995). In low-porosity and low-permeability rocks, fluid drainage is limited to the newly established void network. Pore pressure is thus controlled by the fluid release rate and the drainage rate, which is limited by the permeability of the reaction-generated effective porosity network (Heard and Rubey, 1966; Olgaard et al., 1995). Pore pressure builds up when fluid release rate outpaces drainage. Experiments demonstrate that increasing pore fluid pressures decrease the rate of dehydration (Ko, Olgaard and Wong, 1997; Llana-Fúnez et al., 2012). However, a significant overstep or continued rise in pore pressure can result in hydraulic fracturing, weakening the solid phase (Heard and Rubey, 1966; Olgaard et al., 1995).

2.1.5 Dehydration reaction pathway The reaction progression during gypsum dehydration is very sensitive to temperature, water vapour pressure, confining pressure, pore fluid pressure, heating duration, and sample microstructure. Dehydrating samples in solution, in air, or in vacuum also affects the reaction pathway, particularly for the two hemihydrates. It is therefore not surprising that a large amount of conflicting kinetic results exists in the literature.

The dehydration of gypsum to bassanite has been reported to occur between 50°C – 200°C, over a large pressure range from in-vacuo, various water-vapour pressures, atmospheric pressure and under high pressure (≤ 3.5 GPa) (LeChatelier, 1905; Kelly et al., 1941; Fowler et al., 1968; McConnell et al., 1987; Chang et al., 1999; Prasad et al., 2001; Ballirano and Melis, 2009; Azim et al., 2011; Brantut et al., 2011; Brantut et al., 2012). The bassanite to γ-anhydrite transition occurs between 125°C - 255°C (LeChatelier, 1905; Powell, 1958; Ball and Urie, 1970; Ball and Norwood, 1970; Clifton, 1971; Christensen et al., 2008; Ballirano and Melis, 2009; Jacques et al., 2009; Brantut et al., 2011). The γ-anhydrite to anhydrite transition occurs between 360° - 450°C (LeChatelier, 1905; Clifton, 1971; Hudson- lamb et al., 1996; Prasad et al., 2001; Mirwald, 2008; Jacques et al., 2009). In

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 9

addition, LeChatelier (1905) reports a high-temperature anhydrite polymorph at 1193°C.

Gypsum dehydration can occur via a one-, two- or three-step reaction (Tables 2.2, 2.3).

1) One-step reaction pathways: a) Gypsum  bassanite b) Gypsum  γ-anhydrite c) Gypsum  anhydrite 2) Two-step reaction pathways: a) Gypsum  bassanite  γ-anhydrite b) Gypsum  bassanite  anhydrite 3) Three-step reaction pathways: a) Gypsum  bassanite  γ-anhydrite  anhydrite b) Gypsum  γ-anhydrite  bassanite  γ-anhydrite

c) Gypsum  bassanite  CaSO4.0.15H2O  anhydrite

An experimental challenge in constraining the reaction pathway is posed by the fact that bassanite is crystallographically very similar to γ-anhydrite. The progressive removal of water through the bassanite channels incurs only a slight lattice contraction and therefore a lack of major structural change (Ball and Urie, 1970). Hence, phase distinction by standard powder-XRD is extremely difficult (Gay, 1965; Khalil, Hussein and Gad, 1971; Christensen et al. 2010). This highlights the importance of advanced in-situ studies that can directly monitor changes during phase transition from either: [1] intensity changes of peak reflections using synchrotron powder-XRD (Bezou et al., 1995); or [2] changes in sample mass/enthalpy during thermogravimetric and differential thermal analyses (Bezou et al., 1990). Moreover, γ-anhydrite rehydrates easily (Gay, 1965). This fact can render the identification of hydrous and anhydrous forms challenging, particularly when ex- situ dehydration techniques are used or experimental conditions are not carefully monitored (McConnell et al., 1987, Gay, 1965; Ball and Urie, 1970).

In response to the variable nature of reported reaction pathways, a tabulated summary of gypsum dehydration experiments from the literature is presented below (Tables 2.2, 2.3). The author cautions that while this summary is fairly

10 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

comprehensive, it is by no means completely exhaustive of all experimental works. In addition, experiments were not included where indistinct starting materials, dehydration temperature or experimental apparatus were reported. The main aim of these summary tables was twofold: [1] to provide a concise overview of the variable use of starting materials, experimental methods and experimental conditions; and [2] to highlight the inconsistencies in the reported dehydration temperatures and reaction pathway of gypsum as it dehydrates. The tables have been split into experimental work that observed a one-step dehydration pathway (Table 2.2) and those with a two- or three-step dehydration reaction (Table 2.3). Both tables are ordered in ascending dehydration temperature. The abbreviations G, B and A stand for gypsum, bassanite and anhydrite respectively. Post-experimental XRD for mineral phase confirmation was not reported, as this was standard throughout all experiments.

Several possible reasons for the variation in the reported gypsum dehydration pathways become apparent from this comparison table:

 The use of black-box experiments involving either proxy dehydration measures (discussed further in Section 2.1.8) or post-dehydration sample characterisation. These techniques are only able to report the final product mineral of dehydration.

 The influence of different starting sample microstructure (grain size; sample mass; powder versus single crystal versus whole-rock; synthetic versus natural samples).

 The limited temporal/spatial resolution of some in-situ techniques.

 Differences in experimental heating duration (when reported).

 Differences in experimental conditions (pressure, temperature; dry versus wet; drained versus undrained).

 The relatively easy rehydration of γ-anhydrite.

 The difficulties in differentiating between the mineral phases bassanite and γ-anhydrite.

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 11

Table 2-2: Literature summary of gypsum dehydration following a one-step dehydration pathway, ordered in ascending dehydration temperature. Abbreviations: G (gypsum), B (bassanite), A (anhydrite), s (seconds), min (minutes), hr (hours), atm. (atmospheric), DTA (differential thermal analysis), TGA (thermogravimetric analysis), D (diameter), H (height), VNIR (visible to near infrared), IR (infrared), SR-PXD (synchrotron radiation powder XRD), PH2O (water vapour pressure),

Pc (confining pressure), Pf (pore fluid pressure).

Temperature Dehydration Experimental Cell and Heating duration Experimental conditions Sample Type Reference (°C) pathway Dehydration measure

One step reaction pathway:

In-situ energy dispersive Carbone et al. 41 - 80°C G → γ-A 13 hrs In vacuo Pressed powder pellets XRD (2008) In vacuo; transient P : < several Ultrathin (010) cleaved crystal 50 - 400°C G → γ-A / A - H2O - Sipple et al. (2001) millibars (H: < 50 nm)

Cleaved selenite platetlets (010), Flow ciruit (< 760 mm.Hg), Fowler, Howell, 50 - 150°C G → α-B / β-B 4 - 6 hrs Dry calcination; P : 0 - 333 kPa H2O 20 - 30 μm thick Static cell (>760 mm.Hg) Schiller (1968) Natural selenite and satin spar: Deutsch et al. 60 - 90°C G → B seconds - 9 hrs Dry air, isothermal powdered; DTA, TGA (1994) 3x synthetic powders Natural selenite and satin spar: Deutsch et al. 60 - 90°C B → γ-A 1 - 160 hrs Dry air, isothermal powdered; DTA, TGA (1994) 3x synthetic powders Synthetic powder, g. size: 50 - Ball & Norwood 68 - 142°C α-B → γ-A - P: atm.; P : 0.0013 Pa - 48 kPa DTA H2O 300 μm (1970) 70 - 90°C G → γ-A - In vacuo Powdered fibrous gypsum Proton magnetic resonance Saito (1961) 1 (70°C) - 22 (90°C) Khalil, Hussein & 70 - 90°C G → B - Powder static-TGA + DTA days Gad (1971) Lightly pressed powder pellet Ball & Norwood 81 - 150°C G → A - P : 0.0013 Pa Sample weight loss H2O (synthetic, 40 - 60 μm g. size) (1969)

Lightly pressed powder pellet Ball & Norwood 84 - 115°C G → B - P : 613 Pa - 6 kPa Sample weight loss H2O (synthetic, 40 - 60 μm g. size) (1969) 20 days without seed = no reaction; 10 days 90°C G → A Slurry with distilled water Powder Autoclave Azimi et al. (2011) with seed = 90% reacted

90°C G → A 1 day Slurry with 1.5 M H2SO4 solution Powder Autoclave Azimi et al. (2011) Pc: 300 MPa; constant strain: 10-3-10- Volterra core (D: 10 mm, H: 3 - High T/P gas-medium Barberini et al. 90°C, 127°C G → B - 4 /sec; drained and undrained 10 mm); g. size: 80 - 100 μm torsion apparatus (2005) N flow-through: 50 - 100 cc/min; Precipitated gypsum, g. size: 60 - Vapor-jacketed Pyrex oven + 97 - 140°C G → α-B / β-B ~ 100 mins 2 McAdie (1964) ambient PH2O: 0 - 760 mm.Hg 80 μm sample weight loss Christensen et al. 99°C G → α-B - Hydrothermal (H O) Powder In-situ SR-PXD 2 (2008) Natural polcrystalline samples Gravity convection oven (alabaster, massive, satin spar, 100°C G → B ~ 3 hrs Air; non-isothermal with post analysis: VNIR Harrison (2012) selenite) powdered to size reflectance spectroscopy fraction: < 63 μm Axial compression apparatus P : 140 - 200 MPa; P : 0 - 10 Mpa; Volterra cores; g. size: 80 - 100 Ko, Olgaard, Briegel 105 - 120°C G → B - c f - fluid expulsion water saturated; 4x10-5 /s strain rate μm (1995) measurements Christensen et al. 109 - 140°C G → α-B - Dry heating Powder In-situ SR-PXD (2008) Natural selenite and satin spar: Deutsch et al. 100 - 130°C G → B - Dry air, dynamic Dynamic TGA powdered; 3x synthetic powders (1994)

Triaxial deformation rig - Volterra cores (D: 20 mm); g. Hildyard et al. 100 - 125°C G → B 17 - 21 hrs High effective pressure: 60 - 90 MPa fluid expulsion size: 80 - 100 μm (2011) measurements Synthetic powder and powdered Piston-cylinder high- Yamamoto & 100 - 260°C G → B 2 - 3 hrs P : 4 - 30 kbar H2O selenite pressure apparatus Kennedy (1969) P : 0.1-200 MPa; P : 10-100 Mpa; c f Volterra core (H: 25 mm); Triaxial cell - fluid expulsion Olgaard, Ko, Wong 107 - 150°C G → B 0.5 - 22 hrs drained and undrained; constant g. size: 80 - 100 μm measurements (1995) strain rate: 7x10-7 - 6x10-5 s-1 Lightly pressed powder pellet Ball & Norwood 110 - 152°C G → A - P : 613 Pa - 6 kPa Sample weight loss H2O (synthetic, 40 - 60 μm g. size) (1969) Hydrothermal diamond anvil D O water saturated; P: 343 - 1085 110 - 150°C G → B - 2 Single crystal, g. size: 60 x 80 μm cell; in-situ raman Liu et al. (2015) MPa, undrained spectroscopy Selenite single crystal (010); 0.5 - 110°C G → B +/- γ-A 3 - 34 days 0.49 - 3.75 M NaCl brine saturated Precision oven Michael (2011) 1cm width Pc: 0 - 0.552 GPa; undrained; fixed Volterra cores (D: 10 mm; H: 30 High P/T rock deformation Murrell & Ismail 110 - 170°C G → B - strain rate: ~10-5 / sec mm); g. size: 80 - 100 μm apparatus (1976) Volterra cores (D: 20 mm); Triaxial rig - fluid expulsion Hildyard et al. 110 - 125°C G → B 1 - 5 days Low effective pressure: 4 - 10 MPa g. size: 80 - 100 μm measurements (2011) Gravity convection oven Natural polycrystalline selenite, 115°C G → B ~3.5 hrs Air; non-isothermal with post analysis: VNIR Harrison (2012) weight: ~ 25g reflectance spectroscopy

12 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Table 2.2, continued: Literature summary of gypsum dehydration following a one-step dehydration pathway.

Temperature Dehydration Experimental Cell and Heating duration Experimental conditions Sample Type Reference (°C) pathway Dehydration measure

One step reaction pathway:

Ballirano and Melis 115 - 120°C G → B - Dry heating Synthetic powder, size: 2 - 10 μm In-situ parallel-beam XRD (2009)

115 - 140°C β-B → γ-A - Isothermal, PH2O: 0.0013 Pa - 5.5 kPa Synthetic powder, size: 53 - 75 μm DTA, TGA Ball and Urie (1970)

Voltera core (D: 2.3 mm; H: 8 mm); Time-series synchrotron X- 115°C G → B 310 min Dry heating, drained Fussies et al. (2012) g. size: 80 - 100 μm ray microtomography In-situ time-resolved Volterra core (D: 2 mm; H: 5 mm); 115°C G → B 9 hrs P : 9 MPa; P : 4 Mpa synchrotron X-ray Bedford et al. (2017) c f g. size: 80 - 100 μm microtomography

118°C α-B → β-B - Hydrothermal (H2O) Powder In-situ SR-PXD Christensen et al. (2008)

118°C G → α-B - Hydrothermal (1 M LiCl) Powder In-situ SR-PXD Christensen et al. (2008) Autoclave submerged in an 119 - 122°C G → B 135 mins Water-saturated; P: 1.6 - 1.66 kbar Synthetic powder McConnel et al. (1987) oil bath P : 15 MPa & P : 10 MPa; c f Volterra core (D: 20 mm; H: 50 Triaxial cell - fluid expulsion Llana-Funez et al. 120°C G → B ~700 - 900 s Pc: 50 MPa & Pf: 11 MPa; mm); g. size: 80 - 100 μm measurements (2012) Pc: 110 MPa & Pf: 10 MPa > 2000 s (not fully Volterra core (D: 20 mm; H: 50 Triaxial cell - fluid expulsion Llana-Funez et al. 120°C G → B P : 101 MPa; P : 40 MPa reacted) c f mm); g. size: 80 - 100 μm measurements (2012) >27 hrs (not fully Volterra core (D: 20 mm; H: 50 Triaxial cell - fluid expulsion Llana-Funez et al. 120°C G → B P : 100 MPa; P : 91 MPa reacted) c f mm); g. size: 80 - 100 μm measurements (2012) Volterra core (D: 12 mm; H: 20 Triaxial cell - fluid expulsion 120 - 132°C G → B ~300 mins P : 60 - 190 MPa; P : 10 - 120 Mpa Ko et al. (1997) c f mm); g. size: 80 - 100 μm measurements

123°C G → α-B - Hydrothermal (1 M HNO3) Powder In-situ SR-PXD Christensen et al. (2008)

Ballirano & Melis 125°C B → γ-A - Dry heating Synthetic powder, size: 2 - 10 μm In-situ parallel-beam XRD (2009) P : 2 and 5 kb; axial strain rates: Volterra cores (D: 0.5 in); g. size: 80 125 - 177°C G → G + B - c Triaxial compression Heard & Rubey (1966) 3.3x10-4 - 3.4x10-7 /sec - 100 μm Glass tube immersed in 128°C G → B - - Powder Le Chatelier (1905) paraffin bath Natural polycrystalline samples Gravity convection oven 130°C G → B Overnight Air; non-isothermal (alabaster, massive, satin spar), with post analysis: VNIR Harrison (2012) weight: ~ 100g reflectance spectroscopy Lightly pressed powder pellet 130°C G → A - P : 0.0013 Pa Sample weight loss Ball & Norwood (1969) H2O (synthetic, 40 - 60 μm g. size) Razouk, Salem, Mikhail 150°C G → γ-A - In vacuo Polycrystalline (selenite) IR Spectroscopy (1959) Single crystal, 142 - 217°C α-B → A - P: atm.; P : 0.0013 Pa - 48 kPa DTA Ball & Norwood (1970) H2O g. size: 60 x 80 μm 150°C G → A - In vacuo Powdered fibrous gypsum Proton magnetic resonance Saito (1961)

150°C G → β-B - N2 atm.: ~101 kPa Powder DTA, TGA Clifton (1971) 150°C G → B 2 - 4 hrs Slurry with distilled water Powder Autoclave Azimi et al. (2011) 9 hrs (with anhydrite 150°C G → B + A Slurry with distilled water Powder Autoclave Azimi et al. (2011) seeds) P : 52 - 162 MPa; mean P : 2 Mpa; Volterra - powdered (g. size 75 - 150°C G → B - c f Triaxial cell Leclare et al. (2016) semi-undrained, not isothermal 125 μm) Hydrostatic, P = 10, 50 Mpa; Volterra cores; Triaxial cell - fluid expulsion 150°C G → B - eff Brantut et al. (2012) drained g. size: 80 - 100 μm measurements Glass tube immersed in 168°C B → γ-A - - Powder Le Chatelier (1905) paraffin bath

169°C α- / β-B → A - Hydrothermal (H2O) Powder In-situ SR-PXD Christensen et al. (2008)

165 - 172°C α-B → A - Dry heating Powder In-situ SR-PXD Christensen et al. (2008)

Pc: 0 - .552 GPa; undrained; fixed Volterra cores (D: 10 mm; H: 30 High P/T rock deformation 170 - 470°C B → A - Murrell & Ismail (1976) strain rate: ~10-5 / sec mm); g. size: fine - med apparatus Pc: 0.414 and 0.552 GPa; undrained Gypsum core (D: 10 mm, H: 30 High P/T deformation Murrel and Ismail 170°C G → B - and drained mm); g. size: fine - med apparatus; DTA (1976) P : 2 kb; axial strain rates: Volterra cores (D: 0.5 in); g. size: 80 177°C G → G + B + A - c Triaxial compression Heard & Rubey (1966) 3.3x10-4 / sec - 100 μm

197°C β-B → γ-A - N2 atm.: 101 kPa Powder DTA, TGA Clifton (1971)

25°C/min heat rate < low vacuum SEM chamber: 360 Pa Volterra discs (D: 4 mm; H: 2 mm); In-situ FEI QUANTA600 max: 200°C G → B Brantut et al. (2012) 80°C; 10°C/min < 200°C (water vapour pressure) g. size: 80 - 100 μm ESEM

Volterra cores ( D: 0.5 in); 250°C G → A - P : 5 kb; axial strain: 3.3x10-4 /sec Triaxial compression Heard & Rubey (1966) c g. size: 80 - 100 μm 255°C α-B → γ-A - - Precipitated gypsum DTA, TGA Powell (1958)

Gypsum core (D: 10 mm, H: 30 High P/T deformation Murrel and Ismail 270°C G → A - Pc: 0.276 GPa; undrained and drained mm); g. size: fine - med apparatus; DTA (1976)

290 - 550°C γ-A→ A - - Precipitated gypsum DTA, TGA Powell (1958) 300°C β-B → γ-A - - Precipitated gypsum DTA, TGA Powell (1958)

375°C γ-A → A - N2 atm.: ~101 kPa Powder DTA, TGA Clifton (1971) Single crystal gypusm (cm sized); Controlled transformation gypsum powder: g. size: 576°C G → γ-A ~70 - 100 hrs P : 1 Pa, 500 Pa rate thermal analysis; weight Badens et al. (1998) H2O 18 x 1.3 x 0.7 μm3; set plaster: g. loss measurements size: 15 x 1.2 x 1.7 μm3 600°C G → A - In vacuo Polycrystalline (selenite) IR Spectroscopy Razouk et al. (1959)

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 13

Table 2-3: Literature summary of gypsum dehydration following a two- and three-step dehydration pathway, ordered in ascending dehydration temperature. Abbreviations: G (gypsum), B (bassanite), A (anhydrite), s (seconds), min (minutes), hr (hours), atm. (atmospheric), DTA (differential thermal analysis), TGA (thermogravimetric analysis), D (diameter), H (height), VNIR (visible to near infrared), IR (infrared), SR-PXD (synchrotron radiation powder XRD), PH2O (water vapour pressure),

Pc (confining pressure), Pf (pore fluid pressure).

Temperature Dehydration Experimental Cell and Heating duration Experimental conditions Sample Type Reference (°C) pathway Dehydration measure

Two step reaction pathway:

Lightly pressed powder pellet Ball & Norwood 80.5 - 115°C G → B → A - P : 2.2 - 3.3 kPa Sample weight loss H2O (synthetic, 40 - 60 μm g. size) (1969)

Ca2+ and SO 2- brine saturated Thermal flask immersed in 90.5°C G → B → A 10 days 4 Synthetic powder Ostroff (1964) solution, stirred at 600 rpm thermostated oil bath Air-circulation convection Volterra cores (D: 25 mm; H: 50 oven; sample weight loss, ex- 105 - 150°C G → B → A 42 - 800 hrs Dry heating Milsch et al. (2011) mm); g. size: 80 - 100 μm situ porosity and permeability measurements

Lightly pressed powder pellet Ball & Norwood 107°C G → B → A - PH2O: 0.0013 Pa Sample weight loss (synthetic, 40 - 60 μm g. size) (1969)

Powder: 7x different seived g. sizes 100 - 180°C G → B → γ-A 25 mins - 10 hrs Isothermal TGA Khalil (1982) (from 0.088 - 2.109 mm)

Single crystal gypusm (cm sized); gypsum powder: g. size: Controlled transformation 127°C G → B → γ-A ~50 hrs P : 900 Pa rate thermal analysis; weight Badens et al. (1998) H2O 18 x 1.3 x 0.7 μm3; set plaster: g. loss measurements size: 15 x 1.2 x 1.7 μm3

150°C G → B → A 4 hrs Slurry with 0.2 M H2SO4 solution Powder Autoclave Azimi et al. (2011) 200°C G → B → A 4 hrs Slurry with distilled water Powder Autoclave Azimi et al. (2011) Non-isothermal; Relative humidity 277°C G → B → A Heating rate: ~5 K/min Cleaved selenite - 4 x 4 x 2 mm3 In-situ Raman spectroscopy Sarma et al. (1998) ~60% Water saturated; non-isothermal and Piston-cylinder high- Heating rate: 10 - 60 350°C G → B → A isothermal; heating rate: 10 - 60 K/hr; Synthetic powder pressure apparatus; in-situ Mirwald (2008) K/hr P: 0 - 3.5 GPa DPA Non-isothermal; N flow-through Synthetic powder; g. size: 45 - 106 Strydom et al., 450°C G → B → γ-A Heating rate: 5°C/min 2 TGA, calorimetric analysis (flow rate ~5 cm3/min) μm (1995).

Three step reaction pathway:

G → B → Natural gypsum - powdered; and Hudson-Lamb et al. 97° - 450°C CaSO .0.15H O - Non-isothermal; N flow-through synthetic powder; TGA, calorimetric analysis 4 2 2 (1996) → A g. size: 45 - 106 μm G → γ-A→ B → Non-isothermal; Relative humidity In-situ micro-Raman 177°C Heating rate: ~1°C/min Cleaved selenite - powdered Prasad et al. (2001) γ-A ~60% spectroscopy; TGA Non-isothermal; Capillary system 4x G → B → γ-A → Synthetic powder, In-situ synchrotron angle- 375°C Heating rate: 10 K/min conditions: Open, Open + N ; Sealed; Jacques et al. (2009) A 2 g. size: 53 - 75 μm dispersive X-ray diffraction Sealed + H2O

2.1.6 Microstructural changes during dehydration Dehydration during prograde metamorphism yields reaction-created porosity and in turn permeability throughout reaction progression. However, the details regarding the dynamic evolution of this reaction-induced porosity and how this relates to fluid transport within the crust are still relatively unknown (Rumble, 1994; Ko et al., 1997). In conjunction with experiments performed by Olgaard et al. (1995), Ko et al. (1997) combine hydrological and microstructural techniques to create a reaction progression model of dehydration in polycrystalline gypsum rock (Volterra alabaster, a cylindrical specimen with D: 12 mm; H: 25 mm). Fluid expulsion measurements were taken as gypsum was dehydrated to different completion times (128°C, transiently drained conditions, Pc: 150MPa, Pp: 10 MPa). Plotting expelled

14 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

fluid volume over time produced sigmoidal reaction curves, which were then related to post-dehydration SEM micrographs (Figure 2.2). They divided the reaction into three stages: Stage 1 is characterised by slow fluid expulsion rates during dehydration initiation. Isolated bassanite nuclei form mainly at gypsum grain boundaries. The authors suggested that individual pore pockets surrounding the nuclei trap pore fluid leading to pore fluid pressure growth (Figure 2.2a, c, d). During Stage 2, fluid expulsion increases rapidly before reaching a maximum, which is linked to the elongation and coalescence of pores establishing an interconnected pore network facilitating fluid drainage (Figure 2.2b, c, d). At Stage 3, fluid expulsion slows before plateauing when dehydration has ceased. This is linked to a pore pressure gradient driving fluid flow from the undrained sample end to the drained, +/- sample compaction.

Figure 2-2: Post-dehydration SEM micrographs (a, b) and reaction curves for a drained gypsum dehydration experiment under constant pore pressure (128°C, Pc = 150MPa, Pp = 10 MPa); where (c): Volume of fluid expelled (ΔV/V0 versus time), and (d) the first derivative of (ΔV/V0). The 3 stages show the initial slow increase of fluid expelled (linked to isolated porosity pockets, (a)), followed by a period of rapid increase where the majority of fluid is expelled (linked to coalescence of pore network (b); followed by a final stage of fluid expulsion decrease indicating reaction cessation. Figures from Ko et al. (1997).

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 15

Isolated bassanite nucleation versus sweeping reaction front The above microstructural work indicates random heterogeneous nucleation across the sample. Similar observations were reported during 4D in-situ X-ray tomography of polycrystalline gypsum dehydrated at 115°C (Volterra alabaster, D: 2 mm; H: 5 mm; Pc: 9 MPa, Pf: 4 MPa) by Bedford et al. (2017). They observed bassanite nucleation evenly distributed throughout the sample. Bassanite grains were initially surrounded by isolated ‘porosity moats’, where both grow in size before pores impinge and coalesce (noted at 394 minutes heating). Dispersed bassanite nuclei were also observed in post-experimental photomicrographs of Volterra alabaster, that was dehydrated at 110°C syn-deformation (drained, Pc: 200 MPa, constant strain rate: 3 x 10-4 /s; Stretton, 1996)

However, Wang and Wong (2003) developed a 1D finite-difference model predicting that dehydration occurs as a reaction front that propagates inwards from the drained end of a cylindrical sample. Their model predicted that 100 mins after reaction onset, ~90% bassanite and 7% porosity would be produced at the drained sample end versus ~10% bassanite and ~1% porosity at the sealed end. The model, which was calibrated with experimental data from Ko et al. (1997), predicted a relatively stable linear increase between drainage distance and reaction time. The modelled propagation of a dehydrating reaction front was supported by 2D microstructural observations through post-experimental optical microscopy of rock thin-sections made from a partially dehydrated polycrystalline gypsum sample. A sharp, distinct, inter-granular micron-sized boundary was observed between unreacted gypsum and dehydrated bassanite grains by both Stretton (1996; T: 126°C,

Pc: 200 MPa, no strain applied) and Hildyard et al. (2011; T: 110°C – 125°C, Pc: 100

MPa, Pp: 10 MPa) (Figure 2.3).

Figure 2-3: Photomicrographs from partially dehydrated polycrystalline gypsum identifying a sharp boundary between undehydrated gypsum and dehydrated bassanite. Modified from Stretton (1996) (left image, taken under plane-polarised light) and Hildyard et al. (2011) (right image, taken under cross-polarised light).

16 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

In-situ X-ray micro-tomography monitoring porosity changes of a cylindrical polycrystalline gypsum core (Volterra alabaster, D: 2.3 mm; H: 8 mm), provides unique 3D insights during dehydration at 115°C under dry, drained conditions (Fusseis et al., 2012). These authors confirm the presence of a distinct interconnected porosity front that propagates radially inwards, from the unconfined sample margins to the sample centre over a 4 hour period. Their observations of a sharp porosity increase across a thin reaction front contrasts with the smooth, linear porosity increase modelled by Wang and Wong (2003). A similar margin-inward reaction front was observed in the post-dehydration analysis of polycrystalline gypsum

(110°C, Pc: 60 MPa, Pp: 10 MPa) and serpentine (700°C, Pc: 200 MPa, Pp: 100 MPa), and numerical models by Miller et al. (2003). It is proposed that a grain-scale poromechanical feedback loop occurs where the advancing permeable dehydration front disequilibrates built-up pore-fluid and thermal-elastic stresses, allowing drainage of trapped pore fluid and locally reducing the pressure. This destabilizes gypsum and drives dehydration, allowing the reaction front to propagate further inwards (Miller et al., 2003; Fusseis et al., 2012).

The observed sweeping reaction front of dehydration (Stretton 1996; Miller et al., 2003; Hildyard et al., 2011; Fusseis et al., 2012) is persistent across multiple grains at the micron- and millimetre-scale, however, contrasts the preceding SEM micrographs and X-ray tomography of isolated bassanite nuclei surrounded by a halo of pore space (Olgaard et al., 1995; Ko et al., 1997; Bedford et al., 2017). So what controls how dehydration progresses through the sample? All the above experiments have used Volterra gypsum cores (albeit with slightly different dimensions) and therefore have similar grain sizes and existing porosity, permeability, impurities and pre-existing micro-fractures. There is also no clearly discernible pattern between the two groups in regards to dehydration temperatures, confining or effective pressures

(Pc and Pe, respectively), or sample drainage conditions (Table 2.4). Experiments with observed inter-granular reaction fronts were performed between 110°C – 126°C with samples dehydrated undrained at Pe: 90 MPa (Hildyard et al., 2011), transiently drained (impermeable cap placed on one end of the core, the other end is vented) at

Pe: 50 MPa (Miller, 2003) and Pdiff: 156 MPa (Stretton, 1996), or drained at atmospheric pressures (Fusseis et al., 2012). Isolated bassanite nuclei were observed at temperatures between 107°C – 150°C with samples dehydrated at Pe: 5 MPa

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 17

(Bedford et al., 2017), transiently drained at Pe: 118 MPa (Olgaard et al., 1995), or drained with Pe: 50 – 70 MPa (Ko et al., 1997) and Pc: 200 MPa with a constant strain rate of 3 x 10-4 /s (Stretton, 1996). This highlights the complexity of the coupled kinetic mechanisms involved during gypsum dehydration.

Table 2-4: Literature comparison of the experimental parameters when gypsum dehydration proceeded via an inter-granular reaction front or through isolated bassanite nuclei. Abbreviations: Pc

(confining pressure), Pe (effective pressure), Pf (pore fluid pressure), Pdiff (differential pressure).

Experimental Cell Temperature Dehydration Heating Experimental conditions Sample Type and Dehydration Reaction progress Reference (°C) pathway duration measure

Inter-granular reaction front observed:

Distinct reaction Pc: 100 MPa; Pf: 10 MPa, Volterra core (D: Triaxial rig - fluid front observed - Hildyard

110°C G → B 21 hrs Pe: 90 Mpa; samples 20 mm); expulsion direction of et al. sealed in a copper jacket g. size: 80 - 100 μm measurements propogation (2011) unknown

Pc: 60 MPa; Pp: 10 Mpa; samples jacketed (polyolifin) with a Reaction front 110°C G → B - impermeable cap on one Volterra core Pressure apparatus propogated inwards Miller 2003 end (undrained end) and from drained end permeable cap on the other (drained end) Reaction front Voltera core (D: Time-series propogated inwards Fusseis et 115°C G → B 310 min Dry heating, drained 2.3 mm; H: 8 mm); synchrotron X-ray from the sample al. (2012) g. size: 80 - 100 μm microtomography margins P : 230 MPa, P : 156 c diff Dehydration Mpa; samples sealed in a Volterra core (D: Heard III triaxial Stretton 126°C G → B 90 mins observed first at the copper jacket - one side 9.5 mm; H: 23 mm) apparatus (1996) drained end vented (drained) Isolated bassanite nucleation observed:

Volterra core (H: Triaxial cell - fluid Bassanite formation Olgaard, P : 128 MPa; P : 10 Mpa; 107 - 150°C G → B 0.5 - 22 hrs c p 25 mm); g. size: 80 expulsion is dispersed within Ko, Wong transiently drained - 100 μm measurements the sample (1995)

Pc: 200 MPa; Strain rate: 3 Bassanite formation Volterra core (D: Stretton 110°C G → B - -4 Heard III apparatus is dispersed within x 10 /s; 30% strain; 9.5 mm; H: 23 mm) (1996) drained the sample In-situ time- Volterra core (D: 2 Bassanite formation resolved Bedford et 115°C G → B 9 hrs P : 9 MPa; P : 4 Mpa mm; H: 5 mm); g. is dispersed within c f synchrotron X-ray al. (2017) size: 80 - 100 μm the sample microtomography Volterra gypsum Triaxial cell - fluid Bassanite formation P : 60 - 190 MPa; P : 10 - core (D: 12 mm; H: Ko et al. 120°C - 132°C G → B ~300 mins c f expulsion is dispersed within 120 Mpa; drained 20 mm); g. size: 80 (1997) measurements the sample - 100 μm

Preferred orientation of intra-granular microcracks Brantut et al. (2012) identified two key changes in microstructure during the in-situ dehydration of 2 mm thick Volterra gypsum discs in a low-vacuum SEM chamber equipped with heating stage (from 25°C  200°C). The first change observed was the appearance of thin intra-granular microcracks at ~120°C (Figure 2.4b), followed by grain boundary widening at 143°C (Figure 2.4c). Microcracks appear to form with preferred orientations (Figure 2.4d, e), and often formed as

18 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

evenly spaced, parallel fractures (Figure 2.4b, f). These observations support Sipple et al. (2001a) who reported that dehydration fracture orientations are controlled by the initial crystallographic orientation of gypsum grains. The predominant microcrack orientation was parallel to the (010) plane, that exhibits perfect cleavage along the weakly bonded water layers in the sheeted gypsum crystal structure.

Figure 2-4: SEM micrographs (a-c) were taken in secondary electron mode by Brantut et al. (2012) during in-situ dehydration of Volterra gypsum discs under low vacuum (360 Pa). Initiation of intragranular microcracks is indicated with arrows, seen at 120°C (b), followed by grain boundary widening at 143°C (c). FE-SEM micrographs (d-f) were taken after dehydration showing a preferred orientation of microcracks, carbon-coated samples were imaged with a 10 kV accelerating voltage.

Bassanite growth mechanism The dehydration of gypsum to bassanite can occur topotactically or by dissolution-precipitation. Topotactic transformations occur when the original crystal lattice is mostly retained, and any ionic gains/losses occur with minimal structural rearrangement (Spry, 1969). This produces bassanite pseudomorphs after the initial gypsum grain (Figure 2.4). The (010)/(001) gypsum crystal plane becomes the (001) plane for bassanite (Freyer and Voigt, 2003). Topotactic bassanite growth has been observed in polycrystalline samples (Hildyard et al., 2011; Brantut et al., 2012) and single-crystals (Sipple et al., 2001a, b).

When fluids are present, transformations can proceed through dissolution- precipitation (Ruiz-Agudo et al., 2014). Gypsum dissolves at the mineral-solvent 2+ 2- interface, creating a supersaturated Ca + SO4 + H2O solution. As the stable phase, bassanite precipitates from solution, resulting in a bassanite microfabric unconnected

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 19

to initial gypsum lattice orientations (Freyer and Voigt, 2003). This transformation mechanism has been observed by Olgaard et al., (1995), Ko et al. (1997) and Bedford et al. (2017) during polycrystalline gypsum dehydration, evidenced by ‘pore moats’ surrounding bassanite nuclei, the non-preferred orientation of bassanite grains, and the distinct morphology change and cross-cutting relationship to remaining gypsum (Figure 2.2). Michael (2011) also observed the growth of acicular and platy bassanite from single-crystal selenite dehydrated in brine with no obvious preferred orientation. It has previously been suggested that polycrystalline gypsum will dehydrate topotactically to form β-bassanite (Freyer and Voight (2003) and references therein), and via a dissolution-precipitation mechanism during α-bassanite formation (Freyer and Voight (2003) and references therein). Formation of different bassanite modifications may contribute to the contrasting microstructural observations noted above. However, it is unclear which phase is produced in each of the experiments.

2.1.7 Controls on dehydration Temperature Gypsum dehydration kinetics follow a typical Arrhenius-style dependence on temperature (Arrhenius, 1889):

퐴 (− 푒) 푘 = [퐴푒 푅푇 ] (3)

where:

k = rate constant; R = universal gas constant (J K-1 mol-1); T = temperature (K)

-1 A = pre-exponential factor; 퐴푒 = activation energy (kJ mol ).

Gypsum dehydration rates increase with increasing temperature (Khalil, 1982; Deutsch, Nathan and Sarig, 1994; Ballirano and Melis, 2009). For example, Khalil (1982) show that powdered gypsum dehydrated two times faster at 160°C than at 100°C, and four times faster than at 70°C. A similar effect was observed in fluid expulsion measurements of alabaster gypsum rock. Ko et al. (1997) found that an increase in dehydration temperature from 125°C to 132°C (at constant Pe), produced a six times faster expulsion rate. However, they found only minor differences in the total fluids collected at the end of the experiment (10% increase). The authors link this to observations that the gypsum and bassanite solid-matrix strength is not

20 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

significantly temperature-sensitive. The duration of fluid-collection time was not inherently clear in this study, so perhaps this minor increase in fluid capture reflects both: [1] the faster establishment of a reaction created permeable pore network allowing a faster drainage rate; and/or [2] a faster fluid diffusion rate at higher temperatures.

Heating rates and sample holding cell Changes in heating rates and the type of sample holder during dehydration influence the transition temperatures of gypsum  bassanite and bassanite  γ- anhydrite. Paulik et al. (1992) dehydrated powdered gypsum at five heating rates (0.5 – 10°C/min) and found a steady linear increase in dehydration temperature with increasing heating rate. In another experiment, they tested the effect of five different sample holders (sample mass and heating rate kept constant). They used conical and labyrinth crucibles in both covered and uncovered set-ups, as well as a multi-plate sample holder. Transition temperatures were found to vary between each sample holder and heating rate (Paulik et al., 1992). Similar results were seen in other powdered gypsum dehydration studies where both increasing the heating rate in an open (air flow) capillary system and using a sealed versus open capillary system, increased transition temperatures for both reactions (Gonzàlez-Saborido, 2008; Jacques et al., 2009). Unanimously, neither heating rate nor sample holder geometry affected the anhydrite dehydration temperature. The sensitivity of dehydration kinetics to external factors was therefore attributed to the removal of crystalline water (Jacques et al., 2009).

Initial gypsum microstructure Grain size: Khalil (1982) reports that decreasing grain size increases dehydration rates in powdered gypsum, where seven-grain size fractions (from mean grain sizes (x̄ ): 88 μm - 2.1 mm) were dehydrated under the same conditions. The effective magnitude of rate change, however, was not uniform between all fractions. Fine-grained fractions < 130 μm, were observed to be highly reactive, showing abrupt increases in dehydration rates with decreasing grain size; compared to moderate changes between coarser fractions. This is consistent with solubility studies, which report an increase in gypsum solubilities with decreasing grain size (Sokolov, 1962; Sonnenfeld, 1984; Billo, 1987). Furthermore, Harrison (2012) observed that finer grained gypsum

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 21

powder (< 63 μm) dehydrated at a lower temperature than a coarser sized fraction (63 – 125 μm). Changes in the starting gypsum grain size may account for the variations in dehydration temperatures and the dehydration pathways reported in the literature. Gypsum powder dehydration studies use different size fractions and, more commonly, do not report the particle sizes of their starting materials (Table 2.2). Cave and Holdich (2000), however, found that temperature was a greater controlling factor on dehydration rate than grain size (using five powdered size fractions between 40 – 67 μm); this dominance was consistent between water vapour pressures

(PH2O) in the range 0.001 to 0.35 atm. However, the effects of grain size alone appear variable over their studied experimental conditions and remain unclear.

Rock microstructure: Natural gypsum - Powdered versus Polycrystalline: Harrison (2012) dehydrated four polycrystalline gypsum habits (selenite, massive, satin spar and alabaster) in a gravity convection oven in air, both as natural millimetre-scale samples and as powders (two-grain size fractions: < 63 μm and 63 – 125 μm). For powdered samples, the mass-loss peak (interpreted phase transition via water loss during the gypsum  bassanite transition) was reported at 100°C (< 63 μm) and 115°C (63 – 125 μm). This is consistent with the observations from Khalil (1982) that dehydration temperatures increase with increasing grain size. The polycrystalline samples were found to dehydrate at 130°C for the satin spar, massive and alabaster habits, and selenite dehydrated at 115°C. However, the lower dehydration temperature for selenite could be attributed to its smaller sample mass (~¼ the size of other habits). The above results indicate that powdered gypsum generally dehydrates at lower temperatures than its polycrystalline counterparts. This is supported by the results from other studies where bassanite formation was reported at 115°C for a selenite hand sample (4 x 4 x 2 mm3) (Sarma et al., 1998), and 96°C for powdered selenite (Prasad et al., 2001).

Sample mass Several studies have found a kinetic dependence of sample mass for gypsum dehydration, which can affect both the rate of reaction and the transition temperature. Paulik et al. (1992) observed a steady linear increase in powdered gypsum dehydration temperature for both the gypsum  bassanite and bassanite  γ- anhydrite transitions when sample masses were incrementally increased from 5 mg to 100 mg. In addition, bassanite was found to be the only dehydration product for

22 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

sample aliquots ≤ 10 mg. Cave and Holdich (2000) found a sample mass rate dependence where 40 μm powdered gypsum was dehydrated in sample aliquots of 4 g, 2 g, 0.5 g, 0.4 g, and 0.3 g, in a fluidized bed reactor (PH2O: 0.001 atm) at 140°C. Dehydration reaction rates were ordered from fastest at masses ≤ 0.5 g to slowest at a 4 g sample mass.

Powdered gypsum: Synthetic versus Natural Deutsch et al. (1994) identified distinct differences in reaction rates and IR spectroscopy intensities during the dehydration of five different powdered gypsum microstructures under identical conditions (selenite, satin spar, and three synthetic powders). Synthetic samples dehydrated significantly quicker than natural gypsum samples. Even amongst the synthetic samples, there was significant variation in the dehydration time for both the gypsum  bassanite and bassanite  γ-anhydrite transitions. All sample types were powdered. Therefore, these differences cannot be attributed to grain boundary stressors or variations in microfabrics present in the polycrystalline rock. These results are supported by Yamamoto and Kennedy (1969), who dehydrated both synthetic gypsum and powdered natural selenite and found that natural gypsum consistently dehydrated ~5°C higher than synthetic counterparts, although they do not consider this significant. These effects are most likely attributed to differences in grain size, surface roughness and crystal defects between the samples. Unfortunately, neither study reported grain sizes.

Badens et al. (1998) dehydrated three gypsum microstructures: centimetre- sized natural single crystal gypsum; a set gypsum plaster (57.7% porosity; x̄ : 15 x 1.2 3 3 x 1.2 μm ); and powder precipitated gypsum (x̄ : 18 x 1.3 x 0.7 μm ). When PH2O: 1 Pa, dehydration rates were reported as 0.015 h-1 for both 100 mg gypsum powder and 26.3 mg single crystal gypsum, and 20 mg of set plaster dehydrated at a rate of 0.010 h-1. The similar kinetics of powdered and single crystal gypsum contrast the results of previous studies; however, this could be attributed to sample mass differences.

Effect of salt solutions Gypsum dehydration temperatures are lowered with increasing salinity during hydrothermal dehydration (Ostroff, 1964; Hardie, 1967; Marshall and Slusher, 1966). The formation of anhydrite is also influenced by solution composition. Christensen et al. (2008) found that powdered gypsum dehydrated under dry conditions produced bassanite, γ-anhydrite and anhydrite; water solutions formed γ-anhydrite only, and 1

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 23

M solutions of nitric acid or lithium chloride produced bassanite and anhydrite. Similar results were found by Azim and Papangelakis (2011), where dehydration of powdered gypsum at 150°C for 4 hours in distilled water yielded bassanite, conversely with 0.2 M sulfuric acid a gypsum  bassanite  anhydrite transformation pathway was observed. This effect is further amplified at low temperatures. After 20 days at 90°C in distilled water, powdered gypsum remained unreacted (addition of anhydrite seeds in distilled water produced 90% anhydrite after 10 days). However, full conversion to anhydrite in a 1.5 M sulfuric acid solution at 90°C occurred within 1 day (Azim and Papangelakis, 2011). These results also suggest the presence of a nucleation barrier for anhydrite at low temperatures.

Pressure The transition temperatures during gypsum dehydration are known to increase with increasing pressure (Yamamoto and Kennedy, 1969; McConnell et al., 1987; Mirwald, 2008; Llana-Fúnez et al., 2012; Figure 2.5). Recent in-situ Raman spectroscopy on single gypsum crystals by Liu et al. (2015) found that increasing pressure decreases the dehydration rate of gypsum at isothermal conditions between 110°C - 150°C and 343 - 1085 MPa, using a high-pressure hydrothermal diamond anvil cell. These findings were attributed to an increased binding force of the crystal- bound water at increased pressures.

Figure 2-5: The pressure-temperature stability diagram for bassanite and gypsum within the range of 0 – 800 MPa, and 90°C – 170°C. Equilibrium lines were plotted based on experimental parameters and thermodynamic data provided in McConnell et al. (1987) and Llana-Fúnez et al. (2012).

24 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Pore fluid pressure As discussed earlier, the development of pore fluid pressures within the dehydrating sample is a function of reaction-dependent fluid release rates and the evolution of a permeable porosity network. When a sample is dehydrated under confining pressure (Pc), these variations in pore fluid stresses (Pf) impact the effective pressure (Pe) of the system and can control the mechanical strength of the rock where Pe = Pc - Pf (Olgaard et al., 1995; Llana-Fúnez et al., 2012). Heard and Rubey (1966) deduced the increase in pore fluid pressure during dehydration from the observed ten-fold decrease in gypsum rock strength during triaxial compression tests of polycrystalline gypsum at 5 kbar when the sample was heated from 100°C to 150°C, and at 2 kbar with slightly lower temperatures. Gypsum was jacketed in impermeable sleeves creating an ‘undrained’ dehydrating system. In this set-up, fluids released from dehydration are unable to drain from the system allowing for sufficient Pf build-up that reduces the Pe to the point of rock failure. Murrell and Ismail (1976) observed similar gypsum strength reduction during their undrained gypsum dehydration experiments. They also found that increasing the confining pressure after dehydration had occurred had no effect on rock strength, implying the maintenance of constant Pe. Undrained experiments represent an extreme end- member and would only reflect specific geological settings or circumstances. For comparison, Murrell and Ismail (1976) also dehydrated gypsum under drained conditions (vented jacket) and did not observe the same dramatic strength reduction. One sample was actually found to strengthen mechanically after dehydration. This was interpreted to be the result of trapped fluid in isolated pores, although other authors also contribute this to increased strength in the denser product minerals (Ko et al., 1995; 1997). The contrasting results between end-member experiments creates uncertainty of how rocks in natural geological settings are affected through dehydration.

Evidence from transiently drained experiments suggest that dehydration reactions in crustal rocks can provide a sufficient ‘pulse’ of excess pore pressure (Pe = 0), which does not need to be maintained over long geological time periods to cause rock embrittlement and weakening (Ko et al., 1995; 1997; Olgaard et al., 1995). In these experiments, jacketed samples were sealed at one end, and vented to atmospheric pressure at the other. The evolution of pore fluid pressure was modelled

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 25

with a hydraulic diffusion equation by Olgaard et al. (1995) using experimentally measured fluid release rates and porosity changes. Pore pressure was shown to increase during the initial stages of the reaction, where pore pressure excess was possible in isolated pores before a sufficiently permeable porosity network was established as dehydration progressed allowing for adequate drainage. These simulated pore pressure excesses where linked with the embrittlement and weakening observed experimentally during the beginning stages of gypsum dehydration under drained conditions (Ko et al., 1995; Olgaard et al., 1995). These studies show that the drainage architecture during dehydration reactions in initially low-porosity and low-permeability rocks begins like an ‘undrained system’ where reaction created porosity cannot adequately accommodate the amount of fluid released causing localised pore pressure increases. Elevated pore fluid pressures decrease the dehydration rate until reaching a critical point, where rock strength is reduced, and hydraulic fracturing occurs in grains surrounding these pockets of pore pressure excess (Ko et al., 1997; Miller et al., 2003; Llana-Fúnez et al., 2012; Leclare et al., 2016). Fractures facilitate fluid drainage and decrease effective pressure by increasing the sample permeability. This is coupled with the continuation of the reaction created porosity. The sample thus evolves into a ‘drained system’ as dehydration progresses. Furthermore, Llana-Fúnez et al. (2012) assessed the individual contributions of pore fluid and confining pressure by varying each pressure independently (Pf: 10 - 90 MPa; Pc: 10 - 100 MPa). They showed that pore fluid pressure exerts the dominant control over reaction kinetics. Increasing Pf at constant confining pressure significantly decreased reaction rates. However, increasing confining pressure at constant Pf produced a negligible effect on reaction rates.

Water vapour pressure Variations in water partial pressures during gypsum dehydration can affect the kinetics of the reaction and the dehydration product (McAdie, 1964; Ball and Norwood, 1969). Powdered gypsum dehydrated between 84°C - 88°C under vacuum -8 (Molony and Ridge, 1968) or low PH2O (10 bar; Ball and Norwood, 1969) was found to produce anhydrite; at PH2O = 0.006 bar, both bassanite and anhydrite were stable; and at PH2O: 0.023 bar, bassanite was the only dehydration product (Ball and Norwood, 1969). At higher temperatures and water vapour pressures, Kuntze (1965)

26 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

found a continual increase in transition temperature of bassanite  γ-anhydrite from

~160°C to 200°C as the water vapour pressure was increased from dry N2 flow through to 1 bar. Badens et al. (1998) found that the dehydration reaction pathway varied with water vapour pressure. At ≤ 0.005 bar a one-step conversion took the place of gypsum  γ-anhydrite. However, at 0.009 bar, a two-step transition occurred with bassanite as the intermediate phase. These results were consistently observed across the three microstructures used: set plaster, precipitated powder gypsum and natural single crystal.

Dehydration rates of both α- and β-bassanite were found to decrease with increasing water partial pressures, at all dehydration temperatures between 68°C - 217°C (Ball and Norwood, 1970a) and 115°C - 140°C (Ball and Norwood, 1970b; Ball and Urie, 1970). These findings were coupled with a step-wise increase of activation energies at increasing water partial pressures (McAdie, 1964; Ball and Norwood, 1970a, 1970b; Ball and Urie, 1970). Calculated activation energies were higher and more tightly clustered for α-bassanite (Ball and Norwood, 1970a). These differences were attributed to variations in pore sizes affecting the diffusion of water throughout the sample.

Fowler et al. (1968) also found that water vapour pressure influenced the microstructure (size and shape) of bassanite nuclei formed on dehydrated selenite (010) cleaved gypsum crystals between 1.3 x 10-8 - 1 bar. The smallest hemihydrate growth was observed at 1.3 x 10-7 and 1.3 x 10-5 bar, where the hemihydrate was ~1/10 the size of its nearest neighbour. They infer nuclei growth inhibition at these pressures. Interestingly, growth was not inhibited at the intermediate PH2O of 1.3 x 10-6 bar. The duration of heating and the crystal surface area for each experiment are not clearly defined and may contribute to some of the relative growth difference. With increasing water vapour pressure the overall crystallisation patterns change significantly. Below 0.013 bar, the overall pattern is relatively shapeless, whilst between 0.013 - 0.39 bar an hourglass pattern is dominant, which is then overtaken by dendritic growth patterns at higher pressures. It is unclear whether the change in sample cell (a flow circuit was used < 1 bar, and a static cell was used > 1 bar), could account for these differences.

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 27

2.1.8 Experimental techniques Experimental work on gypsum dehydration can be divided into two categories, those with black-box experimental set-ups and those that involve direct in-situ measurements. Black-box set-ups are defined as experiments where the progression of dehydration is ascertained by proxy measurements during the reaction or simply by post-mortem analysis upon experimental completion. These set-ups are so named because the actual sample characteristics (both mineralogical and microstructural) during the dehydration process remain unknown. Proxy measurements for dehydration reactions include:

[1] Fluid expulsion measurements: the liberated crystal-bound water is collected from the dehydrating sample. This technique often assumes the maximum theoretical reaction porosity has been created and all pores are fully saturated. A limitation of this technique is that the duration of fluid collection time is often unclear, which may lead to an over- or underestimation of reaction rates taking into consideration the variation of fluid diffusion rates through a reaction-dependent pore network under varying temperature and pressure conditions. These techniques often use cylindrical rock cores (~10 – 20 mm in length).

[2] Sample weight loss: the weight loss of samples before, during and after dehydration is compared to either a theoretical post-dehydration weight or used to calculate a rate of weight loss. The sample weight is either measured using analytical balances (McAdie, 1964; Ball and Norwood, 1970; Badens et al., 1998) or by monitoring the extension changes in a silica spiral attached to a cathometer and the jacketed sample (Ball and Norwood, 1969; Ball and Norwood, 1970). These techniques have been mostly used when dehydrating gypsum powders or lightly pressed powder pellets, minimising the complications of fluid diffusion rates through a solid rock pore network. However, it may underestimate the extent of dehydration as it does not take into account trapped fluids in isolated grain-scale pores.

Several styles of in-situ experimental techniques have been used to monitor gypsum dehydration, which either directly measure mineral phase change, observe changes in dehydration microstructures, or measure proxy data such as mass changes or differential temperatures. A brief summary of each technique is given below.

28 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

 Thermogravimetric analysis (TGA) and differential thermal analysis (DTA): these techniques measure the mass of a sample and the differential temperature (between the sample and a reference), respectively, as a function of temperature and time. DTA is a similar technique to differential scanning calorimetry (DSC). TGA and DTA/DSC are often measured simultaneously (Powell, 1958; Clifton, 1971; Ball and Urie, 1970; Strydom et al., 1995; Hudson-Lamb et al., 1996; Badens et al. 1998).

 Infrared (IR) spectroscopy: this technique measures the inelastic scattering of a material illuminated by a laser. It can be used in-situ with spectra collected at fixed time intervals, although the temporal resolution of collection time during dehydration is unclear (Sarma et al., 1998; Prasad et al., 2001; Liu et al., 2015); or during post-mortem analysis (Razouk, Salem and Mikhail, 1960; Harrison, 2012). Most commonly, powdered gypsum samples are used and dehydrated under atmospheric, dry or vacuum conditions. Liu et al. (2015), however, studied the dehydration of single crystal under high pressure (343 – 1085 MPa) using a diamond anvil cell.

 Field emission environmental SEM (ESEM): this technique was employed by Brantut et al. (2012) using a heating stage for in-situ dehydration, taking high-resolution electron micrographs of the free sample surface every 12 seconds during dehydration. The sample is dehydrated under low vacuum

(PH2O: 360 Pa).

 Time-resolved synchrotron X-ray micro-tomography: this method captures 2D radiographs at varying angles around a cylindrical whole-rock sample, which can be combined to reconstruct a 3D model of the internal microstructure of the dehydrating sample with micron-scale resolution. The main limitation of this technique is the relatively limited temporal resolution due to the long collection times required to image the whole sample (15 – 25 mins), and spatial resolution of ~1 micron per voxel edge length. The grey scale image resolution allows for a clear distinction between pore space and solid phases, but cannot differentiate between calcium sulfate phases. Post-dehydration analysis is required for mineral phase identification (Fusseis et al., 2012; Bedford et al., 2017). The

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 29

samples can be dehydrated under various pressure conditions, depending on the user’s experimental apparatus.

 In-situ powder XRD: this technique measures the mineralogical phase change of gypsum during dehydration. It can be used in the laboratory, where diffraction patterns are collected at incremental temperature steps (Carbone et al., 2008; Ballirano and Melis, 2009), or at a synchrotron which allows a higher temporal resolution of pattern collection (~6 – 60 secs) (Christensen et al., 2008; Jacques et al., 2009). The sample can be dehydrated under dry, hydrothermal or vacuum conditions.

Limitations of current experimental approaches A review of previous gypsum dehydration experiments, summarised in Table 2.2 and 2.3, highlights several gaps in the literature.

[1] The predominance of ‘black-box’ or ex-situ experiments

Only 35% of the reported experiments monitor gypsum dehydration using in- situ techniques. The remainder measure reaction progression using proxy measurements or simply by post-dehydration sample analysis. Of these 16 in-situ experiments, only seven provide direct measurements of mineral phase changes or microstructural observations during dehydration.

[2] The lack of geologically realistic conditions during in-situ experimental work

In-situ monitored gypsum dehydration experiments have been performed under the following pressure conditions:

[a] In vacuo or under low vacuum (PH2O: < 900 Pa) conditions:

 Powdered gypsum starting materials - Ball and Norwood, 1969; Ball and Norwood, 1970; Ball and Urie, 1970; Hudson-Lamb et al., 1996; Badens et al., 1998; Prasad et al., 2001; Carbone et al., 2008

 Whole-rock gypsum - Brantut et al., 2012

[b] Atmospheric pressure conditions:

 Powdered gypsum starting materials - Clifton, 1971; Deutsch et al., 1994; Christensen et al., 2008; Ballirano and Melis, 2009; Jacques et al., 2009

30 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

 Single crystal gypsum (relative humidity ~60%) - Prasad et al. 2001

 Whole-rock gypsum (drained) – Fusseis et al., 2012

[c] Atmospheric pressure, hydrothermal conditions:

 Powdered gypsum starting materials - Christensen et al., 2008; Jacques et al., 2009

[d] Under elevated pressures:

 Powdered gypsum starting materials (water saturated; P: 0 – 3.5 GPa) – Mirwald, 2008

 Single crystal gypsum (hydrothermal – D2O saturated; P = 343 – 1085 MPa) – Liu et al., 2015

 Whole-rock gypsum (Pc: 9 MPa; Pf: 4 MPa) – Bedford et al., 2017

The above highlights that majority of in-situ experimental work has been performed either in vacuo / under low vacuum or with powdered gypsum starting materials, which represent unrealistic conditions for gypsum dehydration in the Earth’s crust.

[3] The lack of whole-rock samples

Powdered gypsum starting materials have dominated experimental dehydration work. Of the 46 different studies reported, powdered gypsum samples were used 29 times (synthetic/precipitated gypsum = 22, and powdered gypsum rock/crystal = 7); polycrystalline gypsum 16 times (predominantly Volterra gypsum); and single- crystal gypsum 6 times. Furthermore, only three of the polycrystalline gypsum experiments used in-situ techniques; ten were performed using triaxial deformation cells, where reaction progression is measured by a proxy, and the final two experiments performed post-mortem IR spectroscopy/permeability measurements on dehydrated samples. Furthermore, the three in-situ whole-rock studies have all been microstructurally focused without any kinetic analysis, using in-situ synchrotron micro-tomography (Fusseis et al., 2012; Bedford et al., 2017) or in-situ field emission SEM (Brantut et al., 2012).

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2.2 KINETICS

Kinetics is the study of transformation processes and reaction rates (Lasaga, 2014). All chemical reactions can be decomposed into a series of elementary (single- step) processes. Collectively these steps make up the reaction mechanism (Brantley, Kubicki and White, 2008). Homogeneous reactions occur within a single phase (gas, liquid, solid). Heterogeneous reactions occur at phase interfaces such as water-rock interactions (Brantley et al., 2008). Each reaction step involves a structural and/or compositional transition between molecules where an energy potential barrier, activation energy (Ae), must be overcome (i.e., breaking of atomic bonds) (Lasaga,

2014). The Ae magnitude dictates the rate at which the reaction occurs. The reaction rate can be defined as the rate of product formation or the rate of reactant consumption (Vallance, 2017). Common controlling factors of reaction rates are temperature and pressure, the presence of catalysts, fluids, and the concentration of reactive phases. Solid-state reactions are further affected by the surface morphology (i.e., roughness) and microstructure of the solid material, as both control the surface area and density of available surface-reactive sites (Fischer and Luttge, 2007). Temperature is often the most significant variable related to reaction kinetics. Most chemical reactions exhibit an Arrhenius-style exponential temperature dependence of reaction-rate constant k (Eq. 3).

2.2.1 Rate-controlling mechanisms Elementary reaction steps involve diffusion processes and/or surface reactions. The overall rate-limiting step is defined as the slowest of the elementary processes (Morse and Arvidson, 2002). When the physical process of moving ions to/from the reaction site is rate-limiting, the reaction is diffusion-controlled. However, when the ionic migration, absorption or desorption, or chemical reactions on the sample surface are rate-limiting, the reaction is surface-controlled (Chou et al., 1989; Morse and Arvidson, 2002). Insights into rate-controlling mechanisms can be gained from the experimentally determined Ae. For example, mineral dissolution rates have been studied extensively. Typical surface-controlled reactions exhibit a higher Ae (~62 kJ/mol) compared to diffusion-controlled ones (~20 kJ/mol) (Lasaga, 2014; Brantley et al., 2008).

32 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

2.2.2 Measuring reaction rates Kinetic data is obtained by measuring the change in a physical property of a system over time (Vyazovkin et al., 2014). This property is then converted to a dimensionless value, α (α ∈ [0; 1]), representing the fraction of transformed material (conversion fraction). Chemical kinetics study homogeneous reactions, measuring the changing concentration of reactants/products (Brantley et al., 2008; Weinberg et al., 1997). Reactions are measured in batch/flow-through reactors where solution- suspended reactants are monitored using spectroscopic techniques (Masel, 2001).

Solid-state kinetics is used to study the thermal dehydration of minerals and rocks. Mineral dehydration is heterogeneous: the product fluid phase can interact with both reactant and product solid phases (Vyazovkin et al., 2014). Gypsum dehydrates whereby 1 gypsum (s)  1 bassanite (s) + 1.5 H2O (l/g). Dehydration kinetics are commonly measured experimentally by monitoring changes in sample mass (TGA), temperature (DTA) or the heat of the system (DSC) as a function of time and temperature (Vyazovkin et al., 2014). Experiments can be performed isothermally (constant applied temperature) or nonisothermally (constant heating rate, linear temperature increase). Peaks/deflections in the data indicate when mineral phase transitions have occurred and the directional change of enthalpy (is the reaction endothermic/exothermic?) (Brown and McLaren, 1962). Recently, mineral dehydration reactions have also been studied with in-situ XRD (Carbone et al., 2008; Christensen et al., 2008; Ballirano and Melis, 2009). X-rays diffract from the crystal lattice planes, producing unique diffraction patterns for each material. XRD therefore directly monitors mineral phases and their transitions in crystalline solids as a function of temperature and time.

2.2.3 Kinetic models Rate laws describe the relationship between species concentrations and reaction rate mathematically (Vallance, 2017). Analysis is performed on experimental reaction curves, namely plots of the conversion fraction (α) over time, to determine rate coefficients, k ((time)-1). Solid-state kinetics can be interpreted by a number of physico-geometrical models. These models generally assume [1] isothermal conditions, [2] a single-crystal mineral reactant with simple geometry (sphere/cube), [3] volume conservation, and [4] that the reactant is unaffected by product phases (Galwey and Brown, 1999; Vyazovkin et al., 2014). These models

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 33

represent an oversimplified ideal reaction. These assumptions must be considered for applications to polycrystalline/powdered samples, which contain variable grain size and shape distributions. Kinetic models can be classified based on reaction mechanisms or reaction curve shape. Curve shapes are classified as:

 Constant: the reaction rate is linear (Figure 2.6a)

 Deceleratory: reaction rates decrease with time (Figure 2.6b, e, f)

 Acceleratory: reaction rates increase with time (Figure 2.6c)

 Sigmoidal: the reaction curve is ‘S’ shaped (Figure 2.6d)

Figure 2-6: Isothermal α versus time (min) curves for solid-state reaction models simulated with a rate constant (k) of 0.049 min-1 (after Khawam and Flanagan, 2006). a) zero-order (constant), b) first- to third-order (deceleratory), c) power law (acceleratory), d) Avrami-Erofeyev (JMAEK; sigmoidal), e) geometrical contraction (deceleratory), and f) diffusion (deceleratory).

34 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Reaction-order models These are the simplest models. Reaction rates are proportional to reactant concentration through (similar to homogeneous reactions; Khawam and Flanagan, 2006):

푑훼 = 푘(1 − 훼)푛 (4) 푑푡

The degree to which reactant concentration affects reaction rate dictates reaction order, n. Zero-order reactions are not affected by reactant concentration (Figure 2.6), while higher-order reactions, usually up to n = 3, are strongly coupled to reaction concentration, leading to deceleratory α-curves (Figure 2.6).

Nucleation models Nucleation is the “initial establishment of a new and discrete product particle within the solid reactant” (Galwey and Laverty, 1990). Nucleation preferentially occurs at reactive sites where Ae is minimised (Khawam and Flanagan, 2006). Favoured nucleation sites include lattice imperfections (point defects, dislocations, and kinks), micro-fractures, or crystal impurities (Galwey and Laverty, 1990; Morse and Arvidson, 2002). Nucleation and nuclei growth is assumed to be rate-limiting (Khawam and Flanagan, 2006). Power-law models are the simplest, where nuclei growth is assumed constant (no constraints on nuclei growth), and the nucleation rate obeys a power law yielding acceleratory reaction curves (Pn, Eq. 5, Figure 2.6; Khawam and Flanagan, 2006). However, the most common nucleation-growth model is the Avrami-Erofeyev (or Johnson-Mehl-Avrami-Erofeyev-Kolmogorov, JMAEK) equation. JMAEK includes some additional assumptions where [1] nucleation is randomly (and homogenously) distributed on the reactant, [2] crystal size does not affect nuclei growth rate (growth rate is time-dependent only), [3] ingestion of potential sites by existing nuclei and nuclei coalescence is ignored, and [4] nuclei growth rate is directionally equal (Lasaga, 2014; Khawam and Flanagan, 2006). JMAEK corrects for the growth impingement of nuclei and rate deceleration during the final phase of reaction where the reaction rate slows. This produces a characteristic sigmoidal reaction curve (Figure 2.6). The exponent (n) in both models represents the sum of elementary reactions and dimensions of nuclei growth (Galwey and Brown, 1999).

푑훼 푛−1 = 푘[푛(훼) 푛 ] Pn (5) 푑푡

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 35

푑훼 푛−1 = 푘[푛(1 − 훼)[− ln(1 − 훼)] 푛 ] JMAEK (6) 푑푡

Geometrical contraction models As the reaction initiates, dense nucleation commences rapidly on the sample surface creating a product boundary layer between the nucleus-rich surface and the internally unreacted crystal (Khawam and Flanagan, 2006). Inward progression of the reaction interface towards the sample centre is rate-limiting (Galwey and Brown, 1999), and the reaction is phase-boundary-controlled (Sharp, Brindley and Achar, 1966). The reaction has a negligible induction period resulting in deceleratory reaction curves (Figure 2.6; Galwey and Brown, 1999). A contracting area/disc equation models preferential nucleation on specific crystal surfaces and inwards interface propagation from the margins of a disc/cylinder (R2, Eq. 7). In contrast, a contracting volume/sphere model describes the rapid nucleation on all surfaces of spherical or cubic crystals where the interface progresses inwards at a constant rate (R3, Eq. 8). Diffusion effects are not considered, and particle size effects are included in the rate constant (k) (Khawam and Flanagan, 2006; Galwey and Brown, 1999).

푑훼 1 = 푘[2(1 − 훼)2] R2 (7) 푑푡

푑훼 2 = 푘[2(1 − 훼)3] R3 (8) 푑푡

Diffusion models The mobility of ionic constituents is hindered during solid-state kinetics as they need to diffuse through crystal lattices (Khawam and Flanagan, 2006). The simplest model is a parabolic law describing the kinetics of an infinite, flat, 1D plane where product layer thickness is directly proportional to the conversion fraction (α) (D1, Eq. 9). The 3D Jander equation combines the 1D parabolic law with the contracting volume model (D3, Eq., 10; Jander, 1927). The 3D Ginstling-Brounshtein equation further accounts for molar volume differences between reactants/products (D4, Eq. 11; Ginstling and Brounshtein, 1950).

푑훼 1 = 푘 D1 (9) 푑푡 2훼

2 푑훼 [3(1−훼)3] = 푘 D3 (10) 푑푡 1 [2(1−(1−훼)3)]

36 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

푑훼 3 = 푘 D4 (11) 푑푡 1 2((1− 훼)3−1)

2.2.4 Gypsum dehydration Dehydration kinetics have been investigated extensively using a range of experimental techniques, sample microstructures and experimental conditions (Table 2.5). The table is organised by increasing dehydration temperatures, then by increasing water vapour pressure (PH2O) where applicable. All four solid-state reaction mechanisms have been modelled and empirical Ae range from 35.9 – 246.0 kJ/mol. This variability suggests that gypsum dehydration is kinetically complex and highly sensitive to environmental parameters.

Kinetic models Ball and Norwood (1969) applied several models to gypsum dehydration to interpret best-fit kinetics, finding that mechanisms are highly dependent on both temperature and PH2O. Below 100°C gypsum dehydration was interpreted as phase- boundary controlled (contracting disc model) at low PH2O (0.013 Pa) and nucleation- controlled (JMAEK model) at medium PH2O (613 Pa - 2.27 kPa). Dehydration between 100°C - 110°C was interpreted as diffusion- (1D diffusion model) or phase- boundary-controlled depending on PH2O. However, above ~114°C gypsum dehydration was diffusion-controlled independent of PH2O.

Sigmoidal reaction curves where most common and modelled using JMAEK (Table 2.5). The lowest Avrami exponents (n) were obtained in high-pressure single crystal (n: 0.89 – 1.42; Liu et al., 2015) and polycrystalline gypsum dehydration (n: 0.41 – 0.75; Stretton, 1996). Exponents ~1 are interpreted to be associated with diffusion-controlled reactions (Sharp et al., 1966; Liu et al., 2015). Exponents were found to increase with increasing pressure (Liu et al., 2015) and decrease with decreasing temperature (Stretton, 1996). A mechanism change was inferred from volume diffusion at ~120°C (n: ~0.7) to grain-boundary diffusion-controlled at 90 -

111°C (n: 0.35 - 0.52) (Stretton, 1996). In-vacuo powder pellets (n: ~2, Ae: 76 kJ/mol; Carbone et al., 2008) and atmospheric powder (avg. n: 6, Ae: 109 kJ/mol; Ballirano and Melis, 2009) dehydration were likened to phase-boundary-controlled kinetics (Ae: 79.9 – 92.9 kJ/mol; Ball and Norwood, 1969).

Model-independent Ae calculations were made from the retreat rate of crystal etch-pits (Jordan and Astilleros, 2006), reduced intensity of infrared spectral data

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 37

(Sarma et al., 1998), or when ’x’ percent transformation had occurred (Fowler et al.,

1968; Putnis et al., 1990). Fowler et al. (1968) obtained comparable Ae to McAdie

(1964) under five similar PH2O regimes. Hydrothermal and variable humidity experiments (Ae: 90.3 - 119 kJ/mol) were compared to phase-boundary-controlled reactions at low - med PH2O (2.27 - 3.39 kPa; Ae: 92.9 - 96.6 kJ/mol) by Ball and Norwood (1969) (Putnis et al., 1990; Sarma et al., 1998; Jordan and Astilleros, 2006).

38 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Table 2-5: Literature summary of empirical activation energies for gypsum dehydration ordered firstly by increasing dehydration temperatures and then by increasing water vapour pressure (PH2O).

Kinetic model parameters - JMAK Activation Experimental Cell Temperature Dehydration Experimental Dehydration Sample Type energy and Dehydration Reference (°C) pathway conditions Avrami exponent Rate constant mechanism (kJ/mol) measure (n) (k) (sec-1)

1.4 x10-10 40°C 2.22 -10 44°C 2.23 4.3 x10 Compared to Ball 48°C Pressed powder 2.28 1.8 x10-9 and Norwood In-situ energy Carbone et G → γ-A In vacuo 76 55°C pellets - 200 mg 2.34 7.9 x10-9 (1969) boundary dispersive XRD al. (2008) 59°C 2.40 controlled 1.6 x10-8 80°C 2.42 1.1 x10-7

PH2O: 0.13 Pa 38.5 Fowler, Cleaved selenite Flow ciruit (< 760 P : 13.33 Pa 60.0 Howell, 50 - 150°C G → α-B / β-B H2O platetlets (010), 20 - N / A N / A N / A mm.Hg), Static cell P : 113.33 Pa 123.4 Schiller H2O 30 μm thick (>760 mm.Hg) PH2O: 101.33 kPa 156.9 (1968) Rate equation: dy / Compared to Ball Reduced water Natural single dt = k*f(y) (where and Norwood Thermogravimetric, Putnis et al. 63 - 106°C G → B → γ-A pressure, constant 90.3 N / A crystal gypsum y = fraction of total (1969) boundary IR spectroscopy (1990) N2 flow rate H2O lost) controlled

-6 80°C 3.5 x10 Compared to Ball Ballirano 100°C Synthetic powder, 2.3 x10-5 and Norwood In-situ parallel-beam G → B Dry heating 109 6 and Melis 120°C g. size: 2 - 10 μm -4 (1969) boundary XRD 1.57 x10 (2009) 130°C controlled 4.1 x10-4 Lightly pressed Contracting disc Ball & Boundary 81 - 100°C G → A P : 0.0013 Pa powder pellet (40 - 79.9 model used: -5 -5 Sample weight loss Norwood H2O 4.3 x 10 - 6.5 x 10 controlled 60 μm g. size) [1 - (1 - α)0.5] = kt (1969) Lightly pressed Ball & -5 -4 Nucleation 80.5 -88°C G → B / A PH2O: 613.28 Pa powder pellet (40 - 246.0 2 2.6 x 10 - 1.5 x 10 Sample weight loss Norwood controlled 60 μm g. size) (1969) Lightly pressed Ball & G → B / A Nucleation 81 -88°C P : 2.27 kPa powder pellet (40 - 144.7 2 -5 -5 Sample weight loss Norwood G → B H2O 3.0 x 10 - 7.8 x 10 controlled 60 μm g. size) (1969) Selenite single Compared to Ball Jordan and Various brine crystal (010)), 10 and Norwood 87 - 120°C G → B 119 ± 11 N / A N / A Hydrothermal AFM Astilleros solutions mm2 exposed (1969) boundary (2006) surface area controlled >120°C: volume P : 215 -230 MPa, diffusion c Polycrystalline Stretton 90 -126°C G → B Dif. Stress: 100 - ~ 132 0.41 - 0.75 N / A <110°C: grain Heard III apparatus gypsum (1996) 159 MPa boundary difussion

PH2O: 0 Pa Precipitated 109.2 Zero-order Vapor-jacketed Pyrex Zero-rder reaction: McAdie 97 - 140°C G → α-B / β-B P : 13.31 kPa gypsum, 116.9 N / A nucleation- oven + sample H2O α = kt (1964) PH2O: 101.325 kPa g. size: 60 - 80 μm 201.6 propogation weight loss Volterra cores (D: 25 oven heated, sample Milsch et al. 105 - 150°C G → B → A Dry heating mm; H: 50 mm); g. 78 1.3 - 1.54 -6 Not interpreted 4.9 - 71.8 x 10 weight loss (2011) size: 80 - 100 μm Lightly pressed Parabolic law used: Ball & G → B / A -4 -3 1D Diffusion 107 - 146.5°C PH2O: 0.0013 Pa powder pellet (40 - 35.9 4.01 x 10 - 1.06 x 10 Sample weight loss Norwood G → A α2 = kt controlled 60 μm g. size) (1969) Lightly pressed Ball & Parabolic law used: B → H -4 -3 1D Diffusion 110 - 145°C PH2O: 613.28 Pa powder pellet (40 - 49.5 2.9 x 10 - 1.0 x 10 Sample weight loss Norwood G → A 2 controlled 60 μm g. size) α = kt (1969) D O saturated; Hydrothermal anvil 2 Single crystal, Diffusion Liu et al. 110 - 150°C G → B P: 343 - 1085 MPa, 66.9 0.89 - 1.42 -3 -4 cell; in-situ raman g. size: 60 x 80 μm 0.94 x 10 - 9.2 x 10 controlled (2015) undrained spectroscopy Lightly pressed Contracting disc Ball & -4 -4 Boundary 100 - 110°C G → B PH2O: 2.27 kPa powder pellet (40 - 92.9 model used: 1.9 x 10 - 4.3 x 10 Sample weight loss Norwood controlled 60 μm g. size) [1 - (1 - α)0.5] = kt (1969) Lightly pressed Contracting disc Ball & Boundary 100 - 107°C G → B P : 3.39 kPa powder pellet (40 - 96.6 model used: -4 -4 Sample weight loss Norwood H2O 1.6 x 10 - 2.7 x 10 controlled 60 μm g. size) [1 - (1 - α)0.5] = kt (1969) Fluidised (air, Powder gypsum, 2D Avrami- Cave and

100 - 170°C G → B; G → A CO2), PH2O: 0.001 - median g. size: 48 81 Erofe'ev model: N / A N / A Fluidised bed reactor Holdich 0.35 atm μm kt = [-ln(1 - α)]0.5 (2000) Lightly pressed Ball & Parabolic law used: G → B / A -4 -3 1D/2D Diffusion 110 - 152°C PH2O: 3.39 kPa powder pellet (40 - 50.2 1.9 x 10 - 1.5 x 10 Sample weight loss Norwood G → A 2 controlled 60 μm g. size) α = kt (1969) Lightly pressed Ball & Parabolic law used: -4 -3 1D/2D Diffusion 110 - 146.5°C G → A PH2O: 5.95 kPa powder pellet (40 - 51.0 4.8 x 10 - 1.3 x 10 Sample weight loss Norwood 2 controlled 60 μm g. size) α = kt (1969) Lightly pressed Ball & Parabolic law used: G → B / A -4 -3 1D/2D Diffusion 114 - 150°C PH2O: 2.27kPa powder pellet (40 - 43.9 4.1 x 10 - 1.2 x 10 Sample weight loss Norwood G → A 2 controlled 60 μm g. size) α = kt (1969) Non-isothermal; Cleaved selenite, 4 x Sarma et al. up to 175°C G → B Rel. humidity 92.3 N / A N / A N / A Raman spectroscopy 4 x 2 mm3 (1998) ~60%

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 39

The temperature kinetic divide Kinetically, gypsum behaves markedly different above/below ~100 - 120°C.

Changes in reaction rates

Significantly slower dehydration rates occurred during powdered gypsum dehydration at 75°C compared to higher temperatures (Ballirano and Melis, 2009). In 2 hrs at 150°C, water-saturated powdered gypsum had fully converted to anhydrite. However, 20 days at 90°C incurred no reaction (Azim et al., 2011). For polycrystalline gypsum, full dehydration was observed in 5 hrs at 125°C (Pe: 100 MPa; Ko et al., 1997). However, samples only partially dehydrated after 20 hrs at

120°C (Pe: 140 MPa; Ko et al., 1997) and after 27 hrs at 120°C (Pc: 100 MPa, Pe: 91 MPa; Llana-Fúnez et al., 2012).

Changes in dehydration mechanism

Inferred mechanism changes at ~100 - 110°C (pressed powder gypsum pellets) and ~110 - 120° (polycrystalline gypsum) were already discussed above (Ball and Norwood, 1969; Stretton, 1996). However, a dehydration mechanism switch from first-order reaction model (100°C) to a 2D phase boundary-controlled reaction (110°C) was also interpreted during the isothermal conversion of powdered gypsum to bassanite (Dos Santos et al., 1997). These ‘switch transition temperatures’ and changes in reaction rates are slightly elevated in polycrystalline studies which may be attributed to the effects of grain-scale stresses. However, all three polycrystalline experiments were dehydrated under high-pressure conditions. Therefore, the effects of pressure versus sample crystallinity on dehydration kinetics cannot easily be differentiated.

Effects of PH2O on activation energy

Within each controlled PH2O study, Ae exhibits increases with increasing PH2O.

However, the kinetics are variable between the datasets. Empirical Ae for gypsum dehydration under controlled PH2O can also be differentiated above and below 100°C.

High-temperature experiments exhibit lower Ae within PH2O regimes but are more variable between experimental set-ups. Hydrothermal and high-pressure experiments where PH2O is unknown are not reported (Stretton, 1996; Jordan and Astilleros, 2006; Liu et al., 2015).

40 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Dehydration temperature < 100°C (Table 2.5)

3 -1  144.7 - 246 kJ/mol at medium PH2O (3 x 10 to 1 x 10 Pa) (Ball and Norwood, 1969)

-1 -7  76 - 79.9 kJ/mol at low PH2O (1 x 10 to 1 x 10 Pa) (Ball and Norwood, 1969; Carbone et al., 2008)

Dehydration temperature > 100°C (Table 2.5)

 109 - 201.6 kJ/mol at atmospheric pressure (McAdie, 1964; Fowler et al., 1968; Ballirano and Melis, 2009)

5 3  51 - 123.4 kJ/mol at high PH2O (1x 10 to 3 x 10 Pa) (McAdie, 1964; Fowler et al., 1968; Ball and Norwood, 1969; Putnis et al., 1990; Sarma et al., 1998; Cave and Holdich, 2000)

3 -1  49.5 - 109.2 kJ/mol at medium PH2O (3 x 10 to 1 x 10 Pa) (McAdie, 1964; Fowler et al., 1968; Ball and Norwood, 1969)

-1 -7  35.9 - 38.5 kJ/mol at low PH2O (1 x 10 to 1 x 10 Pa) (Fowler et al., 1968; Ball and Norwood, 1969)

The lower Ae in low PH2O regimes have also been observed in other salt hydrates and were attributed to the Topley-Smith effect (Volmer and Seydel, 1937; Frost, Moon and Tompkins, 1951; Frost and Campbell, 1953). The formation of amorphous/ disordered product phases is favoured at low pressures, which impedes the diffusion of liberated crystal-bound water from the reaction interface. However, higher PH2O regimes are linked to crystalline product formation, which creates adequate drainage architecture (Topley and Smith, 1931, 1935; Frost and Campbell, 1953; L’Vov, 2007). This effect was exaggerated at low temperatures during copper sulphate pentahydrate dehydration (Frost and Campbell, 1953), which may account for the significant Ae drop from > 144 kJ/mol (med PH2O) to ~80 kJ/mol (low PH2O) during low-temperature gypsum dehydration.

Effects of sample microstructure Gypsum microstructure may also affect dehydration kinetics. Single crystal and powdered gypsum dehydrated under similar PH2O produced comparable Ae, although single-crystal data was consistently 10 - 49 kJ/mol lower (Table 2.5; McAdie, 1964; Fowler et al., 1968). Several kinetic models were applied to five powdered gypsum

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 41

microstructures (dry dehydrated at 60°C; Deutsch et al., 1994). A nucleation power- law model fit best for natural gypsum (selenite, satin spar) and one synthetic sample, with the other two synthetics fitting Avrami or second-order reaction models. However, the reported R2 values were very similar between most models (e.g. 0.9952 versus. 0.9806) (Deutsch et al., 1994). This highlights an important caveat: a mathematic model fit to a data series can offer non-unique solutions. Numerous models or combinations of models can adequately fit the same kinetic data making mechanistic interpretations difficult. Molony and Ridge (1968) encountered this, whereby both contracting disc and contracting sphere models equally fit powdered gypsum kinetic data (in vacuo, 85°C).

The kinetic complexity of gypsum dehydration is evident in the literature. The products of dehydration, reaction rates, reaction mechanisms and Ae are all significantly influenced by temperature, PH2O and sample microstructure. Table 2.5 highlights the dominance of powdered gypsum (variable grain sizes), pressed powder pellets or single crystals as sample materials in kinetic experiments. Differences in sample microstructure and experimental techniques may account for the variable Ae and reaction mechanisms reported.

2.3 X-RAY SCATTERING

Scattering techniques are used to characterize the micro- and nanostructure of materials and determine the geometry of particles in solution (Fratzl, 2003; Radlinski et al., 2000b). This is done by analysing the way that objects scatter radiation, which can be from X-rays, neutrons or light (Ingham, 2015). Scattering occurs during wave interference when the incident radiation interacts with contrasting features in the sample. Scattering under these circumstances is assumed to be an elastic process, where no photon energy is lost (Schnablegger and Singh, 2011; Stawski and Benning, 2013). X-rays scatter in regions of electron density contrast; neutrons scatter due to interactions with an atomic nucleus; and the scattering of light is due to contrasts in the refractive index of phases (Jackson, 2008; Ingham, 2015). Rocks are treated as a two-phase system consisting of the rock matrix and the pore network (Debye et al., 1957; Radlinski et al., 2006). X-rays interact with the pore-matrix interface, where the pores act as the ‘scatterers’.

42 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Scattering techniques are governed by a reciprocity law, where particle size and scattering angle have an inverse relationship (Glatter and Kratky, 1982). Therefore, the larger the object interacting with the incident beam, the smaller the scattering angle and vice versa (Ingham, 2015). This inverse relation is reflected by Bragg’s law, where for a fixed wavelength the angle of diffraction and the atomic spacing of the lattice planes are related by (Bragg and Bragg, 1913):

푛휆 = 2푑푠푖푛휃 (12)

where:

n = Integer (denoting the order of the diffraction band); 휃 = Diffraction angle

휆 = Incident radiation wavelength; d = Inter-planar spacing.

2.3.1 How does it work? The set-up of X-ray transmission scattering experiments is depicted in Figure 2.7. A monochromatic, collimated incident beam (i.e. single frequency, parallel travelling X-rays) with wave vector, ki, travels from a radiation source and is directed onto a sample (Kikhney and Svergun, 2015). This incident radiation then interacts with any electron density contrasts in the sample and scatters at a value of 2θ to the incident beam. This scattered radiation now travels along a new wave vector kf. It is collected on highly sensitive photon-counting detectors (Kirby et al., 2013; Kikhney and Svergun, 2015). Scattering is elastic, therefore the magnitude of the incident and scattered wave vectors are equal, only their directions have changed. This change in direction can be measured in reciprocal space as the scattering vector -1 (also called the momentum transfer), Q (A ) = kf – ki (Schnablegger and Singh, 2011). The scattering vector (Q) and scattering angle (2θ) have the following relationship (Glatter and Kratky, 1982; Ingham, 2015):

4 휋 sin(휃) 2휋 푄 = = (13) λ 푑

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 43

Figure 2-7: Schematic of an X-ray scattering experimental set-up. The incoming, incident X-ray (ki) beam (green) penetrates and interacts with the sample and scatters at a value of 2θ to the incident beam. Scattered X-rays (kf) are collected on a 2D detector where a beamstop protects the detector from any transmitted incident X-rays.

2.3.2 SAXS and WAXS Scattering techniques can be used in laboratories and at high-brilliance synchrotron sources. The main X-ray scattering techniques are small-angle X-ray scattering (SAXS) and wide-angle X-ray scattering (WAXS). Both techniques are non-destructive, require little sample preparation and allow for in-situ, real-time measurements with nanometric spatial resolutions and high temporal resolutions (milliseconds – seconds).

Small-angle X-ray scattering (SAXS) measures radiation scattered between 0.066° < 2θ < ~5° which corresponds to length scales from 0.5 – 200 nm (Schmidt, 1991; Radlinski et al., 2005; Ingham, 2015). The exact length scales measured depends on experimental parameters (the distance between the sample and detector) and the incident X-ray wavelength/energy used. SAXS can be inverted for the nano- porosity and pore-size distribution within a material, and therefore provides crucial real-time in-situ measurements of the porosity evolution during dehydration.

Wide-angle X-ray scattering (WAXS) measures radiation scattered at 2θ > 5°, corresponding to real-life angstrom-scale (Ingham, 2015). WAXS is synonymous with transmission-based XRD, characterizing the crystal structure of materials at atomic length scales, which allows for mineral phase identification. WAXS typically has a lower angular resolution than in-situ powder XRD even when collected at synchrotron sources. However, WAXS holds several experimental advantages. Firstly, measurements are not limited to powdered samples at atmospheric pressures.

44 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Whole-rock samples can be used at elevated pressures and temperatures. This is geologically significant when upscaling kinetics to natural systems. In addition, at most synchrotrons, SAXS and WAXS can be collected simultaneously, which is extremely advantageous when monitoring dynamic reactions. The two techniques complement each other, allowing real-time tracking of both the mineral phase transitions and the porosity evolution within the same sample during dehydration.

2.3.3 Application to geology In recent decades popularity has risen to utilise SAXS, SANS (small-angle neutron scattering) and USANS (ultra-small-angle neutron scattering) to characterise the nano- and micro-porosity of rocks. Particular focus has been attributed to sandstones (Thompson et al., 1987; Wong et al., 1986; Schmidt, 1989; Radlinski et al., 2004a), shales (Mildner and Hall, 1986; Wong et al., 1986; Radlinski et al., 1996; Radlinski et al., 2000a, 2000b), and coal (Radlinski and Radlinska, 1999; Radlinksi et al., 2001; Boreham et al., 2003; Radlinski et al., 2004b). The understanding of porosity, permeability and fluid flow in reservoir and source rocks has obvious economic importance for the coal and petroleum industries.

A limited number of experiments using both SAXS/WAXS for geological applications have been reported in the literature. Leu et al. (2016) investigated the pore geometry, pore size distribution, average mineralogy and the presence of any mineral preferred orientations in shales and mudrock. In-situ high-temperature SAXS/WAXS was used in conjunction with TGA/DSC techniques to monitor the dehydration of tobermorite, xonotlite and hillebrandite by Shaw et al. (2000). The use of both techniques to directly monitor high-temperature dynamic processes enabled Shaw et al. (2000) to better understand the dehydration pathways of these calcium silicate minerals.

Four in-situ SAXS/WAXS experiments have been performed on gypsum. Stawski et al. (2016) studied the nucleation and growth of gypsum, bassanite and anhydrite from various supersaturated solution between 12°C – 40°C. Ossario et al. (2017) furthered this work by studying the effects of supersaturation, temperature and the addition of ionic species (Mg2+, citric acid) on the precipitation rate and mechanism of gypsum from solution. The dehydration of fine-grained, powdered gypsum was monitored using in-situ SAXS/WAXS by Cernik et al. (2004a, 2004b). The materials were heated for ~1 hr at a constant heating rate from ambient

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 45

temperature to ~300°C. However, the primary objective of the study was testing the capability of a new beamline to produce high-resolution mineralogical data (Rietveld-refinable) of known reactions (gypsum  bassanite  anhydrite) at elevated temperatures with high temporal resolution (one dataset / second). On this they succeeded, however, little information is reported regarding the results of the reaction.

46 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Chapter 3: Methodology

This chapter details the methodology of quantitative techniques used to analyse the dehydration kinetics of polycrystalline gypsum rock. The objectives of this research project were accomplished over five stages. These stages were performed locally in Brisbane at the Central Analytical Research Facility (CARF) at QUT, and externally at the Australian Synchrotron in Clayton, Melbourne. Dehydration experiments conducted at QUT were black-box experiments, where reaction progression could not be directly monitored but required post-mortem analysis. These experiments were thus labelled ‘ex-situ’ and are complementary to the principal synchrotron work. The pivotal in-situ synchrotron dehydration experiments, using SAXS/WAXS techniques, allow the real-time tracking of metamorphic mineral reactions with high temporal resolution.

The experimental method employed in this thesis will be applied to answer two overarching research questions:

[1] What effect does microstructure have on mineral dehydration?

[2] Does application of a constant pre-stress have an effect on the dehydration rate of polycrystalline gypsum?

The following provides a brief synopsis of each experimental stage.

Stage 1: Preliminary microstructural & chemical characterisation.

Gypsum discs were characterised at CARF, prior to the dehydration experiments, to gain an understanding of the chemical composition and microstructure of the raw starting materials. Initial sample characterisation was important, as artefacts and anomalies in the synchrotron dataset may be caused by the presence of chemical or morphological impurities, preferred crystallographic orientation and/or fractures in the starting materials. Gypsum discs were analysed using powder X-ray diffraction (XRD) to characterise the mineralogy of the samples, and Scanning Electron Microscopy (SEM) for microstructure.

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 47

Stage 2: In-situ time-resolved gypsum dehydration experiments using X-ray scattering

In-situ gypsum dehydration experiments were performed at the Australian Synchrotron (Clayton, VIC), over three proposal rounds: June 2016, February 2017, and July 2017. Gypsum samples were dehydrated under radially drained conditions, with a constant mechanical uniaxial pre-stress, at five temperature steps between 120°C and 170°C. Two uniaxial pre-stresses were tested at each dehydration temperature: [1] low axial pre-stress (cell fastened closed by hand); and [2] high axial pre-stress, where a torque wrench was used to apply an additional 54 Nm torque to close the cell. The quantification of these pre-stress states is discussed in Section 3.4.5. Prior to the synchrotron experiments, we estimated the dehydration time with ex-situ experiments using the Blach cell. This thesis focuses on ten dehydration experiments where time-resolved transmission-XRD (WAXS) was measured concurrently with SAXS. Analysis of the SAXS data is beyond the scope of this thesis.

Stage 3: Post-synchrotron experimental microstructural & chemical characterisation

The reacted discs from synchrotron experiments were characterised at CARF using XRD and SEM to analyse the dehydration-related changes in sample mineralogy and microstructure.

Stage 4: Ex-situ dehydration experiments

After the first two synchrotron proposal rounds, another set of ex-situ dehydration experiments were performed at CARF, mimicking the experimental parameters of in-situ experiments. This was necessary to assess the validity of the indexing methods used to identify mineralogical phases in the synchrotron dataset and post-mortem sample analysis. A time-lag exists between the conduction of experiments at the synchrotron and sample post-analysis at CARF. A possibility, therefore, exists for a back-reaction to occur within this timeframe. The aims of these experiments were: [1] to confirm samples were fully dehydrated (under synchrotron experimental conditions); and [2] assess the preservation of the dehydrated sample microstructure. This was done by immediate XRD and SEM analysis following each ex-situ dehydration experiment.

48 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Stage 5: Temperature Calibrations

A calibration was performed on the Blach cell and external heating unit, which controlled the target cell temperature.

3.1 STARTING MATERIALS

Cylindrical sub-cores of natural, polycrystalline gypsum rock (~13 mm diameter) from Volterra, Italy, were supplied by Dr Harald Milsch of the GFZ German Research Centre for Geosciences. This natural alabaster form of gypsum has been used in rock mechanics for decades, because of its relatively homogeneous microstructure, fine-grained nature (x̄ : 120 μm2), minimal impurities (< 1%), and very low porosity (0.5 - 1%) and permeability (10-16 - 10-21 m2) (Heard and Rubey, 1966, Stretton 1996; Ko et al., 1997; Llana-Fúnez et al, 2009; 2012; Olgaard et al., 1995; Fusseis et al., 2012). Volterra gypsum contains crystallographic preferred orientations locally (Hildyard et al. 2009; Fusseis et al., 2012).

X-ray scattering techniques require minimal sample preparation. However, the attenuation of incident radiation emplaces a constraint on sample thickness. Where possible, a reduced sample thickness is preferred to improve clarity of the true scattering profile of the sample, by: [1] increasing the intensity of transmitted radiation, by minimising the degree of incident radiation absorption by the sample (Pauw, 2013; Ingham, 2015); and [2] decreasing the probability of multiple scattering events which can ‘smear’ the scattering profile (thicker samples increase multi-scattering effects) (Pauw, 2013). Cores were cut into discs using a diamond bladed saw, where a good intensity signal was found with 1 mm thick samples at the temporal resolutions required for dehydration experiments.

Discs were given a sample ID of ‘G’ followed by a number (starting at 1) and stored in individual sample bags. Several measurements were recorded for each disc pre- and post-dehydration: disc mass (g) using an analytical balance; disc thickness (mm) using an electronic micrometre; and disc diameter (mm) using an electronic calliper. Samples were stored in a desiccator post-experiment.

3.2 THE BLACH CELL

The Blach cell contains an Inconel sample chamber, sealed on the upper and lower planes with high-purity beryllium (Be) windows, which confine the sample

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 49

axially. The sample chamber is cylindrical, with an internal diameter of 30 mm. The chamber height is adjustable, depending on sample thickness. Inlets on the sample chamber allow the conduction of fluid-flow experiments and/or monitoring the sample chamber pressure. Figure 3.1a shows the opened cell with the lower Be window exposed, where the sample disc is loaded. A schematic of the open cell is shown in Figure 3.1b. The cell closes by emplacing the upper Be window and silicone ring over the sample (seals the cell), followed by a brass ring, aluminium ring, and finally an Inconel annular, threaded compression nut. The compression nut applies an adjustable, constant mechanical uniaxial pre-stress to the sample. The nut can be closed by hand, or with additional force using a torque wrench. Two Inconel blocks used to heat the sample chamber, encase the sample chamber from the top and bottom (Figure 3.1a). Each block contains two inlets for the insertion of a heating element and a thermometer. This allows independent temperature control of each block.

The Blach cell was specifically designed for X-ray scattering experiments. The deliberate use of rings and annular nuts minimise the volume of material in the penetration pathway of the X-ray beam. This maximises the beam intensity exposed to the sample and detector by reducing unnecessary X-ray attenuation. X-rays during the in-situ dehydration experiments penetrate a total thickness of 7 mm: the upper and lower Be windows (3 mm thick, each) and the sample disc (1 mm) (Figure 3.1c).

Figure 3-1: a) Opened Blach cell exposing the sample chamber. b) Schematic of the Blach cell and the components removed to open the sample chamber. c) Schematic of the X-ray path through the Blach cell sample chamber.

50 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

3.3 STAGE 1: PRELIMINARY MICROSTRUCTURAL AND CHEMICAL CHARACTERISATION.

Characterisation of the gypsum starting materials was performed at CARF, QUT. Gypsum discs were analysed using XRD to characterise the mineralogy of the samples, and SEM for microstructural analysis.

3.3.1 Mineralogy - XRD The PANalytical X’Pert PRO MPD Powder X-ray Diffractometer (XRD) was used for mineral phase identification of pre-experimental discs. Sample aliquots were weighed before adding a corundum internal standard (Al2O3, Baikowski International), with a known weight percentage, and 10 ml of ethanol. A McCrone mill with zirconia beads was used to micronise samples for six minutes, producing a slurry which was dried in a 40°C oven overnight. Once dry, the powders were back- pressed into sample holders.

Diffraction patterns were collected with a Bragg-Brentano geometry at 40 kV and 40 mA using a cobalt source, rotating samples during analysis. 30-minute collection times was used per sample with a step size of 0.016° from 5°- 90° 2θ. Table 3.1 reports the optics configuration.

Table 3-1: PANalytical XRD optics configuration.

Incident optics: Diffracted beam optics:

Mask 15 mm Filter Kβ Divergence slit 0.5° Antiscatter slit 5 mm Antiscatter slit 2° Soller slit 0.04 radian Soller slit 0.04 radian Mineral phases were identified using MDI Jade (Version 4.1) and PANalytical Highscore Plus (Version 4) in conjunction with the following databases: American Mineralogist Crystal Structure Database 2010, PDF4+, ICSD FIZ Karlsruhe 2011, and Crystallographic Open Database. TOPAS (Version 5, Bruker) was used for phase quantification by Rietveld analysis. LaB6 was used to determine the instrument function for specific data collection routine. The reference patterns for gypsum, 00-033-0311 (Natl. Bur. Stand., 1980), and bassanite, 00-041-0224 (Poellmann and Kuzel, 1989) were used for phase identification.

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 51

3.3.2 Microstructure - SEM SEM was used to produce high-resolution micrographs, providing microstructural information of the sample surface including topography (roughness) and morphology (grain and pore size, microfabric). In-situ dehydration experiments were performed using transmission XRD. Traditional SEM methods involving sample carbon coating were therefore avoided to minimise sample contamination. Samples were imaged with the Tescan Mira 3 Variable Pressure Field Emission SEM under low vacuum (40 Pa) with an accelerating voltage of 10 kV, beam intensity of 12 and a working distance between 9 - 14 mm. The high surface roughness of the samples produced edge effects when imaged in pure secondary electron (SE) mode. Therefore, a mixed- mode of 70% backscattered-electron (BSE) signal and 30% SE signal was used. Gypsum discs were loaded onto the sample stage with minimal carbon tape usage.

3.4 STAGE 2: IN-SITU TIME-RESOLVED DEHYDRATION EXPERIMENTS USING X-RAY SCATTERING

Polycrystalline gypsum was dehydrated at five temperature steps between 120°C – 170°C, under radially drained conditions with an applied low or high uniaxial mechanical pre-stress. Gypsum dehydration was monitored in real-time with in-situ X-ray scattering experiments performed at the Australian Synchrotron (Clayton, VIC), on the SR13 ID01 SAXS/WAXS beamline over three proposal rounds: June 2016, February 2017, and July 2017 (proposals 10842, 11757 and 12064, respectively). This thesis focuses on ten dehydration experiments where time- resolved transmission-XRD (WAXS) was measured concurrently with SAXS. WAXS records the scattering intensity over the Q-range 1.887 – 6.202 Å-1. In this Q- range, Bragg peaks are resolved, which represent crystallographic lattice planes (1 Å - 5 Å). Tracking peak evolution provides a technique to monitor, in real-time, mineralogical phase transitions throughout dehydration. SAXS performed on rocks typically measures nanoscale scattering from pores. At short-camera length (discussed further below), the SAXS Q-range overlaps with that of the WAXS detector and thus provides a better resolved Bragg peak of bassanite. This peak was also used for tracking dehydration, as outlined in more detail in Section 3.4.6.

52 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

3.4.1 Synchrotron experimental set-up The SAXS/WAXS instrument uses a pinhole geometry and operates with a flux of 1013 photons per second from an in-vacuum undulator source (3 m length, 22 mm period, and Kmax of 1.56). Figure 3.2 depicts the beamline optics layout as a schematic, detailed in Kirby et al. (2013).

Figure 3-2: Schematic of the beamline optical layout for the SAXS/WAXS beamline at the Australian Synchrotron (after Kirby et al., 2013).

SAXS and WAXS 2D datasets were collected by two separate detectors: a 169 x 179 mm Pilatus 1M and 33 x 169 mm Pilatus 200K, respectively. Both detectors have a pixel size of 172 x 172 μm. Two SAXS sample-camera distances were used during the three experimental rounds at the Synchrotron, a short-camera distance of ~1 m and a long-camera distance of ~7 m. The sample-camera distance (and X-ray energy) affects the angular resolution and range of the collected data. At short- camera distances, the observable Q-range for SAXS equates to a pore size range of ~0.3 - 32 nm and extends to ~300 nm at long-camera distances. Replicating experiments at both camera lengths is therefore necessary to examine the micro-, meso- and macro-porosity evolution during gypsum dehydration. These measurements are important for the larger collaborative research project, outside the scope of this thesis, which combines the in-situ measures of both the dehydration rate (change in mineral phase(s)) with the porosity evolution of the rock. Calibration shots were obtained for quantitative SAXS analysis. However, this thesis works on the raw data only, therefore, the calibration procedure is not described. The beamline set-up limited the simultaneous use of the WAXS and SAXS detectors to short-

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 53

camera length SAXS only (in June 2016 and Feb 2017). Therefore, only these experiments will be discussed throughout this thesis. The SAXS/WAXS instrument set-up is shown in Figure 3.3.

Figure 3-3: The Australian Synchrotron SAXS/WAXS set-up for dehydration experiments at short- camera length.

Slight changes were made to the SAXS/WAXS instrument set-up (X-ray energy, camera length) between proposal rounds. The experimental configurations and resulting detector resolution (ΔQ and Δ2θ), and measurable range of scattering angles are described in Table 3.2. For the reader's ease, measurements are shown in both reciprocal space (Q) and the corresponding values in real-space (d-spacing and 2θ) (Eq. 13).

Table 3-2: SAXS/WAXS instrument configuration, detector resolution and angular resolution across the three Synchrotron proposal rounds.

Proposal X-ray Exposure Energy Wavelength Camera Q-range d-spacing 2θ range ΔQ Δ2θ Detector Round beam size time (keV) (Å) length (m) (Å-1) (Å) (°) (Å-1) (°) 1.6380 - 3.83 - 47.83 - WAXS 0.450 0.0075 0.0212 100 x 100 5.3205 1.18 14.56 Jun-16 5 sec 20 0.619921 μm 0.0286 - 219.58 - 16.31 - SAXS 1.0357 0.0033 0.0093 1.8337 3.42 0.25 1.1715 - 5.36 - 46.33 - WAXS 0.450 0.0061 0.0216 100 x 100 4.1260 1.52 13.02 Feb-17 5 sec 16 0.774901 μm 0.0225 - 279.11 - 16.78 - SAXS 1.0250 0.0027 0.0095 1.5087 4.16 0.25 1.2887 - 4.87 - 45.77 - WAXS 0.477 0.0057 0.0201 250 x 250 4.0770 1.54 14.32 Jul-17 5 sec 16 0.774901 μm 0.0223 - 281.61 - 16.55 - SAXS 1.03286 0.0013 0.0045 1.4885 4.22 0.25

3.4.2 Experimental materials The following equipment was used during in-situ experiments: the Blach cell; heating unit; thermocouple; pressure rig; copper tubing (1.5 cm); silicon ring; quartz

54 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

wool; stainless steel wire; torque wrench; tweezers; thermal glove; and gypsum discs.

Pressure rig A pressure rig was set-up to monitor the pressure inside the cell during dehydration. In June 2016, the rig was set up inside the user cabin and connected to the Blach cell (inside the beamline hutch) via a capillary. The rig was modified and condensed for February 2017. A single pressure gauge and valve were connected directly to the cell inside the beamline hutch. A transducer was used in July 2017, which electronically recorded the pressure with the SAXS/WAXS data.

3.4.3 Loading conditions It was crucial, in regard to data analysis and kinetic modelling, that samples were fully dehydrated during each experiment. The heating durations for the experiments were initially chosen based on the preliminary ex-situ experiments performed at CARF. These durations were then modified on-the-fly as additional in- situ data was collected. Experimental parameters for the ten experiments are shown in Table 3.3. A low pre-stress state was applied to the sample by closing the annular compression nut (screw threading) of the Blach cell by hand (~21 Nm (human grip strength), Xu et al., 2012). The compression nut was further tightened with a torque wrench set to 54 Nm for a high pre-stress state.

Table 3-3: Experimental parameters for in-situ Synchrotron dehydration experiments.

Dehydration Axial Heating duration Sample ID Proposal Round Temperature (°C) pre-stress (mins) G65 Jul-17 119 Low 900 G80 Jul-17 122 High 706 G28 Feb-17 128 Low 126 G18 Feb-17 128 High 90 G29 Jun-16 141 Low 72 G31 Feb-17 141 High 49 G77 Jul-17 151 Low 55 G16 Feb-17 151 High 69 G17 Jun-16 173 Low 72 G23 Feb-17 173 High 30

3.4.4 Sampling Method X-ray scattering was measured during repeated scans of a chosen number of points along each horizontal disc radius. A total of 3 - 5 points were measured on each disc during dehydration. The increase in beam-size between proposal rounds

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 55

(Table 3.2) was due to a change in the experimental configuration of the beamline. The X-ray illumination volume for each point sampled of the 1 mm thick gypsum discs was therefore 0.01 mm3 and 0.0625 mm3 respectively.

Radial scans started in the disc centre and moved towards the margin in equidistant steps (Figure 3.4). Each point was exposed to incident X-rays for 5 seconds. For each experiment, one initial radial scan was taken at room temperature, producing a reference measurement, before heating the cell. During heating, radial scans were taken continuously until the desired heating duration had elapsed.

Figure 3-4: Schematic of the points measured during the dehydration experiment.

3.4.5 Quantification of state of stress There are two sources of stress applied to the sample: [1] the externally applied stress on the disc through mechanical uniaxial confinement by the two beryllium windows when applying torque to close the cell; and [2] the thermal-elastic stress of confined gypsum at elevated temperature. The thermal-elastic and external stress combined estimate the total applied stress on the sample during dehydration. The thermal-elastic stress evolves dynamically as heat increases and the sample transforms.

Thermal-elastic Stress The following computation was performed to estimate the thermal-elastic stress on the sample (Eq. 14; Jaeger, Cook & Zimmerman, 2009, 199). Isotropic material properties were assumed. To average the 3D expansion anisotropy of the gypsum crystal lattice, the linear expansion coefficient (aG) used for gypsum was derived from the volumetric expansion coefficient (av) reported in Ballirano and Melis (2009) (Eq. 15). A 1D gypsum disc was assumed to be completely encased with rigid beryllium.

56 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

휎 = (푎퐺 − 푎퐵푒)(푇1 − 푇0)퐸퐺 (14)

푎 푎 = 푉 (15) 퐺 3

where:

휎 = Stress (Pa); 푇1 = Target temperature (°C); 푇0 = Initial temperature (°C);

-5 -1 푎퐺 = Linear expansion coefficient of gypsum = 2.7 e °C (Ballirano & Melis, -6 -1 2009); 푎퐵푒 = Linear expansion coefficient of beryllium = 11.6 e °C (Davis, 1997, 94);

EG = Young’s modulus of gypsum (Pa) = 41 GPa (Bass, 1995).

External stress Torque was applied to the sample when closing the cell prior to dehydration. To compute the external stress on the sample the applied torque (N.m) must first be calibrated to a measurement of normal force F (N). The applied stress to the sample can then be calculated using the equation:

퐹표푟푐푒 (푁) 푆푡푟푒푠푠 (푃푎) = ⁄퐴푟푒푎 표푓 푑푖푠푐 (푚2) (16)

Torque calibration - the Blach cell A calibration was performed on the Blach cell to relate the torque applied to the compression nut via a torque wrench to an axial normal force (N) exerted onto the sample disc. The Blach cell was filled with distilled water at room temperature. Then, the torque applied at the nut was increased gradually while the fluid pressure was monitored by a Rosemount Pressure transducer (error: < 0.01%, Figure 4.4). The data were fit with a logistic function:

푎 퐹 = 퐹0 + (17) 푇 푏 1+( ) 푇퐹

Where:

F = Force (N); a & b = Function fit constants;

F0 = Function fit force offset (the force present when no torque is applied) (N);

T = Torque applied (ft-pd force); TF = Function fit torque where the slope reaches zero.

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 57

It should be noted that the torque measurements reported on the calibration graph are in imperial units (foot-pounds force) as an American torque wrench was used during the experiment.

3.4.6 Data Analysis The raw SAXS and WAXS data were acquired from the synchrotron as 2D scattering patterns (32-bit tiff files) (Figure 3.5). These patterns were then integrated into radially averaged 1D profiles of scattering intensity (I(Q)) versus scattering vector (Q) using the software package scatterBrain (V. 2.82) (Figure 3.6, 3.7). Gypsum and bassanite are considered to be isotropic (symmetrical) scatterers after visual inspection of 2D scattering patterns. Isotropy is an underlying assumption in the software integration method used to convert the 2D patterns to 1D scattering profiles (dat files). MATLAB (R2018b) was used to analyse the 1D scattering data.

Figure 3-5: False-colour visualisation of the raw 2D scattering patterns collected during gypsum dehydration by the SAXS (left) and WAXS (right) detectors. The key elements shown are the beamstop, Scattering Vector (Q) (green arrow) and Scattered X-ray intensity (scattering patterns). The SAXS Pilatus 1M detector contains 10 modules set up in a 2 x 5 array (7 x 17-pixel gap between modules). The WAXS Pilatus 200K detector contains 2 modules in a 2 x 1 array (7-pixel gap).

58 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

The time evolution of 1D scattering profiles for the gypsum sample G16 (dehydrated at 151°C, high axial pre-stress), from SAXS and WAXS datasets, are shown below as 3D plots of Time (secs) versus scattering vector (Q (Å-1)) versus scattering intensity (counts/sec) (Figure 3.6, 3.7).

Figure 3-6: Stacked 1D WAXS scattering profiles are depicting the time evolution of gypsum disc G16, dehydrated at 151°C with high axial pre-stress for 69 minutes. WAXS measures crystal lattice diffractions (from 2θ = 13.02° - 46.33°).

Figure 3-7: Stacked 1D SAXS scattering profiles are depicting the time evolution of gypsum disc G16, dehydrated at 151°C with high axial pre-stress for 69 minutes. High-Q SAXS (right) measures crystal lattice diffractions (from 2θ = 0.25° - 16.78°), and medium/low-Q SAXS (left) measures scattering from pores.

Method for tracking phase changes in SAXS/WAXS data To monitor dehydration progress, we decided to track the intensity of three scattering peaks of the product phase bassanite. These three peaks correspond to the reflections (110) in the SAXS data, and (020) and (022) in the WAXS data. They

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were chosen because they are isolated in their position in Q-space (so easily tracked automatically), exhibit high scattering intensities (excellent signal-to-noise ratio), and they are crystallographically meaningful. These reflections relate to the pseudo- hexagonal tubes in the bassanite crystal structure that host the remaining water molecules (Figure 2.1). Gypsum crystallographic peaks were not tracked due to the anisotropic thermal expansion effects on the gypsum lattice (Ballirano and Melis, 2009) and, more importantly, because of serious fluctuations in peak intensity, likely due to inhomogeneous deformation and the fact that grains may move in and out of the spatially fixed observation volume during thermal expansion.

The Q-position of bassanite peaks were determined from quantitative XRD on fully dehydrated samples, using 01-074-2787 (Ballirano and Melis, 2001) and database PDF4+. These experimentally measured Q-positions, at both synchrotron wavelengths (0.774901 Å (16 keV) and 0.619921 Å (20 keV)), were then compared to theoretical Q positions calculated for crystallographic reference patterns of bassanite (Ballirano and Melis, 2001; Table 3.4; Appendix C). All three peaks had coincident planes. Therefore, the highest multiplicity plane (making the highest scattering contribution) was chosen. The minor changes in Q-position of peaks between in-situ measured and calculated values are attributed to a discretisation effect. The detector can only observe fixed pixels (= discrete Q-values) with a fixed pixel size of 172 x 172 μm, that equates to a fixed ΔQ (Table 3.2). Therefore, absolute peak position can only be resolved with ± one pixel/one ΔQ.

Table 3-4: Indexing of the measured scattering vector (Q) position of the three unique crystallographic peaks identified in SAXS/WAXS datasets, compared to the theoretical Q position calculated for bassanite reference pattern (Ballirano and Melis, 2001).

Calculated Q of Peak Dataset Q-position at 16 Q-position at 20 keV Bassanite peak Bassanite reference Number measured keV (Å-1) (Å-1) index pattern ( 16 keV (Å-1)) 1 SAXS 1.0463 1.0445 1.0463 110 2 WAXS 1.8029 1.8035 1.8089 020 3 WAXS 2.0779 2.0764 2.0672 220 To track the chosen bassanite peaks, a Matlab script was developed whereby:

1. The user imputes the computed Q-position of the three bassanite peaks.

2. The code searches the final SAXS/WAXS profile (under the assumption the reaction is fully completed) for a peak at each of the three positions to

60 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

within ± 5% of the computed position in WAXS and ± 10% of the computed position in SAXS. E.g. in SAXS, the computed peak is located at Q: 1.0463. Therefore, Matlab performs a search at ± 10% for the largest peak in the Q-interval: [0.9417; 1.1509].

3. Once Matlab has found the peak’s Q-position in the aforementioned intervals, it stores these positions for each experiment.

4. Finally, the code goes back to the first SAXS/WAXS profile and reads the intensity values at the exact peak positions determined in step [3] as functions of time (to give the absolute I-t curves). Therefore, the code assumes that the Ba peaks do not change position with time.

Another MATLAB script then converts absolute intensities to normalised ones as follows:

퐼 (푡)−퐼 (푡=0) 훼 (푡) = (18) max (퐼 (푡)−퐼 (푡=0))

Where:

α = conversion fraction (bassanite proportion); t = time (seconds);

I = scattering intensity.

The normalised intensity curves are assumed to represent the volume fraction of the transformed material, i.e., the relative proportion of bassanite in the system. When ‘Bassanite proportion’ is plotted over time (secs) (α versus t), a sigmoidal reaction curve is produced with a distinct plateau at the end of the experiment.

We interpret the plateaus of the reaction curves to indicate that dehydration is complete. No new product peak reflections are formed nor do the tracked peaks change in position or size. These observations match the results of the following independent tests: [1] the absence of gypsum peaks in the SAXS/WAXS data at the time of bassanite reaction curve plateau, [2] post-experimental XRD and microstructural observations, and [3] ex-situ experiments (Section 3.6). A (semi-) automated Rietveld analysis was not attempted on our scattering data for two main reasons. The limited angular resolution of the detectors did not produce enough data for non-linear peak fitting. In addition, our microstructural observations (Section 4.4.2) show that parent/product crystal sizes can vary greatly and also exhibit locally

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 61

preferred orientations. Both crystal-size and anisotropy effects impede automated Rietveld analysis.

Gypsum dehydration kinetics were modelled from the ‘Bassanite proportion’ reaction curves according to the Avrami (JMAEK) model (Eq. 6). A non-linear least- squares method was performed using least-absolute residuals in the MATLAB Curve Fitting Toolbox (R2018b). The Avrami model is used purely as an empirical mathematical model for reaction progression of sigmoidal dehydration curves. We do not imply the genetic association of a ‘nucleation and growth’ kinetic mechanism. Due to the non-isothermal nature of the synchrotron experimental set-up, the time before the sample reached 97°C was ignored. In other words, for Avrami fitting, the start time = 0 seconds was set to the time when the cell reached 97°C. This temperature was chosen as ~100°C represents the transition into bassanite stability field (McConnell et al., 1987; Prasad et al., 2001; Christensen et al., 2008; Ballirano and Melis, 2009; Harrison, 2012). An Arrhenius fit (Eq. 3) was then modelled to calculate the activation energies for both low- and high-pre-stressed dehydration rates by non-linear least-squares fitting.

3.5 STAGE 3: POST-SYNCHROTRON MICROSTRUCTURAL AND CHEMICAL CHARACTERISATION.

Post-characterisation of the reacted discs was conducted at QUT CARF to gain an understanding of the mineralogy and microstructure related to dehydration. The samples were analysed using XRD and SEM.

3.5.1 Microstructure - SEM Similar to pre-characterisation of the gypsum discs, the dehydrated discs were not polished or carbon-coated prior to SEM analysis. This enabled microstructural observations and analysis of the unaltered sample surface and minimised contamination before XRD analysis. The dehydrated discs were imaged on the Tescan Mira3 FEG-SEM under low-vacuum conditions with the same parameters and loading conditions described in Section 3.3.2. A stitched panorama was produced by taking a series of micrographs (~500 m image width) across the diameter of the disc with a 10% overlap between images.

One disc was broken in half to form a semi-cylinder, exposing a 13 x 1 mm fresh surface of the sample cross-section. One half was then mounted onto a 70°

62 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

sloped sample stub (the fresh surface facing up) to image the internal microstructure of the sample. Once the sloped stub was loaded into the SEM, the sample stage was then tilted a further 20° so that the sample surface was perpendicular to the electron beam.

Grain size ImageJ software (Rasband, 1997 – 2018) was used to measure grain size from SEM micrographs. Measurements were taken from micrographs that contained > 100 grains. A minimum of 30 grains was measured per mineral habit per sample. A grid was superimposed over the image (Figure 3.8a), where a maximum of one grain was chosen per gridded cell. Grains with poor exposure or highly oblique angles to the sample surface were not measured.

Each dehydrated mineral habit required a different method of measurement due to the slight oblique orientation of grains in relation to the sample surface. The long axis of grains can be measured only rarely due to the common overlay and intergrowth of surrounding grains. The grain width was measured for acicular habits (Figure 3.7a). For pseudomorphs, cross-sections were measured along the long axis of tabular pseudomorphs, which are aligned parallel to the c-axis (i.e. parallel to ‘sheets’, Figure 3.7e). Cross-section measurements were of the long and short axes of the exposed grain (Figure 3.7b). Grain width or cross-section was measured for prismatic habits (Figure 3.7c, d), depending on the grain orientation and exposure in the sample. Collective measurements were taken for samples with multiple pseudomorphs. This was due to the limited spatial resolution on micrographs suitable for grain size analysis, to differentiate between types of pseudomorphs.

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Figure 3-8: Examples of the method used to measure the approximate grain size for each post-dehydrated mineral habit from SEM micrographs using ImageJ. Either the width (a, d) or the cross-section (b, c) was measured. Grains orientated highly oblique to the sample surface, or perpendicular to the c-axis (platy habits) were not measured.

64 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

3.5.2 Mineralogy - XRD Following SEM analysis, the samples were prepared for quantitative XRD and analysed using the PANalytical X’Pert PRO MPD Powder X-ray Diffractometer under the same conditions described in Section 3.3.1.

3.6 STAGE 4: EX-SITU DEHYDRATION EXPERIMENTS

Upon completion of the in-situ dehydration experiments at the Australian Synchrotron, a set of ex-situ dehydration experiments were performed at QUT CARF. Two experiments were conducted simulating the 141°C, hand-tight, short- and long-camera length experiments with heating durations of 43 minutes and 133 minutes, respectively. The experiments were scheduled so that immediately after quenching the cell, the samples were vacuum dried and analysed under SEM. Samples were then prepared overnight for XRD analysis the following day.

The aim of these ex-situ experiments was twofold:

[1] Confirm that gypsum was fully dehydrated upon the termination of the experiment (quenching of the cell), as interpreted from the SAXS/WAXS data. There is an inherent time-lag between experiment termination at the synchrotron and quantitative mineral identification through powder-XRD at QUT CARF. Bassanite is metastable at atmospheric conditions. Therefore a possibility, of a back-reaction to gypsum exists through the rehydration of bassanite from residual trapped pore-water or exposure to atmospheric moisture. The latter, however, was minimised by storing samples in a desiccator. The probability of rehydration is vastly reduced during ex- situ experiments as dehydrated samples are immediately dried in-vacuo, and XRD analysis is performed within 24 hours of experiment termination. Confirming complete dehydration within the experimental timeframe is also an important secondary and independent measure to validate the peak tracking method used to monitor reaction progression in the WAXS data.

[2] To investigate the preservation of the dehydrated sample microstructure. As stated above, a delay exists from the reaction termination of in-situ experiments and direct microstructural observation of the samples with SEM. A comparison between sample micrographs of in-situ and ex-situ experiments will highlight the extent (if any) of dynamic structural modifications post-quenching.

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3.6.1 Pre-dehydration characterisation - SEM Prior to dehydration, the gypsum discs were imaged on the Tescan Mira3 FEG- SEM under low-vacuum conditions with the same parameters and loading conditions described in Section 3.3.2. Before loading into the SEM, a corner of the disc was notched with a razor. A stitched panorama was produced by taking a series of micrographs (~500 μm image width, with 10% overlap) across the diameter of the disc perpendicular to the razor notch. This created a detailed panorama of the sample surface microstructure pre-dehydration. The razor notch orientates the panorama to a coordinate system so that the same area can be imaged post-dehydration. This gives direct insight to metamorphic microstructural changes through comparison of the exact same grains pre- and post-dehydration.

3.6.2 Post-dehydration characterisation Immediately after the sample was removed from the quenched Blach cell and weighed, the disc was vacuumed dried to remove any residual moisture prior to SEM mounting. Discs were dried using the Cressington Carbon Coater (208) for 30 minutes at 1.8 x 10-5 mbar. The discs were placed in an alfoil sample-boat to avoid carbon contamination. Vacuum-dried samples were re-weighed.

The dehydrated discs were imaged on the Tescan Mira3 FEG-SEM under low- vacuum conditions with the same parameters and loading conditions described in Section 3.3.2. Panorama micrographs were taken in the same orientation as the pre- dehydration panorama. Following SEM analysis, the samples were prepared for quantitative XRD and analysed using the PANalytical X’Pert PRO MPD Powder X- ray Diffractometer under the same conditions as described in Section 3.3.1.

The results from these ex-situ experiments will be compared to the in-situ synchrotron experiments.

3.7 STAGE 5: TEMPERATURE CALIBRATIONS OF THE BLACH CELL

Several ex-situ temperature calibrations were performed on the Blach cell following an anomalous temperature readout during an in-situ dehydration experiment. This readout revealed a challenge with the mounting of the external temperature sensor at the synchrotron. To ensure that the target temperature within the cell is well known, we measured the temperature evolution of the cell interior for

66 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

six temperature settings of the external heating unit: 129C, 132C, 139C, 140C, 145C and 157C.

The calibrations were conducted by connecting the cell to the external heating unit as in the synchrotron and connecting an electronic temperature logger, which recorded both the internal (cell) and external (surrounding) temperature every second. The apparatus was set-up in an insulated box, to control the ambient temperature. The cell was quenched and dried between each calibration, as done at the synchrotron. Each calibration was run for ~40 minutes.

A regression analysis was performed to determine the empirical relationship between the temperature set at the heating unit and final equilibrium temperature reached within the cell. This calibration was used to compute the target dehydration temperatures of our experiments.

3.8 ETHICS AND LIMITATIONS

Ethical clearance is not required as this project does not involve the research of humans, animals or biosafety.

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Chapter 4: Results

This chapter details the results from:

 Pre- and post-dehydration microstructural and chemical characterisation of the samples (Stage 1 & 3);

 In-situ synchrotron gypsum dehydration experiments (Stage 2);

 The quantification of the mechanical uniaxial pre-stress applied to the sample during dehydration;

 Ex-situ gypsum dehydration experiments (Stage 4);

 Temperature calibrations of the Blach cell (Stage 5).

4.1 STARTING MATERIAL VOLTERRA ALABASTER: MICROSTRUCTURE AND COMPOSITION

Results from quantitative powder-XRD and SEM analysis of Volterra alabaster are presented below.

4.1.1 Mineralogy - XRD Quantitative XRD of Volterra starting material confirm gypsum as the sole dominant crystalline phase, with < 0.8% quartz impurities and minor presence of an amorphous phase (5.8% - 9.1%).

4.1.2 Microstructure - SEM Samples are composed of fine- to very fine-grained euhedral, tabular gypsum which exhibits weak- to moderate localised preferred orientations (Figure 4.1a). Short grain diameters range from 5 – 529 μm, with an average of 68 μm. The sheet- like structure of tabular gypsum is exposed in grains oriented perpendicular to the c- axis (Figure 4.1b). The surface texture of the long axes of tabular gypsum crystals can be smooth, pitted, or partially expose crystallographic planes as either high relief parallel sets of ridges, diamond patterns or steps (Figure 4.1b, c).

68 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Figure 4-1: SEM micrographs of Volterra gypsum microstructure highlighting a) weak-moderate localised preferred orientation of gypsum, b) the sheet-like structure of tabular grains, c) the texture of partially exposed crystallographic planes.

Minor quantities of a stubby white prismatic mineral were observed in all gypsum samples. Semi-quantitative EDS analysis of this mineral indicated strontium sulfate, most likely celestine. The quantity of celestine impurity in Volterra gypsum was insignificant and not detected during quantitative XRD analysis.

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4.2 CELL LOADING CONDITIONS: CALIBRATION OF TEMPERATURE AND AXIAL PRE-STRESS

4.2.1 Temperature calibration The measured Blach cell temperature curves (Figure 4.2) reveal a linear relationship between the set temperature at the heater unit and the cell equilibrium temperature (Figure 4.3). The calibrated cell dehydration temperatures are tabulated in Table 4.1.

Figure 4-2: Curves of temperature over time measured in the cell interior for six different external heater unit settings.

Figure 4-3: Regression analysis of the equilibrium temperature within the cell as a function of temperature at the external heater unit.

70 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Table 4-1: Calibrated Blach cell temperatures and the corresponding heater unit temperature setting for in-situ synchrotron dehydration experiments.

Calibrated Sample ID Heater unit setting (°C) Temperature (°C) G65 127 119 G80 132 123 G28 140 128 G18 140 128 G29 157 141 G31 157 141 G77 170 151 G16 170 151 G17 200 173 G23 200 173 4.2.2 Quantification of low versus high axial pre-stress The total applied stress on the gypsum discs during in-situ dehydration was estimated by computing the thermal stress of confined gypsum at elevated temperatures, and the external mechanical stress applied when closing the Blach cell.

Thermal-elastic stress As stated previously, the experiments are non-isothermal, where bassanite conversion begins in the transient temperature regime. The cell windows remain stationary throughout the experiment. Therefore, bassanite growth relaxes internal stresses. Thus, the upper bound of the thermal-elastic stress on the sample is estimated between 58 - 93 MPa, depending on dehydration temperature (Table 4.2).

The calculated thermal-elastic stress provides a slight overestimation to the actual stress state of the sample. This is because the gypsum discs were radially unconfined and the Be windows are not rigid. This means that along the margins, the thermal-elastic stress will be reduced and tensile (Qiao and Lu, 2015). Data analysis was performed on the central point sampled on each disc for: [1] consistency during experimental comparisons; and [2] to minimise the effects of the radial stress gradient.

Torque calibration - the Blach cell

The function fit parameters for the pressure calibration were: F0 = -27.01 N; a

= 30, 223; b = -1.811; T0 = 119°C. The sigmoidal fit of the calibration data suggests the presence of elastic compression (from the silicone seals) (Figure 4.4). The applied mechanical stress was calculated at 309.51 N for low-pre-stress experiments, and 3, 652.66 N for high pre-stress. This equates to an external stress of ~2.5 MPa

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 71

and ~28 MPa respectively (Table 4.2). Low pre-stress is therefore estimated at ~10% of high pre-stress (human grip ~21 Nm; Xu et al., 2012). Note: the torque wrench used was in imperial units.

Force (N) Force

Torque (ft.pd force)

Figure 4-4: The data from calibration measurements on the Blach cell filled with distilled water, applying incrementally increased torque, via a torque wrench, whilst using a Rosemount Pressure transducer to measure stress. The stress was converted to a force measurement and plotted against the 푎 applied torque. Data were fit with a logistic function: 퐹 = 퐹0 + .Where: F is Force (Newtons); 푇 푏 1+( ) 푇0 F0 = Function fit force offset (the force present when no torque is applied) (Newtons); a & b = Function fit constants; T = Torque applied (ft-pd force); T0 = Function fit torque where the slope reaches zero.

Total applied stress The total estimated applied stress on each of the gypsum discs during dehydration was calculated by combining the thermal-elastic and externally applied stress (Table 4.2).

72 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Table 4-2: Total estimated applied stress on the gypsum discs during synchrotron dehydration experiments, calculated by combining the calculated thermal-elastic stress at each dehydration temperature, and the applied external stress from confining the sample axially in the Blach cell.

Dehydration Upper-bound Thermal- Applied stress Applied stress for Total applied stress Sample Axial Disc area Temperature elastic stress estimate closing the cell applied torque of on the gypsum disc ID Pre-stress (m2) (°C) (MPa) (gypsum) 'hand-tight' (MPa) 40 ftpd (MPa) (MPa) G65 Low 119 1.19 x 10-4 58.53 2.60 0.00 61.13 G80 High 123 1.02 x 10-4 60.93 3.03 35.80 99.77 G28 Low 128 1.29 x 10-4 64.31 2.40 0.00 66.71 G18 High 128 1.26 x 10-4 64.31 2.45 28.89 95.65 G29 Low 141 1.29 x 10-4 72.94 2.40 0.00 75.33 G31 High 141 1.29 x 10-4 72.94 2.40 28.36 103.70 G77 Low 151 1.19 x 10-4 79.17 2.61 0.00 81.78 G16 High 151 1.26 x 10-4 79.17 2.45 28.94 110.56 G17 Low 173 1.29 x 10-4 93.65 2.40 0.00 96.04 G23 High 173 1.27 x 10-4 93.65 2.44 28.76 124.84

4.3 IN-SITU TIME-RESOLVED DEHYDRATION EXPERIMENTS USING X-RAY SCATTERING

In this section, the results from ten in-situ gypsum dehydration experiments performed at the Australian Synchrotron (SAXS/WAXS beamline), will be discussed. Polycrystalline gypsum was dehydrated in the Blach cell at five temperatures between 120°C - 173°C, under radially drained conditions with an applied low or high constant uniaxial pre-stress. 2D filled contour plots (Appendix A), and WAXS 1D scattering profiles (Appendix B) indicate complete dehydration in samples dehydrated ≥ 128°C. Partial dehydration was observed at ~120°C, despite a significantly longer heating duration (≥ 550 minutes longer heating than all other experiments).

For kinetic analysis, the time evolution of bassanite peak reflections (110), (020) and (220) were modelled from bassanite proportion versus time (secs) graphs produced for the eight fully reacted samples from the synchrotron datasets (T: 128°C - 173°C; Figure 4.6 – 4.9). Further discussion of reaction product phase identification is found in Section 4.4.1. The sigmoidal dehydration curves produced track the volume fraction of bassanite in each sample and can be broken down into three sections (Figure 4.5): [1] The first part of the ‘S’ represents the induction period, before dehydration commences, and the relative intensity is zero (i.e. no product phase is present in the system). [2] The steep slope represents the active period of dehydration where nucleation and growth of bassanite increase its relative proportion in the system.

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 73

[3] The final, sub-planar plateau portion of the curve has an intensity of ~1 and indicates complete dehydration to bassanite.

Figure 4-5: A labelled sigmoidal dehydration curve produced as a Relative Intensity versus Time plot. The three unique bassanite peaks (100, 020 and 220 reflections) are tracked over the duration of the experiment. The sigmoidal shape of the curve can be separated into three sections: [1] the induction period; [2] the transient slope region (reflecting active dehydration); [3] the plateau region (indicating complete dehydration).

4.3.1 Kinetic Analysis Avrami model The growth of the (110), (020), and (220) bassanite peaks at the centre of each synchrotron dehydrated gypsum disc, was modelled according to the Avrami equation (JMAEK model). These plots graphically represent an overview of the dehydration reaction for each experiment. The modelled rate coefficients and exponent values are summarised in Table 4.3, and the Avrami fits for samples dehydrated between 128°C – 173°C are presented in Figures 4.6 to 4.9, respectively. The low- and high-pre-stressed samples are plotted together for each dehydration temperature. It should be noted that when modelling the Avrami equation, time = 0 seconds when the cell has reached 97°C. The two discs dehydrated at 120°C, G65 and G80, were not modelled because neither disc had fully dehydrated. A sigmoidal dehydration curve is needed to fit an Avrami model. The incomplete growth of the (110) bassanite peak in G65 is plotted in Figure 4.11.

74 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Table 4-3: Avrami fit (JMAEK model) results for the eight fully dehydration samples.

Temperature Axial Rate coefficient Avrami Sample ID R2 RMSE (°C) pre-stress (k (s-1)) exponent (n) G28 128 Low 3.06 x 10-4 6.32 1.000 0.0053 G18 128 High 6.11 x 10-4 7.19 0.966 0.0730 G29 141 Low 5.38 x 10-4 5.62 1.000 0.0026 G31 141 High 1.43 x 10-3 11.22 0.960 0.0820 G77 150 Low 1.89 x 10-3 8.04 0.919 0.0888 G16 150 High 1.33 x 10-3 8.32 1.000 0.0035 G17 173 Low 1.93 x 10-3 9.75 1.000 0.0027 G23 173 High 2.81 x 10-3 20.51 1.000 0.0098 The JMAEK model fits all eight experiments with a high goodness-of-fit (> 0.91 R2). The main discrepancies between the model and measured data is a tendency for the model to: [1] over-predict the bassanite proportion in the plateau region of the dehydration curve; and [2] under-predict the bassanite proportion in the distinct ‘stepped’ portion of the reaction curve for the low pre-stress intermediate dehydration temperatures (G29, Figure 4.7; and G77, Figure 4.8).The rate coefficients reported in Table 4.3 and the dehydration curves in Figures 4.6 to 4.9 show that for each temperature, highly pre-stressed samples dehydrate faster than samples under a low axial pre-stress. The magnitude of the reaction rate difference lessens with increasing temperature.

Dehydration temperature: 128°C The two samples dehydrated at 128°C, G28 (low axial pre-stress; purple) and G18 (high axial pre-stress; green), are presented below (Figure 4.6). Complete dehydration was observed in both samples, where bassanite peaks have plateaued by ~4,000 seconds in the low pre-stress experiment and ~2,300 seconds in the high pre- stress experiment. These times correlate with the disappearance of gypsum peaks seen in WAXS 2D contour plots (Appendix A). Minor aberrations were observed in G28 peak intensities during dehydration. High pre-stress dehydration has both a shorter induction time and steeper dehydration slope.

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 75

Figure 4-6: A comparison of the reaction rates and Avrami fit of low (purple, G28) and high (green, G18) axially pre-stressed samples, both dehydrated at 128°C. Reaction rate data tracks the growth of the bassanite peaks (110), (020), and (220) from the centre point sampled on each disc.

Dehydration temperature: 141°C The two samples dehydrated at 141°C, G29 (low axial pre-stress; purple) and G31 (high axial pre-stress; green), are presented below (Figure 4.7). Complete dehydration was observed in both samples, where bassanite peaks have plateaued by ~2,500 seconds in the low pre-stress experiment and ~1,000 seconds in the high pre- stress experiment. These times correlate with the disappearance of gypsum peaks seen in WAXS 2D contour plots (Appendix A). A distinct ‘step’ was observed for all crystallographic peaks in the transient slope region of the low pre-stress (G29) dehydration curve. High pre-stress dehydration has both a shorter induction time and steeper dehydration slope.

Figure 4-7: A comparison of the reaction rates and Avrami fit of low (purple, G29) and high (green, G31) axially pre-stressed samples, both dehydrated at 141°C. Reaction rate data tracks the growth of the bassanite peaks (110), (020), and (220) from the centre point sampled on each disc.

76 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Dehydration temperature: 151°C The two samples dehydrated at 151°C, G77 (low axial pre-stress; purple) and G16 (high axial pre-stress; green), are presented below (Figure 4.8). Complete dehydration was observed in both samples, where bassanite peaks have plateaued by ~1,000 seconds in the low pre-stress experiment and ~900 seconds in the high pre- stress experiment. These times correlate with the disappearance of gypsum peaks seen in WAXS 2D contour plots (Appendix A). Similar to G29 (141°C), a ‘step’ was observed for all crystallographic peaks in the transient slope region of the low pre- stress (G77) dehydration curve. This ‘step’ was slightly muted in comparison to G29. A shorted induction time was observed for high pre-stress dehydration, although the dehydration slope for both reaction curves were similar.

Figure 4-8: A comparison of the reaction rates and Avrami fit of low (purple, G77) and high (green, G16) axially pre-stressed samples, both dehydrated at 151°C. Reaction rate data tracks the growth of the bassanite peaks (110), (020), and (220) from the centre point sampled on each disc.

Dehydration temperature: 173°C The two samples dehydrated at 173°C, G17 (low axial pre-stress; purple) and G23 (high axial pre-stress; green), are presented below (Figure 4.9). Complete dehydration was observed in both samples, where bassanite peaks have plateaued by ~700 seconds in the low pre-stress experiment and ~500 seconds in the high pre- stress experiment. These times correlate with the disappearance of gypsum peaks seen in WAXS 2D contour plots (Appendix A). A shorted induction time was observed for high pre-stress dehydration, although the dehydration slope for both reaction curves were similar.

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering 77

Figure 4-9: A comparison of the reaction rates and Avrami fit of low (purple, G17) and high (green, G23) axially pre-stressed samples, both dehydrated at 173°C. Reaction rate data tracks the growth of the bassanite peaks (110), (020), and (220) from the centre point sampled on each disc.

Effects of axial pre-stress: Dehydration activation energy The activation energies were calculated for both the low and high axial pre- stress dehydration rates by fitting the Arrhenius equation (Eq. 3) as follows.

It is straightforward to show that for the Avrami model (Eq. 6):

1 1 푎 (푡 = ) = 1 − ≈ 0.63 (19) 푘 푒

1 Therefore, we plot our empirical results for as a function of dehydration 푘 temperature (Figure 4.10) for low and high pre-stress, respectively, and then obtain the activation energies for both cases by non-linear least-squares fitting.

Figure 4.10 highlights that for dehydration below 160°C, samples under high axial pre-stress dehydrate faster than low-pre-stress samples. This magnitude of divergence increases with decreasing temperature. The difference in reaction rates between low- and high-pre-stress samples is also reflected in the calculated activation energies: 73.8 kJ/mol (R2 = 0.97) and 50.4 kJ/mol (R2 = 0.98), respectively.

78 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Figure 4-10: Compilation of the kinetic results for the samples dehydrated under low and high applied axial pre-stress (centre point). The vertical axis displays the inverse of the reaction constant obtained through the Avrami fit (Table 4.3). It corresponds to the time when 63% of bassanite has been produced in the sample. As seen in Figure 4.6 - 4.9, the Avrami model does not fit the low conversion percentages of ‘stepped’ reaction curves well, however, describes conversions > 50% excellently. The results demonstrate that high-pre-stress samples dehydration faster than low-pre-stressed samples at T < 160°C.

4.4 POST-EXPERIMENTAL CHARACTERISATION

4.4.1 The reaction product (quantitative XRD)

Post-experimental XRD analysis identified bassanite (CaSO4.0.5H2O) as the sole mineral product from in-situ gypsum dehydration. All samples were dehydrated under dry conditions, where β-bassanite is the favoured hemihydrate form and is interpreted as the hemihydrate phase for these experiments (Freyer and Voight, 2003). β-bassanite will simply be referred to as bassanite. Neither anhydrite nor γ- anhydrite were detected in any of the samples during XRD analysis. However, it is difficult to differentiate bassanite and γ-anhydrite with XRD due to marginal differences in their water stoichiometry, coincident peaks and similar crystallography. Therefore, in addition to XRD, the following steps were undertaken to determine the presence/absence of γ-anhydrite in dehydrated samples.

Step 1 – Analyse synchrotron datasets for peak shifts in product phase Mineral transformations can be observed as crystallographic peak shifts (in Q- or 2θ-space), in time-series synchrotron diffraction patterns. During gypsum dehydration, two distinct shifts occur at the gypsum  bassanite and γ-anhydrite 

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anhydrite transitions (Figure 4.13). However, the bassanite  γ-anhydrite transition is evidenced only by a slight peak shift, echoing the minimal structural change between phases (Figure 4.11). Observations of 2D contour plots for 120°C – 173°C dehydration experiments show no evidence of any shifts in bassanite peaks, indicating an absence of γ-anhydrite formation (Appendix A).

Figure 4-11: Adapted surface plot of the three-step gypsum dehydration process from Jacques et al. (2009), using in-situ Synchrotron angle dispersive XRD. The plot displays two distinct crystallographic peak changes during the gypsum  hemihydrate and γ-anhydrite  anhydrite transitions. The transformation of hemihydrate  γ-anhydrite is identified only by a slight shift in the peak 2θ position.

Step 2 – Comparison of product crystallographic peak ratios: 110 versus 100 Bassanite and γ-anhydrite can be differentiated by comparing the relative intensities of 100 and 110 peak reflections (Carbone, Ballirano & Caminiti, 2008; Ballirano & Melis, 2009). These peaks are located at 2θ positions ~15° and 26° respectively, based on a Cukα1 X-ray wavelength. Bassanite and γ-anhydrite are indicated by peak ratios of ~2:1 and ~1:1, respectively. The relative peak ratio method requires bassanite to be indexed using a trigonal crystal system defined unit cell (Abriel & Nesper, 1993). The peak ratios were calculated from the peak diffraction intensity for eleven fully dehydrated gypsum samples (Table 4.4). The majority of samples reflect bassanite 100:110 peak ratios of ~1:1. However, samples G28, G13, and G5 have higher peak ratios (~1.5:1), sitting intermediately between the two mineral ratios. This might indicate the presence of some γ-anhydrite. However, it was observed that peak ratios could vary even between samples dehydrated under similar conditions (G33, G34; G45 and G13; G45 core versus rim). Therefore, with no peak ratios approaching ~2:1, the formation of γ-anhydrite is

80 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

unlikely. The variations in sample peak ratios samples may reflect water movement along hexagonal channels in the bassanite structure or local preferred-orientation effects.

Table 4-4: The 100 vs 110 peak ratios calculated for eleven dehydration experiments. The experimental conditions and crystallographic peaks are listed for each sample.

Temperature Axial Heating 2-Theta Intensity Peak Sample HKL (°C) Pre-stress duration (λ - Co) (counts) Ratio G28 17.03 100 18,222.70 128 Low ~120 mins 1.51 (core) 29.77 110 12,070.98 G28 17.13 100 15,034.29 128 Low ~120 mins 1.47 (rim) 29.87 110 10,196.62 17.16 100 12,449.84 G18 128 High 90 mins 1.28 29.89 110 9,707.67 17.12 100 11,034.06 G26 128 High ~120 mins 1.40 29.85 110 7,904.84 17.17 100 9,809.59 G47 141 Low 51 mins 1.23 29.93 110 8,006.20 17.11 100 19,023.37 G13 141 Low ~120 mins 1.51 29.84 110 12,604.79 G45 17.03 100 6,938.11 141 Low 141 mins 0.97 (core) 29.76 110 7,120.66 G45 17.13 100 9,300.82 141 Low 141 mins 1.21 (rim) 29.87 110 7,715.32 17.13 100 18,225.40 G5 141 High 152 mins 1.58 29.86 110 11,523.43 17.02 100 11,553.20 G16 151 High 69 mins 1.34 29.76 110 8,653.82 17.16 100 12,671.18 G23 173 High 30 mins 1.40 29.89 110 9,058.06 17.09 100 11,672.79 G33 173 High 73 mins 1.33 29.82 110 8,761.38 17.10 100 9,269.90 G34 173 Low 102 mins 1.29 29.84 110 7,167.65 Step 3: Analyse dehydration curves for changes in relative peak intensities There is a significant drop in diffraction intensities for the (010), (020) and (220) peaks when comparing bassanite to γ-anhydrite reference patterns (Table 4.5). Therefore, if γ-anhydrite formed during dehydration, a drop in relative intensity would be seen in the ‘plateau’ region of dehydration curves (Figure 4.6 – 4.). However, only minor intensity fluctuations were observed. The plateau regions remain sub-planar, further indicating the absence of γ-anhydrite. G16 (151°C, high axial pre-stress), was the one exception where a small drop in relative plateau intensity was observed, preferentially seen along the (020) plane (Figure 4.8). It is unlikely that this represents γ-anhydrite formation as the drop was not seen in higher

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temperature experiments (similar heating duration), and the calculated 100:110 peak ratio for G16 was 1.34:1 (Table 4.5).

Table 4-5: The crystallographic details for -bassanite (Ballirano and Melis, 2001) and -anhydrite (Bezou et al., 1995) and their calculated scattering vectors (Q) for the three unique peaks identified in the dehydrated product phase.

Q-Position of β-Bassanite (CaSO4. 0.5H2O) γ-Anhydrite (CaSO4) unique peak at 2θ Diffraction Q-Position at 2θ Diffraction Q-Position at -1 hkl -1 hkl -1 16 keV (Å ) (Cu Kα1 λ) Intensity 16 keV (Å ) (Cu Kα1 λ) Intensity 16 keV (Å ) 1.0463 14.74 1 1 0 100 (999m) 1.0463 14.67 1 1 0 66 1.0405 1.8029 25.64 0 2 0 31 (458m) 1.8098 25.55 0 2 0 5 1.8023 2.0779 29.73 2 2 0 100 (715m) 2.0926 29.59 2 2 0 35 2.0811 Presence/absence of γ-anhydrite? Three independent measures were taken to discern the presence/absence of γ- anhydrite in the dehydrated samples. Unanimously, no evidence was found to indicate a two-step reaction pathway (gypsum  bassanite  γ-anhydrite) during our synchrotron experiments. Therefore it is concluded that bassanite is the sole dehydration product under the experimental conditions used during the dehydration experiments performed for this thesis.

Post-experimental XRD analysis indicated the back-reaction of several synchrotron samples dehydrated above 128°C (> 80% gypsum detected). Back- reaction was also indicated from the SEM micrographs of these samples, which contain a distinctly different microstructure to the original, undehydrated gypsum discs. This difference in microstructure is highlighted in Figure 4.12, where only tabular gypsum habits were observed in all pre-experimental SEM images (left image). Back-reacted gypsum habits, however, are columnar/acicular or swallow-tail contact twins (right image).

82 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Figure 4-12: SEM micrographs are comparing the original Volterra gypsum tabular habits (left), with the columnar and swallow-tail contact twin gypsum habits observed in dehydrated discs that have back-reacted.

The dehydration microstructure of bassanite from ten discs is discussed below where post-XRD confirmed > 93% bassanite (normalised percentage), and there is no microstructural evidence of back-reaction (only relict gypsum grains remain). Some of these experiments were performed with long-camera distance at the synchrotron and are not included in the kinetic analysis. G45 and G47 are the ex-situ samples dehydrated at QUT CARF. SEM micrographs of the two 120°C experiments, G65 and G80, were not obtained.

4.4.2 Microstructure (SEM) Bassanite habits Characteristics of individual crystals: Acicular: Individual crystals appear as fine-grained needles with tube-like channels along their long axes and are smaller in circumference than prisms. Grain width is typically < 5 μm; channel width << 0.5 μm (Figure 4.13a, 4.14a). Small acicular bassanite grains were concentrated around relict saw marks imprinted during cutting of the gypsum cores (Figure 4.13a).

Prismatic: Individual elongate crystals exhibit well-defined crystal faces parallel to the long axis. Bassanite prisms are larger in circumference than acicular crystals and contain multiple internal channels. Grain width is typically 5 - 20 μm. Channels can be simple < 0.5 μm diameter cylindrical/sub-cylindrical, or more complex larger channels (all channels were observed to be < 5-10 μm diameter) (Figure 4.14a, b).

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Tabular single-crystal pseudomorph: Individual crystals of stacked bassanite sheets exfoliating from the gypsum (010)-plane (Sipple et al., 2001a, b) preserve the original Volterra gypsum microstructure (Figure 4.13b).

Figure 4-13: SEM micrographs of acicular (a) and tabular single-crystal pseudomorph (b) bassanite habits. Saw marks remain in some samples from cutting the gypsum sub-cores into experimental discs.

Figure 4-14: SEM micrographs of acicular and prismatic habits in cross-section (a) and prismatic (b) bassanite habits. Bassanite channels can be seen in cross-sections (a).

Characteristic aggregates of crystals: Fibrous multi-crystal pseudomorph: An aggregate of acicular bassanite crystals retain the outer relict grain boundary of the gypsum parent grain (Figure 4.15).

Prismatic multi-crystal pseudomorph: This is an aggregate of prismatic bassanite crystals contained within a relict gypsum grain boundary (Figure 4.16b).

84 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Prismatic/fibrous combination multi-crystal pseudomorph: This term denotes an aggregate of bassanite with both prismatic and acicular crystals within a relict gypsum grain boundary. Crystals have parallel or diverging crystal orientations (Figure 4.16a, c, d).

Figure 4-15: SEM micrographs of fibrous multi-crystal pseudomorph bassanite habits, where the relict gypsum grain boundaries are preserved.

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Figure 4-16: SEM micrographs of prismatic multi-crystal pseudomorphs (b), and combination fibrous/prismatic multi-crystal pseudomorphs (a, c, d), where the relict gypsum grain boundaries are preserved. Crystals within combination pseudomorphs either have parallel (a, c) or diverging orientations (d).

Dehydration temperature: 128°C The microstructure of two samples dehydrated at 128°C (G28: low pre-stress; G26: high pre-stress), is reported below and summarized in Table 4.6. Both samples are composed of idioblastic to subidioblastic, fine to very-fine grained prismatic and very-fine grained acicular bassanite (Figure 4.17). Grains had an average width of 19.1 μm and 1.34 μm, respectively, for each habit for G28 (low axial pre-stress dehydration), and 14.08 μm and 1.68 μm for G26 (high axial pre-stress dehydration). No pseudomorphs or intra-granular dehydration fractures were observed. Occasional intra-granular fractures seen in prismatic grains, perpendicular to the long axis of the grains, however, appear to be mechanical fractures, and not dehydration-related (Figure 4.18). The microstructure is summarised below in Table 4.6.

86 Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Figure 4-17: Post-dehydration SEM micrographs of discs dehydrated at 128°C, under low axial pre- stress (left), and high axial pre-stress (right).

Dehydration microfabrics between low- and high-pre-stressed samples were observed to be fairly similar. The main differences were: [1] prismatic habits dominate at low pre-stress, and acicular at high pre-stress; [2] a slight decrease in the average width of prismatic bassanite was observed at high pre-stress (~4 μm); and [3] localised preferred bassanite orientation is more prevalent at low pre-stress. However, the pervasive relict saw marks observed in the high-pre-stress (G26) sample, obscure true dehydration microstructure as very-fine grain acicular bassanite grains dominate around the saw marks. Inter-grain discolouration was observed in both samples. Partially absorbed relict gypsum grains (4.5 - 6.2% gypsum remaining in samples) are darker grey relative to the light grey bassanite grains. Dissolution textures of gypsum grains are outlined in red (Figure 4.18). Prismatic bassanite orientations were not observed to be crystallographically controlled by gypsum microstructures.

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Figure 4-18: SEM micrographs of prismatic bassanite (light grey grains), and relict partially absorbed gypsum grains (darker grey grains); gypsum dissolution textures are indicated in red.

Table 4-6: A microstructural summary of two discs dehydrated at 128°C, imaged by SEM. Crystallographic information is reported as a normalised percentage for bassanite and gypsum; grain size is semi-quantitative (minimum of 50 grains per habit, per sample measured); and bassanite habits are listed in order of dominance.

Sample Parameters Crystallographic Information Microstructural information Axial Heating Gypsum Grain size: Width = W Evidence of grain Intra-granular dehydration Grain Sample T (°C) Pre- % Bassanite % Gypsum Bassanite habit Cross-section = LA (long axis), SA Microfabric Duration habit boundary widening fractures discolouration stress (short axis)

Prismatic: Inter-grain Relict platy W = 5.6 μm - 39.9 μm, Original grain discolouration seen Core - 99% Core - 1% grains, Prismatic (with channels) x̄ = 19.1 μm, σ = 6.71 μm Moderate localised G28 128 HT 126 mins boundaries not N/A between bassanite Rim - 95% Rim - 5% partially Acicular -rare Acicular: preferred orientation retained. and partially absorbed W = 0.63 μm - 2.19 μm, absorbed gypsum x̄ = 1.34 μm, σ = 0.48 μm

Acicular: Inter-grain Relict platy W = 0.39 μm - 5.69 μm, Rare, weak Original grain discolouration seen grains, Acicular x̄ = 1.68 μm, σ = 1.33 μm G26 128 5x 122 mins 93% 7% localised preferred boundaries not N/A between bassanite partially Prismatic (with chanels) - rare Prismatic: orientation retained. and partially absorbed W = 2.70 μm - 31.90 μm, absorbed gypsum x̄ = 14.08 μm, σ = 6.97 μm

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Dehydration temperature: 141°C The microstructure of four samples dehydrated at 141°C is reported below and summarized in Table 4.7. Three samples were dehydrated under low axial pre-stress (G13, G45, and G47), and G5 under high axial pre-stress.

Low axial pre-stress Bassanite habits in samples dehydrated at 141°C under low axial pre-stress are dominated by fine-grained, idioblastic, tabular single-crystal pseudomorphs (G13, G45, and G47). Fibrous multi-crystal pseudomorphs (G13, G47), and ultra-fine grained acicular habits (G47) were also observed. Pseudomorphs had an average grain size of 83.01 x 38.67 μm (G47), 90.86 x 40.78 μm (G13), and 100.21 x 51.60 μm (G45). Observed microfabrics increased with increasing heating duration from weak-moderate (51 mins) to strong localised preferred orientation (141 mins). Minor relict saw marks are observed in G45; similar to G26, ultra-fine grained acicular bassanite grains dominate around saw marks (x̄ width: 0.99 μm). Figure 4.19 displays an overview image of the microstructure of each disc.

Two dehydration-related microstructural changes were observed in the samples: [1] grain boundary widening, which was moderately common around pseudomorphs (Figure 4.21b); and [2] intra-granular dehydration fractures. These microstructures were not observed in other bassanite habits. Fractures were either radiating, randomly oriented or had a sub-parallel planar orientation which appears to follow the crystallographic (010)-plane along the tabular sheets (Figure 4.20).

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Figure 4-19: Post-dehydration SEM micrographs of discs dehydrated at 141°C, under low axial pre- stress. G13 was imaged twice; first over the disc surface, and then a cross-section of the internal disc microstructure along a freshly broken surface.

Figure 4-20: Dehydration fractures observed in tabular bassanite pseudomorphs.

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Minor amounts of gypsum are identified in the G13 (0.9%) and G47 (0.4%), the shortest heating duration experiments, 125 and 51 mins respectively, from XRD analysis. No gypsum was detected in G45, which was heated for 141 mins. Several partially dehydrated grains were observed in G13 (but not G47). These grains have intra-grain discolouration of mottled smooth, dark grey relict gypsum and fractured, light grey bassanite (Figure 4.21a, b). The same intra-grain discolouration is also observed in the partially dehydrated G4, where XRD analysis identified 28.7% gypsum remaining post-dehydration (Figure 4.21c, d). Relict gypsum in these samples differs from the dissolution textures of inter-grain gypsum seen in G28 and G26 above. Inter- and intra-grain discolouration is only observed in samples where gypsum was identified in the post-XRD analysis.

Figure 4-21: Dehydration fractures observed in tabular pseudomorphs. Grains are partially dehydrated, and intra-granular fractures are isolated within the light grey bassanite domains. Relict gypsum is observed as the smooth, un-fractured, darker grey domains of the grain.

The internal microstructure is observed in cross-sectional SEM micrographs in sample G13. Subidioblastic, fine-grained bassanite grains are fibrous with

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moderate localised shape-preferred alignment. Groups of fibrous grains display highly localised preferred orientations. However, it is unclear whether these grains are pseudomorphs as preserved gypsum grains were hard to identify (Figure 4.22b). Tabular pseudomorphs are absent, even though they appear as the dominant crystal habit on the disc surface. High-magnification micrographs of the sample surface indicate the fibrous nature of some pseudomorphs which appear tabular at lower magnification (Figure 4.22a). Hence, it is possible that tabular pseudomorphs consist of planar sheets of aligned acicular bassanite needles, as suggested by Sipple et al., 2001. SEM micrographs were only taken in cross-section for G13 alone. Therefore, an internal microstructure comparison between samples cannot be made.

Figure 4-22: G13 micrographs of the disc surface (left) and internal cross-section (right), highlighting the difference in microfabric. Internally aggregates of fibrous bassanite dominate. High magnification of surface tabular pseudomorphs (left), indicate a fibrous multi-crystal nature.

An SEM micrograph panorama was taken of the ex-situ dehydrated G45 sample pre- and post-dehydration. Sections of these panoramas were observed to have covered the exact same position on the sample. This gives a unique insight into the microstructural changes that occur during dehydration by looking at the exact same grains, before and after. A snipped of both panoramas is presented in Figure 4.23, where certain sections are enlarged so the reader can both: [1] identify the same grains in unreacted and reacted sample; and [b] observe the change in microstructure. The two main dehydration microstructures, grain boundary widening and dehydration fractures, can be readily observed. Grain boundary widening is observed to be more pronounced along grains whose c-axis lies perpendicular to or is highly oblique to the sample surface.

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Figure 4-23: SEM micrographs of G45 dehydrated at 141°C, low pre-stress. The area under the red line indicates the exact same grains imaged pre- and post-dehydration. The boxed areas show enlarged sections of the initial gypsum microstructure (left), and dehydrated bassanite microstructure (right).

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High axial pre-stress The surface microstructure of G5, dehydrated at 141°C under high axial pre- stress was obscured by pervasive relict saw marks, around which ultra-fine, acicular grain habits dominate (x̄ width: 0.79 μm) (Figure 4.24, right). In areas with no saw marks, fine-grained, idioblastic fibrous multi-crystal pseudomorphs dominate (Figure 4.24, left). Tabular single-crystal pseudomorphs are rare, however, when present contain dehydration fractures along (010) and evidence of grain boundary widening. Pseudomorphs have an average grain size of 19.41 x 11.33 μm. Dehydration microstructures were not observed in the other bassanite habits. No gypsum was detected from XRD analysis.

Figure 4-24: Post-dehydration SEM micrographs of discs dehydrated at 141°C, under high axial pre- stress. Acicular bassanite was observed surrounding pervasive relict saw marks, which dominate the surface of the disc (right).

A comparison between high- and low-pre-stress sample microfabrics is difficult. Similar to samples dehydrated at 128°C, the high pre-stress surface contains pervasive relict saw marks, obscuring the microstructure and causing the dominance of fine-grained acicular bassanite grains.

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Table 4-7: A microstructural summary of four discs dehydrated at 141°C, imaged by SEM. Crystallographic information is reported as a normalised percentage for bassanite and gypsum; grain size is semi-quantitative (minimum of 50 grains per habit, per sample measured); and bassanite habits are listed in order of dominance.

Sample Parameters Crystallographic Information Microstructural information Axial Grain size: Width = W Intra-granular Heating Evidence of grain Sample T (°C) Pre- % Bassanite % Gypsum Gypsum habit Bassanite habit Cross-section = LA (long Microfabric dehydration Grain discolouration Duration boundary widening stress axis), SA (short axis) fractures Pseudomorphs: LA = 37.44 μm - 198.53 μm x̄ = 83.01 μm, σ = 37.19 μm Multiple fractures seen Tabular single-crystal pseudomorph SA = 14.25 μm - 83.62 μm Weak to moderate in most tabular Ultra-fine grain acicular G47 141.4 HT 51 mins 99% 1% N/A x̄ = 38.67 μm, σ = 14.15 μm localised preferred Moderately common pseudomorphs. N/A Fibrous multi-crystal pseudomorphs - orientation Not seen in other rare Acicular: bassanite habits W = 0.43 μm - 1.49 μm x̄ = 0.99 μm, σ = 0.244 μm Pseudomorphs: Relict gypsum part LA = 30.02 μm - 355.63 μm Multiple fractures seen Rare mottled light and Tabular single-crystal pseudomorph Moderate localised G13 141.4 HT 125 mins 99% 1% of intra-grain x̄ = 90.86 μm, σ = 61.86 μm Moderately common in most tabular dark grey intra-grain Fibrous multi-crystal pseudomorphs preferred orientation discolouration SA = 14.77 μm - 160.61 μm pseudomorphs discolouration x̄ = 40.78 μm, σ = 28.15 μm Pseudomorph: Multiple fractures in all LA = 24.67 μm - 384.56 μm Strong localised pseudomorphs G45 141.4 HT 141 mins 100% Not detected N/A Tabular single-crystal pseudomorph x̄ = 100.21 μm, σ = 75.09 μm Moderately common N/A preferred orientation Not seen in acicular SA = 15.64 μm - 160.44 μm grains x̄ = 51.60 μm, σ = 30.05 μm Acicular: W = 0.26 μm - 1.84 μm x̄ = 0.79 μm, σ = 0.39 μm

Prismatic: Acicular LA = 3.96 μm - 13.55 μm Multiple fractures seen Primsatic (with channels) x̄ = 8.79 μm, σ = 2.58 μm Weak to moderate Rare in in most tabular G5 141.4 5x 152 mins 100% Not detected N/A Fibrous multi-crystal pseudomorphs SA = 3.13 μm - 10.33 μm localised preferred pseudomorphs, not pseudomorphs (rare). N/A Tabular single-crystal pseudomorph - x̄ = 6.08 μm, σ = 1.69 μm orientation seen in other habits. Not seen in other rare bassanite habits Pseudomorphs: LA = 8.40 μm - 49.23 μm x̄ = 19.41 μm, σ = 8.25 μm SA = 4.01 μm - 25.87 μm x̄ = 11.33 μm, σ = 4.76 μm

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Dehydration temperature: 151°C SEM micrographs of one sample dehydrated at 151°C were obtained where back-reaction had not occurred (G16). The surface microstructure was largely obscured by pervasive relict saw marks around which ultra-fine, acicular grain habits dominate (x̄ width: 0.66 μm) (Figure 4.25, right). Fine grained, idioblastic prismatic crystals (x̄ : 4.31 x 3.21 μm), and multi-crystal pseudomorphs (x̄ : 51.25 x 31.96 μm), both fibrous and prismatic, were dominant in unobstructed areas (Figure 4.25). Tabular single-crystal pseudomorphs were rare, however, when present contain dehydration fractures after (010) and evidence of grain boundary widening. Dehydration microstructures were not observed in the other bassanite habits. No gypsum was detected from XRD analysis. The microstructure is summarised below in Table 4.8.

Figure 4-25: Post-dehydration SEM micrographs of G16, dehydrated at 151°C under high axial pre- stress. The surface microstructure was largely obscured by pervasive relict saw marks (left).

All low-pre-stress samples dehydrated at 151°C had back-reacted. Therefore, a comparison between low- and high-pre-stress dehydration microstructures could not be made.

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Table 4-8: A microstructural summary of one disc dehydrated at 151°C, imaged by SEM. Crystallographic information is reported as a normalised percentage for bassanite and gypsum; grain size is semi-quantitative (minimum of 50 grains per habit, per sample measured); and bassanite habits are listed in order of dominance.

Sample Parameters Crystallographic Information Microstructural information Axial Heating Gypsum Grain size: Width = W Evidence of grain Intra-granular dehydration Grain Sample T (°C) Pre- % Bassanite % Gypsum Bassanite habit Cross-section = LA (long axis), SA Microfabric Duration habit boundary widening fractures discolouration stress (short axis)

Acicular: W = 0.21 μm - 1.36 μm, x̄ = 0.66 μm, σ = 0.26 μm

Prismatic: Acicular LA = 1.11 μm - 11.10 μm, Prismatic (with channels) Multiple fractures seen in most x̄ = 4.31 μm, σ = 2.15 μm Rare, weak Fibrous multi-crystal pseudomorph platy pseudomorphs (rare). G16 151 5x 69 mins 100% Not detected N/A SA = 1.05 μm - 7.40 μm, localised preferred N/A N/A Prismatic multi-crystal pseudomorph Not seen in other bassanite x̄ = 3.21 μm, σ = 1.49 μm orientation Platy single-crystal pseudomorph - habits rare Pseudomorphs: LA = 24.34 μm - 103.84 μm, x̄ = 51.21 μm, σ = 20.22 μm SA = 10.67 μm - 87.86 μm, x̄ = 31.96 μm, σ = 16.70 μm

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Dehydration temperature: 173°C The microstructure of three samples dehydrated at 173°C is reported below and summarized in Table 4.9. One sample was dehydrated under low axial pre-stress (G34) and two under high axial pre-stress (G23, G33) (Figure 4.26). No gypsum was detected from any sample during XRD analysis.

Figure 4-26: Post-dehydration SEM micrographs of discs dehydrated at 173°C under low axial pre- stress (G34) and high axial pre-stress (G23, G33). Low pre-stress Fine-grained, idioblastic, tabular single-crystal pseudomorphs (x̄ : 70.40 x 34.59 μm) were the only bassanite habit to be observed in G34. A weak to moderate localised shape-preferred orientation was observed, and grain boundary widening was moderately common (Figure 4.27, right). Pseudomorphs contained multiple dehydration fractures per grain, which were either sub-parallel, planar

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crystallographically controlled fractures along tabular bassanite sheets (Figure 4.27, left), or radiating fractures (Figure 4.27, right).

Figure 4-27: Sub-parallel crystallographically controlled (left) and radiating (right) dehydration fractures in G34.

High pre-stress Fine-grained, idioblastic bassanite pseudomorphs were observed in G23, dehydrated for 30 mins (x̄ : 45.22 x 24.71 μm), and G33 (x̄ : 64.98 x 34.32 μm), dehydrated for 73 mins. Pseudomorphs ranged from fibrous multi-crystal, fibrous- prismatic combination multi-crystal, prismatic multi-crystal and tabular single- crystal. The surface microstructure was largely obscured by pervasive relict saw marks in G23, around which ultra-fine, acicular grain habits dominate. A minor amount of saw marks were observed on the G33 disc surface. A weak localised preferred orientation was observed; grain boundary widening was moderately common; and pseudomorphs contained multiple dehydration fractures per grain (Figure 4.28).

Figure 4-28: Curved and linear dehydration fractures in G33.

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Table 4-9: A microstructural summary of three discs dehydrated at 173°C, imaged by SEM. Crystallographic information is reported as a normalised percentage for bassanite and gypsum; grain size is semi-quantitative (minimum of 50 grains per habit, per sample measured); and bassanite habits are listed in order of dominance.

Sample Parameters Crystallographic Information Microstructural information

Axial Grain size: Width = W Intra-granular Heating Evidence of grain Sample T (°C) Pre- % Bassanite % Gypsum Gypsum habit Bassanite habit Cross-section = LA (long Microfabric dehydration Grain discolouration Duration boundary widening stress axis), SA (short axis) fractures

Pseudomorph: Multiple fractures in all LA = 26.23 μm -217.36 μm Weak to moderate pseudomorphs G34 173.3 HT 102 mins 100% Not detected N/A Tabular single-crystal pseudomorph x̄ = 70.40 μm, σ = 41.21 μm localised preferred Moderately common N/A Not seen in acicular SA = 16.22 μm - 120.28 μm orientation grains x̄ = 34.59 μm, σ = 19.91 μm

Fibrous multi-crystal pseudomorph Acicular Pseudomorphs: Multiple fractures seen Fibrous-prismatic multi-crystal LA = 14.88 μm -94.61 μm Rare, weak Moderartely in most G23 173.3 5x 30 mins 100% Not detected N/A pseudomorphs x̄ = 45.22 μm, σ = 18.42 μm localised preferred common with pseudomorphs. N/A Tabular single-crystal pseudomorph SA =7.70 μm - 64.28 μm orientation pseudomorphs. Not seen in acicular Prismatic multi-crystal pseudomorphs x̄ = 24.71 μm, σ = 12.64 μm grains (rare)

Pseudomorphs: Tabular single-crystal pseudomorph Multiple fractures in all LA = 22.05 μm -159.56 μm Fibrous-prismatic multi-crystal Weak localised pseudomorphs G33 173.3 5x 73 mins 100% Not detected N/A x̄ = 64.98 μm, σ = 32.51 μm Moderately common N/A pseudomorph preferred orientation Not seen in acicular SA = 16.80 μm - 66.80 μm Acicular - rare grains x̄ = 34.32 μm, σ = 13.75 μm

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Chapter 5: Discussion

The following chapter details the discussion and interpretation of results reported in Chapter 4. This will be broken down into four sections. Firstly, bassanite dehydration microstructures will be discussed, and a hypothesis put forth regarding their formations. Then the two main research objectives will be evaluated based on experimental findings and compared to the literature. These were: a) the effect of pre-stress on gypsum dehydration, and b) the effect of gypsum microstructure on dehydration kinetics. Finally, several experimental limitations will be discussed (in addition to those previously mentioned throughout the thesis).

5.1 BASSANITE MICROSTRUCTURES

Three main bassanite morphologies were observed: [1] prismatic bassanite (Figure 5.1a), [2] multi-crystal pseudomorphs (MCP) (Figure 5.1b, c), and [3] single-crystal pseudomorphs (SCP) (Figure 5.1d). Prismatic habits display cross- cutting relationships with respect to relict gypsum grains and do not retain gypsum microfabrics. This habit was dominant at 128°C under low (G28) and high pre-stress (G26). In contrast, gypsum microfabrics were preserved by bassanite pseudomorphs (SCP and MCP). SCP show the highest degree of structural retention of the gypsum lattice, with significant preservation of cleavage planes and outcropping crystallographic planes (Figure 5.1d). SCP was the dominant morphology for low- pre-stress experiments at 128°C (G4), 141°C (G13, G45 and G47), and 173°C (G34). MCPs incur more significant structural modifications. A single gypsum grain is replaced by an aggregate of smaller bassanite grains whilst the original grain boundary is retained (Figure 5.1c, d). The preferential and parallel orientation of bassanite fibres within pseudomorphs suggests there is a preservation of the gypsum lattice, suggested to be the gypsum c-axis (Freyer and Voight, 2003). ‘Exfoliation’ of the (relatively weak) gypsum (010) crystallographic planes is thought to occur from contraction along [010] caused by the anisotropic thermal behaviour of the gypsum lattice (Sipple et al., 2001a, b). Thermal expansion is largest along the b-axis, perpendicular to the (010) crystallographic planes (Schofield et al., 1996; Ballirano and Melis, 2009). The preferential expansion is likely caused by the weakening of

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hydrogen bonds along the sheets of lattice-bound water which run parallel to (010) (Figure 2.1; Schofield et al., 2000). Expansion of the (100) surface, coupled with exfoliation is also thought to contribute to ‘bending’ and partitioning of the (010) planes into needle-like grains orientated with long-axes parallel to (100) (Sipple et al., 2001a, 2001b). This may explain the relict c-axis preferential orientation of acicular and prismatic bassanite aggregates within MCP (Figure 5.1b, c). Pseudomorphs that contain diverging bassanite crystal orientations are uncommon and may reflect crystal intergrowths or twinning/kinks in the original gypsum lattice. MCP was the dominant morphology for high-pre-stress experiments at 141°C (G5), 151°C (G16), and 173°C (G23, G33).

Figure 5-1: Main bassanite morphologies observed in SEM micrographs post-dehydration: (a) prismatic bassanite grains, (b, c) multi-crystal pseudomorphs, and (d) single-crystal pseudomorphs.

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Mineral transformations are controlled by two main mechanisms: solid-state diffusion and dissolution-precipitation (Putnis, 2002; Ruiz-Agudo et al., 2014). The topotactic retention of crystallographic structure and microfabric is generally used as evidence for solid-state diffusion mechanisms (Ruiz-Agudo et al., 2014). However, oxygen isotope tracing during hydrothermal pseudomorphic transformations of Na- feldspar  K-feldspar (O’Neil and Taylor, 1967; Mérigoux, 1968) and kaolinite + K+  muscovite (O’Neil, 1977), indicate complete recrystallization of the product phase despite observed topotaxy. An interfacial-coupled dissolution-precipitation mechanism is suggested to explain the preservation of parent phase crystallographic structures (O’Neil and Taylor, 1967; O’Neil, 1977). A thin fluid film interface between the parent and product phase acts as a reaction front (O’Neil, 1977). The parent phase dissolves in the fluid phase and immediately, the product phase re- precipitates retaining the parent crystal structure (Putnis and Putnis, 2007). Increasing dissimilarity in the structural relationship between parent and product minerals can lead to a polycrystalline product of one or more phases (Putnis and Putnis, 2007).

Considering the parent (gypsum) and product (bassanite) phases have remained the same throughout all experiments, what then explains the observed changes in bassanite morphology? An uncoupled dissolution-precipitation reaction can also occur. Therefore, it is proposed that the three morphologies represent different stages of coupling/uncoupling along this continuum between these two end-members. Dehydration under dry conditions dictates that the fluid phase present during decomposition is reaction-controlled crystal-liberated water. The thickness of the interfacial fluid reaction front is then regulated by the degree of coupling/uncoupling. Equal rates of dissolution and precipitation would produce a fluid interface only several monolayers thick (Putnis, 2002). The reaction becomes surface-controlled, where dissolution of the parent phase is rate-limiting, controlling bassanite growth (Xia et al., 2009; Lasaga, 2014; Ruiz-Agudo et al., 2014). However, a faster dissolution rate will increasingly thicken the fluid film. A thicker reaction rim increases the transportation length-scale of ionic species between the parent and product phase, and the reaction becomes diffusion-controlled (Ruiz-Agudo et al., 2014). It is difficult to observe these atomistic-scale mechanisms experimentally. However, key insights were gained from SEM micrographs of partially dehydrated

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samples (Figure 5.2, 5.3). These are interpreted for each morphology in the three proposed stages of rate-coupling identified:

a) Tightly-coupled dissolution-precipitation: Gypsum dissolves at an equal rate to bassanite formation allowing topotactic preservation of the parent phase producing SCP’s. Bassanite would precipitate via the Frank-van-der- Merwe crystal growth mechanism, where nucleation occurs layer-by-layer across the parent phase boundary (Sitter et al., 2008). An extremely thin fluid film reaction front is likely needed for the comprehensive inheritance of crystallographic structure (Figure 5.2a).

i. Microstructural observations: Dehydration occurs in isolated grains, randomly distributed throughout the sample. An intra-grain reaction front is identified from micrographs by changes in colour and texture between the phases. Gypsum domains are darker grey and smooth (no fractures), and bassanite domains are a lighter grey, containing multiple dehydration fractures (Figure 5.3a, b). Reduction in solid molar volume is accommodated by fracturing in the product phase and inter-granular grain-boundary widening (Figure 5.1d).

b) Moderately-coupled dissolution-precipitation: Gypsum dissolves at a slightly faster rate than bassanite precipitates, producing MCP’s. The fluid interface thickness embodies the ‘Goldilocks Principle’. It is thicker than in tightly-coupled processes (a). Multiple bassanite grains nucleate, and some gypsum structural information is lost. Yet, the interface is thin enough to allow the transference of c-axis orientation and relict gypsum grain boundaries to the product phase (Figure 5.2b, 5.3a, b).

i. Microstructural observations: Similar to SCP, dehydration occurs in isolated grains, randomly distributed throughout the sample. However, a more distinct, sharp, sub-micron sized, intra-grain reaction front propagates inwards from the grain boundaries (Figure 5.3c, d). Product phase channel-like nano-/micro-pores and inter- granular grain-boundary widening accommodated solid volume reduction (Figure 5.1b; Figure 5.3b).

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c) Uncoupled dissolution-precipitation: Gypsum dissolves considerably faster than bassanite precipitates. The fluid interface is significantly thicker than during coupled reactions. A Volmer-Weber crystal growth mode is favoured where bassanite nucleates as small clusters on the gypsum surface forming ‘islands’ (Sitter et al., 2008). Parent microfabrics are not retained, and bassanite grows in randomly oriented euhedral prismatic habits (Figure 5.2c).

i. Microstructural observations: Dehydration occurs randomly throughout the sample. Large, prismatic bassanite grains cross-cut relict gypsum grains. Gypsum grains display dissolution textures with no clear reaction front. The boundary between phases is separated by a ‘porosity moat’ (Figure 5.3e, f). The long-axis of a single bassanite grain can cross-cut multiple gypsum grains. This suggests preferable growth along the bassanite c-axis (long axis of prisms) which propagates the reaction. Intra-grain porosity (channel-like micro-pores) and inter-grain porosity (‘moats’) accommodate solid volume change.

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Figure 5-2: Schematic of (a) tightly-coupled dissolution-precipitation processes which form single- crystal bassanite pseudomorphs preserving gypsum grain boundaries and crystallography. (b) Moderately-couple dissolution-precipitation which form multi-crystal bassanite pseudomorphs preserving gypsum grain boundaries, bassanite fibres have a preferred orientation along the relict gypsum c-axis. (c) Uncoupled dissolution-precipitation where bassanite forms euhedral, prismatic habits with no retention of gypsum microstructure.

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Figure 5-3: SEM micrographs of partially dehydrated gypsum. Relict gypsum is darker grey (Gyp) compared to lighter grey bassanite (Bas). Bassanite morphologies are either single-crystal pseudomorphs (SCP) with intra-granular fracturing (a, b), multi-crystal pseudomorphs with intra- granular porosity (MCP) (c, d), or prismatic with inter- and intra-granular porosity (e, f).

Prismatic bassanite has a larger grain size, but a reduced number of grains compared to bassanite aggregates in MCP’s. This indicates low nucleation and high growth rates of bassanite, yielding a smaller number of large product crystals. This is compared to the (relatively) high-nucleation, low-growth rate in MCP, which yields a

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larger number of smaller crystals. The switch in rate between the two mechanisms is possibly attributed to the nucleation barrier imposed by the thicker fluid interface 2- required to form prismatic bassanite. This requires Ca2+ and SO4 ions to diffuse over larger length-scales (Ruiz-Agudo et al., 2014; Bedford et al., 2017). In addition, the gypsum crystal lattice provides a structural ‘template’ with preferential nucleation sites for bassanite formation in MCP (De Yoreo and Vekilov, 2003).

5.1.1 Dehydration reaction fronts Intra-granular reaction fronts in SCP and MCP are autocatalytic. A feedback mechanism is established from the precipitation of a stable phase (bassanite) which favours the inward propagation of the reaction from the grain boundary (Galwey, 2000; Putnis and Putnis, 2007). The feedback loop promotes parent phase dissolution increasing the fluid saturation with respect to the product, further favouring product precipitation (Putnis, 2002). Interface advance is, however, conditional on reaction- created porosity in the product phase to maintain a parent-fluid reaction boundary (Ruiz-Agudo et al., 2014). Both SCP and MCP exhibit inter-granular grain- boundary widening. Interestingly, differences were observed for intra-granular porosity that is created through fracturing in SCP and by porous bassanite grains in MCP. This may be attributed to the uncoupling/coupling of dissolution-precipitation. Two types of intra-granular fracturing is observed in SCP. Crystallographically- controlled sub-parallel (010)-planar fractures are associated with solid volume shrinkage and exfoliation of (010) planes (Figure 5.4b). However, most segments of radial fractures do not appear to be crystallographically controlled and are thought to be hydraulic fractures created by intra-granular pore-fluid overpressures (Figure 5.4a). During SCP formation, precipitating bassanite mimics the gypsum lattice. However, because gypsum has negligible porosity, the only intra-granular transportation architecture established for the liberated crystal-bound fluids is (010) exfoliation. Localised increases in pore-fluid pressure are created if these shrinkage cracks cannot accommodate the volume of fluids produced. This can lead to hydraulic fracturing within the product phase (Olgaard et al., 1995), and possibly further propagation of exfoliation along (010). Fracture pathways facilitate fluid drainage, reducing the effective pressure, allowing the dehydration front to propagate further into the parent phase (Fusseis et al., 2012). Conversely, with MCP, localised grain-scale stresses are mitigated by the slight uncoupling of dissolution-

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precipitation. Fewer lattice ‘building instructions’ are transcribed. Therefore, bassanite growth is less restricted, and changes in solid volume can be accommodated through pore formation.

Figure 5-4: SEM micrographs of intra-granular fractures observed in bassanite single-crystal pseudomorphs. Fractures are either non-crystallographically-controlled radiating, hydraulic fractures (a), or exfoliation fractures along the (010) plane (b).

Previous microstructural analysis of the gypsum  bassanite transformation indicates that dehydration can occur via two pathways. The inwards propagation of a sharp, inter-granular reaction front, initiated at unconfined sample margins (Fusseis et al., 2012), or the drained end of jacketed samples (Stretton, 1996; Miller, 2003). Alternatively, heterogeneous nucleation has been observed under hydrostatic (Olgaard et al., 1995), drained (Stretton, 1996; Ko et al., 1997) and confined (Bedford et al., 2017) dehydration conditions. Our dehydration experiments were conducted similarly to the set-up of Fusseis et al. (2012) with radially unconfined gypsum samples. It was therefore hypothesised that dehydration would occur as a spatially-dependent reaction front propagating inwards from the margin of the sample. However, no spatial dependence was observed in the dehydration kinetics between the centre, mid- and margin point sampled for dehydration between 128°C - 173°C at low or high pre-stress (Figure 5.5). For several samples, the margin point dehydrated the slowest. Furthermore, microstructural observations indicate prismatic bassanite forms from isolated and dispersed bassanite nucleation. Bassanite grains are surrounded by a ‘porosity moat’, similar to Bedford et al. (2017), with no clear reaction front observed (Figure 5.3f). Intra-granular reaction fronts isolated within grains were observed in SCP and MCP.

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Figure 5-5: Normalised dehydration curves of bassanite proportion ((110) peak) over time (sec) highlighting the lack of spatial dependence of reaction rates between the centre (circles), mid- (crosses) and margin point (diamonds) sampled. Kinetics of samples dehydrated at 128°C (purple), 141°C (green), 151°C (blue) and 173°C (red) are shown.

Interestingly, G65 (120°C, low pre-stress) was the only sample exhibiting a spatial dependence of the dehydration pattern. There was a significant reaction delay and change in absolute intensities between points sampled across the disc (Figure 5.6). The centre of the sample reacts the slowest and has the lowest raw scattering intensities. A step-wise increase in recorded intensity and dehydration rate is observed progressing outwards to the sample margin. This compares with the results obtained by Fusseis et al. (2012; T: 115°C), where pressure diffusion processes were suggested to control reaction front advancement. A reaction front develops at the unconfined margins where fluid drainage is possible. Reaction-controlled porosity and permeability create new drainage pathways driving the reaction front inwards. Pore-fluid overpressures in the sample interior may suppress further bassanite nucleation until reached by the reaction front (Miller, 2003). Conversely, the opposite spatial dependence was observed for G80 which was dehydrated under high pre-stress at 123°C. The fastest kinetics occurred at the sample centre and midpoint, and the margin dehydrated the slowest (Figure 5.6). This might indicate that G65 and G80 dehydrate via different kinetic processes. However, it is unclear whether the loss of spatial-dependant reaction progression is due to increased pre-stress or a slightly

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elevated temperature (3°C difference). Unfortunately, these samples were not analysed by SEM, so microstructural observations are not available.

Figure 5-6: Raw dehydration curves of the peak intensity of (110) over time (sec) highlighting the lack of spatial dependence of reaction rates for gypsum dehydrated at 120°C under high pre-stress (G80), and the spatial dependence of rates at 120°C, low pre-stress (G65). The centre (purple), mid- (blue) and margin points (red) sampled are shown.

5.1.2 What controls dissolution-precipitation coupling? Several trends are observed from microstructural observations. Firstly, prismatic bassanite habits were only dominant at 128°C (both high and low pre- stress). Secondly, for temperatures T: 141°C – 173°C, low pre-stress dehydration produces SCP, and high pre-stress dehydration produces MCP. This highlights a possible correlation between the magnitude of pre-stress applied to the sample and the coupling of dissolution-precipitation. However, a duplicate experiment at 128°C and low-pre-stress (G4) produced SCP, compared to its sibling G28 with prismatic products. The only change in experimental conditions was a difference in the final sample chamber partial pressure reading (267 kPa for G28 and 117 kPa for G4). Chamber pressure fluctuations during dehydration are a combination of changes in the: [1] partial pressure of air molecules due to increasing temperature, [2] total product volume increase of 7.8% during dehydration (bassanite (s) + H2O (l); Ko et al., 1997), and [3] contributions of the partial pressure of water vapour. The inlet valve on the Blach cell was improperly closed during G4 dehydration. This means that the internal sample chamber in the cell was vented to the atmosphere, preventing the build-up of partial pressures (air, water vapour) inside the cell. Could these pressure differences inside the sample chamber influence the dehydration mechanism of

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gypsum? And what is the influence of pressure on the phase stability of reaction- liberated water?

Phase stability of H2O

To determine the phase of liberated water, the pressure-temperature (P-T) conditions at the final stage of the experiment (before the cell is quenched) were plotted against pure water vapour pressure curves (Figure 5.7). Water vapour curves were produced with the Antoine equation (Antoine, 1888):

푃 = 10exp((퐴 − 퐵)⁄(퐶 + 푇)) (20)

Where: P = sample chamber partial pressure (converted to kPa), A/B/C = constants for pure water, T = sample chamber temperature (°C). Different constants were used from 0°C – 100°C (low-pressure: A: 8.07131, B: 1730.63, C: 233.426) and 100°C – 180°C (high-pressure: A: 8.14019, B: 1810.94, C: 244.485) (NIST, 2018). The curves represent a thermodynamic equilibrium between liquid and gaseous pure water, where the rates of evaporation and condensation are equal (Brantley, Kubicki and White, 2008). When samples plot in the ‘liquid’ region, condensation is thermodynamically favoured, compared to the ‘vapour’ region where evaporation is favoured. It is noted that fluids released during dehydration will 2- contain dissolved Ca2+ and SO4 . Therefore, true equilibrium may deviate slightly from plotted vapour pressure curves.

Figure 5-7: Sample pressure-temperature readings from dehydration experiments, prior to quenching, are plotted with the vapour pressure curves for pure water, calculated using the Antoine equation (Eq. 20). Shaded samples indicate the dominant bassanite morphology observed in SEM micrographs, where: green = single-crystal pseudomorphs, blue = multi-crystal pseudomorphs (MCP), and orange = prismatic habits. SEM analysis was not performed on non-shaded samples.

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The dehydrated samples cluster into three regions in P-T space (Figure 5.7), each corresponding to different bassanite morphologies. Low temperature- intermediate pressure samples plot along the liquid-vapour water phase boundary (G18, G26, and G28). These samples contained prismatic bassanite (no pseudomorphism), indicated in orange (proposed mechanism: uncoupled dissolution- precipitation). High-pressure samples plot in the upper ‘vapour’ region. MCP morphologies were observed, indicated in blue (proposed mechanism: moderately coupled dissolution-precipitation), except G13 (SCP) which had the lowest pressure in the cluster. Low-pressure samples plot in the lower ‘vapour’ region, where SCP morphologies were observed, indicated in green (proposed mechanism: tightly coupled dissolution-precipitation). The anomalously low-pressure recordings were caused by improper closure of inlet valves (G4, G34) and different pressure monitoring set-ups (G29, G17). A longer capillary length was used to connect the Blach cell to the pressure gauge in June 2016. This increased the dead volume within the sample chamber for gaseous molecules to distribute and therefore, recorded lower pressures than subsequent experiments with a shorter capillary length (i.e. smaller chamber volume). This is important, as Figure 5.7 highlights a correlation between the pressure of the cell, the magnitude of pre-stress to the sample and the degree of dissolution-precipitation coupling. High-pre-stress samples are correlated with higher pressure readings and MCP morphologies (blue, Figure 5.7), and low- pre-stress samples correlate with anomalously low-pressure readings and SCP morphologies (green, Figure 5.7). However, this correlation is explained by the vented/larger volume sample chambers. This is reinforced by low-pre-stress samples G28 and G1, with negligible recorded pressure difference to their high pre-stress counterparts (Figure 5.7). This suggests that the coupling/uncoupling of dissolution- precipitation depends on the liquid/vapour phase of water in the system.

The phase of fluids during dehydration may have the following implications for the dehydration mechanism:

1. The removal rate of fluids away from the reaction front.

2. The thickness of the interfacial fluid film.

2+ 2- 3. The saturation of the fluid boundary with respect to Ca and SO4 ions.

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At low pressures and high temperatures, the evaporation of water is thermodynamically favoured. The lower density and reduced surface tension of water vapour relative to liquid water allows vapour to migrate through a permeable pore network faster and with higher accessibility to small pores. During dehydration, lattice-bound fluid release rates increase with the establishment of a permeable, porous drainage architecture. Water vapour migration can thus occur sooner as smaller developing pore channels are inaccessible to liquid water. High evaporation rates within the cell lead to proportionally more water vapour versus liquid water in the system. This will result in faster removal of fluids from the reaction front, creating a relatively thin interfacial fluid-film, and a higher degree of fluid supersaturation promoting bassanite precipitation. It is suggested that these conditions lead to the tightly-coupled dissolution-precipitation that forms SCP observed in low-pressure samples (Section 5.1). At higher pressures, evaporation rates lessen, increasing the availability of liquid water and the removal of fluids from the reaction front slows. The interfacial fluid-film thickens, and the solution saturation decreases. This would result in the loss of some parent-phase crystallographic information leading to MCP formation in high temperature, high- pressure samples. Conversely, at the liquid-vapour water phase boundary, equilibrium is approached between the rates of evaporation and condensation. Fluid drainage rates slow, thickening the fluid interface, producing a higher degree of fluid under-saturation. Under these conditions the reaction becomes diffusion-controlled, and the parent phase structural information is lost. This is seen in low temperature- intermediate pressure samples where no pseudomorphs were observed.

The phase stability of water in the dehydrating system is therefore thought to control the coupling/uncoupling of dissolution-precipitation and in turn bassanite microstructure. Correlations between dominant dehydration morphologies and sample pre-stress is coincidental. However, SEM analysis was not performed on all samples. Therefore, microstructural observations are limited to a subsample of dehydrated discs.

5.2 THE EFFECT OF PRE-STRESS ON POLYCRYSTALLINE GYPSUM DEHYDRATION KINETICS

High-pre-stress samples consistently dehydrated faster at all temperatures (120°C: 173°C) (Figure 4.6 – 4.9, 5.5). However, the magnitude of kinetic

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differences decreases with increasing temperature (Figure 4.11). The change in dehydration kinetics is reflected in the activation energies (Ae) calculated for each pre-stress set, 73.8 kJ/mol (low pre-stress) and 50.40 kJ/mol (high pre-stress). As discussed below, the Ae calculated here are semi-quantitative, representing lower- bound estimates only, and should not be used for estimating rate constants outside the considered temperature regime.

These results contrast with single-crystal isothermal dehydration using a hydrothermal diamond anvil cell. Dehydration kinetics between 110°C – 150°C showed a linear negative pressure dependence (P: 343 – 1085 MPa; Liu et al., 2015). This kinetic change was attributed to the increased crystal binding forces under higher pressure, where lattice bonds are harder to break, and water removal is more difficult leading to slower reaction rates (Liu et al., 2015). What was not considered, however, is that significant increases in pressure (~700 MPa) at a constant temperature may simply keep the sample in the gypsum stability field (Figure 2.5).

This would account for their kinetically negative pressure dependence. An Ae of 66.9 kJ/mol was obtained. However, it is unclear at what experimental pressure these were calculated. Conversely, higher Ae has been calculated during single crystal dehydration at lower pressures than performed by Liu et al. (2015) (Table 2.5): 92.3 kJ/mol (non-isothermal, Tmax: 175°C, relative humidity ~60%; Sarma et al., 1998), 119 ± 11 kJ/mol (87°C – 120°C, hydrothermal brine; Jordan Astilleros, 2006), 90.3 kJ/mol (63°C – 106°C, constant N2 flow; Putnis et al., 1990), and 156.9 kJ/mol

(50°C – 150°C, PH2O: atm.; Fowler et al., 1968). However, these variations in Ae may be caused by changes in the temperature ranges tested, the grain size of starting materials and differences in experimental parameters. This makes comparing kinetics datasets difficult. A negative pressure dependence was observed when higher Ae were calculated with increasing PH2O from vacuum to atmospheric conditions. This was found for both single crystal (38.5  156.9 kJ/mol; Fowler et al., 1968), and powdered gypsum (109.2  201.6 kJ/mol; McAdie, 1964) (Table 2.5). The rise in Ae with PH2O was thought to reflect changes in nuclei growth patterns caused by variations in water adsorption properties at the reaction interface as water vapour saturation increased (Fowler et al., 1968).

A key limitation in our experimental set-up should be considered before interpreting kinetic differences relating to pre-stress: a constant, mechanical, uniaxial

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pre-stress was applied to gypsum samples. This pre-stress was applied when closing the cell, where beryllium windows compress the sample axially. These windows remain fixed in position during dehydration. Therefore, they do not move with the sample as the solid volume changes during dehydration, relaxing pre-stress. The volume change is accommodated by the establishment of porosity and fracturing as opposed homogeneous sample contraction. In the latter case, the sample would detach from at least one Be window, becoming a free surface, eliminating axial pre- stress. However, dehydrated discs usually stuck to the Be windows (in some cases a razor was needed to remove the sample), implying constant contact throughout dehydration.

5.2.1 Possible explanations for pre-stress-sensitive kinetics There are several possible explanations for the observed change in dehydration kinetics between low- and high-pre-stressed samples:

 Changes in dehydration mechanism.

 Dehydration is facilitated by pressure-solution at high pre-stress.

 High mechanical pre-stress causes cataclasis.

 High pre-stress facilitates exfoliation of the (010) gypsum planes.

Change in dehydration mechanism As discussed above, microstructural observations indicate that dehydration was surface- and diffusion-controlled during SCP (low- pre-stress samples) and prismatic bassanite formation (128°C, low and high pre-stress), respectively. MCP formation (high-pre-stress samples) exist somewhere between these two endmembers. However, the change in mechanism was associated with variations in sample chamber partial pressures rather than the magnitude of pre-stress applied to the samples. The coupling/uncoupling of dehydration processes was not thought to affect reaction kinetics. Yet, the reduction in Ae from low- to high- pre-stressed dehydration does match the expected Ae decrease as reaction mechanisms move from surface- to diffusion-controlled (Lasaga, 2014; Brantley et al., 2008). This implies that the coupling/uncoupling of dissolution-precipitation may affect gypsum dehydration rates. However, Ae cannot be assumed to characterize a single reaction mechanism (Lasaga, 2014; Brantley et al., 2008). This is demonstrated by the mechanism switch

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at 128°C. Both samples dehydrated via uncoupled dissolution-precipitation (Figure 5.3e, f), but gypsum still reacted around two times faster under high pre-stress. This indicates that the magnitude of pre-stress is the dominant controlling factor on dehydration kinetics.

Pressure-solution Pressure-solution, or stress-induced solution transfer, is the preferential dissolution from regions of high differential stress and precipitation at low-stress regions, where interstitial fluids act as a conduit for dissolved materials (Vernon, 2004). Localised contact-pressure variations at grain-grain contacts increase internal lattice stresses, which increases the minerals solubility relative to its non-stressed state (Robin, 1978). Increased uniaxial pre-stress enhances localised grain-scale stresses, especially in a material with anisotropic thermal-elastic properties such as gypsum (Ballirano and Melis, 2001) exhibiting a random grain orientation. These internal stresses may promote the dissolution-precipitation dehydration mechanism through pressure-solution. Common microstructural evidence for pressure-solution includes: truncated fossils/phenocrysts, stylolites, and indented grain contacts (Passchier and Trouw, 2005). These microstructures were not observed in dehydrated samples, where high-pre-stress pseudomorphs preserved the original grain shape (Figure 5.1, 5.3). However, at the grain-scale, dissolution-precipitation is initiated at the grain boundary. Pressure-solution may, therefore, help to initiate this process, where reaction-created porosity might relax high contact stresses locally, allowing grain shape retention at the scale of observation.

Mechanical pre-stress cataclasis The application of high mechanical pre-stress may reduce the energy barrier associated with bassanite nucleation by deforming gypsum grains (Vernon, 2004). Cataclasis would increase available sites for nucleation and assist local fluid migration (Vernon, 2004). Microcracks would likely be ‘healed’ during dehydration by the precipitating bassanite grains. However, spallation (sheeted fractures) around the unconfined sample margins were notably absent from all samples, and no further evidence for cataclasis was observed in SEM micrographs of partially dehydrated gypsum grains at high pre-stress (Figure 5.1e). Therefore, cataclasis is ruled out as a mechanism for enhancing kinetics at high pre-stress.

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Pre-stressed gypsum High pre-stress may enhance dehydration by facilitating (010)-plane exfoliation and grain-boundary widening, particularly, for gypsum grains with a c- axis either perpendicular or at a high angle to, the direction of uniaxial pre-stress. b- axis expansion would likely be inhibited for grains with c-axis orientations parallel to the pre-stress direction. However, it is possible that the build-up of localised thermal- elastic stress (upper bound estimate ~58 - 93 MPa (Section 4.2.2)) induced from the obstruction of b-axis expansion, might generate pressure-solution within these grains. In addition, high uniaxial pre-stress creates a heterogeneous strain gradient within the sample. This would likely increase the density of ‘geometrically necessary dislocations’, which form to accommodate the curvature of a crystal lattice undergoing non-uniform deformation (Gao and Huang et al., 2003; Hughes et al., 2003). Dislocations are preferential low-energy nucleation sites (Morse and Arvidson, 2002; Khawam and Flanagan, 2006). Therefore, an increase in dislocation density will increase the surface reactivity of gypsum grains, promoting dehydration.

It is suggested that both pressure-solution (from lattice expansion inhibition and grain-grain contacts) and the effects of sample pre-stress contribute to the observed positive dependence of pre-stress and gypsum kinetics, where high-pre- stressed samples dehydrate faster.

5.2.2 Low pre-stress ‘stepped’ dehydration curves Reaction curves of low-pre-stress samples dehydrated at intermediate temperatures (G29: 141°C, G77: 151°C) exhibit a distinct ‘stepped’ region, which was not resolved in any high-pre-stress experiments (Figure 4.6 – 4.9, 5.5). A slight deviation in the G17 (173°C) reaction curve was noted. However, the reaction kinetics were too fast for accurate temporal resolution of a ‘step’ (if present). Dehydration curves track the relative intensities of bassanite crystallographic peaks over time, representing in-situ reaction kinetics. Therefore, a stepped curve indicates a period of reaction deceleration. The ‘step’ occurred at the same conversion proportion (~20% dehydration) for all crystallographic peaks tracked ((110), (020), (220)) in both samples. This indicates that the dehydration reaction itself was impeded, opposed to an anisotropy in growth kinetics between lattice planes.

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Unfortunately, SEM micrographs were not obtained for samples with stepped kinetic data (G29, G77 ± G17), leaving their bassanite microstructures unresolved. However, experimental parameters correlate with SCP morphologies observed in G4, G13, G47 and G45 (all 141°C, low pre-stress) and G34 (173°C, low pre-stress). These samples lack kinetic data as they were either dehydrated ex-situ (G45, G47) or using the synchrotron long-camera length set-up in February 2017, which only measured SAXS without resolving diffraction peaks (G4, G13). However, G29 and G17 plot in the same low-pressure region as G4 and G34 (Figure 5.7), indicating SCP would be the likely dehydration morphology (pressure readings not obtained for G77). Intra-granular dehydration fractures are prevalent in SCP morphologies. These fractures were not observed in other bassanite habits, suggesting that they are coupled with SCP processes (Section 5.1). It is therefore suggested that changes in dehydration rates at ‘steps’ may relate to pore-fluid pressure build-up and hydraulic fracturing during SCP formation.

Dehydration kinetics are largely controlled by pore-fluid pressure (Pf), where reaction rates decrease with increasing Pf (Olgaard et al., 1995; Ko et al., 1997; Miller et al., 2003; Llana-Funéz et al., 2012). Furthermore, it has been demonstrated that the dehydration of low-porosity, low-permeability polycrystalline gypsum can initially act as an ‘undrained system’ when inadequate drainage structures are developed (Ko et al., 1995; Olgaard et al., 1995). Negligible intra-granular porosity is created in bassanite SCP’s as a high proportion of the non-porous gypsum lattice is retained (Section 5.1). This would create localised regions of elevated Pf during the initial stages of dehydration leading to a reduction in reaction rate, observed as reaction curve ‘steps’ (Figure 5.5). Dehydration rates plateau until a critical point is reached when Pf overpressures reduce the rock strength and bassanite fractures hydraulically. The effective pressure is then reduced via fracture-drainage pathways, allowing advancement of the dehydration interface. This denotes the acceleratory region after the stepped plateau in the reaction curves. The absence of a stepped region in the margin point of G29 (141°C; Figure 5.5) suggests sufficient alleviation of Pf at the unconfined sample margins. Similarly, the margin-inwards reaction advance observed in G65 (120°C, low pre-stress; Figure 5.5) indicates mitigation of effective pressure via diffusion-controlled processes. Dehydration ‘steps’ were therefore not seen in high-pre-stress experiments or in G28 (128°C, low pre-stress)

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because sufficient intra-/inter-granular porosity was created in MCP and prismatic bassanite habits to mitigate Pf.

5.3 THE EFFECT OF MICROSTRUCTURE ON MINERAL DEHYDRATION

The dehydration of in-situ Volterra gypsum samples is compared to the dehydration rates of powdered gypsum by Ballirano and Melis (2009). Ballirano and Melis (2009) analysed the kinetics of powdered synthetic gypsum (x̄ = 2 μm) dehydrated using in-situ laboratory parallel-beam powder XRD, under dry conditions between 75°C and 130°C. The two low-pre-stress synchrotron samples G65 and G28 are compared to the Ballirano and Melis (2009) 120°C and 130°C powdered experiments, respectively. A plot (Figure 5.8) comparing the whole-rock and powdered dehydration data for the two temperatures uses the following data:

[1.a] Whole-rock gypsum, measured data: The growth of the (020) bassanite peak from the centre point of G28 (dotted violet line = 128°C, hand-tight) and margin point of G65 (dotted green line = 119°C, hand-tight).

[1.b] Whole-rock gypsum, Avrami fit function: The Avrami fit function reported in Table 4.4 was plotted for G28 (dashed purple line), where n = 6.31 and k = 3.06e-5 /sec. As dehydration was incomplete for G65, a dimensional Avrami model

(Eq. 21) was used (dashed green line) to predict both Imax, the maximum completion intensity of bassanite peaks (plateau portion of the ‘S’ curve) and the rate constant, k (sec-1):

푛 훼 = 퐼푚푎푥(1 − exp(−푘푡 )) (21)

where:

Imax = Maximum peak intensity;

α = Volume fraction of transformed material (bassanite proportion) over time; k = Rate coefficient (kinetic parameter dependent on temperature) (sec-1); t = Time (seconds); n = Avrami exponent.

The exponent was calculated as n = 6.05, and rate constant, k = 1.90e-5 /sec (R2: 0.99; RMSE: 78.47).

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[2] Powdered gypsum, Avrami fit function: The experimental values reported in Ballirano and Melis (2009) from their kinetic analysis using the Avrami model (Eq. 6). They report an average exponent n = 6 and rate coefficients of 1.57e-4 s-1 and 4.1e-4 s-1 for the isothermal dehydration of 120°C (solid green line) and 130°C (solid purple line), respectively. The reaction curves for these two experiments were plotted using the Avrami equation (Eq. 6).

Figure 5-8: Dehydration reaction curves highlight that powdered gypsum (solid lines) dehydrates faster than polycrystalline gypsum (solid lines) under similar conditions. Note that the activation energy calculated for polycrystalline gypsum (Figure 4.32), does not include 120°C reaction, as the sample was not fully dehydrated. *Kinetic data for powdered gypsum was taken from Ballirano and Melis (2009).

At both temperatures, powdered gypsum reacts faster than polycrystalline gypsum rock (Figure 5.8). The effect of microstructure on gypsum dehydration is most apparent at 120°C, where powdered gypsum has a faster rate coefficient than polycrystalline by a factor of eight. Powdered gypsum has fully dehydrated to bassanite in less than 3 hours. In contrast, the polycrystalline sample still contained ~40% gypsum after 15 hours of heating. This difference in dehydration rates between polycrystalline and powdered gypsum is not apparent from the calculated activation energies (Ae) for the two sets of experiments. The Ae for polycrystalline dehydration at low axial pre-stress is 73.9 kJ/mol (T: 128°C - 173°C), and the reported value for powder dehydration is 109 kJ/mol (T: 75°C - 130°C; Ballirano & Melis, 2009).

These Ae suggest that polycrystalline gypsum would dehydrate faster than powdered. However, this is not the case, as observed in Figure 5.8.

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This contrast in Ae may reflect difference in the kinetic behaviour of gypsum at different temperature ranges. As discussed in Section 2.2.4, there is a significant change in dehydration rates and reaction mechanism above and below ~100°C for powdered gypsum and ~120°C for polycrystalline. The Ae reported by Ballirano and Melis (2009) will, therefore, be influenced by these low-temperature processes. Their calculated rate coefficients differ by an order of magnitude between dehydration at 80°C (k: 3.5e-6), 100°C (k: 2.3e-5), and 120°C (k: 1.57e-4). However, there is only a negligible increase from 120°C to 130°C where k = 4.1e-4. Our synchrotron 120°C experiment is kinetically similar (k: 1.9e-5) to the 100°C experiment of Ballirano and Melis (2009).

Other low-temperature dehydration experiments at atmospheric pressure report similarly high Ae to Ballirano and Melis (2009): 156 kJ/mol for single crystals (20 – 30 micron thick, T: 50°C – 150°C; Fowler et al., 1968), 119kJ/mol for hydrothermal single crystals (T: 87°C – 120°C, Jordan and Astilleros, 2006), and 201.6 kJ/mol for precipitated gypsum powder (grain size: 60 – 80 µm, T: 97°C – 140°C; McAdie, 1964). Polycrystalline gypsum dehydrated between 90°C – 126°C under high differential stress (100 – 159 MPa) also reported an Ae of 132 kJ/mol. Conversely, high-temperature dehydration at atmospheric pressures have a reduced Ae similar to our low-pre-stressed samples: 92.3 kJ/mol for single crystals (4 x 4 x 2 mm3, non- isothermal heating to 175°C, RH ~60%; Sarma et al., 1998) and 78 kJ/mol for Volterra alabaster (T: 105°C – 150°C; Milsch et al., 2011). These variations reinforce the difficulty in extrapolating kinetic data outside the temperature range studied.

Our synchrotron experiments are not directly analogous to those of Ballirano and Melis (2009), as the axial confinement of polycrystalline samples produces an estimated applied pressure of ~61 - 91 MPa during low-pre-stress dehydration (Section 4.2.2). However, the unconfined dehydration of Volterra gypsum cores by

Milsch et al. (2011) produces a comparable Ae (78 kJ/mol) to our low-pre-stress samples (73.8 kJ/mol). This indicates that our Ae still provides a useful comparison between kinetic datasets.

5.3.1 Why do the kinetics of powdered and polycrystalline gypsum differ? Gypsum dehydration kinetics are affected by several intrinsic (sample microstructure, grain size, sample mass) and extrinsic (temperature, pressure, heating

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rate, sample holder geometry) factors (Section 2.1.7). Changes in these parameters between datasets may account for some of the variations in dehydration rates, reaction mechanism and activation energies reported above. Harrison (2012) studied the effect of sample microstructure on gypsum dehydration kinetics and found that powdered gypsum consistently dehydrated at lower temperatures than its polycrystalline counterparts (Section 2.1.7). This demonstrates the individual effect of microstructure when extrinsic experimental parameters remain constant. Furthermore, similar results have been reported for other salt hydrates. Single crystal

NiSO4·6H2O dehydrated eight times faster than its powdered form during vacuum gravimetry (Thomas and Renshaw, 1969). Fluid expulsion from powdered

Li2SO4·H2O was reportedly ten times greater than from single crystals (Galwey et al., 1994). Alum (KCr(SO4)2·12H2O and KAl(SO4)2·12H2O) crushed powders dehydrated five times faster than single crystal alums (Galwey and Guarini, 1993). So, why does sample microstructure affect dehydration kinetics?

Possible explanations for kinetic differences between rocks and powdered samples The geometry and number of reaction interfaces initiated during dehydration are influenced by the available reactive surface area of the sample (Galwey, 2003; Brantley et al., 2008). The overall reaction kinetics are proportional to the extent of these active reaction interfaces (Galwey, 2003). Grain surfaces are constrained by the rock matrix in polycrystalline materials. Therefore, nucleation is preferentially favoured at grain boundaries where associated transformational pre-stress energies are minimised (Yund and Hall, 1970; Rubie and Thompson, 1985). Localised grain- grain contact pressures further reduce the ‘free’ surface area at grain boundaries available as nucleation sites (Robin, 1978; Wheeler, 1987). However, the grain surfaces of powdered samples are unconfined, resulting in a significant increase in the available surface area for nucleation (Galwey, 2000). Similar observations are found in mineral dissolution studies where powdered samples react an order of magnitude faster than single crystals of calcite (Arvidson et al., 2003) and dolomite (Luttge et al., 2003). This was related to the limited surface area of single crystals available for reaction. Furthermore, the absence of grain-contacts in powdered aliquots establishes a permeable drainage network prior to dehydration. Therefore, unlike low-permeable polycrystalline samples, powdered gypsum dehydration kinetics are not impeded by increases in pore-fluid pressure (Section 5.2.2; Olgaard

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et al., 1995; Llana-Funéz et al., 2012). This ‘free’ movement of dehydration fluids through powdered gypsum also increases the probability of grain-fluid contact throughout the sample. The diffusion coefficients of solids are significantly increased in the presence of water (Lasaga, 2014). Therefore, the dehydration of unreacted grains might be promoted by exposure to fluids produced elsewhere in the sample. In addition, the preparation of powdered samples by mechanical abrasion/grinding can damage grain surfaces and increase the number of surface dislocations, creating a high number of available low-energy nucleation sites (Rubie and Thompson, 1985). Ballirano and Melis (2009) used a synthetic gypsum powder, likely produced from precipitation from a supersaturated solution in a laboratory setting. It is unclear whether grinding was used to separate the grain-size fraction used in their experiments (2 – 10 μm).

The grain size of initial sample materials also controls the available surface area for dehydration initiation. Khalil (1982) found that decreasing grain size increased the dehydration rate in powdered gypsum. This is consistent with solubility studies, which report an increase in gypsum solubilities with decreasing grain size (Sokolov, 1962; Sonnenfeld, 1984; Billo, 1987). The powdered gypsum used by Ballirano and Melis (2009) had an average grain size of 2 μm. This is significantly smaller than the ~120 μm average grain size reported for Volterra gypsum (Heard and Rubey, 1966, Stretton 1996; Ko et al., 1997). Therefore, the observed kinetic differences of powdered and polycrystalline gypsum may be influenced by both grain-scale stresses and grain size. This highlights a major limitation when comparing kinetic datasets. Variations in both the sample microstructure (powder, single crystal, polycrystalline) and sample grain sizes make it difficult to detect the influence of isolated parameters on dehydration kinetics. To the author’s current knowledge there is a lack of reported kinetic analysis of powdered gypsum with a comparable grain size to Volterra gypsum (Table 2.5). The grain sizes of dehydrated gypsum range from 2 – 10 μm (Ballirano and Melis, 2009), 40 – 60 μm (Ball and Norwood, 1969; Cave and Holdich, 2000), 60 – 80 μm (McAdie, 1964), or are not reported (Carbone et al., 2008). Therefore, it is recommended for future work that powdered Volterra gypsum be dehydrated in the Blach cell under the same conditions used for polycrystalline samples. A 13 x 1 mm cylindrical, permeable spacer can be used as a sample holder, ensuring a similar sample mass is dehydrated

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(Section 2.1.7), and the powder remains in-situ. This experimental set-up would allow a direct comparison of the microstructural control on dehydration kinetics between polycrystalline and powdered gypsum with the same grain size distribution.

5.4 LIMITATIONS

Non-isothermal conditions

Gypsum was dehydrated under non-isothermal conditions. Therefore, part of the conversion occurs in the thermally transient regime, at lower temperatures than the equilibrium cell temperature used in the Arrhenius fit. This is highlighted below where the 63% conversion time was plotted on the uncalibrated in-situ temperature measurements (Figure 5.9). The effects of this are most prevalent at the highest temperatures. Therefore, both the fitted rate constants and the Arrhenius fit are lower-bound estimates. These data points are not truly valid for estimations of activation energies and should not be used to extrapolate to higher temperatures. However, the estimated apparent activation energies provide a useful comparison with literature data and act as a semi-quantitative pointer towards rate constants in the studied temperature range.

Figure 5-9: The non-isothermal conditions of the kinetically analysed low (solid lines) and high pre- stress (dashed lines) dehydration experiments are plotted using uncalibrated temperature measurements. The plateau region indicates the stabilisation of target temperature. The black linear line depicts the bassanite – gypsum transition temperature at 97°C (Section 3.4.6; Ballirano and Melis, 2009). Coloured symbols indicate the time at which 63% of the reaction has taken place (circles: low pre-stress, squares: high pre-stress). Note: G65 and G80 were still unreacted when quenched.

An electronically controlled hydraulic piston has been developed for the Blach cell. This will enable isothermal dehydration experiments to be conducted in the cell

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via a ‘pressure-drop’ method (Llana-Fúnez et al., 2012). Constant pressure can be applied to keep samples within the gypsum stability field while the cell is heated to the target temperature. Once the cell has reached an equilibrium temperature, the piston is released, reducing the pressure into the bassanite stability field where dehydration can commence.

Calculations of high Avrami exponents The Avrami exponent (n) is a compound parameter representing contributions of the nucleation mechanism and the number of nuclei growth dimensions (Criado and Ortega, 1987; Ballirano and Melis, 2009). Exponent values are generally reported within the range of 1 – 4. Values ≤ 3 can indicate 1- to 3-dimensional growth with either a constant rate or instantaneous nucleation (Criado and Ortega, 1987). An exponent of 4 indicates a constant nucleation rate and equal nuclei growth in 3-dimensions (Criado and Ortega, 1987; Galwey, 2000). Higher exponents of 6 - 8 were calculated for dehydration under all pre-stressed states at 128°C and 151°C, and low pre-stress at 141°C (Table 4.3). These correlate with values reported by Ballirano and Melis (2009): n = 4.5 – 7.4. Very high exponents (n: 8 – 20) were calculated for our synchrotron experiments with the fastest kinetics (k: 1.4 x 10-3 – 2.8 x 10-3) where the reaction slopes are sub-vertical, and dehydration is completed almost entirely in the transient heating regime (Table 4.3; Figure 4.7 – 4.9). This means that the reaction rates accelerate continuously as temperature increases and dehydration proceeds. This, in turn, should result in an increasing slope in the conversion curves, which, in the static Avrami model, can only be accommodated by an increase in the exponent. In addition, exponents > 4 have been linked to autocatalytic nucleation where the rate of nucleation increases as the reaction occurs (Gualtieri, 2001; Christian, 2002).

Microstructural observations of intra-granular reaction fronts indicate that dehydration is autocatalytic, which support the high exponents (Section 5.1.1). However, our experiments deviate from several key assumptions to the JMAEK model: they are non-isothermal; microstructural observations indicate the prevalence of grain-boundary nucleation (non-homogeneous nucleation), and the sample is polycrystalline with variations in grain-size and grain-shape (Kelton, 1997; Vyazokin et al., 2014). The Avrami model is used here purely as an analytical expression for reaction progression of sigmoidal dehydration curves. Therefore, little consideration

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will be paid to the genetic implications of the Avrami exponent.

Recording sample chamber pressure Several techniques were used to measure the evolving sample chamber partial pressures during dehydration. This meant that pressure readings between synchrotron proposal rounds were not directly comparable. A pressure gauge with a long capillary length (June 2016) allowed intermittent pressure readings throughout dehydration as the pressure gauge was accessible in the user cabin. However, the long capillary length extended the dead-volume within the sample chamber leading to minimal variations in pressure throughout the experiment. In February 2017, a shorter capillary length was used allowing better resolution of dehydration-induced pressure fluctuations (smaller dead-volume) (Figure 5.7). A shortcoming was that the gauge was located in the hutch, and therefore, inaccessible during the reaction. This prompted the use of an electronic transducer in July 2017, allowing in-situ pressure readings throughout dehydration. However, the poor resolution of the transducer failed to measure pressure changes. A short-capillary pressure gauge is recommended for future experiments.

Recording sample temperature The use of a thermocouple (insulated with quartz wool) produced several erroneous temperature measurements, requiring temperature calibrations to be performed (Section 4.2). A new version of the Blach cell, however, is under development which will have an inbuilt thermocouple inlet, improving the accuracy of temperature measurements.

Poor temporal resolution for fast kinetics Three to five sample points were measured for each dehydrated disc. The aim of this was to maintain adequate spatial resolution to identify the propagation of an inter-granular reaction front as observed by Fusseis et al. (2012). However, this led to poor temporal resolution during high-temperature dehydration (151°C, 173°C). Only 10 – 15 SAXS/WAXS measurements were taken during the active period of dehydration of these experiments (steeply sloped section of reaction curve). It is recommended for future experiments that a single spatial point in the sample centre is measured to resolve the kinetics in these regions more accurately. Moreover, exposure time could be decreased if sample thickness was reduced, also providing denser sampling in time.

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Chapter 6: Conclusions

The following conclusions were drawn from microstructural and kinetic analysis of in-situ time-resolved synchrotron SAXS/WAXS experiments dehydrating polycrystalline gypsum:

1. Three distinct bassanite morphologies were observed: single-crystal pseudomorphs (SCP), multi-crystal pseudomorphs (MCP), and idiomorphic prismatic bassanite. It is hypothesised that each morphology forms along a spectrum of rate-coupled dissolution-precipitation mechanisms:

a. Tightly-coupled processes where dissolution and precipitation rates are equal forms SCP. SCP exhibit topotactic preservation of gypsum microfabrics.

b. Moderately-coupled processes where gypsum dissolution occurs at a slightly faster rate than bassanite precipitation produces MCP. MCP retain gypsum grain boundaries, and the long-axes of bassanite fibres are orientated parallel to the relict c-axis.

c. Uncoupled processes where dissolution significantly outpaces precipitation and prismatic bassanite forms prismatic bassanite. No gypsum microfabrics are retained, and prismatic habits cross-cut relict gypsum grains.

2. The phase of water in the sample chamber (liquid/vapour) during dehydration appears to influence which bassanite morphology is formed.

3. A distinct ‘stepped’ region was observed in the reaction curves of low-pre- stress samples dehydrated at intermediate temperatures (141°C, 151°C) after ~20% transformation had occurred. A plateau in the reaction curve indicates that dehydration was temporarily impeded. Hydraulically fractured bassanite SCP were only observed under these experimental conditions. Therefore, dehydration ‘steps’ are linked to a localised pore- fluid pressure build-up during SCP formation. This slows dehydration until

Pf overpressures reduced the rock strength and fracture bassanite grains. Further work is needed to investigate the phase relationship of liberated

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crystal-bound fluids and its effect on dehydration microstructure that in

turn has control over the mitigation of dynamic reaction-induced Pf fluctuations.

4. Both SCP and MCP exhibit distinct, micron-scale intra-granular reaction fronts which propagate inwards from the grain boundary.

5. The propagation of a margin-inward spatially-dependent inter-granular reaction front (akin to Stretton, 1996; Miller, 2003; Fusseis et al., 2012) was only observed during dehydration at 120°C under low pre-stress. Microstructural analysis and in-situ kinetic data indicates dispersed, heterogeneous nucleation for all other samples.

6. High-pre-stress samples consistently dehydrated faster at all temperatures tested. This was reflected in the calculated activation energies: 73.8 kJ/mol (R2: 0.97) and 50.4 kJ/mol (R2: 0.98) for low- and high-pre-stressed states of gypsum, respectively (T: 128°C - 173°C). High-pre-stress is thought to create a heterogeneous strain gradient within the sample that facilitates: a) exfoliation of the (010) gypsum planes (Sipple et al., 2001a, b) and grain- boundary widening, b) localised pressure-solution at grain-grain contacts, and c) a surface-density increase of ‘geometrically necessary dislocations’ (Gao and Huang et al., 2003; Hughes et al., 2003) which act as preferential low-energy nucleation sites.

7. Sample microstructure plays a key role in dehydration kinetics. Our polycrystalline gypsum dehydrates slower than literature reported powdered samples. The magnitude of kinetic differences increases with decreasing temperature. At 120°C powdered gypsum has a faster rate coefficient than polycrystalline by a factor of eight. This is attributed to the lack of grain-scale stresses, an increase in available reactive-surface area, and a decrease in grain size in powdered samples.

These results provide key insights into the complexity of polycrystalline gypsum dehydration and promote the importance of whole-rock in-situ kinetic studies. There has been an over-reliance of powdered gypsum starting materials to study dehydration kinetics. It has been found that polycrystalline dehydration rates are significantly influenced by grain-scale stresses, which are notably absent in

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powdered samples. These grain-scale stresses are exacerbated by an increase in axial pre-stress. This has important implications when upscaling dehydration kinetics to understanding crustal-scale fluid migration and reaction-induced embrittlement of hydrous mineral host rocks.

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Appendices

APPENDIX A: DEHYDRATION CONTOUR PLOTS

Filled 2D contour plots of the raw WAXS data graphically represent the mineralogical phase transitions of each experiment during dehydration. The log of the scattering intensity (counts/sec) is plotted against dehydration time (secs) versus scattering vector (Q (Å-1)). These plots present an overview of the dehydration reaction for each experiment (centre sample point used).

Plots are grouped by dehydration temperature, with the low- and high-axial pre-stressed samples shown on the same page for direct comparison. Crystallographic peaks are seen as linear features. The greyscale depicts their scattering intensity where darker shades indicate higher intensity. There is a variable amount of white - light grey background scattering between the peaks. Three peak types can be seen: [1] gypsum peaks; [2] bassanite peaks; and [3] constant background peaks from the Be windows. Each plot has the two WAXS unique bassanite peak reflections labelled, 020 and 220, which were tracked for kinetic analysis. Red stars are plotted to indicate when bassanite peaks are first observed. Note that some bassanite peaks appear before others, suggesting a preferred growth along particular crystallographic planes.

146Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Dehydration Temperature: 120°C The two samples dehydrated at 120°C, G65 (low axial pre-stress) and G80 (high axial pre-stress), are presented below (Figure A-1). Neither sample is fully dehydrated when the experiment is terminated, after ~16 hrs (G65) and ~11 hrs (G80).

Figure A- 1: WAXS 1D scattering profile contour plots for samples dehydrated at 128°C with low axial pre-stress (G28 - top), and high axial pre-stress (G18 - bottom). The labelled peaks 020 and 220 were tracked for kinetic analysis. The red stars indicate the time bassanite peaks first appear. The high-Q peaks with a constant intensity result from Be cell window scattering.

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Dehydration Temperature: 128°C The two samples dehydrated at 128°C, G28 (low axial pre-stress) and G18 (high axial pre-stress), are presented below (Figure A-2). Complete dehydration was observed in both samples, where gypsum peaks have disappeared by ~4,000 seconds in the low-pre-stress experiment (top) and ~2,300 seconds in the high-pre-stress experiment (bottom).

Figure A- 2: WAXS 1D scattering profile contour plots for samples dehydrated at 128°C with low axial pre-stress (G28 - top), and high axial pre-stress (G18 - bottom). The labelled peaks 020 and 220 were tracked for kinetic analysis. The red stars indicate the time bassanite peaks first appear. The high-Q peaks with a constant intensity result from Be cell window scattering.

148Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Dehydration Temperature: 141°C The two samples dehydrated at 141°C, G29 (low axial pre-stress) and G31 (high axial pre-stress), are presented below (Figure A-3). Complete dehydration was observed in both samples, where gypsum peaks have disappeared by ~2,400 seconds in the low-pre-stress experiment (top) and ~1,200 seconds in the high-pre-stress experiment (bottom).

Figure A- 3: WAXS 1D scattering profile contour plots for samples dehydrated at 141°C with low axial pre-stress (G29 - top), and high axial pre-stress (G31 - bottom). The labelled peaks 020 and 220 were tracked for kinetic analysis. The red stars indicate the time bassanite peaks first appear. The high-Q peaks with a constant intensity result from Be cell window scattering.

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Dehydration Temperature: 151°C The two samples dehydrated at 151°C, G77 (low axial pre-stress) and G16 (high axial pre-stress), are presented below (Figure A-4). Complete dehydration was observed in both samples, where gypsum peaks have disappeared by ~1,300 seconds in the low-pre-stress experiment (top) and ~900 seconds in the high-pre-stress experiment (bottom).

Figure A- 4: WAXS 1D scattering profile contour plots for samples dehydrated at 151°C with low axial pre-stress (G77 - top), and high axial pre-stress (G16 - bottom). The labelled peaks 020 and 220 were tracked for kinetic analysis. The red stars indicate the time bassanite peaks first appear. The high-Q peaks with a constant intensity result from Be cell window scattering.

150Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Dehydration Temperature: 173°C The two samples dehydrated at 173°C, G17 (low axial pre-stress) and G23 (high axial pre-stress), are presented below (Figure A-5). Complete dehydration was observed in both samples, where gypsum peaks have disappeared by ~780 seconds.

Figure A- 5: WAXS 1D scattering profile contour plots for samples dehydrated at 173°C with low axial pre-stress (G17 - top), and high axial pre-stress (G23 - bottom). The labelled peaks 020 and 220 were tracked for kinetic analysis. The red stars indicate the time bassanite peaks first appear. The high-Q peaks with a constant intensity result from Be cell window scattering.

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APPENDIX B: WAXS 1D SCATTERING PROFILES: FINAL VS. INITIAL

The initial and final 1D WAXS scattering profile were overlain on an Intensity (counts/s) versus Q (Å-1) plot for each dehydration experiment. The initial profile indicates the mineral phase of the starting material, i.e. gypsum (blue), and the final profile shows the mineral phase(s) in the sample when the experiment was terminated and the cell quenched (orange). Plots are grouped by dehydration temperature, with the low- and high-pre-stressed samples shown on the same page for direct comparison.

Dehydration Temperature: 120°C The two samples dehydrated at 120°C, G65 (low axial pre-stress) and G80 (high axial pre-stress), are presented below in Figure B-1. Both were only partially dehydrated. Therefore, final scattering profile for these two experiments contains the crystallographic peaks for both gypsum and bassanite.

152Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Figure B- 1: The initial (blue) and final (orange) 1D WAXS scattering profiles are overlain from the dehydration experiments at ~120°C with low axial pre-stress (G65 - top), and high axial pre-stress (G80 - bottom). Both are only partially dehydrated where the final profiles for both contain gypsum and bassanite. The bassanite crystal planes (020) and (220) are labelled in both graphs.

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Dehydration Temperature: 128°C The initial and final 1D WAXS scattering profiles of two samples dehydrated at 128°C, G28 (low axial pre-stress) and G18 (high axial pre-stress), are presented below in Figure B-2. Both samples were fully dehydrated during the in-situ experiment.

Figure B- 2: The initial (blue) and final (orange) WAXS 1D scattering profiles are overlain from dehydration experiments at 128°C with low axial pre-stress (G28 - top), and high axial pre-stress (G18 - bottom). The bassanite crystal planes (020) and (220) are labelled in both graphs.

154Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Dehydration Temperature: 141°C The initial and final 1D WAXS scattering profiles of two samples dehydrated at 141°C, G29 (low axial pre-stress) and G31 (high axial pre-stress), are presented below in Figure B-3. Both samples were fully dehydrated during the in-situ experiment.

Figure B- 3: The initial (blue) and final (orange) WAXS 1D scattering profiles are overlain from dehydration experiments at 141°C with low axial pre-stress (G29 - top), and high axial pre-stress (G31 - bottom). The bassanite crystal planes (020) and (220) are labelled in both graphs.

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering155

Dehydration Temperature: 151°C The initial and final 1D WAXS scattering profiles of the two samples dehydrated at 151°C, G77 (low axial pre-stress) and G16 (high axial pre-stress), are presented below in Figure B-4. Both samples were fully dehydrated during the in- situ experiment.

Figure B- 4: The initial (blue) and final (orange) WAXS 1D scattering profiles are overlain from dehydration experiments at 151°C with low axial pre-stress (G77 - top), and high axial pre-stress (G16 - bottom). The bassanite crystal planes (020) and (220) are labelled in both graphs.

156Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Dehydration Temperature: 173°C The initial and final 1D scattering profiles of the two samples dehydrated at 173°C, G17 (low axial pre-stress) and G23 (high axial pre-stress), are presented below in Figure B-5. Both samples were fully dehydrated during the in-situ experiment.

Figure B- 5: The initial (blue) and final (orange) WAXS 1D scattering profiles are overlain from dehydration experiments at 173°C with low axial pre-stress (G17 - top), and high axial pre-stress (G23 - bottom). The bassanite crystal planes (020) and (220) are labelled in both graphs.

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APPENDIX C: CALCULATED Q VALUES FOR BASSANITE

Scattering vector (Q) values were calculated for gypsum in the following steps:

Step 1 - Obtain bassanite crystallographic data and 2θ calculation:

Bassanite crystallographic data was sourced from the PDF4+ database (Ballirano et al., 2001). This database allowed the conversion of theta to a user input X-ray wavelength. Crystallographic data were then exported for the two wavelengths used at the Australian Synchrotron (0.77490 Å and 0.619921 Å). These results are reported under the ‘PDF4+ Data’ columns in Table C-1.

Step 2: Calculate the scattering vector (Q)

The scattering vector (Q) expected at each wavelength was calculated in Excel from the 2θ values exported from PDF4+. Theta was calculated by θ = 2θ / 2. Theta was converted from degrees to radians by: θ (radians) = θ(π / 180). Q was then calculated using the following scattering vector equation (Glatter and Kratky, 1982) (Eq. 13).

The calculated Q values for X-ray wavelengths 0.77490 Å and 0.619921 Å are reported under the ‘Calculated data’ columns in Table C-1. It should be noted that only results within the measured scattering range are reported.

158Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Table C-1: 2θ and calculated bassanite Q values for Synchrotron λ: 0.77490 Å and 0.619921 Å.

PDF4+ Data Calculated data for λ: 0.77490 Å Calculated data for λ: 0.619921 Å 2θ d I H K L θ (°) θ (radians) Q θ (°) θ (radians) Q 5.078 8.74625 2m 1 0 1 2.539 0.044 0.718 5.053 0.035 0.718 5.078 8.74625 m -1 0 1 2.539 0.044 0.718 5.053 0.035 0.718 7.0126 6.33518 3 0 0 2 3.506 0.061 0.992 6.984 0.049 0.992 7.3986 6.00512 999m 1 1 0 3.699 0.065 1.046 7.370 0.052 1.046 7.3986 6.00512 m 2 0 0 3.699 0.065 1.046 7.370 0.052 1.046 10.1659 4.37313 24m -1 1 2 5.083 0.089 1.437 10.145 0.071 1.437 10.1659 4.37313 m -2 0 2 5.083 0.089 1.437 10.145 0.071 1.437 10.2125 4.35324 32m 1 1 2 5.106 0.089 1.443 10.192 0.071 1.443 10.2125 4.35324 m 2 0 2 5.106 0.089 1.443 10.192 0.071 1.443 10.3839 4.28155 10m 2 1 1 5.192 0.091 1.467 10.364 0.072 1.468 10.3839 4.28155 m -2 1 1 5.192 0.091 1.467 10.364 0.072 1.468 11.1748 3.97941 14m 1 0 3 5.587 0.098 1.579 11.161 0.078 1.579 11.1748 3.97941 m -1 0 3 5.587 0.098 1.579 11.161 0.078 1.579 11.6133 3.82963 3 -3 0 1 5.807 0.101 1.641 11.603 0.081 1.641 11.6445 3.81941 3 3 0 1 5.822 0.102 1.645 11.635 0.081 1.645 12.3349 3.60638 15 0 1 3 6.167 0.108 1.742 12.333 0.086 1.742 12.8151 3.47179 458m 0 2 0 6.408 0.112 1.810 12.819 0.089 1.810 12.8151 3.47179 m 3 1 0 6.408 0.112 1.810 12.819 0.089 1.810 13.8168 3.22117 15m 1 2 1 6.908 0.121 1.951 13.835 0.096 1.951 13.8168 3.22117 m -1 2 1 6.908 0.121 1.951 13.835 0.096 1.951 14.0517 3.16759 1 0 0 4 7.026 0.123 1.984 14.074 0.098 1.984 14.4158 3.08798 10 2 1 3 7.208 0.126 2.035 14.445 0.101 2.035 14.5975 3.04975 55 -3 1 2 7.299 0.127 2.060 14.630 0.102 2.060 14.6473 3.03944 95m 0 2 2 7.324 0.128 2.067 14.680 0.102 2.067 14.6473 3.03944 m 3 1 2 7.324 0.128 2.067 14.680 0.102 2.067 14.8282 3.00256 715m 2 2 0 7.414 0.129 2.093 14.865 0.103 2.093 14.8282 3.00256 m 4 0 0 7.414 0.129 2.093 14.865 0.103 2.093 15.274 2.91542 2 -3 0 3 7.637 0.133 2.155 15.320 0.107 2.155 15.3455 2.90193 3 3 0 3 7.673 0.134 2.165 15.393 0.107 2.165 15.8826 2.80439 636m -1 1 4 7.941 0.139 2.240 15.942 0.111 2.240 15.8826 2.80439 m -2 0 4 7.941 0.139 2.240 15.942 0.111 2.240 15.9213 2.79761 509m 1 1 4 7.961 0.139 2.246 15.982 0.111 2.246 15.9213 2.79761 m 2 0 4 7.961 0.139 2.246 15.982 0.111 2.246 16.4049 2.71568 68m 4 0 2 8.202 0.143 2.314 16.478 0.114 2.314 16.4049 2.71568 m -2 2 2 8.202 0.143 2.314 16.478 0.114 2.314 16.5367 2.69419 7m 4 1 1 8.268 0.144 2.332 16.613 0.115 2.332 16.5367 2.69419 m -4 1 1 8.268 0.144 2.332 16.613 0.115 2.332 17.0538 2.61307 13m 1 2 3 8.527 0.149 2.405 17.144 0.119 2.405 17.0538 2.61307 m -1 2 3 8.527 0.149 2.405 17.144 0.119 2.405 17.3679 2.56617 7m 3 2 1 8.684 0.152 2.448 17.468 0.121 2.448 17.3679 2.56617 m -3 2 1 8.684 0.152 2.448 17.468 0.121 2.448 17.9615 2.48202 1m 1 0 5 8.981 0.157 2.531 18.080 0.125 2.531 17.9615 2.48202 m -1 0 5 8.981 0.157 2.531 18.080 0.125 2.531 18.7389 2.37992 7 0 1 5 9.369 0.164 2.640 18.884 0.131 2.640 18.8769 2.36267 2m 5 0 1 9.438 0.165 2.659 19.027 0.132 2.659 18.8769 2.36267 m -5 0 1 9.438 0.165 2.659 19.027 0.132 2.659 19.023 2.34469 27 -3 1 4 9.512 0.166 2.680 19.179 0.133 2.680 19.0794 2.33782 52m 0 2 4 9.540 0.166 2.688 19.238 0.133 2.688 19.0794 2.33782 m 3 1 4 9.540 0.166 2.688 19.238 0.133 2.688 19.2709 2.31481 3 -4 1 3 9.635 0.168 2.714 19.437 0.134 2.714 19.3469 2.3058 4 4 1 3 9.673 0.169 2.725 19.516 0.135 2.725

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering159

Table C-1: Continued.

PDF4+ Data Calculated data for λ: 0.77490 Å Calculated data for λ: 0.619921 Å 2θ d I H K L θ (°) θ (radians) Q θ (°) θ (radians) Q 19.669 2.2684 34m 1 3 0 9.835 0.172 2.770 19.851 0.137 2.770 19.669 2.2684 m 4 2 0 9.835 0.172 2.770 19.851 0.137 2.770 20.0045 2.23074 7 -3 2 3 10.002 0.175 2.817 20.200 0.139 2.817 20.0595 2.22468 17 3 2 3 10.030 0.175 2.824 20.258 0.140 2.824 20.135 2.21643 8 -2 1 5 10.068 0.176 2.835 20.336 0.140 2.835 20.1958 2.20983 10 2 1 5 10.098 0.176 2.843 20.400 0.141 2.843 20.4593 2.18166 38 -2 2 4 10.230 0.179 2.880 20.675 0.143 2.880 20.5088 2.17645 21m 2 2 4 10.254 0.179 2.887 20.727 0.143 2.887 20.5088 2.17645 m 4 0 4 10.254 0.179 2.887 20.727 0.143 2.887 20.8908 2.13708 133m 5 1 2 10.445 0.182 2.940 21.127 0.146 2.940 20.8908 2.13708 m -1 3 2 10.445 0.182 2.940 21.127 0.146 2.940 21.0085 2.12524 13m 2 3 1 10.504 0.183 2.956 21.250 0.146 2.956 21.0085 2.12524 m -2 3 1 10.504 0.183 2.956 21.250 0.146 2.956 21.1445 2.11173 90 0 0 6 10.572 0.185 2.975 21.393 0.147 2.975 21.3112 2.0954 2 -5 0 3 10.656 0.186 2.999 21.568 0.148 2.999 21.3976 2.08704 1 5 0 3 10.699 0.187 3.011 21.659 0.149 3.011 22.0443 2.02653 12 0 3 3 11.022 0.192 3.100 22.340 0.154 3.100 22.1697 2.01521 2m 1 2 5 11.085 0.193 3.118 22.472 0.154 3.118 22.1697 2.01521 m -1 2 5 11.085 0.193 3.118 22.472 0.154 3.118 22.275 2.00581 8 6 0 0 11.138 0.194 3.132 22.583 0.155 3.132 22.3212 2.00171 10 3 3 0 11.161 0.195 3.139 22.632 0.155 3.139 22.4133 1.99359 8m -1 1 6 11.207 0.196 3.152 22.729 0.156 3.152 22.4133 1.99359 m -2 0 6 11.207 0.196 3.152 22.729 0.156 3.152 22.8971 1.95201 9m 5 2 1 11.449 0.200 3.219 23.242 0.159 3.219 22.8971 1.95201 m -5 2 1 11.449 0.200 3.219 23.242 0.159 3.219 23.2615 1.92184 8 -2 3 3 11.631 0.203 3.269 23.628 0.162 3.269 23.2933 1.91925 8 2 3 3 11.647 0.203 3.274 23.662 0.162 3.274 23.3481 1.91481 19 -6 0 2 11.674 0.204 3.281 23.720 0.163 3.281 23.4081 1.90997 40m 6 0 2 11.704 0.204 3.290 23.784 0.163 3.290 23.4081 1.90997 m -3 3 2 11.704 0.204 3.290 23.784 0.163 3.290 23.4397 1.90743 38m 3 3 2 11.720 0.205 3.294 23.818 0.163 3.294 23.4397 1.90743 m -6 1 1 11.720 0.205 3.294 23.818 0.163 3.294 24.0119 1.86262 7 4 1 5 12.006 0.210 3.373 24.428 0.167 3.373 24.1655 1.85096 212m -4 2 4 12.083 0.211 3.395 24.592 0.168 3.395 24.1655 1.85096 m -5 1 4 12.083 0.211 3.395 24.592 0.168 3.395 24.2647 1.8435 360m 1 3 4 12.132 0.212 3.408 24.698 0.169 3.408 24.2647 1.8435 m 4 2 4 12.132 0.212 3.408 24.698 0.169 3.408 24.6652 1.81402 2m 4 3 1 12.333 0.215 3.464 25.127 0.172 3.464 24.6652 1.81402 m -4 3 1 12.333 0.215 3.464 25.127 0.172 3.464 24.7567 1.80742 2 -3 1 6 12.378 0.216 3.476 25.225 0.172 3.476 24.8157 1.80319 3m 0 2 6 12.408 0.217 3.484 25.289 0.173 3.484 24.8157 1.80319 m 3 1 6 12.408 0.217 3.484 25.289 0.173 3.484 24.9591 1.79299 3m -1 0 7 12.480 0.218 3.504 25.443 0.174 3.504 24.9591 1.79299 m -5 2 3 12.480 0.218 3.504 25.443 0.174 3.504 25.0335 1.78775 5m 1 0 7 12.517 0.218 3.515 25.523 0.174 3.515 25.0335 1.78775 m 5 2 3 12.517 0.218 3.515 25.523 0.174 3.515 24.6652 1.81402 m -4 3 1 12.333 0.215 3.464 25.127 0.172 3.464 24.7567 1.80742 2 -3 1 6 12.378 0.216 3.476 25.225 0.172 3.476 24.8157 1.80319 3m 0 2 6 12.408 0.217 3.484 25.289 0.173 3.484 24.8157 1.80319 m 3 1 6 12.408 0.217 3.484 25.289 0.173 3.484 24.9591 1.79299 3m -1 0 7 12.480 0.218 3.504 25.443 0.174 3.504 24.9591 1.79299 m -5 2 3 12.480 0.218 3.504 25.443 0.174 3.504

160Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Table C-1: Continued.

PDF4+ Data Calculated data for λ: 0.77490 Å Calculated data for λ: 0.619921 Å 2θ d I H K L θ (°) θ (radians) Q θ (°) θ (radians) Q 24.6652 1.81402 m -4 3 1 12.333 0.215 3.464 25.127 0.172 3.464 24.7567 1.80742 2 -3 1 6 12.378 0.216 3.476 25.225 0.172 3.476 24.8157 1.80319 3m 0 2 6 12.408 0.217 3.484 25.289 0.173 3.484 24.8157 1.80319 m 3 1 6 12.408 0.217 3.484 25.289 0.173 3.484 24.9591 1.79299 3m -1 0 7 12.480 0.218 3.504 25.443 0.174 3.504 24.9591 1.79299 m -5 2 3 12.480 0.218 3.504 25.443 0.174 3.504 25.0335 1.78775 5m 1 0 7 12.517 0.218 3.515 25.523 0.174 3.515 25.0335 1.78775 m 5 2 3 12.517 0.218 3.515 25.523 0.174 3.515 25.4953 1.75589 1 -6 1 3 12.748 0.222 3.578 26.020 0.177 3.578 25.5828 1.74998 5m 6 1 3 12.791 0.223 3.590 26.114 0.178 3.590 25.5828 1.74998 m -5 0 5 12.791 0.223 3.590 26.114 0.178 3.590 25.7939 1.7359 54 6 2 0 12.897 0.225 3.620 26.342 0.180 3.620 25.8477 1.73235 20m 0 4 0 12.924 0.226 3.627 26.401 0.180 3.627 25.8477 1.73235 m -4 0 6 12.924 0.226 3.627 26.401 0.180 3.627 25.8957 1.72919 12 -2 2 6 12.948 0.226 3.634 26.453 0.180 3.634 25.9642 1.72471 6m 2 2 6 12.982 0.227 3.643 26.527 0.181 3.643 25.9642 1.72471 m 4 0 6 12.982 0.227 3.643 26.527 0.181 3.643 26.2372 1.70707 5m 0 3 5 13.119 0.229 3.681 26.823 0.183 3.681 26.2372 1.70707 m -7 0 1 13.119 0.229 3.681 26.823 0.183 3.681 26.3769 1.69819 21m 1 4 1 13.188 0.230 3.700 26.974 0.184 3.700 26.3769 1.69819 m -6 0 4 13.188 0.230 3.700 26.974 0.184 3.700 26.4446 1.69392 135 -3 3 4 13.222 0.231 3.709 27.048 0.184 3.709 26.4898 1.69108 82m 3 3 4 13.245 0.231 3.715 27.097 0.184 3.715 26.4898 1.69108 m 6 0 4 13.245 0.231 3.715 27.097 0.184 3.715 26.6266 1.68255 7m -2 1 7 13.313 0.232 3.734 27.246 0.185 3.734 26.6266 1.68255 m -4 3 3 13.313 0.232 3.734 27.246 0.185 3.734 26.6826 1.67908 4m 2 1 7 13.341 0.233 3.742 27.307 0.186 3.742 26.6826 1.67908 m 4 3 3 13.341 0.233 3.742 27.307 0.186 3.742 26.7342 1.6759 5 -6 2 2 13.367 0.233 3.749 27.363 0.186 3.749 26.8522 1.66867 45 7 1 0 13.426 0.234 3.765 27.491 0.187 3.765 26.8867 1.66657 53 5 3 0 13.443 0.235 3.770 27.529 0.187 3.770 26.9168 1.66474 52 2 4 0 13.458 0.235 3.774 27.562 0.187 3.774 27.2694 1.64361 3 -2 3 5 13.635 0.238 3.823 27.947 0.190 3.823 27.315 1.64092 5 2 3 5 13.658 0.238 3.829 27.997 0.190 3.829 27.7546 1.61543 5 -7 1 2 13.877 0.242 3.889 28.478 0.193 3.889 27.8577 1.60957 11m 2 4 2 13.929 0.243 3.904 28.592 0.194 3.904 27.8577 1.60957 m 5 3 2 13.929 0.243 3.904 28.592 0.194 3.904 28.1179 1.59497 1 -7 0 3 14.059 0.245 3.939 28.878 0.196 3.939 28.2186 1.58939 1m 1 2 7 14.109 0.246 3.953 28.989 0.196 3.953 28.2186 1.58939 m 1 4 3 14.109 0.246 3.953 28.989 0.196 3.953 28.4328 1.57766 3m 3 4 1 14.216 0.248 3.983 29.225 0.198 3.983 28.4328 1.57766 m -3 4 1 14.216 0.248 3.983 29.225 0.198 3.983 28.733 1.56152 1 -5 2 5 14.367 0.251 4.024 29.557 0.200 4.024 28.8419 1.55575 2 5 2 5 14.421 0.252 4.039 29.678 0.201 4.039 28.9627 1.5494 6m -4 2 6 14.481 0.253 4.055 29.811 0.201 4.055 28.9627 1.5494 m -5 1 6 14.481 0.253 4.055 29.811 0.201 4.055 29.0218 1.54631 7 -1 3 6 14.511 0.253 4.063 29.877 0.202 4.063 29.0673 1.54394 9m 4 2 6 14.534 0.254 4.070 29.928 0.202 4.070 29.0673 1.54394 m 5 1 6 14.534 0.254 4.070 29.928 0.202 4.070 29.3273 1.53055 25m 1 1 8 14.664 0.256 4.105 30.217 0.204 4.105 29.3273 1.53055 m 2 0 8 14.664 0.256 4.105 30.217 0.204 4.105 29.4388 1.52488 9 -6 2 4 14.719 0.257 4.120 30.341 0.205 4.120 29.5375 1.5199 18m 0 4 4 14.769 0.258 4.134 30.451 0.205 4.134

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering161

APPENDIX D: CALCULATED Q VALUES FOR GAMMA-ANHYDRITE

Scattering vector (Q) values were calculated for γ-anhydrite in the following steps:

Step 1 - Obtain γ-anhydrite crystallographic data and 2θ calculation:

Anhydrite crystallographic data was sourced from the PDF4+ database (Bezou et al., 1995). This database allowed the conversion of theta to a user input X-ray wavelength. Crystallographic data were then exported for the two wavelengths used at the Australian Synchrotron (0.77490 Å and 0.619921 Å). These results are reported under the ‘PDF4+ Data’ columns in Table D-1.

Step 2: Calculate the scattering vector (Q)

The scattering vector (Q) expected at each wavelength was calculated in Excel from the 2θ values exported from PDF4+. Theta was calculated by θ = 2θ / 2. Theta was converted from degrees to radians by: θ (radians) = θ(π / 180). Q was then calculated using the following scattering vector equation (Glatter and Kratky, 1982) (Eq. 13).

The calculated Q values for X-ray wavelengths 0.77490 Å and 0.619921 Å are reported under the ‘Calculated data’ columns in Table D-1. It should be noted that only results within the measured scattering range are reported.

162Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering

Table D-1: 2θ and calculated γ-anhydrite Q values for Synchrotron λ: 0.77490 Å and 0.619921 Å.

PDF4+ Data Calculated data for λ: 0.77490 Å Calculated data for λ: 0.619921 Å

2θ d I H K L θ (°) θ (radians) Q θ (°) θ (radians) Q 14.67 33.59 6.0388 2 0 0 7.335 0.064 1.040 7.335 0.051 1.040 14.67 66.41 6.0384 1 1 0 7.335 0.064 1.041 7.335 0.051 1.041 20.37 1.48 4.3606 1 1 1 10.185 0.089 1.441 10.185 0.071 1.441 25.55 11.91 3.4864 3 1 0 12.775 0.111 1.802 12.775 0.089 1.802 25.55 5.39 3.4862 0 2 0 12.775 0.111 1.802 12.775 0.089 1.802 29.27 3.96 3.0509 3 1 1 14.635 0.127 2.059 14.635 0.102 2.059 29.27 3.15 3.0507 0 2 1 14.635 0.127 2.060 14.635 0.102 2.060 29.59 16.85 3.0194 4 0 0 14.795 0.129 2.081 14.795 0.103 2.081 29.59 35.21 3.0192 2 2 0 14.795 0.129 2.081 14.795 0.103 2.081 32.03 16.72 2.7943 2 0 2 16.015 0.139 2.249 16.015 0.111 2.249 32.03 31.82 2.7942 1 1 2 16.015 0.139 2.249 16.015 0.111 2.249 32.89 2.01 2.7232 4 0 1 16.445 0.143 2.307 16.445 0.114 2.307 32.89 4.17 2.723 2 2 1 16.445 0.143 2.307 16.445 0.114 2.307 38.5 3.81 2.3381 3 1 2 19.250 0.166 2.687 19.250 0.133 2.687 38.5 1.31 2.338 0 2 2 19.250 0.166 2.687 19.250 0.133 2.687 41.41 1.83 2.1804 4 0 2 20.705 0.179 2.882 20.705 0.143 2.882 41.41 3.29 2.1803 2 2 2 20.705 0.179 2.882 20.705 0.143 2.882 42.1 1.25 2.1461 5 1 1 21.050 0.182 2.928 21.050 0.145 2.928 42.11 1.83 2.146 4 2 1 21.055 0.182 2.928 21.055 0.145 2.928 42.11 1.29 2.1459 1 3 1 21.055 0.182 2.928 21.055 0.145 2.928 43.05 4.39 2.1013 0 0 3 21.525 0.185 2.990 21.525 0.148 2.990 45.04 1.4 2.0129 6 0 0 22.520 0.194 3.121 22.520 0.155 3.121 45.04 1.7 2.0128 3 3 0 22.520 0.194 3.122 22.520 0.155 3.122 47.41 2.19 1.9176 6 0 1 23.705 0.203 3.277 23.705 0.162 3.277 47.41 4.6 1.9174 3 3 1 23.705 0.203 3.277 23.705 0.162 3.277 49.29 7.92 1.8487 5 1 2 24.645 0.211 3.399 24.645 0.168 3.399 49.29 8.79 1.8486 4 2 2 24.645 0.211 3.399 24.645 0.168 3.399 49.3 9.04 1.8485 1 3 2 24.650 0.211 3.399 24.650 0.168 3.399 52.49 2.59 1.7432 6 2 0 26.245 0.224 3.604 26.245 0.179 3.604 52.5 1.83 1.7431 0 4 0 26.250 0.224 3.605 26.250 0.179 3.605 54.05 5.84 1.6965 6 0 2 27.025 0.230 3.704 27.025 0.184 3.704 54.06 10.83 1.6964 3 3 2 27.030 0.230 3.704 27.030 0.184 3.704 61.41 1.43 1.5097 8 0 0 30.705 0.260 4.162 30.705 0.207 4.162 61.42 1.9 1.5096 4 4 0 30.710 0.260 4.162 30.710 0.207 4.162

Insights into the kinetics of solid gypsum dehydration from Wide- and Small-angle Synchrotron X-ray Scattering163