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Water solubility and bubble growth dynamics in rhyolitic silicate melts at atmospheric pressure Ryan, Amy 2014

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WATER SOLUBILITY AND BUBBLE GROWTH DYNAMICS IN RHYOLITIC SILICATE MELTS AT ATMOSPHERIC PRESSURE  by Amy Ryan  B.A., The Colorado College, 2010  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Geological Sciences)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)   November 2014  © Amy Ryan, 2014   ii Abstract This thesis is a high-temperature, low-pressure experimental study that quantifies the temperature-dependence of water (H2O) solubility in a rhyolitic melt at atmospheric pressure, and assesses the sensitivity of the water exsolution and bubble growth processes to thermodynamic and kinetic parameters. In the investigation of H2O solubility I defined the magnitude of retrograde solubility (-7.1x10-3 wt% H2O per 100°C) and estimated the enthalpy and entropy of the H2O exsolution reaction (ΔHo = +17.8 kJ mol-1, ΔSo = 107 J K-1 mol-1). I also modelled the implications of retrograde solubility for the glass transition temperature (Tg) and outline the potential effect on cooling volcanic bodies at surface- and conduit-relevant pressures if cooling is slow enough to facilitate H2O resorption. In my investigation of bubble growth dynamics and the vesiculation process in my experimental products I recalibrated the estimates of H2O exsolution enthalpy and entropy (ΔHo = +18.5 kJ mol-1, ΔSo = 108 J K-1 mol-1). Additionally I identified the viscosity (η) dependence of average volumetric growth rate (dV/dt) (log dV/dt = -0.79 log η + 4.95) and have calculated the time to develop 60% porosity for melts of varying viscosities at conduit-relevant pressures that are up to 15% oversaturated with H2O. By dismantling a complex system and individually investigating the behaviours of dissolved and exsolved H2O I have developed models that can be used to study volcanic hazards past, present and future.    iii Preface This thesis comprises two manuscripts based on an experimental project I completed within the Centre for Experimental Studies of the Lithosphere (CESL) during my time at UBC. Hugh Tuffen at the Environment Centre at Lancaster University donated the raw material for this study. Dr. James K. Russell proposed the experimental methodology and Elizabeth Friedlander initially tested it in 2010 as a part of her coursework at UBC.  During my MSc I replicated and expanded the initial experimental suite from 2010 and completed most analyses. Specialized imaging and analysis by fourier transform infrared spectroscopy (FTIR) was completed by collaborators Dr. Alexander R.L. Nichols at the Research and Development Center for Ocean Drilling Science at the Japan Agency for Marine Earth Science and Technology (JAMSTEC). Dr. Kai-Uwe Hess at the Department of Earth and Environmental Sciences at Ludwig-Maximilians-Universität (LMU) performed X-ray computed tomography (XCT) imaging. These results are included in both manuscripts. Dr. James K. Russell helped develop and refine the thermodynamic and kinetic modeling portion of both manuscripts, and contributed to the idea- and figure-development processes. I wrote initial drafts of each manuscript and subsequently received revisions and comments from co-authors.    A version of Chapter 2, titled ‘Experiments and models on H2O retrograde solubility in volcanic systems’, has been accepted and is in print in the journal American Mineralogist. Authors: Ryan, A.G., Russell, J.K., Nichols, A.R.L., Hess, K.-U. and Porritt, L.A.   Chapter 3 is being prepared for submission with the title ‘Bubble growth in rhyolitic melts: experiments and models’. Potential authors: Ryan, A.G., Russell, J.K., Hess, K.-U., Dingwell, D.B., and Phillion, A.B.    iv Table of Contents  Abstract .......................................................................................................................................... ii Preface ........................................................................................................................................... iii Table of Contents ......................................................................................................................... iv List of Tables .............................................................................................................................. viii List of Figures ............................................................................................................................... ix List of Symbols ............................................................................................................................ xii Acknowledgements .................................................................................................................... xiii Chapter 1: Introduction ............................................................................................................... 1 1.1 Motivation ........................................................................................................................ 1 1.2 Thesis Structure ............................................................................................................... 4 Chapter 2: Experiments and Models on H2O Retrograde Solubility in Volcanic Systems .... 6 2.1 Overview ........................................................................................................................... 6 2.2 Introduction ...................................................................................................................... 7 2.3 Materials ........................................................................................................................... 8 2.4 Experimental Methods .................................................................................................. 11 2.5 Analytical Methods ........................................................................................................ 14 2.5.1 Physical properties .................................................................................................... 14 2.5.2 XCT ........................................................................................................................... 15 2.5.3 FTIR .......................................................................................................................... 16   v 2.6 Results of High T Experiments ..................................................................................... 17 2.6.1 Porosity-time patterns ............................................................................................... 18 2.6.2 FTIR H2O maps ......................................................................................................... 20 2.6.3 Calculated H2O contents in glasses ........................................................................... 22 2.7 Discussion ....................................................................................................................... 27 2.7.1 Retrograde solubility: Comparison to published models .......................................... 27 2.7.2 Retrograde solubility: The effect on Tg .................................................................... 29 2.7.3 Implications for volcanic processes .......................................................................... 32 2.8 Implications .................................................................................................................... 37 2.9 Acknowledgements ........................................................................................................ 38 Chapter 3: Bubble Growth in Rhyolitic Melts: Experiments and Models ............................ 39 3.1 Introduction .................................................................................................................... 39 3.2 Materials ......................................................................................................................... 41 3.2.1 Starting material ........................................................................................................ 41 3.2.2 Vesiculation experiments and results ........................................................................ 41 3.3 Methods .......................................................................................................................... 44 3.3.1 3D image acquisition ................................................................................................. 44 3.3.2 Image analysis ........................................................................................................... 45 3.3.3 Data treatment and sources of error .......................................................................... 46 3.4 Results ............................................................................................................................. 49 3.4.1 Porosity ...................................................................................................................... 49 3.4.2 Bubble number density .............................................................................................. 49 3.4.3 Bubble size distribution ............................................................................................. 51   vi 3.5 Discussion ....................................................................................................................... 59 3.5.1 Nucleation dynamics ................................................................................................. 59 3.5.1.1 BND: Potential nucleation events ....................................................................... 59 3.5.1.2 BND: Sensitivity to oversaturation and temperature ........................................... 60 3.5.2 Growth dynamics ...................................................................................................... 61 3.5.3 Thermodynamic driving force ................................................................................... 63 3.5.4 Growth rates .............................................................................................................. 66 3.5.5 Implications for volcanology .................................................................................... 71 3.6 Conclusion ...................................................................................................................... 71 Chapter 4: Conclusion ................................................................................................................ 73 References .................................................................................................................................... 75 Appendices ................................................................................................................................... 86 Appendix A H2O Solubility and Surface Tension Data Compilation ................................ 86 A.1 H2O Solubility at 0.1 MPa ........................................................................................... 86 A.2 Surface Tension ........................................................................................................... 87 Appendix B Mass Loss in Samples ........................................................................................ 88 Appendix C Bubble Size Distribution for Internal Pressure Calculations ........................ 91 Appendix D Derivation of Thermodynamic Values ............................................................ 92 D.1 Enthalpy and Entropy of H2O Exsolution ................................................................... 92 Appendix E Recalculating Enthalpy (ΔH°) and Entropy (ΔS°) and Chemical Affinity (A)................................................................................................................................................... 94 Appendix F XCT Image Processing ...................................................................................... 98   vii F.1 ‘Tomoview’: Instructions ............................................................................................. 98 F.2 Image Processing Effectiveness ................................................................................. 105 F.3 Avizo® Fire: Instructions .......................................................................................... 106 Appendix G XCT Images and Histograms ......................................................................... 108 Appendix H EMP Analysis .................................................................................................. 115 H.1 Introduction ............................................................................................................... 115 H.2 Methods ..................................................................................................................... 116 H.3 Results ....................................................................................................................... 116 H.4 Interpretation ............................................................................................................. 117 Appendix I Supplementary Sample Photos and SEM Images ......................................... 119 I.1 Sample Photos ............................................................................................................. 119 I.2 SEM Images ................................................................................................................ 119 I.3 XCT Images ................................................................................................................ 121	     viii List of Tables  Table 2.1 Major anhydrous element composition of obsidian from Hrafntinnuhryggur, Krafla, Iceland. .......................................................................................................................................... 10	  Table 2.2 Experimental conditions and properties of all pre- and post-experiment cores ........... 12	  Table 2.3 Model values of residual H2O in glasses from 1 atm isothermal vesiculation experiments ................................................................................................................................... 23	  Table 3.1 Major element compositions of Hrafntinnuhryggur obsidian, Krafla, Iceland. ............ 42	  Table 3.2 Experimental conditions and physical property data by 2D and 3D image analysis for experimental products. .................................................................................................................. 48	  Table 3.3 Computed values of initial chemical affinity and measured normalized volume change at equilibrium for varying temperatures. ...................................................................................... 66	  Table 3.4 Computed values of viscosity, H2O diffusion rate and Peclet numbers at varying water contents and temperatures. ............................................................................................................ 67	  Table A.1 Compilation of all published equilibrium concentrations of H2O for a range of temperatures at atmospheric pressure. .......................................................................................... 86	  Table A.2 Compilation of all published values of surface tension (σ) between H2O bubbles and silicate melts. ................................................................................................................................. 87 Table H.1 Average composition of obsidian from Hrafntinnuhryggur, Krafla, Iceland by EMPA at UBC ........................................................................................................................................ 115      ix List of Figures  Figure 1.1 Histogram of experimental H2O solubility data for a range of melt compositions and temperatures at pressures less than 50 MPa. ................................................................................... 3	  Figure 2.1 Images of starting material and experimental run products from the 1000°C suite of experiments ..................................................................................................................................... 9	  Figure 2.2 Summary of 1 atmosphere, isothermal, vesiculation experiments .............................. 13	  Figure 2.3 Summary of experimental data from all six suites of isothermal experiments, plotted as porosity vs. time. ....................................................................................................................... 19	  Figure 2.4 Colour contour maps of residual H2O contents of glassy sample cores measured by FTIR for 1000°C experiments ...................................................................................................... 21	  Figure 2.5 Volume and H2O content changes in each sample during experiments ...................... 24	  Figure 2.6 Residual H2O contents as mole fraction and experimental temperature ..................... 28	  Figure 2.7 Isobaric H2O solubility curves predicted by Liu et al. (2005) model and plotted as T  vs. H2O content for a range of P ................................................................................................... 30	  Figure 2.8 Model isobaric (0.01 - 20 MPa) rehydration-cooling paths in volcanic systems and corresponding glass transition temperatures ................................................................................. 31	  Figure 2.9 Coupled effects of retrograde solubility and ‘rehydration quench’ in surficial deposits and within volcanic conduits ........................................................................................................ 35	  Figure 3.1 Images of starting material and experimental run products from the 1000°C suite of experiments ................................................................................................................................... 43	  Figure 3.2 XCT image processing using ImageJ and Avizo® Fire. ............................................. 46	  Figure 3.3 Porosity and bubble number density for all experimental products ............................ 50	    x Figure 3.4 Cumulative volume fraction of bubbles of a given radius at various porosities for all experimental products ................................................................................................................... 52	  Figure 3.5 BSD statistics against porosity for all experimental products ..................................... 53	  Figure 3.6 Cumulative BND against bubble radii at various porosities for all experimental products ......................................................................................................................................... 54	  Figure 3.7 Cumulative BND fraction against bubble radii experimental products in each temperature suite. .......................................................................................................................... 56	  Figure 3.8 Cumulative BND fraction against bubble radii for plateau samples in each T suite .. 58	  Figure 3.9 Thermodynamic driving force in T-suites. .................................................................. 64	  Figure 3.10 Volume of exsolved H2O and average volumetric growth rates from supersaturation and viscosity .................................................................................................................................. 68	  Figure 3.11 Average volumetric growth rates and the time to 60% porosity in T-P-H2O space .. 70 Figure 4.1 Summary cartoon of the change in dissolved H2O content, melt viscosity, bubble fraction, average volumetric growth rate and magma viscosity with depth in a rhyolitic volcanic conduit and surficial deposit..........................................................................................................73 Figure B.1 Change in sample mass (Δm) vs. change in sample volume (ΔV) for all experiments at all temperatures (900-1100°C) .................................................................................................. 90	  Figure C.1 Bubble size distribution showing volume fraction against bubble radius (mm) for three samples (4 hr, 7.5 hr, 13 hr) from the 1000°C experimental suite. ...................................... 91 Figure G.1 XCT images, histograms and bubble size distributions for all experimental products separated by temperature suite .................................................................................................... 108	  Figure H.1 Lateral variations in SiO2, Al2O3, Na2O and K2O in the starting material and experimental product .................................................................................................................. 118   xi Figure I.1 Photos of the exterior surfaces/rinds of experimental products ................................. 119 Figure I.2 SEM images of bubble shape and distribution in experimental products .................. 122 Figure I.3 XCT images of bubble populations in 1000°C plateau samples showing partial bulk collapse. ...................................................................................................................................... 123       xii List of Symbols CHAPTER 2 a constant in the Redlich-Kwong equation of state; corrects for the attractive potential of molecules b  constant in the Redlich-Kwong equation of state; corrects for volume D  diffusion rate (m2 s-1) mf  final mass (g) mi  initial mass (g) Δm  difference between initial and final mass (mg) nb  moles of exsolved H2O in bubbles (mol) ni  moles of dissolved H2O in the starting material (mol) nr  moles of dissolved H2O in the residual glass (mol) P  pressure (atm or MPa) Pe  external pressure (atmospheric pressure) (Pa) Pi  pressure within bubbles (Pa) R  universal gas constant r  radius T  temperature (°C or K) Texp  experimental temperature (°C) Tg  glass transition temperature (°C) Tg[anhydrous] anhydrous glass transition temperature (°C) Tg*  normalized glass transition temperature (°C); Tg* = Tg/Tg[anhydrous] Tmelt  melt temperature (°C) ΔT  difference between the starting and final experimental temperature (°C) t  time (h or s) Δte  time to achieve the equilibrium plateau Vf  final volume (cm3) Vi  initial volume (cm3) ΔV  difference between initial and final volume (cm3) XH2O  concentration of H2O in glass (mol fraction or wt%) ΔH°  standard state enthalpy (kJ mol-1) ΔS°  standard state entropy (J K-1 mol-1) φf  final porosity (%) φi  initial porosity (%)  η  viscosity (Pa s) ηeff  effective viscosity (Pa s) ηmelt  melt viscosity (Pa s) µH2O  chemical potential of H2O ν’  vesiculation rate (cm3 h-1); ν’=dV/dt ρf  final density (g cm-3) ρi  initial density (g cm-3)  ρm  melt density (kg m-3)   xi σ  surface tension (N m-1)  CHAPTER 3 A  chemical affinity (kJ mol-1) Ai  initial chemical affinity (kJ mol-1) BND  bubble number density (mm-3); BND=nB/Vi  BSD  bubble size distribution D  diffusion rate (m2 s-1) dV/dt  average volumetric growth rate; dV/dt=[ΔV/Vi]teq-1 LD  diffusion lengthscale (m); LD=(4Dt)0.5 nB  number of bubbles P  pressure (atm or MPa) ΔP  overpressure (Pa) Pe  Peclet number; Pe=(ΔPr2)/(ηD) r  radius (µm) T  temperature (°C or K) Tg  glass transition temperature (°C) t  time (h or s) teq  time to equilibrium concentration of H2O (s) Vi  initial volume (cm3 or mm3) ΔV  difference between initial and final volume (cm3 or mm3) ΔV/Vi  normalized volume change v’  initial vesiculation rate (cm3 h-1) ΔH°  standard state enthalpy (kJ mol-1) ΔS°  standard state entropy (J K-1 mol-1) η  viscosity (Pa s) ΣBNDf  cumulative bubble number density fraction ΣVf  cumulative volume fraction τD  diffusive timescale for H2O in the melt (s) =r2/D τη  relaxation timescale of melt (s); =η/ΔP φ  porosity (%)  APPENDIX D amH2O  activity of H2O in a melt b  y-intercept; from the equation for a line y = mx+b fvH2O  fugacity of H2O vapor K1  equilibrium constant m  slope; from the equation for a line y = mx+b P  pressure (Pa) PH2O  partial pressure of H2O (Pa) R  universal gas constant T  temperature (K) xH2O  concentration of H2O (mol fraction) ΔG°(T,P) standard state free energy change   xii ΔH°(T,P) standard state enthalpy (kJ mol-1) ΔS°(T,P) standard state entropy (J K-1 mol-1) µmH2O  chemical potential of H2O in a melt  µvH2O  chemical potential of H2O in a vapor  APPENDIX E A  chemical affinity (kJ mol-1) amH2O  activity of H2O in a melt b  y-intercept; from the equation for a line y = mx+b f vH2O  fugacity of H2O vapor f oH2O  standard state fugacity of H2O vapor KH2O  equilibrium constant m  slope; from the equation for a line y = mx+b P  pressure (Pa) PH2O  partial pressure of H2O (Pa) R  universal gas constant T  temperature (K) xH2O  concentration of H2O (mol fraction) ΔGr°  standard state free energy change of a reaction ΔG°(T,P) standard state free energy change ΔH°(T,P) standard state enthalpy (kJ mol-1) ΔS°(T,P) standard state entropy (J K-1 mol-1) µmH2O  chemical potential of H2O in a melt  µvH2O  chemical potential of H2O in a vapor ρH2O  water density  xiii Acknowledgements  First and foremost I would like to thank Kelly Russell for his support, guidance, enthusiasm and insight. Prior to this MSc I never thought I would dabble in several of the fields I have (e.g. physical chemistry, thermodynamics) and my success can certainly be attributed to your patience and encouragement. Your drive to explore and question what we think we know is inspirational and infectious.   I would also like to thank the various people who helped me get to this point including my supervisory and examining committees (Lucy Porritt, James Scoates, Mark Jellinek, Lori Kennedy, Dante Canil), coauthors (Kai Hess, Alex Nichols, Andre Phillion) and staff at UBC and LMU (Joern Unger, Doug Polson, David Jones, Sebastian Wiesmaier, Andre Schottler Himmel). Additionally a big thank you to my office mates, VPL alumni, fellow grad students and various keen friends who’ve helped to keep me inquisitive, excited and sane, particularly Luke Hilchie, Dan Gainer, Evan Smith, Stephan Kolzenburg, Dave Newton, Matt Manor, Lauren Harrison, Betsy Friedlander and Fabian Wadsworth.     A very special thank you to my undergraduate supervisor and friend Steve Quane, who is to blame for me being a geologist in the first place. Thanks for derailing me from Religious Studies 7 years ago.  Finally I would like to express my deep gratitude to my roommate, friends and family for supporting me through this crazy two years. I’m sure you’re all sick of hearing about bubbles so I’ll shut up now.    I have received funding for my MSc from AmeriCorps, the Mineralogical Association of Canada and the University of British Columbia.   1 Chapter 1: Introduction 1.1 Motivation  Water (H2O) has a profound effect on the physical properties of a silicate melt or magma. Dissolved within a melt H2O reduces the melt density, viscosity, surface tension, and solidus temperature (Goranson 1931; Friedman et al. 1963; Burnham and Davis 1971; Hess and Dingwell 1996; Zhang 1999; Gardner et al. 2013). The presence of H2O vapor-filled bubbles further reduces the bulk density and can reduce or increase the effective viscosity of a magma body depending on strain rate (Sparks 1978; Bagdassarov and Dingwell 1992; Manga et al. 1998; Robert et al. 2008; Vona et al. 2013). These physical properties exert strong control on many processes attending magma ascent, eruption and post-emplacement (Toramaru 1989; Bottinga and Javoy 1990; Proussevitch and Sahagian 1998; Sparks et al. 1999; Quane et al. 2009). It follows that a nuanced understanding of the behavior of dissolved and exsolved H2O in silicate melts is necessary to characterize many aspects of a volcanic systems.   There are three directions that studies of H2O behavior in silicate melts may take: (1) to describe the behavior of dissolved H2O exclusively by quantifying and modeling solubility limits and diffusion rates (e.g. Burnham and Jahns 1962; Dingwell et al. 1984; Zhang et al. 1991; Dixon et al. 1995; Holtz et al. 1995; Moore et al. 1998; Newman and Lowenstern 2002; Baker et al. 2005; Papale et al. 2006; Zhang et al. 2007), (2) to describe the behavior of exsolved H2O exclusively by characterizing and modeling bubble nucleation and growth dynamics (e.g. Sparks 1978; Hurwitz and Navon 1994; Toramaru 1995; Bagdassarov et al. 1996; Navon et al. 1998; Gardner et al. 2000; Mourtada-Bonnefoi and Laporte 2004; Proussevitch and Sahagian 2005; Baker et al. 2012; Gardner et al. 2013); and (3) to integrate the behaviors of dissolved and exsolved H2O to study the vesiculation process or a larger topic, such as the rheology of bubbly   2 magmas (e.g. Bagdassarov and Dingwell 1992; Manga et al. 1998; Blower et al. 2001b; Rust and Manga 2002; Llewellin and Manga 2005; Quane and Russell 2005; Robert et al. 2008; Vona et al. 2013).  Clearly each of these investigative avenues dovetails in to the next. As a result several authors have sought to couple studies of dissolved and exsolved H2O. However it can be difficult to use a single methodology for exploring different portions of the ‘H2O behavior spectrum’. For example, experimental studies of H2O solubility or bubble growth have traditionally required the use of metal capsules which inhibits the opportunity to track bubble growth, whether by in-situ imaging or by gathering data after quenching (e.g. Burnham and Jahns 1962; Burgisser and Gardner 2005; Baker et al. 2006). Some experimental studies of bubble growth are completed by analyzing the growth of previously nucleated single bubbles in glass samples, eliminating the chance to extract thermodynamic data about H2O exsolution or nucleation dynamics (e.g. Bagdassarov et al. 1996; Liu and Zhang 2000). Parametric studies of and numerical models for bubble growth dynamics often model the time-dependent concentration of H2O in the silicate melt, but H2O solubility is frequently described by oversimplified equations like Henry’s law, which does not account for changes in temperature or composition (e.g. Sparks 1978; Lensky et al. 2004; Proussevitch and Sahagian 2005). Forensic field-based studies of the vesiculation process are inherently limited by the fact that the materials available for analysis are the final products created by a potentially complex series of natural processes (e.g. Castro et al. 2005; Watkins et al. 2012; Wright et al. 2012). Well-constrained high-temperature high-pressure experimental studies are the most direct way to investigate the behavior of dissolved and exsolved H2O in silicate melts. Previous    3 Figure 1.1 Histogram of experimental H2O solubility data for a range of melt compositions and temperatures at pressures less than 50 MPa. Studies used for the histogram are listed as ‘Sources’. There is a paucity of low-pressure experimental data, which leave H2O solubility models unconstrained at conduit relevant pressures. 50 MPa approximates ~2.5 km depth assuming a magma/rock density of 2.0 g cm-3.  experimental studies cover a wide range of pressures, temperatures and compositions found in natural magmatic systems. However, low-pressure experimental studies are relatively rare, especially at 1 atm, or 0.1 MPa (Figure 1.1) (Zhang 1999; Liu et al. 2005; Robert et al. 2008; Kennedy et al. 2010). As a result many predictive H2O solubility models, derived from experimental data, are either poorly constrained (Liu et al. 2005; Zhang et al. 2007) or unconstrained at atmospheric pressure (Moore et al. 1998; Papale 1999; Yamashita 1999; Newman and Lowenstern 2002). As concentrations of dissolved H2O derived from these models are used to model other physical properties or processes, many aspects of volcanology may be inaccurately modeled at conduit-relevant conditions, here defined as <50 MPa or ~2.5 km depth (Yamashita 1999; Blower et al. 2001b; Di Matteo et al. 2004).    4 For this thesis I have undertaken a coupled study of H2O solubility and bubble growth dynamics at atmospheric pressure in order to fill gaps in the current body of literature. Using a natural H2O-oversaturated rhyolitic obsidian and a simple experimental methodology (i.e. unjacketed foaming experiments (c.f. Figure 2.1)) I have been able to explore the behavior of both dissolved and exolved H2O at a range of elevated temperatures and atmospheric pressure. This experimental study is unique because of the simplicity of the methodology, the low-pressure experimental conditions, and the use of non-destructive 3D X-ray computed tomography (XCT) to image and analyze bubble populations that result from high-temperature foaming experiments. By using non-destructive analytical techniques the utility of each experimental product is increased, which ultimately allows for simultaneously quantification of H2O solubility and bubble nucleation and growth dynamics at atmospheric pressure in a single suite of experiments.   1.2 Thesis Structure This thesis has two chapters that separately explore the behaviors of dissolved and exsolved H2O in a single experimental dataset: Chapter 2 constrains the change in the solubility limit of dissolved H2O within a homogeneous rhyolitic melt with temperature at atmospheric pressure, and outlines the implications of the temperature dependence of H2O solubility in the greater field of volcanology. Chapter 3 addresses the mechanisms of H2O vapor exsolution through the lenses of bubble nucleation and bubble growth dynamics at atmospheric pressure. The dovetailing nature of these two topics of course leads to some redundancies within the chapters, but also presents the opportunity to speculate about the coupled effect of dissolved and exsolved H2O on magma rheology. This is addressed in the concluding chapter.   5 There are seven appendices of supplementary material pertinent to the material presented in Chapters 2 and 3. Appendix A includes a table of all available H2O solubility data at atmospheric pressure, as well as published surface tension measurements/calculations for silicate melts. Appendix B contains additional information about the experimental method. Appendix C is a rough bubble size distribution, used to derive a mean bubble size for calculations in Chapter 2. Appendix D includes the series of equations used to extract estimates for the enthalpy and entropy of H2O exsolution from Chapter 2. Appendix E includes the equations used to recalculate the enthalpy and entropy of H2O exsolution from Chapter 3, as well as the equations to calculate chemical affinity. Appendix F is a set of instructions for running the MATLAB-based ‘Tomoview’ and Avizo® Fire image processing programs described in Chapter 3, as well as an overview of the effectiveness of various image processing programs. Appendix G is a collection of supplementary XCT images and histograms for materials used in Chapter 3. Appendix H contains compositional data for the starting material and experimental products measured by electron microprobe analysis at the University of British Columbia. Appendix I is a collection of supplementary photographs, scanning electron microscope images and XCT images.    6 Chapter 2: Experiments and Models on H2O Retrograde Solubility in Volcanic Systems 2.1  Overview We present a suite of 36 high-temperature (900-1100°C), experiments performed on 10 x 10 mm unjacketed cores of rhyolitic obsidian from Hrafntinnugryggur, Krafla, Iceland under atmospheric pressure. The obsidian is bubble- and crystal-free with an H2O content of 0.11(4) wt%. The obsidian cores were heated above the glass transition temperature (Tg), held for 0.25-24 hours, then quenched. During the experiment the volume of the samples increased as H2O vapour-filled bubbles nucleated and expanded. Uniquely, the bubbles did not nucleate on the surface of the core, nor escape, conserving mass during all experiments. Within each isothermal experimental suite, the cores increased in volume with time until they reached a maximum, after which continued heating caused no change in volume (measured by He-pycnometry). We interpret these T-t conditions as representing thermochemical equilibrium between the melt and exsolved vapour. These experiments are modelled to recover the 1 atmosphere, temperature-dependent solubility of water in the rhyolite melt. Our results define the magnitude of retrograde solubility (-7.1x10-3 wt% H2O per 100°C) and provide estimates of the enthalpy and entropy of the H2O exsolution reaction (ΔHo = 17.8 kJ mol-1, ΔSo = 107 J K-1 mol-1).  We conclude by modelling the implications of retrograde solubility for the glass transition temperatures (Tg) of cooling volcanic systems at pressures relevant to volcanic conduits and the Earth’s surface. All volcanic systems cool; the effects of retrograde solubility are to allow melts to rehydrate by H2O dissolution as they cool isobarically, thereby depressing   7 Tg and expanding the melt window. Ultimately, the melt is quenched at higher H2O contents and lower temperatures when the isobaric retrograde solubility curve ‘catches’ the evolving Tg.    2.2 Introduction  All magmas contain dissolved volatiles that strongly affect the thermodynamic and physical properties of melt and dramatically influence magmatic and volcanic processes (Navon et al. 1998; Mysen and Acton 1999; Sparks et al. 1999; Gardner et al. 2000; Di Matteo et al. 2004; Zhang et al. 2007; Giordano et al. 2008). Exsolution of a fluid phase, where the dissolved volatile reaches supersaturation, affects the bulk properties of magmas, drives many volcanic eruptions, and controls the duration, magnitude, rate and style of eruption (e.g., effusive vs. explosive) (Webster and Botcharnikov 2011; Watkins et al. 2012). Water (H2O) is the most prevalent, and usually the dominant, volatile species in volcanic systems making the low pressure solubility limits of H2O in silicic melts relevant to many eruptive and post-eruptive volcanic processes (Sparks et al. 1999; Castro et al. 2005; Robert et al. 2008; Kennedy et al. 2010).   There are a plethora of H2O solubility studies on melts at pressures >50 MPa (Burnham and Jahns 1962; Silver et al. 1990; Dixon et al. 1995; Carroll and Blank 1997; Moore et al. 1998; Yamashita 1999; Holtz et al. 2000; Newman and Lowenstern 2002; Papale et al. 2006; Zhang et al. 2007). There are, however, surprisingly few lower pressure (i.e. < 5 MPa) studies of H2O solubility in silicate melts (Friedman et al. 1963; McMillan et al. 1986; Silver et al. 1990; Liu et al. 2005). This lack of data has been pointed out by numerous authors, including Zhang (1999), Liu et al. (2005), Robert et al. (2008) and Kennedy et al. (2010), yet the data gap persists. A compilation of all 1 atmosphere, H2O solubility data is presented in Appendix A and comprises   8 28 values deriving from three experimental studies. These experiments are particularly important for two reasons. Firstly these pressures correspond to a wide variety of volcanic environments (conduits, domes, ignimbrites, lavas) and thus a range of processes (welding, sealing/permeability collapse and flow dynamics). Secondly, these low pressure solubility experiments are critical for constraining models of H2O solubility in silicate melts as a function of temperature, pressure, and composition (Yamashita 1999; Di Matteo et al. 2004; Liu et al. 2005).   Here we present a series of 0.1 MPa, high-temperature (T) experiments wherein cores of obsidian are heated isothermally above the glass transition temperature (Tg) for controlled amounts of time. These experiments allow progressive bubble nucleation and growth with time until thermochemical and mechanical equilibria between the melt and the exsolved H2O fluid are reached (Figures 2.1 and 2.2). Thus, each series of isothermal experiments illustrates the rates of volatile exsolution (volume change) and, ultimately, defines the solubility of H2O in the rhyolite melt at atmospheric pressure (Figure 2.2a). These experiments have been used to create a thermodynamic model for the 0.1 MPa temperature dependence of H2O solubility (retrograde solubility). Furthermore, we explore the effects of retrograde solubility on Tg: resorption of H2O during cooling depresses Tg thereby expanding the ‘melt window’ in volcanic systems and causing melts to quench at higher H2O contents and lower temperatures.  2.3 Materials Our experiments use rhyolitic obsidian from Hrafntinnugryggur, Krafla, Iceland as described and chemically analysed by Tuffen and Castro (2009) (Table 2.1). Their work showed the Hrafntinnugryggur obsidian sampled from a <0.05 km3 outcrop to have a uniform major    9  Figure 2.1 Images of starting material and experimental run products from the 1000°C suite of experiments. Photographs of (a) the undeformed starting material and experimental run-products (b,c,d). Calculated final porosities and dwell time are listed in the upper left corner of the images. The scale bar at right in photos is marked in mm. X-ray computed tomography (XCT) images from the center of the starting material (e) and the same experimental products (f,g,h). The field of view in each XCT image is 18.2 mm across. The initial heterogeneity in the distributions of bubbles (b,f) is related to cryptic flow banding in the starting material (see text for explanation).  element chemical composition independent of a diversity of outcrop textures and colors. They reported, based on synchrotron Fourier transform infrared spectroscopy (FTIR) analysis, that the H2O contents across the outcropping of Hrafntinnugryggur obsidian varied from 0.11-0.37 wt%. They argued that the variability in H2O content was a reflection of differences in post-eruption quench paths (Tuffen and Castro 2009).   10   S11ba UBC-Std4b Method EMPA XRF SiO2 75.23 74.77 TiO2 0.23 0.23 Al2O3 12.00 12.31 Fe2O3 - 0.69 FeO 3.28 2.48 MnO 0.11 0.11 MgO 0.10 0.14 CaO 1.66 1.64 Na2O 4.15 4.28 K2O 2.75 2.60 P2O5 - 0.03 Total 99.51 99.28 FeOT 3.28 3.10 aElectron microprobe analysis of glass (Tuffen and Castro, 2009). bBulk XRF analysis of glass by ALS-Chemex.  Table 2.1 Major anhydrous element composition of obsidian from Hrafntinnuhryggur, Krafla, Iceland.  All experimental cores for this study derive from a single ~1000 cm3 block of pristine obsidian donated by Hugh Tuffen (pers comm 2008). The starting glass is texturally isotropic and homogeneous except for minor occurrences of cryptic flow-banding, and is essentially bubble- and crystal-free. Table 2.1 is a comparison of the anhydrous bulk chemical composition of the obsidian block measured by X-ray fluorescence to the electron microprobe (EMP) measured composition of Tuffen and Castro (2009). Independently, we have measured the water content of the obsidian block by FTIR (see below) to be 0.11(4) wt% and adopt this value for our work below (Table 2.1).  Cylindrical sample cores of obsidian (10 x 10 mm) were drilled, trimmed, and the ends ground to make parallel polished end-surfaces (Figure 2.1).  The cores were then dried at ~150°C   11 for 2 to 24 hours prior to measuring core volume (Vi) with precision digital callipers (σ ± ~2x10-3 cm3) and mass (mi) with a high precision balance (σ ± ~0.006 mg) (Table 2.2). The average density (ρi) of the starting material, based on 43 cores, was 2.394 g cm-3 (σ ± ~0.024 g cm-3). The porosity (φi) of the initial obsidian cores is below detection.   2.4 Experimental Methods A total of 36 high-temperature, 1-atmosphere experiments were performed on cores of obsidian in a Nabertherm HTC 08/15 furnace (Figure 2.2b). Each experiment had a prescribed dwell time ranging from 0.25-24 hours at a constant experimental temperature (Texp) varying from 900-1100°C (Figure 2.2b; Table 2.2). Our range of Texp is > 100°C above the calorimetric glass transition temperature (Tg = 690°C ± 20) of the Hrafntinnugryggur obsidian as determined by (J. M. Castro et al. 2008). The obsidian cores were placed into the furnace on a pre-heated ceramic base thereby ensuring that the obsidian cores heated uniformly once they were in the furnace (i.e. the ceramic plate did not behave as a heat sink). Two independent K-type thermocouples were used to monitor the internal temperature of the furnace and showed the temperature to be ±5-10°C of its set temperature. Once the prescribed dwell time was reached the ceramic plate and vesiculated obsidian core were removed from the furnace allowing them to quench to below the nominal Tg (i.e. 690°C) within 10-15 seconds (measured by thermocouples). There was no change in the geometry of the expanded glass cores during cooling (Figure 2.1).      12 LABEL Texp (°C) t (h) mi (g) mf (g) ρf (g cm-3)a ΔV (cm3) ϕf (%)b AR-IK-28 0 0 1.702 1.702 2.394 0 0 AR-IK-39 900 5.0 1.600 1.600 2.372 0.02 3.07 AR-IK-40 900 7.5 1.575 1.575 2.056 0.12 15.15 AR-IK-46 900 9.0 1.571 1.570 2.053 0.12 15.10 AR-IK-54 900 12.3 1.824 1.824 1.856 0.23 23.34 AR-IK-49 900 13.0 1.953 1.952 2.105 0.11 11.56 AR-IK-52 900 16.8 2.210 2.209 1.807 0.30 24.66 AR-IK-24 900 20.0 1.639 1.637 1.344 0.53 43.25 AR-IK-50 900 24.0 1.764 1.763 1.340 0.56 42.77 AR-IK-44 925 2.5 1.676 1.676 2.313 0.03 4.24 AR-IK-42 925 5.0 1.732 1.731 1.797 0.25 25.71 AR-IK-43 925 12.0 1.713 1.712 1.462 0.47 39.74 AR-IK-45 925 20.0 1.827 1.826 1.188 0.78 50.60 AR-IK-51 925 24.0 1.612 1.611 1.415 0.46 40.24 AR-IK-10 950 1.5 1.720 1.719 1.916 0.16 18.25 AR-IK-7 950 4.0 1.676 1.675 1.215 0.67 48.83 AR-IK-48 950 6.0 1.654 1.653 1.131 0.78 53.36 AR-IK-11 950 12.5 1.648 1.647 1.007 0.94 57.41 AR-IK-25 950 20.0 1.872 1.871 1.100 0.92 53.87 AR-IK-21 1000 0.5 1.675 1.675 1.901 0.19 21.23 AR-IK-17 1000 1.5 1.617 1.617 1.275 0.59 46.54 AR-IK-22 1000 1.5 1.819 1.817 1.109 0.88 53.71 AR-IK-16 1000 2.5 1.632 1.630 0.796 1.37 66.69 glass 4 1000 4.0 2.324 2.322 0.895 1.58 60.74 AR-IK-12 1000 4.0 1.716 1.714 0.906 1.17 61.64 AR-IK-20 1000 4.0 1.714 1.713 0.888 1.22 63.05 AR-IK-34  1000 4.0 1.728 1.726 0.799 1.43 66.40 AR-IK-18 1000 7.5 1.531 1.529 0.822 1.22 65.80 AR-IK-27 1000 13.0 1.884 1.883 0.936 1.22 60.87 AR-IK-32 1050 0.5 1.736 1.736 1.950 0.17 18.80 AR-IK-33 1050 1.2 1.734 1.733 1.008 1.00 58.17 AR-IK-47 1050 3.0 1.680 1.679 0.843 1.30 65.22 AR-IK-23 1050 4.0 1.701 1.699 0.712 1.68 70.42 AR-IK-35 1050 5.0 1.726 1.724 0.759 1.54 68.00 AR-IK-30 1100 0.5 1.731 1.730 1.115 0.85 54.92 AR-IK-31 1100 1.0 1.730 1.728 0.696 1.78 71.60 AR-IK-36 1100 2.0 1.725 1.723 0.762 1.54 67.91 aMean density (2.394 g cm-3) is based on an initial porosity below detection. bϕf = 100 ΔV/Vf , where Vf is the final volume.  Table 2.2 Experimental conditions and properties of all pre- and post-experiment cores including: time (t), initial and final mass (m), final density (ρf), volume change (ΔV) and final porosity (ϕf)   13 Figure 2.2 Summary of 1 atmosphere, isothermal, vesiculation experiments. (a) Conceptual diagram of experiments showing a single curve recording volume change as a function of time at fixed T. Individual experiments for prescribed dwell times plot as points defining segments of curve: initial state, rapid growth as system expresses its supersaturated state, decreasing growth as system approaches equilibrium, and cessation of exsolution/constant bubble volume at equilibrium. (b) The experimental grid for all experiments plotted as T vs. t. Each isothermal suite of experiment comprises 3 to 10 runs at different dwell times.  In order to prevent fracturing of the cores when they were introduced into the furnace we modified our procedure for the high T (>1000°C) suites of experiments. Specifically, the cores were introduced into the furnace at lower temperatures and then heated slowly (5-12.5°C min-1) to Texp. Replicate experiments involving isothermal heating at Texp vs. ramping up to Texp produced cores with equivalent density, indicating that the final vesiculation was a product only of Texp and time.  We performed two other ancillary experiments. The first tested the influence of sample dimensions and surface roughness on the vesiculation process and vesicle retention. For this experiment (glass 4; Table 2.2) an angular chip of obsidian featuring smooth conchoidal fracture surfaces was allowed to vesiculate using the same method described above. Replicate T-t time volume change  (a)water solubility limitexsolution/bubblegrowthequilibrium plateauConstant T0 5 10 15 20 25900 950 1000 1050 1100 t (h)T (o C)(b)  14 experiments involving the obsidian chip and two sample cores produced products having identical (± 0.01 g cm-3) densities. We take this agreement to indicate that the machined surfaces of the cores do not change the bulk behaviour of the material by facilitating H2O escape or enhancing vesiculation (Appendix I). We also ran three reversed experiments at 950°C, 1000°C and 1050°C to test the reproducibility of our results (e.g. AR-IK-34, AR-IK-47 and AR-IK-48). The reversed experiments approached the final vesiculated state from lower and higher temperatures to test that the state is path-independent. Samples were introduced at temperatures below Texp, then heated above Texp and allowed to vesiculate for 0.25-1 hours. Presumably at this point the cores exsolved more H2O due to a decrease in solubility relative to Texp. The cores were then cooled back down at a rate of 2-3°C min-1 to Texp and allowed to dwell at Texp for 0.5-2.5 hours. The samples were removed and quenched as described above. The reversed experiments have densities that vary by ~0.1 g cm-3 from the ‘unreversed’ experimental products (points on the equilibrium plateaus at 950°C, 1000°C and 1050°C (Table 2.2)). Thus, the final density of the sample is not greatly influenced by the T-path of the experiment, but rather is dependent on Texp and dwell time. This, however, would not be valid for T-t curves in the growth regime because the slopes of the growth curves are different for different T’s, and the total time would be an integrated path of one growth curve plus another (Figure 2.3).   2.5 Analytical Methods 2.5.1 Physical properties For each experimental run product we measured final mass (mf ) and volume (Vf ) (Table 2.2); volumes of the irregular swollen cores (Figure 2.1) were measured with a Micromeritics   15 AccuPyc II 1340 helium pycnometer having an analytical uncertainty ± 0.04%. Masses were measured with a high precision balance (σ ± ~0.006 mg). The final density (ρf) of the materials was derived from these two measurements. The propagated uncertainties on the calculated values of density, volume change, and porosity are ~6x10-4 g cm-3, 0.02 cm3 and 1.38%, respectively and are corroborated by replicate measurements.  2.5.2 XCT  We selected a suite of twenty three undeformed samples and experimental run products for imaging by X-ray computed tomography (XCT) and for parallel analysis of water contents by FTIR. XCT 3D high-resolution images were acquired using a GE phoenix® v|tome|x s 240 micro-CT scanner at the Institute of Medical Engineering at the Technische Universitat Munchen (IMETUM) facility, Germany using a high-power X-ray tube and a drx-250 rt detector system. Experimental conditions: 1000 images for 360° (average of 3 single images, one image skipped), exposure time: 333 ms, voltage: 80 kV, current: 130 µA, using a 0.2 mm VA-steel filter.   The resulting set of radiographs was then used to generate a 3D image using the inverse radon transformation (Deans, 2007); the resulting object has a 18.5 µm voxel size. The resulting raw 2D and 3D TIFF images were then processed using ImageJ (Abramoff et al. 2004; Schneider et al. 2012) to optimize contrast in the greyscale images (Figure 2.1). To isolate bubble populations within the sample for further analysis, the individual datasets were then segmented and analyzed using the Avizo® Fire program (version 8) by the FEI Visualization Sciences Group. These analyses were used to calculate an average bubble radius between all samples (0.322 mm; Appendix C) for subsequent internal pressure calculations (see below).   16 2.5.3 FTIR Six samples, including the starting glass and glassy run products, were prepared as 100-330 µm-thick wafers and analyzed by FTIR for total water content at the Institute for Research on Earth Evolution (IFREE) at the Japan Agency for Marine Earth Science and Technology (JAMSTEC). Analyses were performed in the mid-IR region over 512 scans at a resolution of 8 cm-1 using a heated ceramic (globar) infra-red source, a Ge-coated KBr beamsplitter and a liquid-nitrogen cooled HgCdTe2 (MCT) detector. The wafers were placed on an H2O-free IR-invisible KBr window. Background analyses were taken through the window, before the wafer of glass was positioned in the beam path to measure sample spectra. The results are H2O contents averaged from eleven to sixteen individual ‘spot tests’ on the starting material and five experimental products from the 900°C, 950°C, 1000°C, 1050°C and 1100°C temperature suites (AR-IK-24, AR-IK-25, AR-IK-18, AR-IK-23, AR-IK-31) (Table 2.3). H2O contents (wt%) were calculated using the height above a linear baseline of the peak at 3550 cm-1, a density for rhyolite of 2350 g l-1 (Stevenson et al., 1994), a molar absorption coefficient of 90 l mol-1 cm-1 for rhyolite (Hauri et al., 2002) and thickness estimated from the peak at 1830 cm-1 (following Miwa and Toramaru, 2013). Thickness was not measured directly due to the fragility of the experimental products and the difficulty of positioning the measuring needle on the analyzed spot due to the small areas of glass between vesicles.  In addition, 2D micro-distributions in water content were measured in five samples (Figure 2.4) including the starting material (AR-IK-UND) and four duplicated experimental run products from the 1000°C experimental suite: BF-IK-16, heated for 0.5 hours to a final porosity of 40.7%; BF-IK-2, heated for 1.5 hours to a final porosity of 57.6%; BF-IK-1, heated for 2.5 hours to a final porosity of 62.0%; and BF-IK-3.5, heated for 6 hours to a final porosity of 66.5%   17 (Figure 2.4). Wafers of these samples were prepared to a thickness of 200-330 µm and color contour FTIR spectroscopic images of the residual H2O content were collected using the same set up as above and a liquid-nitrogen cooled Focal Plane Array (FPA) MCT detector. The FPA MCT detector produces 350 x 350 µm images each made up of 4096 spectra, giving a resolution of about 5.5 µm. Five to twenty of these images were combined to produce mosaics covering larger areas (von Aulock et al., 2013). H2O contents (wt%) were calculated from spectra as for the spot tests. Thus images of the 3550 cm-1 peak normalized by the 1830 cm-1 peak, assuming constant density and molar absorption coefficients (i.e., compositional homogeneity), are proportional to actual H2O concentration and take into account any change in thickness across a wafer (von Aulock et al., 2014). There are imaging artefacts related to the use of this technique which produce high-H2O concentration rims around the edge of bubbles. This is likely related to the thinning of the glass at the edge of the bubbles, which may effect absorption.  2.6 Results of High T Experiments  Exposure to temperatures above Tg (900-1100°C) produces variably expanded bubble-rich run products featuring smooth outer surfaces free of scalloping (Figure 2.1). The high-T experiments cause exsolution of volatiles in the obsidian because the Icelandic glasses were initially quenched with water contents above their 1 atmosphere solubility limits. The extent of exsolution of H2O fluid at constant T is manifest by a change in volume (increased porosity) that depends on the experimental dwell time and on the 1 atmosphere solubility of H2O at that T (Figure 2.1). The bubbles formed are assumed to be 100% H2O.  The range in ΔV is 0.02-1.78 cm3 and is a direct indication of bubble formation and growth (Table 2.2). Mass changes (Δm) between the starting core and final cooled experimental   18 product are small but quantifiable (0.19 to 2.26 mg) and are positively correlated to ΔV (Appendix B). We ascribe the mass loss to the escape of the exsolved H2O upon quenching as a result of microfracturing in the cores (see Appendix B). The smooth exterior surfaces of the cores and the bubble distributions illustrated by XCT (Figure 2.1) indicate that the bubbles form  and grow during the experiment but fail to perforate the core walls to degas. This fact allows us to treat each experiment as a closed system where the original H2O is conserved and partitioned between the bubbles and the residual melt. The corollary to this is that all volume change is a direct proxy for the volumetric amount of volatile exsolution at 1 atmosphere and T in a fixed amount of time (Figure 2.3).  2.6.1 Porosity-time patterns   Each isothermal suite of experiments shows a systematic increase in sample volume, expressed as porosity (φf), with increasing dwell time (t) until a maximum stable sample volume (e.g. porosity) is attained (Figure 2.2a, 2.3). We interpret the initial increase in sample volume (the curvilinear portion in Figure 2.2a; 2.3) to be the kinetically controlled bubble nucleation and growth regime and a response to an initial H2O-oversaturation at 1 atm and Texp. The plateau in sample volume (the horizontal portion of curve in Figure 2.2a; 2.3) marks the cessation of exsolution and bubble growth and is due to equilibrium being reached. This fixed maximum porosity is indicative of the H2O solubility limit for that temperature at 1 atm. In this way we use volume change as an expression of the amount of H2O that is exsolved from the melt to achieve equilibrium. Thus, porosity is inversely proportional to the equilibrium concentration of H2O in the glass.  The rate of change of sample volume (v' = dV/dt) and the time (Δte) to achieve the equilibrium plateau depend on experimental temperature. Specifically, the value of v' and Δte are    19    Figure 2.3 Summary of experimental data from all six suites of isothermal experiments, plotted as porosity (φf) vs. time (t), including starting material (at t=0): (a) 900°C, (b) 925°C, (c) 950°C, (d) 1000°C, (e) 1050°C, (f) 1100°C (cf. Table 2.2). Each isothermal suite of experiments shows a non-linear increase in porosity with t defining a monotonic sharply increasing curve that reaches a final plateau. With increasing T, the peak growth rate (ν’) increases (as calculated from the maximum slope of the curve). The final plateau value of H2O (grey bar) also increases with increasing temperature. For several suites (e.g. 925°C), the last datum shows a slight relative decrease in porosity, suggesting partial collapse of the sample as the dwell times approach the relaxation timescale of the melt. In all cases analytical uncertainties (1σ) fit within symbols. Also reported are the computed values of viscosity (η; Giordano et al. 2008) and diffusion rate of H2O (D; Zhang et al. 2007) at the experimental temperatures based on the measured H2O content of 0.11 wt%.  quantified by the slope and length of tangent lines to the curvilinear portions in Figure 2.3. At higher temperatures sample volume increases rapidly (v', steep slope) and the plateau is reached in a short amount of time (Δte, e.g., 1-2 hours at 1050°C; Table 2.2, Figure 2.3). At lower ! "! #! $!"!%$!%&!%'!%(%)*+q% ,%%)-+).+/!!%01203%d%4%56#$%)7.%8+9%4%:6:5;ï"$%)<#8ï"+=>%4%!6!$%?<$@*6%(A=>v’BΔteB! & "! "& #! #&"!%$!%&!%!!%"%)#+q% $%%)-+)%+&#&%'()'*%d%+%!6,!%)-.%/+0%+%&6:"1ï"$%)2#/ï"+3D+%!6!4%52$@#! 6 "! "6 #!"!%$!%6!%'!%!%)"+q% #%%)-+)?+/$!%%1&%'%d%4%'6$$%)7.%(+9%4%)6$;ï"$%)*#(ï"++,%4%!6"5%?*$@"! $ "!"!%$!%$!%'!%!%)"+q% #%%)-+)-+"!!!%%.&%'%d%/%)60!%)12%(+3%/%06"4ï"$%)*#(ï"++,%/%"6!0%5*$@"! " # $ : &"!%$!%&!%!!%(%)*+q% ,%%)-+"!&!%01203%d%4%66$:%)7.%8+9%4%"6$;ï"#%)<#8ï"+=>%4%!6/$%?<$@*)A+(e)B! !6$ " "6$ #"!%$!%$!%7!%!%)"+q% #%%)-+""!!%$%&$'%d%(%)6*$%)+,%-+.%(%"6/0ï"#%)1#-ï"+23%(%#6*#%41$@")#+(f)BRyan t al. (2014) FIGURE 3  20 temperatures the bubble nucleation and growth rates are substantially slower (flatter slope) and it takes longer to reach the equilibrium plateau (e.g., 20-25 hours at 900°C; Table 2.2, Figure 2.3). The variations in the porosity-time patterns show the relationship between bubble growth rates and temperature and are reflections of the effect of temperature on melt viscosity (η). More importantly for this research, the final plateau value of the φf-t curves increases with experimental temperature, from ~42% at 900°C to ~70% at 1100°C (Table 2.2, Figure 2.3). Thus the maximum porosity value is inversely proportional to T and is a qualitative expression of the retrograde solubility of H2O.    Some of the longest-term experiments do show signs of partial collapse. For example, in the 925°C suite of experiments (Figure 2.3b), the core volume is reduced by 10% in the 4 hours of dwell time after reaching the equilibrium solubility limit. This additional time at Texp is enough to allow for some viscous relaxation of the sample, especially given the effect of porosity on the effective viscosity of the core (Quane et al. 2009). A porosity of 50% reduces the predicted bulk viscosity of the core by an order of magnitude (log ηmelt: 7.90 Pa s (Giordano et al. 2008); log ηeff: 7.10 Pa s (Quane et al. 2009)) thus decreasing the relaxation timescale of the vesicular core and facilitating partial collapse. That said, not all cores experience collapse. The 1000°C suite of experiments are stable for 13 hours; 7 hours after reaching the equilibrium plateau the sample shows an apparent porosity decease of less than 2-3%.  2.6.2 FTIR H2O maps FTIR contour maps were created for polished wafers cut from cores of starting material and the run products of the 1000°C experiments held at Texp for 0.5, 1.5, 2.5 and 6 hours (Figure 2.4). The H2O contour map for the starting material shows a weak (<0.01 wt%) variation of H2O content, creating relatively ‘water-rich’ and ‘water-poor’ bands 100-200 µm in width (Figure   21 2.4a). At shorter run durations, the banding has a minor influence on bubble nucleation behaviour and bubble distribution (Figure 2.1b,f), however, with increasing time the run products show homogeneous H2O-distributions (Figure 2.4b,c,d,e). This indicates that over the dwell time of the experiments the dissolved H2O is readily mobilized to produce a homogeneous distribution of residual H2O. Figure 2.4 Colour contour maps of residual H2O contents of glassy sample cores measured by FTIR for 1000°C experiments: (a) starting material (t=0), (b) t=0.5 h, (c) t=1.5 h, (d) t=2.5 h, (e) t=6 h. Final porosity is shown in parentheses. Photos of the glass wafers used for analysis are shown next to each map with a red box showing the analysis location. The colour scale bar denotes H2O content. The starting material is weakly inhomogeneous and shows diffuse banding correlative with slight variations in H2O content. Experimental products on the other hand show nearly homogeneous distributions of H2O in the sample, even after only 0.5 h at 1000°C. Circular high or low H2O content areas are bubbles that either intersect or lie just below the surface of the glass wafer. The high H2O content rims around these bubbles are artefacts of the variable thickness of the glass at the edge of the bubble (see text for explanation). All scale bars are 350 µm for FTIR contour maps, and 5 mm for photos of glass wafers.  As stated above, we attribute the high H2O concentration rims to artefacts related to the imaging process. To verify this assumption we have assessed the potential for diffusion-limited resorption of H2O from the bubbles to the melt during the quenching of the samples: using the relationship between diffusion coefficients (D), time (t) and diffusion length scale (LD) (LD = 0 hr (0%)0.5 h (40.7%)1.5 h (57.6%)2.5 h (62.0%)6 h (66.5%)0.200.000.100.050.15total H 2 O(a)(b)(c)(d)(e)Ryan t al. (2014) FIGURE 4  22 (4*D*t)0.5) we expect trivial effective diffusion length and thus an insignificant amount of rehydration.    FTIR spot analyses of the starting material and experimental products at equilibrium at 900°C, 950°C, 1000°C, 1050°C and 1100°C quantify the equilibrium concentration of H2O in the rhyolitic glass at 1 atm for these temperatures. These measurements show a change in the H2O content of the residual glass with increasing Texp from an initial 0.114 wt%  (s.d. 0.013) to 0.098 wt% (s.d. 0.010), 0.087 wt% (s.d. 0.009), 0.093 wt% (s.d. 0.008), 0.090 wt% (s.d. 0.006) and 0.108 wt% (s.d. 0.010) for 900°C, 950°C, 1000°C, 1050°C and 1100°C respectively (Table 2.3).  The 2D FTIR contour maps are most useful for demonstrating the homogeneous distributions of H2O in the run products. Unfortunately, the individual spot analyses are not precise enough to quantify the changes in H2O contents. The lack of precision is at least partly due to the complexity of measuring highly vesicular samples.  2.6.3 Calculated H2O contents in glasses  In our analysis of the experimental data we assume that volume expansion of the sample results only from bubble formation and expansion and that thermal expansion of the melt  (potentially captured during quenching) can be neglected. This assumption is justified because the maximum volume change predicted for the melt being heated to 1100°C is 0.65% (Bagdassarov and Dingwell, 1992), which is within our measurement uncertainties for porosity  (1.38%). Similarly, we ignore the potential slight variations in glass density caused by different quench rates (nature vs. experiment; Vollmayr et al. 1996). Here, we use the volume change (ΔV; Figure 2.5a) to compute the total H2O exsolved from the melt at the experimental conditions by determining the internal pressure of the bubbles (Pi) and using the Redlich-Kwong equation of   23  Measured Properties Calculated Properties Sample H2Oc  mid ΔV (m3) ϕf (%)e nif  nbg nrh H2Ogf ΔH2Oi AR-IK-28 0.114 1.702 0 0 1.08E-04 - - 0.114  AR-IK-39  1.600 2.07E-08 3.07 1.01E-04 2.16E-07 1.01E-04 0.114  AR-IK-40  1.575 1.16E-07 15.15 9.97E-05 1.21E-06 9.85E-05 0.113  AR-IK-46  1.571 1.16E-07 15.10 9.94E-05 1.21E-06 9.82E-05 0.113  AR-IK-54  1.824 2.29E-07 23.34 1.15E-04 2.39E-06 1.13E-04 0.112  AR-IK-49  1.953 1.07E-07 11.56 1.24E-04 1.12E-06 1.22E-04 0.113  AR-IK-52  2.210 3.01E-07 24.66 1.40E-04 3.15E-06 1.37E-04 0.111  AR-IK-24 0.098 1.639 5.27E-07 43.25 1.04E-04 5.50E-06 9.82E-05 0.108 -0.010 AR-IK-50  1.764 5.63E-07 42.77 1.12E-04 5.88E-06 1.06E-04 0.108  AR-IK-44  1.676 3.07E-08 4.24 1.06E-04 3.14E-07 1.06E-04 0.114  AR-IK-42  1.732 2.48E-07 25.71 1.10E-04 2.53E-06 1.07E-04 0.111  AR-IK-43  1.713 4.65E-07 39.74 1.08E-04 4.76E-06 1.04E-04 0.109  AR-IK-45  1.827 7.78E-07 50.60 1.16E-04 7.96E-06 1.08E-04 0.106  AR-IK-51  1.612 4.58E-07 40.24 1.02E-04 4.68E-06 9.73E-05 0.109  AR-IK-10  1.720 1.64E-07 18.25 1.09E-04 1.64E-06 1.07E-04 0.112  AR-IK-7  1.676 6.73E-07 48.83 1.06E-04 6.74E-06 9.93E-05 0.107  AR-IK-48  1.654 7.79E-07 53.36 1.05E-04 7.80E-06 9.69E-05 0.106  AR-IK-11  1.648 9.39E-07 57.41 1.04E-04 9.40E-06 9.49E-05 0.104  AR-IK-25 0.087 1.872 9.16E-07 53.87 1.18E-04 9.17E-06 1.09E-04 0.105 -0.018 AR-IK-21  1.675 1.87E-07 21.23 1.06E-04 1.80E-06 1.04E-04 0.112  AR-IK-17  1.617 5.90E-07 46.54 1.02E-04 5.68E-06 9.67E-05 0.108  AR-IK-22  1.819 8.80E-07 53.71 1.15E-04 8.47E-06 1.07E-04 0.106  AR-IK-16  1.632 1.37E-06 66.69 1.03E-04 1.31E-05 9.02E-05 0.099  glass 4  2.324 1.58E-06 60.74 1.47E-04 1.52E-05 1.32E-04 0.102  AR-IK-12  1.716 1.17E-06 61.64 1.09E-04 1.12E-05 9.73E-05 0.102  AR-IK-20  1.714 1.22E-06 63.05 1.08E-04 1.17E-05 9.68E-05 0.102  AR-IK-34   1.728 1.43E-06 66.40 1.09E-04 1.38E-05 9.55E-05 0.100  AR-IK-18 0.093 1.531 1.22E-06 65.80 9.69E-05 1.18E-05 8.51E-05 0.100 -0.007 AR-IK-27  1.884 1.22E-06 60.87 1.19E-04 1.18E-05 1.07E-04 0.103  AR-IK-32  1.736 1.67E-07 18.80 1.10E-04 1.55E-06 1.08E-04 0.112  AR-IK-33  1.734 1.00E-06 58.17 1.10E-04 9.26E-06 1.00E-04 0.104  AR-IK-47  1.680 1.30E-06 65.22 1.06E-04 1.20E-05 9.43E-05 0.101  AR-IK-23 0.090 1.701 1.68E-06 70.42 1.08E-04 1.56E-05 9.21E-05 0.098 -0.007 AR-IK-35  1.726 1.54E-06 68.00 1.09E-04 1.43E-05 9.49E-05 0.099  AR-IK-30  1.731 8.52E-07 54.92 1.10E-04 7.60E-06 1.02E-04 0.106  AR-IK-31 0.108 1.730 1.78E-06 71.60 1.09E-04 1.59E-05 9.36E-05 0.097 0.010 AR-IK-36   1.725 1.54E-06 67.91 1.09E-04 1.37E-05 9.54E-05 0.100   aInitial water content is based on FTIR analysis. bCalculated internal pressure (Pa) [Pi=Pe+2σ r-1]. cMeasured H2O content (wt%) in cores by FTIR. dInitial mass (g) of sample core. ePorosity of sample  based on volume change. f,g,hCalculated moles of H2O dissolved in initial sample, exsolved as bubbles and remaining in sample, respectively. iMeasured - calculated H2O content of glass run products.  Table 2.3 Model values of residual H2O in glasses from 1 atm isothermal vesiculation experiments. We assume an initial H2O content of 0.114 wt.%a, constant surface tension (0.081 N m-1), and an average mean bubble radius of 0.322 mm for an internal pressure of 101828 Pab. Residual H2O is calculated from sample volume change (ΔV) using the Redlich-Kwong equation of state (see text for full explanation).    24 Figure 2.5 Volume and H2O content changes in each sample during experiments. (a) Observed changes in sample volume (ΔV/Vi) plotted against experimental T (°C) for all experiments (Table 2.2). The isothermal experiments show an increase in ΔV/Vi with increasing dwell time (arrow at right). Samples below the equilibrium plateau part of the curve (cf. Fig. 2a; Fig. 3) are open symbols; equilibrium plateau samples are closed. (b) The calculated H2O contents (wt%) of the residual glass in each sample vs. T (°C) for all experiments (Table 2.3). Residual H2O contents of the glass decrease with increasing dwell time within each isothermal set of experiments and with increasing T. Symbols as in (a).  state to calculate the H2O vapour content in the bubble fraction. We then compute the H2O content of the residual melt by difference, thereby establishing the 1 atmosphere solubility of H2O in the rhyolite melt, and the T-dependence of the H2O solubility at 1 atmosphere. We compute the internal pressure of the bubbles using a modified form of the Rayleigh-Plesset equation:  𝑃? − 𝑃? = 𝜌? 𝑟 ?????? + ?? ™ ™ ? + ??? ™ ™ + ???   (Eq. 2.1) where Pi is the pressure within the bubble (Pa), Pe is the external pressure of the system (Pa), ρm is the density of the melt (kg m-3), r is bubble radius (m), t is time (s), η is melt viscosity (Pa s) and σ is the surface tension of the melt (N m-1) (Sparks 1978; Barclay et al. 1995; Toramaru 900 1000 11000.090.100.110.12H 2O (wt%)T  (oC)(b) t900 1000 11000 1 2 3 ∆V/V iT  (oC)(a)tRyan et al. (2014) FIGURE 5  25 1995; Navon et al. 1998; Liu and Zhang 2000; Blower et al. 2001b; Proussevitch and Sahagian 2005). Some terms in Eq. 2.1 can be considered negligible under specific conditions and eliminated. For the purposes of our calculations, we eliminate the terms for inertial and viscous forces based on the following: i) our experiments are isobaric and static, thus, Pe is a constant 105 Pa and inertial forces (1st term) are negligible; ii) viscous forces form an important resistance during bubble growth (Proussevitch and Sahagian, 1998) but as the bubbles achieve their final equilibrium state viscous forces become irrelevant and can be ignored (2nd term). There are two situations where the surface tension term (3rd term; Eq. 2.1) dominates in the calculation of internal pressure. The first is where bubbles are small and at a critical radius (the bubble radius where the gas phase in a bubble is equilibrated with the melt (Toramaru 1995)) of ~10-3 cm (Sparks 1978; Prousevitch et al. 1993; Barclay et al. 1995; Liu and Zhang 2000). The second case is where bubbles are no longer growing and have achieved their equilibrium size (Toramaru 1989; 1995). Given the negligible effects of inertial and viscous forces on the final distribution of bubbles (e.g., on the equilibrium plateau) we calculate internal pressure from: 𝑃? = 𝑃? + ???   (Eq. 2.2) Surface tension (σ) acts as a force that opposes an increase in the surface area of a phase and, here, exists between the silicate melt and the supercritical fluid produced by exsolution of dissolved H2O. A recent review of surface tension data by Gardner and Ketcham (2011) has shown a small T-dependence for melt-fluid σ (9x10-5 N m-1 °C-1). A compilation of all published σ values for hydrous (3.5-9.3 wt% H2O) compositions from basaltic andesite to rhyolite to phonolite also fell within the narrow range of 0.042-0.110 N m-1 (Walker and Mullins 1981;   26 Mourtada-Bonnefoi and Laporte 1999; Bagdassarov et al. 2000; Mangan and Sisson 2000; Mourtada-Bonnefoi and Laporte 2002; 2004; Mangan and Sisson 2005; Gardner and Ketcham 2011; Gardner 2012; Gardner et al. 2013). Conversely values for σ increase dramatically from hydrous (0.042-0.110 N m-1) to anhydrous silicate melts (0.282-0.371 N m-1) (Walker and Mullins 1981; Bagdassarov et al. 2000). Water appears to be more important than melt composition and temperature, therefore, in lieu of published data at low water contents (i.e. <1 wt%) we used the average value for all hydrous data (0.081 N m-1). For this surface tension value, the calculated internal pressure of bubbles (Pi) is 101828 Pa (Table 2.3) for an average bubble radius (r) of 0.322 mm (from XCT imaging; Figure 2.1; Appendix C). The error in Pi associated with the selection of values for σ and r is small: a 3-fold increase or decrease in r cause ~1% change in Pi. Similarly using an anhydrous surface tension value of 0.3 N/m increases Pi by ~1.5%.   Using this Pi value, the initial number of moles of H2O in the glass of each sample (ni) (Table 2.3), the change in sample volume (ΔV; Figure 2.5a) and the Redlich-Kwong equation of state we calculate the moles of H2O vapour in the bubbles formed during each experiment (nb) using the following equation: ??? + 𝑃? = ?  ??????? − ??  ????   ??????    (Eq. 2.3) where a and b are constants that correct for the attractive potential of molecules and for volume, respectively (Redlich and Kwong 1949), R is the universal gas constant and T is temperature in Kelvin (Table 2.3). Solving for nb we compute the number of moles of H2O in the residual glass (nr) by subtracting nb from the number of moles of H2O in the core at the start of the experiment (ni) and then convert to a value of wt% H2O in the residual glass (Table 2.3). The calculated   27 residual water contents of the glass mirror the relative change in sample volume with time and temperature (Figure 2.5). Minimum H2O values in each temperature suite correspond to data that lie on the equilibrium plateau and decrease with increasing temperature.   2.7 Discussion 2.7.1 Retrograde solubility: Comparison to published models  Figure 2.6a plots ln xH2O against reciprocal temperature for all experimental suites as well as a linear model fitted to the data points that define our equilibrium plateaus (solid symbols) from 900-1050°C (Figure 2.3a,b,c,d,e):  ln xH2O = 1069.6/T – 6.4637  (Eq. 2.4)  where xH2O is the mole fraction of water in the glass and T is the experimental temperature (K).  We have chosen to remove the 1100°C data point, which does not fall on the well-defined linear trend. At 1100°C the time to equilibrium (Δte) competes with the viscous relaxation timescale, effectively meaning the 1100°C is at the limit of the experimental-window using this methodology. Even though the experimental t-window is small (2 hours; Figure 2.3f) we suspect that we failed to capture the maximum volume expansion of the plateau sample at this temperature.   Figure 2.6b shows our data and model against all published 0.1 MPa H2O solubility data (Table A.1) and the models produced by Newman and Lowenstern (2002), Liu et al. (2005) and Zhang et al. (2007). Our data extend from 900-1100°C and are consistent with the experimental data of Liu et al. (2005) over the same temperature range and down to 700°C. In addition, our model, which estimates the magnitude of the 0.1 MPa of retrograde solubility at ~ -7.1x10-3 wt%   28 H2O per 100°C from 700-1200°C (Figure 2.6b), fits not only our data, but when extrapolated to lower temperature, also captures some of that produced by Liu et al. (2005). In contrast, the Liu   Figure 2.6 Residual H2O contents as mole fraction (XH2O) and experimental temperature. (a) Calculated values of ln XH2O vs. 1000/T (K). Closed symbols denote plateau samples. The linear best-fit line for 900-1050°C plateau samples is shown as a solid black line. Thick grey line is measured H2O content of starting material. (b) The residual H2O contents as ln XH2O vs. 1000/T (K) for the plateau samples from this study (closed circles) as well as all published 0.1 MPa rhyolitic data (Appendix A), including Liu et al. (2005) (open circles), Friedman et al. (1963) (open triangles) and McMillan et al. (1986) (open square). Broken lines show published models (500-1250°C). Solid line is our linear best-fit. The models of Moore et al. (1998) and Papale et al. (2006) plot below the field of view. Our best-fit model agrees well the data from Liu et al. (2005), as well as with the Liu et al. (2005), Zhang et al. (2007) and Newman and Lowenstern (2002) H2O solubility models. All models fail to capture all the Friedman et al. (1963) and McMillan et al. (1986) data.   et al. (2005) and Zhang et al. (2007) models, which yield similar estimates of the magnitude of retrograde solubility over the same temperature range (~ -7.8 x 10-3 wt% H2O per 100°C and ~ -0.72 0.76 0.80 0.84−5.65−5.55−5.45ln(X H2O)1000/T  (K)  1100oC 900oC(a)0.7 0.8 0.9 1.0 1.1 1.2 1.3−7.5−7−6.5−6−5.5−5−4.5ln(X H2O)1000/T  (K)   Liu et al. (2005) Zhang et al. (2007) Newman andLowenstern (2002) linear best−fit 1250oC 500oC(b)Ryan et al. (2014) FIGURE 6  29 13.9 x 10-3 wt% H2O per 100°C, respectively; Figure 2.6b) do not fit our data or all of the Liu et al (2005) dataset. The Newman and Lowenstern (2002) model agrees well with our data despite being constrained by almost no experimental data at 0.1 MPa. On this basis, we are confident that our data and model accurately capture the 0.1 MPa retrograde solubility within our experimental window (900-1100°C) and to lower temperatures (i.e. 700-900°C). The consistency in the data and the calculated values of retrograde solubility shown between the Liu et al. (2005) model and our results suggests that the Liu et al. (2005) model is the best of the multi-pressure models, at least at low pressures.  Based on the empirical fit shown as Eq. 2.4 we have calculated the implied standard state enthalpy and entropy values for the exsolution of H2O from the melt: ΔHo = +17.8 kJ mol-1; ΔSo = 107 J K-1 mol-1 (see Appendix D). The positive value of ΔHo shows that this reaction is endothermic, resulting in a very slight decrease in the temperature of the system. Liu et al. (2005) derived similar exsolution enthalpy values (13.2-16.5 kJ mol-1 at 0.1-11 MPa) and concluded that exsolution does not have a significant effect on the temperature of the rhyolitic melt.  2.7.2 Retrograde solubility: The effect on Tg  Below, we have explored the wider implications of retrograde solubility for volcanic processes. Figure 2.7 shows the calculated isobaric solubility curves for a rhyolite melt over a range of pressures (0.1-40 MPa) as modeled by Liu et al. (2005). At constant temperature, H2O solubility is strongly controlled by and increases with pressure. Additionally, each isobaric curve shows the increase in the solubility of water with decreasing temperature (1000-400°C). At atmospheric pressure the effect is slight, as evidenced by the near vertical slope of the isobaric curve from both models. However, at higher pressures the slopes of the isobaric curves become   30 increasingly negative. Ultimately the change in the negative slopes of the T-XH2O curves maps out the change in the magnitude of retrograde solubility with pressure. This shows that, as volcanic systems cool, the capacity for H2O dissolution in melts increases substantially with increasing pressure, allowing for increasing melt rehydration.    Figure 2.7 Isobaric H2O solubility curves (grey lines) predicted by Liu et al. (2005) model and plotted as T (°C) vs. H2O content (wt%) for a range of P (numbers on lines, in MPa). Our model is the thick black line at 0.1 MPa. Thin solid black curve is glass transition temperature (Tg (°C) of the rhyolite melt with increasing H2O content (Giordano et al. 2008). The intersection of the Tg curve with the isobars marks the maximum possible H2O content of the melt at a given pressure. Here, the drop in Tg with increasing H2O content is insufficient to accommodate further H2O resorption, thereby, causing a ‘rehydration quench’ of the melt to a glass.  Figure 2.7 also shows values of Tg calculated for the Hrafntinnugryggur rhyolitic melt as a function of water content using the viscosity (η) model of Giordano et al. (2008) (Tg ~ T where η = 1012 Pa s).  The addition of water to anhydrous melts causes a strong initial reduction in Tg but at higher water contents the rate of decrease in Tg lessens (Hess and Dingwell, 1996).  The calculated glass transition curve cuts across the pressure dependent water solubility curves at high angle to create a series of [T-XH20] intersection points. These intersections mark the termination of isobaric H2O solubility curves for volcanic systems. As the melt cools moving 0 0.5 1 1.5 2 2.5 3 3.54005006007008009001000H2O (wt%)T or Tg (oC)4030201052.510.1Ryan et al. (2014) FIGURE 7  31 down the isobaric solubility curves, it redissolves magmatic volatiles, causing the Tg of the hydrated melt to decrease continuously, thereby, expanding the melt (vs. glass) window. This effect of H2O content on Tg creates a positive feedback loop, or ‘chase scenario’ where the decreasing T of the system chases the falling Tg (Figure 2.8 inset). Ultimately, however, the decrease in Tg with increasing water content (i.e. slope of Tg curve) is insufficient to avoid intersection with the steep isobaric retrograde solubility curves at volcanic to subvolcanic temperatures. Thus, during cooling the isobaric retrograde solubility curve intersects the H2O-dependent Tg curve and the melt is quenched to a glass (i.e. ‘rehydration quench’; Figure 2.8 inset).   Figure 2.8 Model isobaric (0.01 - 20 MPa) rehydration-cooling paths in volcanic systems and corresponding glass transition temperatures (Tg).  Inset shows diverse paths for volcanic systems to intersect their Tg's, including: i) cooling at rates faster than the melt changes composition (‘thermal quench’, A), ii) exsolution and loss of H2O causing a rise in melt Tg (‘degassing quench’, C), and iii) cooling paths allowing for H2O resorption and reducing melt Tg (‘rehydration quench’, B). Schematic arrows in main figure show simplified volcanic processes including: isobaric thermal quench (A), rehydration quench (B1) and degassing quench (C) at elevated pressure; isothermal eruption (arrow labelled ‘pyroclastic fallout’) followed by cooling and rehydration (B2); and isothermal accumulation (arrow labelled ‘ignimbrite’) promoting isobaric cooling and rehydration (B3). The grey arrows show the variations in H2O content and Tg depending on the external pressure and cooling rate of different volcanic processes (see text for explanation).  0 1 2 34006008001000H 2 O (wt%)T or Tg (o C)1052.510.1 20Tg ( o C)400400 100 0degassing quench(C)thermal quench (A)Tmelt (o C)rehydration quench(B)1000(C)! (A)! (B 1 )!(B 2 )!(B 3 )!PYROCLASTIC FALLOUT!IGNIMBRITES!Ryan et al. (2014) FIGURE 8  32 At this point H2O content is ‘frozen in’ corresponding to the T-P-XH2O coordinate of the intersection; below the Tg curve the predicted isobaric H2O solubility curves become metastable extensions (dashed lines; Figure 2.7). The values defined by the intersection of the solubility and Tg curves are maximum H2O contents for dissolution of H2O fluid (solute) into the silicate melt (solvent). This is because the melt solubility curves are for a solvent (Tmelt > Tg) having a specific set of thermochemical and structural properties distinct from the corresponding glass (<Tg). The Tg limitation on water solubility in silicate melt is, however, not relevant to secondary, non-magmatic (re)hydration processes that operate at temperatures below Tg (e.g., devitrification, perlitization, palagonitization), where glasses with substantially higher water contents can be created (i.e. Anovitz et al. 2008). This lower temperature rehydration of silicate glass is demonstrated serendipitously by the 550°C experiments of Liu et al. (2005) which resulted in anomalously high, but reproducible, H2O contents. Liu et al. (2005) recognized these values as a 550°C ‘solubility’ limit but, because the experiments were below the glass transition curve, did not include these data in their H2O solubility (melt) model. The mechanisms for hydration of volcanic glasses below Tg are incompletely understood but must be the result of alternative means of water dissolution (Anovitz et al. 2008; Giachetti and Gonnermann 2013).   2.7.3 Implications for volcanic processes The glass transition is an important limiting value for the temperature conditions at which many volcanic processes take place. Above Tg, rates of nucleation, crystallization and vesiculation are fast enough to significantly affect magmatic processes. Conversely, where the T-  33 Xmelt path of the melt intersects the Tg of the melt, glass forms and many magmatic and volcanic processes effectively cease.  There are a variety of ways in which volcanic systems approach and intersect their glass transition (Fig. 2.8; inset). Conventionally, volcanic systems can be cooled at rates faster than they can vesiculate and crystallize to the point that the isochemical melt reaches its Tg to form glass (thermal quench). All volcanic systems exsolve gas as they rise to the Earth's surface and the associated loss of H2O from the melt due to degassing can cause a rapid and substantial rise in the Tg of the melt thereby reducing the melt window (Fig. 2.8, inset). Where the degassing-induced rise in Tg intersects the melt temperature (Tg = Tmelt) the melt transitions to glass (degassing quench). The retrograde solubility of H2O provides a means of expanding the melt field relative to the glassy state. In a wide range of volcanic systems where cooling timescales are slow enough to facilitate H2O diffusion in silicate melts, the melts have the opportunity to resorb H2O as they cool. The consequence of this is to reduce the effective Tg of the melt allowing for further uptake of H2O with cooling. Ultimately, however, the reduction in Tg with increasing H2O content is insufficient to avoid intersecting the isobaric solubility curve where a rehydration quench of the melt occurs.  Figure 2.8 shows several potential cooling paths in a schematic volcanic system and their effect on the final H2O content of the quenched melt, including: i) conventional thermal quenching (A), and ii) slower cooling along the retrograde solubility curve until the glass transition temperature curve is intersected (i.e. rehydration quench; B1, B2 and B3). The differences in the final H2O content and Tg of the melt arising from thermal vs. rehydration quenching increase substantially with increasing pressure.    34 Retrograde solubility mainly plays a role in volcanic systems where cooling is slow enough to support vapour-melt equilibrium. For rehydration to occur the system must also contain H2O-rich fluids available for resorption. Highly efficient degassing of volcanic systems (Sparks et al. 1999) would favour a degassing quench over rehydration quenching. We have identified three volcanic environments where the retrograde solubility of H2O can play an important role, including: welding of pyroclastic deposits, flow of silicic lavas, and the forensic recovery of fragmentation depths.  Studies of welding processes and timescales have emphasized the role H2O plays in inducing or prolonging welding (Friedman 1963; Sparks et al. 1999; Giordano et al. 2005; Grunder and Russell 2005; Keating 2005; Robert et al. 2008; Kolzenburg and Russell, 2014).  Sparks et al. (1999) discussed the role of load P in causing rehydration of vitric juvenile pyroclasts in ignimbrite sheets. The rehydration causes a concomitant viscosity reduction and, thus, facilitates welding. The ‘gas retention regime’ of their conceptual model requires pore fluid pressure to equal load pressure, implying very low permeability or extremely rapid compaction. Their isothermal conceptual model did not consider an alternative explanation involving the effects of retrograde solubility, which has a marked effect even at low pressures (i.e., < 20 MPa; Figure 2.9a). In a 100 m thick ignimbrite sheet for example (e.g., Fish Canyon Tuff, Rio Caliente, Cerro Galan, Bishop Tuff (Cas and Wright, 1988)) discounting the effects of retrograde solubility leads to an underestimation of the final H2O content of a melt by 0.1 wt% at 2 MPa, assuming an isothermal system at 800°C (Figure 2.9b). Because there is a concordant decrease in Tg with increasing H2O, assuming an isothermal body also overestimates the effective viscosity of the material. For example, in a model for an ignimbrite (i.e. 2 MPa) that considers rehydration along the cooling path rather than an isothermal (800°C) system, Tg decreases by ~15°C, thereby   35 expanding the melt window and prolonging welding (Figure 2.9b). Figure 2.9c is an extension of these same curves to conduit-relevant depths of 2 km. At these pressures (up to 40 MPa), the difference between the H2O content and Tg of an isothermal and a cooling system is 1 wt% H2O and ~75°C, respectively. At 40 MPa the Tg of the melt on the retrograde solubility path is nearly half the value of the corresponding anhydrous glass transition of the melt. This remarkable decrease in Tg will dramatically change the timescales for welding of materials filling the volcanic conduit (Russell and Quane, 2005; Kolzenburg and Russell, 2014). Although the overall   Figure 2.9 Coupled effects of retrograde solubility and ‘rehydration quench’ in surficial deposits and within volcanic conduits. (a) Solid grey line represents the isothermal (800°C) P-dependence of H2O solubility (e.g., Sparks et al., 1999). The increase in load pressure allows for increased H2O solubility but does not include the effects of retrograde solubility in a cooling melt (arrow) leading to underestimation of final H2O contents. (b) Differences in H2O contents (wt%); black lines) and Tg values normalized to their anhydrous values (grey lines) as a function of P for an isothermal melt (800°C melt; dashed lines) vs. a cooling melt (solid lines) for a 100 m thick ignimbrite sheet or lava. The difference in curves shows the effects of ‘rehydration quenching’ on H2O contents and Tg of the melt. Over 100 m H2O resorption in the cooling melt increases the H2O content by ~0.1 wt% and depresses Tg by 15°C relative to an isothermal melt. (c) The difference between H2O content and Tg in an isothermal (800°C) versus a cooling melt in the context of the upper conduit (2000 m). Lines as in (b). Over 2000 m there is a ~1.0 wt% increase in H2O content and a ~50°C decrease in Tg in a cooling melt relative to an isothermal one.  1 2 35  10 15 20 25 30 35       0.6 0.7 0.8 0.9 1.0 −250 −500 −750 −1000 −1250 −1500 −1750  0 0.2 0.4 0.60.5 1  1.5       0.85 0.9 0.95 1.0 −20 −40 −60 −80   0 1 2 3400600800100051 0  15  20 2 5 3 0 3 5  25 0 500 750 1000 1 2 50 1500 175 00 .5 11 .5  20 40 6 0 80Pressure (MPa)Depth (m)H 2 O (wt%)H 2 O (wt%)Pressure (MPa)Depth (m)Tg/Tg a n h y d r o u s Tg/Tg a n h y d r o u sT orTg (o C)(a)(b)(c)H 2 OTgH 2 OTgRyan et al. (2014) FIGURE 9  36 effect of retrograde solubility is small relative to the P-dependence of H2O solubility, it increases the melt window in a cooling pyroclastic body substantially and will greatly facilitate welding.    Similarly, P- and T-dependent H2O concentrations may play an important role in explaining the transport and cooling timescales of rhyolitic lava flows. Two primary models have been proposed to explain the eruption and emplacement of these dense (i.e. low porosity), high viscosity melts: extensive degassing in the conduit prior to eruption (Jaupart and Allegre 1991; Gonnermann and Manga 2003; Yoshimura and Nakamura 2008 ; Castro et al. 2012) vs. initial extrusion of an inflated magmatic foam that subsequently collapses to form a dense lava (Eichelberger et al. 1986; Westrich et al. 1988; Westrich and Eichelberger 1994). Several mechanisms have also been invoked to explain the lateral extent of these high-viscosity magmas: extremely efficient heat retention (Manley, 1992; Tuffen et al. 2013) vs. changes in magma rheology related to the presence and distribution of bubbles (Eichelberger et al. 1986; Castro and Cashman, 1999; Vona et al. 2013). Retrograde solubility could also explain some of the enigmatic behaviour and textures found in rhyolite flows. Once erupted to the surface, whether as a relatively dense or foamed body, rhyolite will begin to cool and resorb H2O as dictated by P (i.e. flow thickness) and T (eruption temperature and cooling history) conditions (Figure 2.9a). This resorption process, which could possibly eradicate foamed textures (Westrich and Eichelberger 1994), would lead to a decrease in viscosity, as well as depression in Tg, prolonging the life of a flowing viscous body (Figure 2.9b). Coupled with thermal efficiency and the effect of bubbles on magma rheology, retrograde solubility could explain the impressive lateral extent of some rhyolite lava flows.  Forensic investigations of storage and fragmentation depths and eruption dynamics are commonly based on measured H2O contents in melt inclusions or glasses to estimate pressure   37 (Atlas et al. 2006; Rust and Cashman 2007; Wright et al. 2007). H2O contents coupled with H2O distribution and textural data have also been used to identify specific pressure cycling events, such as at Mono Craters, California (Watkins et al. 2012). These studies could be further constrained by considering the T-dependence of H2O solubility as noted by McIntosh et al. (2014). As in welding studies, many forensic volcanology studies have assumed isothermal conditions (Rust and Cashman 2007; Wright et al. 2007) constrained by geothermometry (Rust and Cashman 2007; Watkins et al. 2012). Strong thermal quenching is necessary in each instance to ensure that the isothermal pressure estimates from H2O contents are valid. However, as many of these volcanic centers are dynamic and complex, there is always the possibility of re-equilibration at different P-T conditions than those recorded elsewhere in a sample. At the very least, H2O-P curves that include considerations of retrograde solubility can provide lower and upper bounds on estimated fragmentation depths (Figure 2.9c).   2.8 Implications  This high temperature experimental study produced new data on the solubility of H2O in silicate melts under conditions where the published data are sparse (i.e. 0.1 MPa). These data are used to create a simple thermodynamic model for H2O solubility from 700-1200°C at 0.1 MPa and the enthalpy and entropy of exsolution of H2O. The data and model corroborates the low-pressure data and model for H2O solubility of Liu et al. (2005).   The results of this study also highlight the importance of retrograde solubility in volcanology. Pressure changes in volcanic systems lead to dramatic changes in water solubility, especially during ascent, and ultimately control eruption processes. However, volcanic systems generally move from high to low temperature and the inverse relationship between temperature   38 and water solubility plays a critical role in many post-eruption processes. Our work shows that the effects of retrograde solubility and the potential for rehydration quenching should be considered when interpreting volcanic processes recorded by surficial deposits or within volcanic conduits and feeders.   2.9 Acknowledgements  The NSERC Discovery and Discovery Accelerator Supplements programs and the German Academic Exchange Service funded this work via grants held by JKR. The senior author acknowledges scholarship and travel funding from AmeriCorps, the Mineralogical Association of Canada and the University of British Columbia. We are indebted to Hugh Tuffen (Lancaster University, UK) who generously donated to us a block of obsidian from Hrafntinnuhryggur, Krafla, Iceland, and to Andre Phillion (University of British Columbia Okanagan, BC, Canada) for access to the floating license for Avizo® Fire. We would like to thank Felix von Aulock and an anonymous reviewer for the thorough and constructive reviews, which significantly improved this manuscript.     39 Chapter 3: Bubble Growth in Rhyolitic Melts: Experiments and Models 3.1 Introduction  The nucleation and growth of bubbles attending magma vesiculation drives magma ascent and controls eruption style (explosive vs. effusive eruptions). The processes and rates of bubble nucleation and growth in silicate melts have been modeled by theoretical calculations (e.g. Sparks 1978; Toramaru 1989; Barclay et al. 1995; Toramaru 1995; Proussevitch and Sahagian 1998; Blower et al. 2001b; Lensky et al. 2004; Proussevitch and Sahagian 2005; L'Heureux 2007; Huber et al. 2013), empirically constrained by experimental observation and measurement (e.g. Hurwitz and Navon 1994; Bagdassarov et al. 1996; Lyakhovsky et al. 1996; Navon et al. 1998; Mourtada-Bonnefoi and Laporte 1999; Gardner et al. 2000; Larsen and Gardner 2000; Liu and Zhang 2000; Mourtada-Bonnefoi and Laporte 2004; Gardner and Ketcham 2011; Baker et al. 2012; Gonnermann and Gardner 2013) and deduced from field observations (e.g. Cashman and Mangan 1994; Klug and Cashman, 1994; Gaonac'h et al. 1996; Mangan and Cashman 1996; Giachetti et al. 2010). These studies have demonstrated that there is a diversity of competing processes and rates inherent in the vesiculation process.   A number of studies have sought to link certain nucleation or growth mechanisms, as well as growth rates, to melt physical properties. Two physical properties that have marked effects on the formation of a bubble population are melt viscosity and volatile supersaturation (Sparks 1978; Toramaru 1995; Navon et al. 1998; Liu and Zhang 2000; Lensky et al. 2004; Burgisser and Gardner 2005; Bai et al. 2008). Where melt viscosity is low (~ <105 Pa s) bubbles can grow, move and interact (e.g. coalesce with other bubbles) with relative ease in the melt (Sparks et al., 1994; Baker et al. 2006; Gonnermann and Manga 2007; Bai et al. 2008). However where melt viscosity is higher (~ >107 Pa s) bubble nucleation can be delayed, bubble size and   40 interactions are limited, and significant overpressure can develop (Bagdassarov et al. 1996; Stevenson et al. 1997; Navon et al. 1998; Proussevitch and Sahagian 1998; Gardner et al. 2000; Gonde et al. 2011). Additionally bubble growth rate is inversely related to melt viscosity (Sparks 1978; Lyakhovsky et al. 1996; Navon et al. 1998; Proussevitch and Sahagian 1998; Blower et al. 2001b; Masotta et al. 2014). In melts where the degree of supersaturation is high the system is functioning far from chemical equilibrium, exsolves significant amounts of gas, and can prompt continuous or ‘runaway’ nucleation, which generates a closely-packed population of bubbles that may grow quickly (Sparks et al., 1994; Lyakhovsky et al. 1996; Mangan and Cashman 1996; Larsen and Gardner 2000; L'Heureux 2007). Where volatile supersaturation is relatively low smaller volumes of gas are exsolved, nucleation may be limited to a single event, and the thermochemical drive for bubble growth by diffusive mass transfer is low (Bagdassarov et al. 1996; Baker et al. 2006; L’Heureux 2009).   Here we present a unique dataset from which we constrain the effects of kinetics on bubble growth dynamics. These experiments are most relevant to rhyolitic melts at low pressures and elevated temperatures but provide hard constraints on the thermodynamics and kinetics of bubble nucleation and growth at low degrees of H2O supersaturation (+5-15% above the H2O solubility limit) and moderate viscosities (~105-109 Pa s). The dataset derives from a previous study of H2O solubility at atmospheric pressure (1 atm) wherein H2O-oversaturated rhyolitic glass cores were allowed to vesiculate at fixed temperatures from 900-1100°C for variable amounts of time. After quenching, samples were imaged using X-ray computed tomography (XCT), a state-of-the-art non-destructive 3D imaging technology that allows for precise quantification of the volume of exsolved gas, as well as, the number of bubbles (bubble number density; BND) and the bubble size distribution (BSD).    41 These cores provide ‘snapshots’ of bubble nucleation and growth over a fixed amount of time at a controlled temperature. Thus, the processed images of bubbles in these cores provide the critical data to constrain the dynamics of bubble production in rhyolitic melt at temperatures above the glass transition temperature (Tg). Additionally our findings can be used to predict the total volume of H2O exsolved and the average volumetric growth rate as functions of thermodynamic oversaturation and viscosity.   3.2 Materials  3.2.1 Starting material  The starting material for this study is fresh natural rhyolitic obsidian from Hrafntinnuhryggur, Krafla, Iceland donated by Hugh Tuffen (pers comm 2008). The glass is essentially bubble- and crystal-free, texturally homogeneous, and has been described and chemically analyzed by Tuffen and Castro (2009). Table 3.1 is a comparison of the anhydrous chemical composition of the obsidian block used in these experiments (X-ray fluorescence analysis) to the electron microprobe (EMP) measured composition of Tuffen and Castro (2009). Water content measured by Fourier transform infrared spectroscopy (FTIR) is 0.11(4) wt%, which lies above the 1 atm modelled H2O solubility limit at temperatures greater than 900°C (Chapter 2). The chemical composition of the glass does not change with exposure to high temperature (Appendix H).   3.2.2 Vesiculation experiments and results A full description of the experimental method and results can be found in Chapter 2. For vesiculation experiments 10 x 10 mm cylindrical obsidian cores of known mass and volume were placed on a ceramic base (preheated to the experimental temperature) in a Nabertherm HTC    42   S11ba UBC-Std4b Method EMPA XRF SiO2 75.23 74.77 TiO2 0.23 0.23 Al2O3 12.00 12.31 Fe2O3 - 0.69 FeO 3.28 2.48 MnO 0.11 0.11 MgO 0.10 0.14 CaO 1.66 1.64 Na2O 4.15 4.28 K2O 2.75 2.60 P2O5 - 0.03 Total 99.51 99.28 FeOT 3.28 3.10 aElectron microprobe analysis of glass (Tuffen and Castro, 2009). bBulk XRF analysis of glass by ALS-Chemex.  Table 3.1 Major element compositions of Hrafntinnuhryggur obsidian, Krafla, Iceland, the starting material for the high-T experiments. Compositional data from the experimental products is available in Appendix H. The difference in composition between and within samples is less than the analytical uncertainty (Appendix H).   08/15 furnace at temperatures (T) between 900-1100°C for prescribed dwell times (t) of 0.25-24 hours. After reaching the appropriate dwell time the ceramic base and obsidian core were removed from the furnace and quenched below the measured calorimetric glass transition temperature of the melt (Tg = 690°C ± 20 (Castro et al. 2008)) within seconds without any modification to their shape and volume. The final mass and volume of the foamed cores were then measured using a high precision balance and a Micromeritics AccuPyc II 1340 helium pycnometer, respectively.    43 During exposure to high-T’s the volume of the sample increases with time (Figure 3.1). In these isothermal experiments sample volume increases until it plateaus at a stable maximum value. The final maximum volume of sample and the rate at which this volume is achieved increases with increasing T. Uniquely bubbles do not nucleate on the surface of the core or escape, so each experimental product can be viewed as a closed-system (see Appendix I). Therefore these experimental products give ‘snapshots’ of vesiculation, and thus bubble populations, in temperature-time space. Figure 3.1 Images of starting material and experimental run products from the 1000°C suite of experiments. Photographs of (a) the undeformed starting material and experimental run-products (b,c,d). Dwell time and calculated volume changes (ΔV, %) are listed in the upper left corner of the images. The scale bar is marked in mm.   44 In Chapter 2 we interpret the increase in sample volume to be the initially oversaturated system exsolving excess dissolved volatiles (assumed to be 100% H2O), inducing bubble nucleation and growth. The apparent rate and total amount of vesiculation increases with increasing T. In Chapter 2 we interpret the plateau in sample volume at a stable maximum to be the cessation of exsolution and bubble nucleation/growth as the equilibrium concentration of H2O for that T at 1 atm has been reached. Thus volume change (sample porosity) is inversely proportional to the equilibrium concentration of H2O in the glass. The results of these experiments established the 1 atm solubility limits as a function of T. Three vesiculated samples from Chapter 2 of varying porosity (AR-IK-10: 18.3%, AR-IK-11: 57.4%, AR-IK-16: 66.7%) were thin-sectioned and selected for 2D imaging by scanning electron microscopy (SEM) using the Philips XL-30 Scanning Electron Microscope at the University of British Columbia. These 2D images were used as reference materials to check data from 3D image analysis and are available in Appendix I. Twenty two of the remaining thirty three experimental products from the vesiculation experiments were selected for XCT analysis (Table 3.2).  3.3 Methods  3.3.1 3D image acquisition XCT is a non-destructive 3D imaging technique that is becoming increasingly more popular for analyzing complex geologic materials (Baker et al. 2012). In this study, 3D high-resolution images at a voxel size of 18.5 µm were acquired using a GE phoenix® v|tome|x s 240 micro-CT scanner at the Institute of Medical Engineering, Technische Universitat Munchen (IMETUM). For each scan, 1000 radiographs, scanning 360 degrees, were acquired at an   45 exposure time of 333 ms using a voltage of 80 kV, a current of 130 µA, and a 0.2 mm VA-steel filter. The resulting set of radiographs was then reconstructed using the inverse radon transformation (Deans, 2007) to generate a 3D image of the internal structure of the vesicular glass cores.  3.3.2 Image analysis Image analysis was performed to characterize the bubble growth in the obsidian cores. In the original 3D reconstructed datasets, X-ray attenuation is expressed as a greyscale value, with brighter shades of grey corresponding to increased attenuation (Figure 3.2a). Using ImageJ 1.47v (Abramoff et al. 2004; Schneider et al. 2012), the image contrast was adjusted so that the solid materials (glass and any microlites) appear nearly white while air (bubbles within the core, air outside the core) appears nearly black (Figure 3.2b). To reduce the potential of losing information by exaggerating contrast, this parameter was increased only to the point where noise was removed without drastically changing bubble shape and size. To remove the void space surrounding the cores from the image, the image was inverted in ImageJ and the area outside the core was filled in using a flood fill.   We used the Avizo® Fire software (v.8) to process the optimized set of greyscale images. This program includes a number of 2D and 3D image filtering, processing and segmenting tools and is capable of advanced analysis and visualization. To process these sets of XCT data, a grey-scale threshold was applied to the images to identify the bubbles as the entity of interest (Figure 3.2c). Bubbles that sit next to one another were separated using a watershed algorithm, which effectively reconstructs bubble walls that fall below the resolution limit of the XCT (Figure 3.2d). Each bubble was then labeled with a unique identifier (Figure 3.2e), counted, and characterized in terms of its volume and surface area. A 3D view of the individually identified   46 bubbles is also provided (Figure 3.2f). After collecting data for the bubbles within each core, we applied a similar process to the inverted images to collect volume data for the glass in the cores.  3.3.3 Data treatment and sources of error Two types of errors frequently arise related to image resolution: ‘Type I’ errors result from overestimating the number of 1-voxel entities in the core due to greyscale-thresholding. Much like a pixelated photograph, a ‘voxelated’ 3D entity cannot faithfully capture curves or structures smaller than the resolution (Figure 3.2g). As a result, while thresholding it is possible to accidently separate single voxels from the entity to which they should belong, inflating the   Figure 3.2 XCT image processing using ImageJ and Avizo® Fire. (a) Raw TIFF image output by XCT imaging. Greyscale color is based on X-ray attenuation (solid glass is white and air is black). (b) Optimized TIFF. Contrast is enhanced so that the image is nearly binary. (c) Inverted TIFF. This isolates bubbles for analysis in Avizo® Fire. (d) Thresholded TIFF. The greyscale values that show bubbles are identified as the values of interest and highlighted in blue by Avizo® Fire. (e) Separated TIFF. Avizo® Fire separates bubbles using a watershed segmentation algorithm, then highlights individual entities with different colors. (f) Final 3D rendering. (g) Type I errors (circled in white) in a high magnification 3D image. The resolution of the XCT images causes bubbles to appear cubic at high magnification. FOV for a-f is 18.2 mm across.  Raw TIFF Optimized TIFF Inverted TIFF Thresholded TIFF Separated TIFF 3D Rendering !" #" $"%" &" '"(a) (b) (c)(d) (e) (f)(g)  47 number of 1-voxel entities identified by image processing software. Similarly if there are structures in a sample that are smaller than the resolution of the XCT data (e.g. bubble walls) it is possible that image processing will artificially and erroneously lump separate entities together, generating ‘Type II’ errors (‘fake megabubbles’). The ‘Separate Objects’ command in Avizo® Fire is very effective and produces few Type II errors relative to other image processing software we tested for this study (‘3D Object Counter’ plugin in ImageJ (Bolte and Cordelières 2006); ‘Particle Analyzer’ tool in the BoneJ (v 1.3.12) plugin for ImageJ (Doube et al. 2010); ‘Tomoview’ (Flaws et al. 2011); Appendix F).   To combat these resolution-related artefacts, 2D image analysis has been used to verify bubble size distributions for each core. Type I errors are eliminated by examining the three sets of high-magnification SEM images of several vesicular samples (AR-IK-10, AR-IK-11, AR-IK-16) and identifying and measuring the smallest bubbles present in each sample (Appendix I). In each sample the minimum bubble radius is ~25 µm. The volume of a sphere with this minimum radius (~65450 µm3; ~10 voxels) is then used to distinguish real bubble size distribution data from Type I errors (e.g. Phillion et al. 2008). Similarly, any Type II errors in the Avizo® Fire data are eliminated by looking through the raw XCT data for each core and measuring the radius of the largest bubble identified using the ‘Analyze Particles’ plugin in ImageJ 1.47v (Abramoff et al. 2004; Schneider et al. 2012). The volume of a sphere with this maximum radius is then used as the cut off for accurate size distribution data. Using these data treatment processes we can overcome most resolution-related errors and recover the bubble size distribution and approximate bubble number within each core.  To check the reproducibility of our results one low (AR-IK-32) and one high (AR-IK-23) porosity sample were reprocessed from the initial ‘optimization’ phase to check the user’s ability   48 to pick the same nearly-binary color scheme. These second sets of optimized TIFFs were then processed through Avizo® Fire using the same methodology described above.  LABEL Texp (°C) t (h) Vglass (mm3)a VB (mm3)b rmax (mm)c ϕ (%)d nBe BND (nB/Vglass) AR-IK-24 900 20 536.8 406.8 0.606 43.11 6379 9.2 AR-IK-44 925 2.5 649.8 30.336 0.303 4.46 10622 15.3 AR-IK-42 925 5 706.5 219.59 0.460 23.71 7573 10.6 AR-IK-43 925 12 604.7 441.48 0.553 42.20 10558 15.0 AR-IK-45 925 20 678.6 716.8 0.587 51.37 6582 8.7 AR-IK-51 925 24 608.5 476.85 0.585 43.93 3917 5.8 AR-IK-7 950 4 689.8 591.3 0.564 46.16 17676 25.1 AR-IK-48 950 6 807.1 780.0 0.789 49.15 8457 12.4 AR-IK-25 950 20 582.6 944.0 0.564 61.84 14295 18.2 AR-IK-21 1000 0.5 645.7 133.8 0.335 17.16 20759 29.9 AR-IK-22 1000 1.5 842.1 727.0 0.426 46.33 12156 16.0 AR-IK-20 1000 4 626.4 1104.7 0.761 63.82 13936 19.6 AR-IK-34 1000 4 637.1 1210.4 0.771 65.52 13681 18.9 AR-IK-18 1000 7.5 611.1 950.0 1.003 60.86 9470 14.9 AR-IK-27 1000 13 717.2 1247.6 1.506 63.50 23061 29.3 AR-IK-32 1050 0.5 680.7 96.9 0.418 12.46 13551 18.7 AR-IK-33 1050 1.17 673.1 900.3 0.523 57.22 9890 13.8 AR-IK-47 1050 3 645.8 1198.0 0.762 64.97 11042 15.9 AR-IK-23 1050 4 502.0 1390.9 0.574 73.48 13788 19.5 AR-IK-35 1050 5 592.1 1354.6 0.698 69.58 12793 17.6 AR-IK-31 1100 1 508.0 1595.8 0.579 75.85 15876 22.5 AR-IK-36 1100 2 538.1 1434.4 0.703 72.72 11404 15.7 aVolume of glass in each experimental product given by 3D image analysis using Avizo® Fire bVolume of bubbles in each experimental product given by 3D image analysis using Avizo® Fire cMaximum bubble radius in each core measured by 2D image analysis using ImageJ dϕ = [VB/(Vglass+VB)]*100 eNumber of bubbles identified in each experimental product using Avizo® Fire   Table 3.2 Experimental conditions and physical property data by 2D and 3D image analysis for experimental products.      49 3.4 Results 3.4.1 Porosity  Two datasets were collected for each core imaged by XCT: one is for the bubble population within the core while the second is for the glass within the core. A ratio of the total volume of the bubbles to the sum of the volumes of the glass and the bubbles gives the porosity (φ) of the material as calculated by image analysis (Table 3.2). Figure 3.3a shows φ calculated by image analysis compared to φ measured by He-pycnometry. Data points lie along or near the 1:1 line on the figure, indicating agreement between the two methods for measuring the porosity of the samples.  Figure 3.3b shows the change in sample φ with time (t) for each temperature (T) suite. In each T suite there is an increase in φ with time until a maximum is achieved. After this maximum porosity value, φ plateaus or, rarely, decreases slightly. The plateau value of φ increases with increasing T and is an expression of H2O retrograde solubility (Chapter 2). The slope of the initial curved portion of each trendline is the initial vesiculation rate (v’), which increases with experimental temperature from 0.02 to 1.60 cm3/h. This positive relationship between vesiculation rate and T indicates that the rate of at least one aspect of the vesiculation process is strongly dependent on T.  3.4.2 Bubble number density Bubble number density (BND) is a normalized measure of the number of bubbles in a sample and is calculated by dividing the number of bubbles in the sample by the volume of the melt (BND = nB/Vi (mm3)) (Proussevitch et al. 2007).The change in BND with time and temperature is shown in Figure 3.3c and listed in table 3.2. BND, represented by the size   50  Figure 3.3 Porosity and bubble number density for all experimental products. (a) Porosity measured by Avizo® Fire (φAF (%)) against porosity measured by He-pycnometry (φHP (%)). Closed symbols are replicate measurements for one low- and one high-porosity sample. The black 1:1 line and replicate measurements show that XCT image analysis using Avizo® Fire reproduces results from physical measurements by He-pycnometry. (b) Porosity (φ  (%)) against time (t (h)) for all T suites. Symbols: closed circles: 900°C, open circles: 925°C, closed squares: 950°C, open squares: 1000°C, closed diamonds: 1050°C, open diamonds: 1100°C. Solid black curves are hand drawn to delineate datasets. Isothermal suites of experiments show non-linear increases in φ  with t until the curve reaches a plateau value. With increasing T the rate of vesiculation (v’, the slope of the curves at low t) and the final plateau value (the maximum φ  value) increase. The change in the maximum plateau value is the result of T-dependence of H2O solubility (Chapter 2). (c) Bubble number density (BND (number of bubbles per volume of initial volume of glass (nB/mm3Vi)); shown as symbol size) with time (t (h)) and temperature (T (°C)). BND, calculated using statistics generated by Avizo® Fire, generally increases with T and is often at a maximum at short dwell times. There is no systematic behavior with increasing t.     0 5 10 15 20 2520406080t (h)q (%)  900oC 925oC 950oC 1000oC 1050oC 1100oC0 20 40 60 8020406080φ HP (%)φ AF (%)0 5 10 15 20 25900950100010501100t (h)T (o C)BND (N/mm3)− 5− 10− 15 − 20− 25(a)(b)(c)  51 of the symbol, is generally greater with increasing temperature, from maximum values of 9.2 at 900°C to 22.5 at 1100°C. Within each T suite BND is generally at a maximum at short experimental dwell times, but otherwise shows no clear pattern with increasing time, and varies by 1 order of magnitude over the whole dataset (5.8 to 29.9).  3.4.3 Bubble size distribution  Bubble size distributions (BSDs) are a way of efficiently displaying textural data and can be plotted as normalized bubble volume or bubble number fractions per bubble size (Shea et al., 2010). Figure 3.4 shows the changes in the cumulative volume fraction (ΣVf) with bubble size (shown as bubble radius (r) in µm) as φ increases. There are three apparent changes in the cumulative volume fraction-size curves with increasing φ: (1) the curve shifts to the right between 0 and 40% porosity, indicating a decrease in the volume contribution of small bubbles  (25-200 µm in radius) (2) the largest bubble size generally increases with increasing φ, and (3) the maximum slope of the curves increases with increasing φ, reaching the greatest value in the 70-75% porosity range. An increase in the slope of the curve indicates a restriction in the volumetrically-dominant size range in the sample.   The calculated median, graphic standard deviation (which provides a measure of sorting) and skewness (Cas and Wright, 1987) for the bubble size distributions show little dependence on T, BND or φ (Figure 3.5). However there is a weak positive correlation between median bubble size and φ to ~ 40% porosity. Above 40% the median value becomes constant and the sorting of the bubble population (the graphic standard deviation) apparently decreases with φ. Finally, the maximum values of skewness are achieved at high φ values (Figure 3.5).     52 Figure 3.4 Cumulative volume fraction of bubbles of a given radius (r (µm)) at various porosities (φ) for all experimental products. BSD statistics are shown in the upper left corner: median bubble size (rmed), graphic standard deviation (i.e. a measure of sorting) (rσ), and skewness (rα). (a) At low porosities (φ=0-25%) the volumetrically-dominant size range is between 25 and 400 µm. The maximum bubble radius does not exceed 500 µm. Each curve has a similar slope in semilog space. (b) At intermediate porosities (φ=40-59%) the volumetrically-dominant size range has increased and restricted to 150-400 µm. The maximum bubble radius has increased to 800 µm. Compared to BSDs for low porosity samples (shown as grey lines) the slope of the curves has increased, reflecting the more-restricted BSD. rmed, rσ and rα have increased relative to the low porosity BSD. (c) At high porosities (φ=60-75%) the volumetrically-dominant portion of the BSD has increased and remained restricted (200-500 µm). The maximum bubble radius has increased, in one sample, to 1500 µm. Relative to the BSDs for low and medium porosity samples (grey lines) the slope of the BSDs for high porosity samples is at a maximum and is nearly the same for all BSDs, irrespective of temperature. rmed, rσ have remained the same while rα has generally increased. 1 0 2 1 0 300.20.40.60.81r ( μm)ΣV f  φ = 60 − 75%r med  = 50 − 291 μmr σ = 67 − 155 μmr α = 0.7 − 5.41 0 2 1 0 300.20.40.60.81r ( μm)ΣV f  φ = 40 − 59%r med  = 61 − 297 μmr σ = 68 − 129 μmr α = 1.7 − 4.71 0 2 1 0 300.20.40.60.81r ( μm)ΣV f  φ = 0 − 25%r med  = 54 − 143 μmr σ = 34 − 81 μmr α = 2.0 − 2.4(a)(b)(c)  53  Figure 3.5 BSD statistics against porosity (φ (%)) for all experimental products. (a) Median bubble sizes, shown as radius (r (µm)), initially increase with increasing φ then stabilize between 200-300 µm. Error bars are the graphic standard deviation of each BSD and represent the sorting of the bubble population. At elevated porosities the graphic standard deviation generally decreases. Three intermediate to high porosity samples (40-65%) have very low median values. Each of these samples has an anomalously high concentration of bubbles in the smallest size fraction (r=25 µm), which we attribute to errors related to imaging. (b) Skewness does not show a strong relationship to φ, though maximum skewness values generally increase with porosity. Positive skewness values reflect right-skew in BSDs, or distribution tails extended toward large bubble sizes.                0 2 0 4 0 6 0 8 0246φ (%)SKEWNESS0 2 0 4 0 6 0 8 001 0 02 0 03 0 04 0 0φ  (%)r (μm)MEDIAN(b)(a)  54 Figure 3.6 Cumulative BND (nB/Vi) against bubble radii (r (µm)) at various porosities (φ) for all experimental products. (a) At low porosities (φ=0-25%) BSDs are monotonically increasing smooth curves with steep initial slopes and short final plateaus, extending to ~450 µm. The maximum slope of BSDs for samples from 0-20% porosity are the same but the maximum slope of a ~25% porosity sample is less. Steep slopes are indicative of greater concentrations of the size range. (b) At intermediate porosities (φ=40-59%) BSDs are S-shaped and have a nearly flat portion of the curve up to 200 µm, shallow to moderately steep slopes from 200-350 µm and plateaus to the largest bubble sizes (up to 800 µm). At large bubble sizes the distribution of bubbles (points in the curve) becomes more diffuse: only individual bubbles have grown past ~550 µm, instead of the whole population growing equally. Relative to low porosity samples (shown as grey curves) bubbles less than 200 µm are uncommon and the size range of the most numerous bubbles is greater. There are 2 BSDs in this porosity range (and one at the higher porosity range) that show anomalously high concentrations of bubbles in the smallest size range (~25 µm in radius). We attribute these enrichments to errors related to image resolution and image processing. (c) At high porosities (φ=60-75%) BSDs for all samples are similar and include two steep slopes (one between 25 and 75 µm, the other between 200 and 400 µm) and two plateaus. The maximum bubble radius has increased, in one sample, to 1500 µm. Only individual bubbles are growing above ~550 µm. High porosity samples are slightly enriched in the smallest bubble size, have greater maximum bubble sizes, and greater concentrations of bubbles in the 200 to 400 µm size range, relative to intermediate porosity samples.   55 The cumulative bubble number density (ΣBNDf) of bubble sizes also change systematically with porosity (Figure 3.6): with increasing φ, both overall and within T suites, there are four distinct curves that appear:  (1) low porosity samples (5-20%) have smooth curves with nearly constant steep slopes followed by short plateaus. These curves have the smallest maximum bubble size.  (2) at intermediate porosities (25%) the slope of the curves decreases and the maximum bubble size increases.  (3) at higher porosities (40-60%) a kink develops in the curve and the BND of the small size fraction (<200 µm in radius) decreases dramatically. The maximum slope of the curve is less than that of curves for low porosity samples. The maximum bubble size continues to increase.  (4) in high porosity samples (61-75%) the kink in the curve becomes stronger. There is an increase in the BND of the smallest size fraction and there are two distinct plateaus, one for small bubbles (50-200 µm in radius) and one for larger bubbles (>350 µm in radius). The maximum slope of the curve is generally greater than the maximum slope of the curve for 40-60% porosity samples, but less than the slope for 5-20% porosity samples. The maximum bubble size of these samples is the greatest.   Three experiments have anomalously high BND values for the smallest size fraction (<40 µm in radius) although the patterns are similar to other experiments. In replicate tests of these datasets (i.e. reprocessing through Avizo® Fire) the anomalously high BND values at small size fractions sometimes disappear. Therefore the high BND values in this size fraction are likely the result of errors associated with segmenting and analyzing the XCT data.    56 Figure 3.7 Cumulative BND fraction against bubble radii (r (µm)) experimental products in each temperature suite: (a) 900°C, (b) 925°C, (c) 950°C, (d) 1000°C, (e) 1050°C and (f) 1100°C. BND here is cumulative number of bubbles per volume of the initial glass with radii greater than r. The dwell time (h) and porosity (%) of each sample are listed in legends in the lower left of each figure. Plateau samples (Figure 3.3b; Figure 3.8) are marked with a star in each T suite. Low porosity samples (porosities less than 20%) (black solid curves in (b), (d) and (e)) have short horizontal plateaus at small bubble sizes, then smooth curves to maximum bubbles sizes (~300 to 400 µm). Curves for samples with porosities greater than 20% have nearly horizontal portions to ~200 µm, then steeply decreasing curved portions to maximum bubble sizes (~400 to 1500 µm). In isothermal suites below 1000°C ((a), (b), (c)) the curved portion of each BSD moves right with t to nearly the same position, with a similar steep slope (e.g. 12, 20 and 24 h curves in the 925°C suite, 4 and 20 h curves in the 950°C suite). In isothermal suites at or above 1000°C curves move right with t, the maximum slope of the curve increases with t, then develops a ‘kick out’ (e.g. 4, 7.5 and 13 h curves in the 1000°C suite, 4 and 5 h curves in the 1050°C suite). These ‘kick outs’ develop at dwell times greater than that needed to reach a plateau value and result from a degree of gravitational settling.  1 0 2 1 0 30.00010.0010.010.11r ( μm)ΣBND(>r)f  20 h; 43%900 o C1 0 2 1 0 30.00010.0010.010.11r ( μm)ΣBND(>r)f  2.5 h; 4%5 h; 24%12 h; 42%20 h; 51%   24 h; 44%925 o C1 0 2 1 0 30.00010.0010.010.11r ( μm)ΣBND(>r)f  4 h; 46%20 h; 62%950 o C1 0 2 1 0 30.00010.0010.010.11r ( μm)ΣBND(>r)f  0.5 h; 17%1.5 h; 46%4 h; 64%7.5 h; 61%13 h; 64%1000 o C1 0 2 1 0 30.00010.0010.010.11r ( μm)ΣBND(>r)f  0.5 h; 12%1.17 h; 57%4 h; 73%5 h; 70%1050 o C1 0 2 1 0 30.00010.0010.010.11r ( μm)ΣBND(>r)f  1 h; 76%2h; 73%1100 o C(a)(b)(c)(d)(e)(f)  57 Figure 3.7 is the change in a modified version of the ΣBNDf - r curves in log-log space within T suites (ΣBND(>r)f - r). As noted in Figure 3.6 in all T suites there is a shift in the shape of curves at φ > 40%: below 40% curves are concave-down and decrease smoothly to maximum values from 300 to 500 µm, indicating there are numerous bubbles in small size fraction (<200 µm); above 40% the BND of small bubbles decreases and there is a restriction in the size range of the larger bubbles, which are expressed as a horizontal plateau that terminates near 200 µm and a steeply dipping nearly-linear curve to maximum bubble sizes (400-1000 µm), respectively.  Between T suites another relationship develops: in the 925°C and 950°C suites the final portions of most ΣBND(>r)f - r curves are nearly linear and have similar maximum slopes (Figure 3.7). In the 1000°C, 1050°C and 1100°C suites however the final portions of the curves transition from nearly linear to curved with progressively decreasing slopes as t increases past the time to reach equilibrium (starred curves in Figure 3.7). In these experimental cores the experimental dwell times is approaching the viscous relaxation timescale of the melt (τη) and cores suffer a degree of gravitational settling, which is expressed as a decrease in the slope of curves at r values greater than 600 µm. Because these features in the tails of the curves are not related to continued vesiculation, the modification to the BSDs, which causes the numerically-dominant bubble size range to be slightly less restricted and the maximum bubble size to increase, is ignored in the analysis of the curves. XCT images of the bubble populations in collapsed cores are available in Appendix I.   Lastly, Figure 3.8 shows ΣBND(>r)f - r curves and XCT images for selected plateau samples. We have used the plateau samples from each T suite at the first instance where sample porosity reaches the plateau φ value. This figure shows that the final portions of each curve have   58 very similar slopes and maximum bubble sizes. The consistency of these curves suggests that where φ reaches plateaus in each T suite the bubble size distribution is essentially the same (core photos in Figure 3.8).  Figure 3.8 Cumulative BND fraction against bubble radii (r (µm)) for plateau samples in each T suite (starred labels in Figure 3.7). These samples have reached the T-dependent of H2O solubility at 1 atm for each T-suite (Chapter 2). In each BSD the horizontal plateau at small bubble sizes extends to roughly 200 µm, then curves decrease steeply with nearly the same slope to maximum bubble sizes between 500-600 µm. The maximum negative slopes of the curves are nearly identical but represent wide T (900-1100°C) and porosity ranges (43-76%). The similarity in these BSDs can be ascribed to shared saturation states and thermochemical equilibrium. XCT images of the cores show the similarities between the bubble populations in plateau samples. Scale bars are 4 mm.  1 0 2 1 0 30.00010.0010.010.11r ( μm)ΣBND(>r)f  900 o C925 o C950 o C1000 o C1050 o C1100 o C9 0 0  º C 9 2 5  º C 9 5 0  º C1 0 0 0  º C 1 0 5 0  º C 11 0 0  º C  59 3.5 Discussion 3.5.1 Nucleation dynamics 3.5.1.1 BND: Potential nucleation events In our experiments we have observed few systematic changes in bubble number densities (BND) with time (t) in individual temperature suites. Generally at low t, BND is at a maximum but otherwise does not vary with t (Figure 3.3c). This suggests that processes that increase BND, including continuous or multiple significant periods of nucleation, are not occurring. Instead nucleation seems to primarily occur as a large discrete event at the start of the high-T experiments.   While the change in BND with t is not systematic, small fluctuations in BND with t, coupled with ΣBNDf - r curves, may reveal more subtle nucleation and bubble-interaction dynamics: Figure 3.6 shows an increase in the maximum size of individual large bubbles in samples with increasing porosity (φ>25%), which are likely the result of some form of coalescence, potentially Ostwald ripening given the textural evidence against physical coalescence (Appendix I). Some form of coalescence occurring early in the vesiculation process could also account for the slight initial drop in BND from the minimum t to the next experimental product in each T-suite (Figure 3. 3c). Also evident in Figure 3.6 is a slight increase in the amount of small bubbles in high porosity samples (φ>60%). This change in ΣBNDf - r curves, coupled with the slight increase in BND that occurs at maximum time in some of the high T suites (where samples achieve greater than 60% porosity) (Figure 3.3), suggests there may be a small late-stage nucleation in some samples after a certain porosity is achieved.   60 These signals are weak but persistent and may speak to the more nuanced nucleation and bubble-interaction dynamics in our experimental system. 3.5.1.2 BND: Sensitivity to oversaturation and temperature  Calculated BND values from this study are low relative to other experimental of bubble nucleation and growth in silicate melts. Our BND values range from ~5-30 N/mm3 which is 1-2 orders of magnitude lower than those found in other experimental studies (e.g. Hurwitz and Navon 1994; Gardner et al. 2000; Larsen et al. 2004; Mourtada-Bonnefoi and Laporte 2004; Burgisser and Gardner 2005; Baker et al. 2006; Gonde et al. 2011; Gonnermann and Gardner 2013). We attribute this discrepancy to the difference in the degree of H2O supersaturation: the starting material for this study initially contains 0.11(4) wt%, which is 0.01-0.02 wt% oversaturated relative to the 1-atmosphere solubility limits identified in Chapter 2. The materials from other experimental studies of nucleation on the other hand are vesiculated by decompression and have initial H2O concentrations often greater than 4 wt% (e.g. Mourtada-Bonnefoi and Laporte 2004; Gardner and Ketcham 2011; Gonnermann and Gardner 2013).  These observations suggest the magnitude of BND in any study, though moderated by surface tension (Gonnermann and Gardner 2013), is strongly correlated with the degree of oversaturation. Gonnermann and Gardner (2013) have previously proposed this relationship, as they observed a positive relationship between the BND of their experimentally-produced material and the supersaturation pressure. Additionally this conclusion is in line with the observed positive relationship between BND and decompression rate in nucleation experiments: where decompression rate is high the initial magnitude of supersaturation is also high, prompting a larger nucleation event and an elevated BND value (Hurwitz and Navon 1994; Gardner et al. 2000; Mourtada-Bonnefoi and Laporte 2004; Gardner and Ketcham 2011; Gonde et al. 2011;   61 Gardner et al. 2013). However in a recent study by Gardner et al. (2013) the authors observed a large range in BND for melts of different compositions at similar temperatures, degrees of supersaturation and surface tension values, which perhaps is the result of a range of melt viscosities. Ultimately some aspects of nucleation dynamics are still poorly understood.  We have also assessed the sensitivity of BND to changes in T using our different experimental T-suites: where the amount of H2O oversaturation is equivalent between T suites  (e.g. at plateaus) systematic changes in BND could be related to the temperature of the system. However BND does not show a strong relationship to T (Figure 3.3). Baker et al. (2006) and Gonde et al. (2011) have also noted that BND values show little or no sensitivity to T.  3.5.2 Growth dynamics  Figures 3.4, 3.5 and 3.6 have demonstrated that bubble size distributions (BSDs) vary systematically with increasing porosity, effectively tracking the evolution of bubble populations through the vesiculation process. Figure 3.7 shows the change in the bubble population with time/porosity in each T-suite. Combining observations from these figures we can infer several potential growth mechanisms that operate in our samples:  1. Following the initial nucleation event there is growth of the newly formed bubbles, as evidenced by the right-shift in Figures 3.4a, and 3.6a, and the increase in the median size of bubbles (Figure 3.5a). Growth however does not seem to occur at an equal rate for all bubble sizes, given the decrease in the slope of the curves in Figure 3.6a and the change in the curve shapes with T-suites in Figure 3.7 (e.g. 1000°C suite). Equal growth of bubbles by the same increment would result in a right-shift of the curve without a change in the slope in Figures 3.6 and 3.7.    62 2. As noted above some form of coalescence likely starts around 20% porosity, evidenced by the right-shift in the tails in Figures 3.4b and 3.6b and the appearance of single big bubbles >550 µm. This coalescence, likely Ostwald ripening given textural evidence (Appendix I), may cause the kink in Figure 3.6b: if small bubbles are preferentially scavenged to form large single bubbles, it will create a nearly flat slope at small bubble sizes without dramatically changing the slope of the rest of the curve.  3. Between 20 and 40% porosity bubble growth continues but the size range of bubbles is very quickly restricted, as shown by the steepening of the slope of curves in Figures 3.4b and 3.6b. Between 40 and 75% porosity the number of bubbles/volume fraction of bubbles between ~200-500 µm increases, but the size range is even more restricted given the steep slopes in Figures 3.4c, 3.6c and 3.7, and the decrease in the sorting of the BSDs (Figure 3.5a).  The similarity of BSDs with φ between T-suites suggests common growth mechanisms that are not heavily influenced by T.  The similarity between the BSDs (ΣBND(>r)f - r curves) and core photos for the plateau samples from all our T-suites (Figure 3.8) demonstrates the insensitivity of growth dynamics to small changes in initial H2O supersaturation. To achieve effectively the same bubble size distribution the bubble populations must be formed by the same growth mechanisms, irrespective of the difference in initial supersaturation in 900°C and 1100°C experimental materials (+5% and +15% the T-dependent 0.1 MPa H2O solubility limits, respectively (Chapter 2)). Therefore we can describe the envisioned growth mechanisms outlined above as insensitive to both T and H2O supersaturation over the ranges achieved in this study.    63 Previous forensic field and experimental studies have sought to link specific patterns in BSDs to nucleation and growth dynamics, and overarching volcanological processes (Marsh 1988;  Toramaru 1990; Cashman and Mangan 1994; Gaonac'h et al. 1996; Mangan and Cashman 1996; Marsh 1998; Larsen and Gardner 2000; Blower et al. 2001a; 2002; Proussevitch et al. 2007; Shea et al. 2010; Baker et al. 2012). Toramaru (1989), Blower et al. (2002), Baker et al. (2006), Bai et al. (2008) and Shea et al. (2010) have observed that melts at similar saturation states and with similar nucleation dynamics achieve similar BSDs. Additionally BSDs similar to those produced here (ΣVf – r curves, e.g. Figure 3.4; ΣBND(>r)f - r curves, e.g. Figures 3.7 and 3.8) have been described as forming from single nucleation events where limited ripening and coalescence has occurred and where the system degasses efficiently (i.e. physical properties of the system allow for near-equilibrium conditions) (Blower et al. 2002; Shea et al. 2010).  Therefore the mechanisms we have identified here agree well with previous BSD analysis. 3.5.3 Thermodynamic driving force  Thus far we have examined changes in nucleation and growth dynamics with respect to experimental (T, t) and physical properties (φ, H2O oversaturation) without quantifying the thermodynamic or kinetic parameters of the system. The next two sections examine the effects of chemical affinity (A), which is effectively the thermodynamic driving force for a chemical reaction, and melt viscosity (η), which is the primary kinetic moderator of the system, on nucleation and growth dynamics as well as growth rates.    In Chapter 2 we calculated the enthalpy (ΔHo) and entropy (ΔSo) of the H2O exsolution reaction using the slope and y-intercept of a linear-regression model (c.f. Figure 2.6). In this study we have used a similar methodology to recalculate ΔH° and ΔS° using independently    64 Figure 3.9 Thermodynamic driving force in T-suites. (a) Exsolution reaction equilibrium constant (ln(KH2O)) against T (1000/T (K)). Experimental products that lie off the equilibrium plateau (Figure 3.3b) and are still oversaturated in H2O are shown as open circles while plateau samples from T-suites are shown as closed symbols. A linear best-fit line for plateau samples defines the relationship between the equilibrium concentration of H2O and temperature, following the method used in Chapter 2. Enthalpy (ΔH°) and entropy (ΔS°) values recalculated from this best-fit line are given in the upper right corner (Appendix E). The 1100°C plateau sample has not been included in the linear-regression model (see Chapter 2). (b) Calculated chemical affinity (A (kJ mol-1)) against the mole fraction of H2O dissolved in the melt (ln(xH2O)). The initial A values for the melt as a function of the initial H2O content and T are shown as crossed circles. Remaining symbols as in (a). Solid black and grey lines with slopes greater than 0 show − 5.7 −5.6 −5.5 −5.4−0.2−00.20.4ln(x H 2 O )A/RT1200 o C 1100 o C900 o C800 o C1000 o CRESORPTIONVESICULATION− 5.7 −5.6 −5.5 −5.4−20246ln(x H 2 O )A (kJ mol−1 )800 o C1000 o C1200 o CRESORPTIONVESICULATION900 o C1100 o C0.72 0.76 0.80 0.84 0.8810.811.011.211.411.61000/T (K)ln(K H 2O)  H o = 1 8 . 4 9  k J  m o l − 1S o = 1 8 0 . 0  J  K − 1  mol −1ΔΔ(a)(b)(c)Δ H º  =  1 8 . 4 9  k J  m o l -1Δ S º  =  1 0 8 . 0  J  K -1    65 the relationship between A and ln(xH2O) for different temperatures (Appendix E). The horizontal line is where the system achieves equilibrium (A=0) and defines transition from volatile vesiculation to resorption. (c) A/RT against ln(xH2O). Symbols and graph form as in (b). The slope of the isothermal model curves is 2 and chemical affinity has been normalized to remove the effect of T.    calculated vapor densities and fugacities (Figure 3.9a; Appendix E). The recalculated values for ΔH° and ΔS° are 18.49 kJ mol-1 and 108.0 J K-1 mol-1, respectively. Using these values as well as calculated fugacities we have derived chemical affinity (A) for the starting material and each experimental product (Table 3.3; Figure 3.9b,c). These values again demonstrate the differencein the degree of H2O oversaturation that is a result of H2O retrograde solubility at 0.1 MPa (~1.6 kJ mol-1 per 100°C), and show that in our plateau experiments we have achieved thermodynamic equilibrium (where A=0). We have also identified a thermodynamic threshold where the degree of oversaturation cannot promote more than 1 major nucleation event (A= ~ 4 kJ mol-1).   These results are unique in bubble growth and nucleation literature: previous estimates of ΔH° and ΔS° for H2O exsolution are limited (e.g. Yamashita 1999; Liu et al. 2005)) and the thermodynamics of nucleation and growth, though frequently numerically modeled (e.g. Toramaru 1989; 1995; Proussevitch and Sahagian 1998; 2005; L'Heureux 2007) are not often experimental derived (e.g. Stevenson et al. 1997; Gonnermann and Gardner 2013). With respect to nucleation dynamics, previous authors have noted that continuous nucleation or multiple nucleation events are difficult to achieve in experiments (Gardner et al. 1999; Blower et al. 2002; Baker et al. 2006). However a thermodynamic threshold where multiple nucleation events can occur has yet to be established. While this A value (~4 kJ mol-1) is not particularly significant in terms of delineating the thermodynamic threshold for single vs. continuous nucleation, it is a step towards identifying the energy required by different nucleation regimes. Similarly we have   66 demonstrated that ~4 kJ mol-1 is not a sufficient change in the thermodynamic driving force of the system to cause a change in growth dynamics.   Finally we have established the relationship between the initial thermodynamics driving force (Ai) (Table 3.3) and the normalized volume change achieved at the time of equilibrium (ΔV/Vi) (Table 3.3): Figure 3.10a shows the positive relationship between these variables. The linear equation for this relationship is effectively a predictive tool for volume change by H2O exsolution given an initial saturation state.   T (°C)a Ai (kJ mol-1)b ΔV/Vic 900 1.01 0.762 925 1.42 1.024 950 1.84 1.168 1000 2.67 1.911 1050 3.50 2.381 1100 4.33 2.521 aExperimental temperature. bInitial chemical affinity. cNormalized change in sample volume at equilibrium.  Table 3.3 Computed values of initial chemical affinity and measured normalized volume change at equilibrium for varying temperatures.  3.5.4 Growth rates  Growth of a bubble is achieved by expansion of an over-pressurized bubble against the viscosity of the melt (η) and by diffusion of dissolved H2O into the bubble, which is controlled by the diffusion rate of H2O (D) (Sparks 1978; Toramaru 1995; Blower et al. 2001b). As these physical properties have unique T-dependence (Zhang et al. 2007; Giordano et al. 2008) there must be a temperature at which a growth regime limited by η develops over a growth regime   67 limited by D. The Peclet number roughly predicts the regime-switch in a system and is defined as  𝑃𝑒 = ∆𝑃  𝑟?𝜂  𝐷  where Pe is the dimensionless Peclet number, ΔP is the bubble overpressure (Pa), r is a representative radius of the bubbles (m), η is the viscosity of the melt (Pa s) and D is the diffusion rate of H2O in the silicate melt (m2 s-1). Because the Pecelt number is a ratio of the bubble expansion (η/ΔP) and diffusive timescales (r2/D) (Stevenson et al. 1997), a value of 1 roughly marks the transition from D-limited (D-controlled) (Pe >> 1) to η-limited (η-controlled) growth (Pe < 1) (Stevenson et al. 1997). T (°C)a teq (s)b H2Oeq (wt%)c log η (Pa s)d log DH2O (m2 s-1)e r (mm)f LD (mm)g τη (s)h τD (s)i Pej 900 7.20E+04 0.108 8.10 -12.35 0.20 0.36 2.50E+05 8.95E+04 0.36 925 7.20E+04 0.106 7.89 -12.27 0.16 0.39 1.54E+05 4.77E+04 0.31 950 7.20E+04 0.105 7.42 -12.19 0.15 0.43 5.23E+04 3.48E+04 0.67 1000 1.44E+04 0.100 6.83 -12.08 0.16 0.22 1.34E+04 3.08E+04 2.29 1050 1.44E+04 0.098 6.28 -11.94 0.14 0.26 3.79E+03 1.71E+04 4.51 1100 3.60E+03 0.097 5.77 -11.82 0.11 0.15 1.17E+03 7.99E+03 6.83 aExperimental temperature. bTime to the equilibrium concentration of H2O in seconds. cEquilibrium concentrations of H2O for the experimental temperature (Chapter 2).  dMelt viscosity values calculated from Giordano et al. (2008). eDiffusion rates for H2O in silicate melt are calculated from Zhang et al. (2007). fAverage space between bubbles in the plateau samples from each T-suite, meaured using ImageJ.  gThe diffusion lengthscale for H2O in the melt (LD = (4 D teq)0.5).       hCharacteristic timescale for viscous relaxation of the melt (τη = η ΔP-1 where ΔP is 503 Pa (Chapter 2)).  iCharacteristic timescale for H2O diffusion through the melt (τD = r2 D-1 where r is space over which H2O must diffuse, in this case the average distance between bubbles in the experimental core).  jThe ratio of the characteristic timescales for diffusion to the timescale for viscous relaxation (Pe = τD τη-1 (Stevenson et al., 1997)).    Table 3.4 Computed values of viscosity, H2O diffusion rate and Peclet numbers for Hrafntinnuhryggur (Krafla, Iceland) melt at varying water contents and temperatures.   68  Figure 3.10 Volume of exsolved H2O and average volumetric growth rates from supersaturation and viscosity. (a) The normalized change in volume (ΔV/Vi) against the degree of supersaturation (i.e. initial chemical affinity (Ai (kJ  mol-1))) for plateau samples (Figure 3.7, 3.8). Solid line is a linear best-fit regression model to describe the relationship of the relative volume of H2O exsolved to supersaturation at 0.1 MPa. The equation for this model is given in the lower right corner. (b) Average volumetric growth rate for all plateau samples (dV/dt = (ΔV/Vi) teq-1) against viscosity (log η; calculated from Giordano et al. (2008); Table 3.4). The solid line is a best-fit linear regression model, which is given in the lower left corner. Porosity values at the plateaus are listed in parentheses. Because these variables define an inverse Arrhenian relationship an increase in the viscosity of the melt results in a decrease in the growth rate or the same logarithmic magnitude.      0 1 2 3 4 50.511.522.53A i  (kJ mol −1 )V/V i   (1100 o C)(1000 o C)V/V i  = 0.57A i  + 0.22(900 o C)ΔΔ5.5 6.5 7.5 8.510 −210 −110 010 1log ηdV/dt (h −1 )1100 o C 1000 o C 900 o C(~70%)(~65%)(~60%)(~45%)log dV/dt = −0.79 log η + 4.95(~75%)(a)(b)  69  Peclet numbers for our melt at these experimental temperatures range from 0.31 to 6.83 using viscosity values from the GRD calculator (Giordano et al. 2008) and diffusion rates calculated from the equation produced by Zhang et al. (2007) (Table 3.4). Thus our material does not definitively sit in either the η- or D-controlled regime from 900-1100°C. However a comparison of the timescales for viscous relaxation (τη) and diffusion (τD) shows τη is of the same order of magnitude or longer than the dwell time required to reach an equilibrium concentration of H2O in the melt (teq). τD is also of the same order of magnitude as teq and τη but is frequently less than the dwell time to equilibration (Table 3.4). Additionally calculated diffusion lengthscales (LD = (4 D t)0.5) (Table 3.4) show that the time necessary to achieve equilibrium at each T is sufficient for H2O to diffuse into and between bubbles, given the average distance between bubbles (r) in these highly vesicular samples (Table 3.4). This indicates η is primarily the growth rate-limiting parameter in our experiments.    Figure 3.10b shows the inverse relationship between the average growth rate (log dV/dt = log ([ΔV/Vi] teq-1)) and viscosity (log η). This correlation demonstrates the role of kinetics in the exsolution process: while A controls the final volume of H2O exsolved (Figure 3.10a), exsolution is moderated by η and functions on a similar timescale to that of the relaxation timescale of the melt (τη). Experimental and numerical studies have previously identified and described this relationship (Sparks 1978; Lyakhovsky et al. 1996; Navon et al. 1998; Proussevitch and Sahagian 1998; Blower et al. 2001b; Masotta et al. 2014) but it has yet to be quantified in this manner. The linear scaling of these parameters in log-log space means that where viscosity spans several orders of magnitude (Table 3.4), average growth rate will as well.       70  Figure 3.11 Average volumetric growth rates and the time to 60% porosity in T-P-H2O space. (a) Temperature or Tg (°C) against water content for a range of pressures (light grey steeply dipping curves, (c.f. Figure 2.7)). Thick and thin shallowly dipping curves are isoviscous. Tg (log η=12) is the solid black and delineates the melt and glass (shaded grey) fields. Average volumetric growth rates given by the equation in Figure 3.10b are shown on the right side of the figure for select viscosities. The change in growth rate is the same order of magnitude as changes in viscosity in T-P-H2O space. (b) Same view and symbols as (a). Shaded fields represent 15% supersaturation for select isobars (MPa) (a comparable degree of supersaturation to this study). In these shaded fields the relationship between average volumetric growth rate and viscosity derived in this study can be used to calculate the time needed for the system to vesiculate to 60% porosity (t60% = 1.5 / (dV/dt))). At low viscosities (log η = 5) 60% porosity is achieved in less than 10 minutes, while near Tg the system needs nearly 6 years to produce 60% bubbles. Again, these vales are applicable to rhyolitic melts at conduit-relevant pressures and low degrees of supersaturation.    0 1 2 34006008001000H 2 O (wt%)T or Tg (o C)0 1 2 34006008001000H 2 O (wt%)T or Tg (o C)GLASSMELT1 0 -4.1 s - 1  1 0 -3.3 s -1 1 0 -4.9 s - 1  1 0 -6.5 s - 1  1 0 -8.1 s -1 1 0 -2.6 s - 1   9  m  5 5  m  5 . 7  h  3 5  h  5 6  d  5 . 8  y 0.1 1 2.5 5 1 0 2 0 3 0 4 0(b)(a)  71 3.5.5 Implications for volcanology When a silicate melt ascends to the surface, vesiculation occurs as a consequence of volatile supersaturation. As H2O exsolves from the system the bubble fraction of the magma and the melt viscosity will increase as dictated by P- and T-dependence of H2O solubility and the T- and H2O-dependence of viscosity, respectively (Figure 3.11a). Given the relationships observed in this study along with the findings of Chapter 2 we can predict average vesiculation rate for rhyolitic melts as a function of melt viscosity in T-P-H2O space where the degree of supersaturation is comparable to that in this study (+5-15% H2O solubility limit) (Figure 3.11b).  Similarly, using the same relationships we can derive the time necessary at achieve 60% porosity in the same system (t60% = 1.5 / (dV/dt))). This porosity value approximates a fragmentation threshold and, given the linear-scaling relationship in log-log space, can be achieved in less than 9 minutes at low viscosities (log η=5) and nearly 6 years at Tg (log η = 12). This vast contrast in the time needed to reach a porosity value that approaches the fragmentation threshold yet again demonstrates the profound importance of viscosity in a magmatic system.  3.6 Conclusion In this experimental study we have used XCT data for foamed rhyolitic obsidian cores to identify and describe bubble nucleation and growth dynamics over a range of temperatures (900-1100°C) and initial states of oversaturation (5-15% greater than H2O solubility limits) at atmospheric pressure. Additionally we have recalculated thermodynamic constants for the H2O exsolution reaction (ΔHo, ΔSo) and used chemical affinity values to assess the sensitivity of nucleation and growth mechanisms to changes in the thermodynamic driving force. Finally we have quantified average volumetric growth rates, and developed a kinetic model to describe the   72 change in growth rate with melt viscosity and the time needed to reach a critical porosity value in T-P-H2O space where H2O supersaturation is low (<15%). These models, though for the moment limited to low-pressure rhyolitic melts at low levels of superaturation, have the potential to serve as the basis for models that describe or forecast the vesiculation process in magmatic systems at conduit-relevant pressures.       73 Chapter 4: Conclusion The behavior of H2O in a silicate melt is of critical importance in the field of volcanology. Dissolved H2O has a profound effect on the physical properties and rheology of the melt, while exsolved H2O is the most significant driving force for magma ascent and volcanic eruption. Characterizing the behavior of both dissolved and exsolved H2O at a wide range of pressures, temperatures and conditions is absolutely vital for the geologic community’s understanding of the complex volcanic systems found in nature.  In this thesis I have used foamed rhyolitic obsidian from high temperature experiments to explore the temperature dependence of H2O solubility at atmospheric pressure (Chapter 2), and the dynamics and rates of bubble formation with respect to H2O supersaturation and viscosity (Chapter 3). By conducting these highly constrained experiments at atmospheric pressure using well-characterized natural experimental materials I have been able to systematically isolate and identify the relationships of H2O to several external and intrinsic properties of the rhyolitic silicate melt. This simple set of high temperature experiments again demonstrates the utility of experiments in attacking the fundamental questions and problems that arise in volcanology. I believe a similar campaign or an expansion of this study could be used to continue to explore the coupled behavior of dissolved and exsolved H2O present in a magma. I have partitioned my study of H2O behavior to H2O solubility and growth dynamics, but an integration of these two topics would shed light on another fundamental question in volcanology: the effect of bubbles on magma rheology (Figure 4.1). With the behavior of H2O solubility at atmospheric pressure well described in Chapter 2, and the rate of average volumetric growth and total volume change modeled for different temperature regimes in Chapter 3, an experimental high temperature deformation study of foamed rhyolitic obsidian could be used to differentiate the   74 effects of dissolved H2O and the volume of bubbles on the bulk rheology of a magma. Such a study would be a significant contribution to the field of volcanology and would be extremely useful for models that forecast volcanic hazards.   Figure 4.1 Summary cartoon of the change in dissolved H2O content (H2Om), melt viscosity (ηmelt), bubble fraction (ϕ), average volumetric growth rate (dϕ/dt) and magma viscosity (ηmagma) with depth in a rhyolitic volcanic conduit and surficial deposit. On the left is a cartoon of a volcanic conduit from with depths for nucleation, fragmentation and emplacement noted with thick grey dashed lines. Above the depth of emplacement a cartoon of a welding ignimbrite sheet is shown on the right side of the conduit. On the right are simplified changes in various physical properties with depth (left is low, right is high; solid line is the magma in the conduit or the eruption column, dashed line is the glassy material in the welding ignimbrite sheet): the change in H2Om is dictated by a T- and P-dependent H2O solubility model (Chapter 2, e.g. Liu et al., 2005). In a cooling ignimbrite sheet retrograde solubility may cause H2O resorption, which will cause H2Om to increase (Chapter 2). Because ηmelt is heavily dependent on H2Om, accurate modeling of ηmelt (e.g. Giordano et al., 2008) requires a constrained T- and P-dependent H2O solubility model that is suitable to surficial pressures (e.g. Liu et al., 2005). ϕ is also an expression of H2O solubility (Chapter 2) and is controlled by the thermodynamics of the exsolution process (Chapters 2, 3). In a cooling ignimbrite sheet where resorption is occurring ϕ will change dramatically (Chapter 2), potentially producing dense glassy rhyolitic flows. As determined in this body of work dϕ/dt is inversely proportional to ηmelt and controls the time to a critical fragmentation threshold (Chapter 3). Thus accurately modeled ηmelt has the potential to be a predictor for the timescale from nucleation to fragmentation (Chapter 3). The ultimate aim is to produce a comprehensive model for ηmagma (e.g. Quane et al., 2009) that accounts for the parameters explored in this thesis. 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A.1 H2O Solubility at 0.1 MPa Melt Composition T (°C) H2O (wt%)a Source rhyolite (Bandelier Tuff) 635 0.15 Friedman et al. (1963) rhyolite (Bandelier Tuff) 735 0.10 rhyolite (Bandelier Tuff) 735 0.10 rhyolite (Bandelier Tuff) 785 0.05 rhyolite (Bandelier Tuff) 835 0.02 synthetic calcium aluminosilicate 1200 0.121 McMillan et al. (1986) rhyolite (Mono Craters) 552 0.186 Liu et al. (2005) rhyolite (Mono Craters) 698 0.126 rhyolite (Mono Craters) 750 0.116 rhyolite (Mono Craters) 851 0.106 rhyolite (Mono Craters) 850 0.105 rhyolite (Mono Craters) 850 0.104 rhyolite (Mono Craters) 999 0.102 rhyolite (Mono Craters) 1000 0.099 rhyolite (Mono Craters) 1000 0.098 rhyolite (Newberry Volcano) 552 0.180 rhyolite (Newberry Volcano) 698 0.124 rhyolite (Newberry Volcano) 750 0.115 rhyolite (Newberry Volcano) 851 0.106 rhyolite (Newberry Volcano) 850 0.105 rhyolite (Newberry Volcano) 850 0.103 rhyolite (Newberry Volcano) 999 0.102 rhyolite (Newberry Volcano) 1000 0.100 synthetic haplogranite 552 0.187 synthetic haplogranite 698 0.119 synthetic haplogranite 851 0.102 synthetic haplogranite 999 0.099 synthetic haplogranite 1000 0.094 aCalculated difference in H2O solubility due to the difference in composition between rhyolitic glass from this study and glasses from Liu et al. (2005) is 3E-5 wt% (Zhang et al. 2007).  Table A.1 Compilation of all published equilibrium concentrations of H2O for a range of temperatures at atmospheric pressure.    87 A.2 Surface Tension Melt Composition SiO2 (wt%) H2O (wt%) T (°C) σ (N m-1) Source basalt 50.28 0.00 1500 0.355 Walker and Mullins (1981) basalt 51.29 0.00 1497 0.354 andesite 61.79 0.00 1510 0.352 limburgite 43.31 0.00 1499 0.348 basalt 49.66 0.00 1296 0.371 rhyolite 77.35 4.70 800 0.104 Mourtada-Bonnefoi and Laporte (1999) rhyolite 77.35 4.75 800 0.104 rhyolite 77.35 6.80 800 0.104 rhyolite 77.35 7.00 800 0.104 rhyolite 77.35 7.70 800 0.104 haplogranite 78.60 9.26 800 0.073 Bagdassarov et al. (2000) haplogranite 78.60 8.90 900 0.084 haplogranite 78.60 8.90 1000 0.090 haplogranite 78.60 8.91 1100 0.097 haplogranite 78.60 8.92 1200 0.103 haplogranite 78.60 0.00 1150 0.351 rhyolite 75.60 0.00 1150 0.282 rhyolite 75.64 5.20 900 0.110 Mangan and Sisson (2000) rhyolite 76.51 6.90 800 0.106 Mourtada-Bonnefoi and Laporte (2004) dacite 69.30 5.70 1000 0.042 Mangan and Sisson (2005) dacite 68.80 5.20 1000 0.060 dacite 68.70 4.80 1000 0.073 dacite 68.70 4.80 900 0.043 rhyolite 76.53 4.98 1085 0.088 Gardner and Ketcham (2011) rhyolite 76.53 4.98 975 0.087 rhyolite 76.53 4.98 875 0.078 rhyolite 76.53 4.98 825 0.078 rhyolite 76.53 4.98 775 0.088 dacite 66.93 3.51 1150 0.083 phonolite 61.47 5.37 875 0.061 Gardner (2012) phonolite 61.47 5.37 1150 0.052 trachyte 62.57 4.50 1150 0.073 Gardner et al. (2013) dacite 69.85 4.72 1150 0.072 rhyolite 76.53 5.05 1150 0.066 phono-tephrite 51.13 4.44 1150 0.072 basaltic andesite 54.12 4.63 1150 0.067 dacite 66.93 3.51 1150 0.065  Table A.2 Compilation of all published values of surface tension (σ) between H2O bubbles and silicate melts.     88 Appendix B   Mass Loss in Samples We attribute the measured mass loss in our samples to the integration of two signals: (1) mass loss due to diffusion of H2O out of the sample over the experimental timescale, and (2) mass loss due to H2O leaking out of the sample through cracks formed during quenching.  We have modelled the magnitude of mass loss in our experimental cores that can be ascribed to H2O diffusion (and escape) through the cylinder walls over the time of the experiment (Crank, 1975, pg. 74).  The dimensionless concentration (x/x0) of the diffusing agent (i.e. H2O) can be mapped as a function of dimensionless radius (r/r0) from the exterior wall of the cylinder inwards for the parameter α where: 𝛼   =     ?∙?    ???       (Eq. B.1) We have used Zhang et al. (2007) to select the appropriate diffusion rates (D; m2/s) for our experiments (1.7E-12 to 4.5E-13 m2s-1) and used the maximum times of each experiment for t (s). For our 1 cm diameter experimental cores and their maximum dwell times we obtain α values between 10-5 to 10-3.These calculations indicate that for a maximum time and temperature, H2O loss due to diffusion through the cylinder walls will never affect a thickness greater the exterior 1 mm of the core. This is substantially thicker than the maximum "bubble depleted" margin (0.4 mm) observed in any of our run products. Furthermore, the maximum drop in concentration is to 50% of the original H2O content. This partial diffusion-controlled degassing would correspond to a mass loss of 0.37 mg if we accept the modelling limits (0.5 mm rinds depleted of H2O) and 0.16 mg if we use the observed rinds (0.2 mm). As these values are well below the observed mass loss (Figure B.1) we again assert that diffusion is not the primary mechanism for mass loss. We believe mass loss due to H2O leaking through cracks formed during quenching is the   89 dominant mechanism. Though we do not have images to confirm the presence of microfractures in our samples we have several observations that give us confidence in this interpretation: (1) if H2O mass loss were occurring during the high-T experiments a majority of the H2O vapor filling bubbles would be lost and bubbles would collapse as the melt around them relaxes. However as these experimental products have measured final porosities up to 70% we are confident that at the time of quenching H2O vapor must still be present within bubbles; (2) the very systematic positive relationship between volume change and mass loss for all experiments (including those before the plateaus) suggests the mechanism responsible of mass loss is related to the volume of bubbles at the time of quenching rather than the time or temperature of an experiment; (3) because samples are quenched below Tg within 10-15 seconds of removal from the furnace it’s likely that the quenched glass surrounding bubbles is extremely fragile and potentially unstable. Romano et al. (1996) noted microfractures developing around isolated H2O-filled vesicles in quenched glasses due to contraction of the glass around the vesicles during quenching. In these experiments escape of H2O along microfractures after quenching caused a decrease in glass density, which was most pronounced in the time between quenching and the post-experiment physical property measurements. We believe a similar mechanism is responsible for mass loss in our samples, though it may be amplified by the close proximity of bubbles (and thus thin glass walls) in our higher porosity samples.    90  Figure B.1 Change in sample mass (Δm) vs. change in sample volume (ΔV) for all experiments at all temperatures (900-1100°C). The maximum mass loss that can be ascribed to diffusion out of the cores is shown as a grey box. The strong positive correlation between the measured mass loss and volume gain is ascribed to post-experiment leakage of exsolved H2O during quenching. There is no correlation to experimental temperature (purple: 900°C; blue: 925°C; light blue: 950°C; green: 1000°C; yellow: 1050°C; red: 1100°C) indicating that mass loss depends only on the magnitude of volume increase (i.e. vesiculation) and that the core can effectively be viewed as a closed-system during the high-T experiment.      0 0.5 1 1.5 2−2.5−2.0−1.5−1.0−0.50∆ V (cm3)∆ m (mg)  91 Appendix C  Bubble Size Distribution for Internal Pressure Calculations  Figure C.1 Bubble size distribution showing volume fraction against bubble radius (mm) for three samples (4 hr, 7.5 hr, 13 hr) from the 1000°C experimental suite. The average bubble radius for all bubbles used for internal pressure calculations (0.322 mm) is shown as a red point on each plot. The volumetrically-dominant size range for a majority of samples lies between 0.2 and 0.5 mm.     0.1 0.2 0.3 0.4 0.5 0.600.20.40.60.81r (mm)Volume fraction  4 h7.5 h13 h1000 oC  92 Appendix D  Derivation of Thermodynamic Values D.1 Enthalpy and Entropy of H2O Exsolution At equilibrium there is equality of chemical potentials (µ) between H2O dissolved in the melt (m) and exsolved as a vapor (v) 𝜇???? = 𝜇????    (Eq. D.1) The corresponding free energy balance for this equilibrium is 0 = ∆𝐺(?,?)? + 𝑅𝑇  𝑙𝑛 ??????????   (Eq. D.2) where ∆𝐺(?,?)?  is the standard state free energy change for the equilibrium represented by Eq. D.1, 𝑓????  is the fugacity of H2O vapour, and  𝑎????  is the activity of H2O in the melt. Expansion of Eq. D.2 in terms of standard state values of enthalpy and entropy yields: 0 = ∆𝐻(?,?)? − 𝑇∆𝑆(?,?)? + 𝑅𝑇  𝑙𝑛 ??????????   (Eq. D.3) The activity of H2O in the melt can be approximated as the square of H2O content measured, assuming all H2O is speciated as OH at low pressure, low concentrations and high temperatures. This assumption is corroborated by Silver and Stolper (1988), Ihinger et al. (1999) and Zhang et al. (2007) and coincides with previous H2O solubility models (Nicholls, 1980; Burnham 1994; Sahagian and Proussevitch 1996). Thus, 𝑎???? = [𝑥???]?  (Eq. D.4) The fugacity of H2O vapour is the fugacity for H2O in the vapour at the experimental conditions divided by the standard state conditions: a pure ideal gas at atmospheric pressure (i.e. 101325 Pa). Assuming that the bubbles in our experiments contain pure H2O fluid at the model internal bubble pressure (cf. Table 2.3):   93  𝑓???? =   ????™ ℣ ␥ = ™ ℣ ␣™ ℣ ␥ ≅ 1   (Eq. D.5) Substituting these values in to equation D.3 yields 0 = ∆𝐻(?,?)? − 𝑇∆𝑆(?,?)? + 𝑅𝑇  𝑙𝑛 ?[????]? (Eq. D.6) The corresponding equilibrium constant (𝐾?) is 𝐾? = ?[????]? = [𝑥???]?? = 𝑒𝑥𝑝?∆??™ 𝑒𝑥𝑝∆???   (Eq. D.7) This can be rearranged to form the Arrhenian equation: 𝑙𝑛  𝑥??? = ∆??? ™ + ?∆????    (Eq. D.8) where slope (m) and intercept (b) are:  𝑚 = ∆????   (Eq. D.9) 𝑏 = ?∆????   (Eq. D.10) We obtained estimates for ∆𝐻? and ∆𝑆? from fitting Eq. D.8 to our experimental data over the temperature range 900 to 1050°C (cf. Fig. 2.6a).          94  Appendix E  Recalculating Enthalpy (ΔH°) and Entropy (ΔS°) and Chemical Affinity (A) At equilibrium there is equality of chemical potentials (µ) between H2O dissolved in the melt (m) and exsolved as a vapor (v) 𝜇???? = 𝜇????   (Eq. E.1) The corresponding free energy balance for this equilibrium is 0 = ∆𝐺(?,?)? + 𝑅𝑇 ln𝐾???  (Eq. E.2) or 0 = ∆𝐻(?,?)? − 𝑇∆𝑆(?,?)? + 𝑅𝑇   ln𝐾???  (Eq. E.3) where ΔG°(T,P) is the standard state free energy change for the equilibrium represented by Eq. E.1 ΔH°(T,P) is the standard state value of enthalpy, ΔS°(T,P) is the standard state value of entropy and KH2O is the equilibrium constant:  𝐾??? = ????(?,?,?)? /????( ™?   ?,?   ™? ,???)??????   (Eq. E.4) where f vH2O(T,P,X) is the fugacity of H2O vapour at the temperature, pressure and composition of interest, f °H2O(298 K,1 atm,X=1) is the standard state fugacity of H2O vapour (f °H2O =1), and amH2O  is the activity of H2O in the melt. The activity of H2O in the melt can be approximated as the square of H2O content measured, assuming all H2O is speciated as OH at low pressure, low concentrations and high temperatures: 𝑎???? = [𝑥???]?  (Eq. E.5) Thus the equilibrium constant becomes  𝐾??? = ????(?,?,?)?[????]?   (Eq. E.6)   95 Using the Redlich-Kwong EOS and the WebGasEOS calculator by the Lawrence Berkeley National Laboratory I calculated f vH2O(T,P,X) for each experimental temperature (Texp) and the internal pressure of the bubbles (Pi; 101828 Pa (Chapter 2)), assuming X=1 (see values below).  I also used the Redlich-Kwong EOS and the WebGasEOS calculator to estimate the density of H2O vapour at these conditions. Multiplying these density values (see values below) by the molar mass of H2O and the measured volume change in each experimental core (ΔV from Chapter 2) we can derive the moles of H2O in the bubbles present in samples. By difference we can calculate the moles in the residual glass and xH2O for each sample.  Plotting lnKH2O against 1/Texp (K) for plateau samples (excluding the 1100°C plateau) and fitting these points with an Arrhenian best-fit line (Figure 3.9) allow us to model ΔH° and ΔS° because of the following relationships:  ln𝐾??? = ?∆??™ + ∆???   (Eq. E.7) 𝑚 = ?∆???   (Eq. E.8) 𝑏 = ∆???   (Eq. E.9) where m and b are the slope and y-intercept of the Arrhenian best-fit line, respectively.  In our experiments H2O dissolved in the melt (m) is being exsolved as a vapor (v) until equilibrium is reached. Thus the dominant reaction is the following:  𝜇???? → 𝜇????   (Eq. E.10) Chemical affinity (A), which is effectively the chemical driving force for a reaction, is related the to Gibbs free energy of a reaction (ΔrG) by the following relationship  𝐴 = −∆?𝐺  (Eq. E.11) where   96 ∆?𝐺 = ∆?𝐺°+ 𝑅𝑇 ln𝐾???  (Eq. E.12) where ΔrG° is the standard state Gibbs free energy of the reaction, R is the universal gas constant, T is temperature, and KH2O is the equilibrium constant. As discussed above KH2O is related to f vH2O and amH2O. KH2O can thus be rewritten as  ln𝐾??? = ln ????(?,?,?)?????( ™?   ?,?   ™? ,???)? − ln 𝑎????   = ln ????(??,? ™? ,???)? ? − 2ln(𝑥???) (Eq. E.13) Because the standard state Gibbs free energy of the reaction (ΔrG°) is as follows ∆?𝐺° = ∆𝐻(?,?)? − 𝑇∆𝑆 ?,?? + 𝑅𝑇 ln ???? ??,? ™? ,???? ? − 𝑅𝑇 2ln(𝑥???)  (Eq. E.14) affinity can be calculated using the following equation: 𝐴 = −∆𝐻 ?,?? + 𝑇∆𝑆 ?,?? − 𝑅𝑇 ln ???? ??,? ™? ,???? ? + 𝑅𝑇 2ln(𝑥???)  (Eq. E.15) Values used in this equation, including the recalculated model ΔH° and ΔS° values, are listed below.   VALUES Fugacity f vH2O(900C,Pi,X=1) = 0.99977 f vH2O(925C,Pi,X=1) = 0.99979 f vH2O(950C,Pi,X=1) = 0.99981 f vH2O(1000C,Pi,X=1) = 0.99984 f vH2O(1050C,Pi,X=1) = 0.99987 f vH2O(1100C,Pi,X=1) = 0.99989 f vH2O(1100C,Pi,X=1) = 0.99989   97 Density ρH2O(900C,Pi,X=1) = 0.0001881 ρH2O(925C,Pi,X=1) = 0.0001842 ρH2O(950C,Pi,X=1) = 0.0001804 ρH2O(1000C,Pi,X=1) = 0.0001733 ρH2O(1050C,Pi,X=1) = 0.0001668 ρH2O(1100C,Pi,X=1) = 0.0001607 Enthalpy and Entropy ΔH°(T,P) = 18.49 kJ mol-1 ; assumed to be independent of temperature ΔS°(T,P) = 108.0 J K-1 mol-1 ; assumed to be independent of temperature     98 Appendix F  XCT Image Processing The goal of this appendix is to provide a manual for ‘Tomoview’ (thus far there is not one and very few instructions available from LMU), discuss the effectiveness of ‘Tomoview’ and other programs relative to Avizo® Fire, and outline the steps used in Avizo® Fire to produce the dataset analyzed in Chapter 3.  F.1  ‘Tomoview’: Instructions  ‘Tomoview’ is a MATLAB-based program developed at Ludwig-Maximilians-Universität (LMU) in Munich, Germany (Flaws et al. 2011). It is designed to process and segment 3D XCT data using a relatively simple, relatively fast, free program. Like other 3D image processing programs (e.g. ‘3D Object Counter’ plugin in ImageJ (Bolte and Cordelieres, 2006), Particle Analyzer’ tool in the BoneJ (v 1.3.12) plugin for ImageJ (Doube et al. 2010), BLOB3D (Ketcham, 2005), Pore3D (Brun et al., 2010), Avizo® Fire (by the FEI Visualization Sciences Group)) ‘Tomoview’ uses combinations of greyscale thresholding, filtering and watershed-based segmentation algorithms to isolate and quantify different materials within stacks of XCT data.  The ‘Tomoview’ program can only be accessed through the LMU Mineralogy server after a user account is established through Ludwig-Maximilians-Universität (LMU). Within the remote connection portal the user can access the XCT data files through the ‘Storage 1’ shortcut on the desktop, then the ‘ct’ folder, the ‘XCT’ folder, then the individual run folder (often begins with ‘mgm###’ followed by a sample name keyed in by whoever collected the XCT data using the GE phoenix® v|tome|x s 240 micro-CT scanner at the Institute of Medical Engineering at the Technische Universitat Munchen (IMETUM) facility at the TUM Research Campus in Garching, Germany).    99 Within the specific run folder there are several important files/folders to identify amongst the ~2000 files in each folder:  • an .AVI file: a video of corrected .TIFF files, down the z-axis,  • a .PCA file: a notepad document that contains run conditions and the image resolution (labeled as ‘VOXELSIZEX’ and ‘VOXELSIZEY’ and given in mm)  •  the folder containing the merged/corrected set of .TIFF files (often has ‘recon’ in the folder name).   To increase the processing speed copy and paste the folder containing the corrected .TIFF files to the desktop. Also create an ‘output’ folder so you can keep modified .TIFF sets separate.  Open ImageJ either by opening a single .TIFF file or by finding the program in the Applications menu. In ImageJ import the full sequence of corrected .TIFF files (File>Import>Image Sequence…, select any image in the set, hit ‘Open’). A ‘Sequence Options’ dialog box will open. Hit ‘OK’ without making changes. ImageJ will now open all .TIFF files together in sequence, looking down the z-axis. The user can view the x- and y-axes by switching to orthogonal view (Image>Stacks>Orthogonal Views…). Travelling from the first to the last image the user will move ‘up’ through the sample, from the sample base to the air above the sample.  Convert the image to 8-bit (Image>Type>8-bit). Then optimize the contrast in the image. The easiest way to do this is to zoom in to the image to an area where the different phases to be identified are present. Adjust the contrast and brightness (Image>Adjust>Brightness/Contrast) using the ‘Auto’ function, followed by increasing the ‘Minimum’ and reducing the ‘Maximum’ until the image is more or less binary, or at least until each phase has a distinct greyscale value. It is preferable to make the image almost-binary rather than binary because it gives more leeway to   100 the user in subsequent processing stages. Hit ‘Apply’ when contrast is suitable. Save the new ‘optimized’ .TIFF images as an image sequence (File>Save As>Image Sequence) in the ‘output’ folder on the desktop. It can be helpful to give these .TIFF files a name like ‘optimized’ or ‘binary’ to keep them straight from other .TIFF sets.   Open MATLAB. Change the ‘Current Folder’ to D:\tomoview. In the command space type writeVOX to initialize the conversion from .TIFF files to a single .VOX file. A dialog box will open. Open the ‘optimized’ .TIFF files. A preview of the .TIFF file stack will appear in a new dialog box in MATLAB after the image sequence is selected. In the first dialog box change the drop-down menu labeled ‘Voxel Size’ from ‘pixel’ to ‘um’ and input the resolution in microns in the space to the left. Make sure the ‘Downsampling’ drop-down menu reads 1:1. Hit ‘Save’ and MATLAB will begin writing the .VOX file. A progress bar will appear and fill several times as the file is being written. MATLAB will list the final elapsed time when the writing process is complete. This can take anywhere from a few seconds to an hour depending on the traffic on the LMU Mineralogy server.   In the MATLAB command window type tomoview to open the ‘Tomoview’ dialog window. Open the .VOX file and a preview will appear in the dialog box.   Within ‘Tomoview’ there are four tabs that allow the user to edit and analyze the .VOX file. In the ‘Read’ tab, the user can switch viewing directions using the drop-down menu in the upper left corner of the dialog box. Using the ‘Outline’ tool the user can select a subvolume to analyze (the selection should be verified in each field of view to make sure it is correct). For these analyses I selected as much of the sample as I could without getting interference from the sample stand or the top of the sample (these areas will appear grainy and pixelated in some fields of view. In this tab the user will also need to set the ‘downsampling’ ratio: the ratio 1:1 does not   101 subject the selected volume to downsampling and will give the highest resolution data possible. To move on to the next tabs the user will need to hit the ‘(G)et Vol’ button. A progress bar will appear and fill when this step is complete. Again this can take minutes to tens of minutes depending on the traffic on the LMU Mineralogy sever. The exact dimensions in pixels of the selected volume can be retrieved by typing size(core.V) in the MATLAB command window.   In the ‘Process’ tab the user can apply a variety of filters (‘Smooth’, ‘Sharpen’, ‘Median’, ‘Deblur’), change body morphology (‘Erode’, ‘Dilate’, ‘Open’, ‘Close’) and segment the greyscale data using a watershed algorithm. Additionally the user can change the fields of view using the drop-down menus in the upper right. To see the changes in the dataset based on any filters or segmentation applied, change the field of view to ‘Segmented’. A list of applied filters/changes will appear in the grey box in the lower left corner. Due to a bug in the program a pre-applied filter and segmentation scheme always appear in this space. The erroneous filter can be removed by selecting it and hitting the ‘Remove’ or ‘Clear All’ buttons.  When segmenting the data, the user inputs a greyscale gradient threshold that the program will use to divide the image in to 3D areas of ‘like’ greyscale. This segmentation scheme can be used to identify and define different materials in the subsequent ‘Materials’ tab, or to distinguish air outside the sample from the solid material and bubbles within the core. For these samples no filters or changes to morphology were applied, and a gradient of 0.010 or 0.001 was used and tracked over an infinite distance (‘0.010:Inf’ or ‘0.001:Inf’ in ‘Tomoview’). The ‘0.001:Inf’ setting produces the highest degree of segmentation possible in the .VOX file and was used to try to capture the thin bubble walls that likely exist between individual bubbles. Unfortunately this sensitivity can also result in over-segmentation where naturally occurring   102 greyscale gradients (e.g. at the edge of bubbles) are identified as a number of entities rather than a single entity.  To apply a segmentation scheme, filters or morphology changes hit their respective ‘Add’ button and make sure they are listed in the grey box in the lower left corner. Hit the ‘(P)rocess’ button to proceed with segmentation. A progress bar will appear and fill when the process is complete. Of all the steps involved in ‘Tomoview’ processing, this step takes the longest and often causes ‘Tomoview’ and MATLAB to temporarily freeze. When it is complete a preview will appear in the upper box on the right side. If the segmentation is satisfactory click on the ‘Materials’ tab.  In the ‘Materials’ tab the user can identify and define different materials in the sample. This can be done using one of three histograms: ‘Processed’, ‘Segmented’, and ‘Volume’. The ‘Processed’ histogram, which shows greyscale against voxel quantity, uses information from the greyscale in the .TIFF files used to generate the .VOX file. The ‘Segmented’ histogram, which shows greyscale against voxel quantity, uses the segmentation criteria applied by the user in the ‘Process’ tab. The ‘Volume’ histogram displays greyscale against volume. By selecting different areas on any of the histograms the user can highlight different materials within the sample. For these analyses, the ‘Processed’ histogram was the only one used to define materials. Because no filters or changes to morphology were applied in the ‘Process’ tab, the greyscale data has not been altered since the optimized contrast was set in ImageJ. The sources of error then are related to the image resolution (see below) and the user’s ability to pick the area on the histogram that best defines one material without including information from others. The user can alter the morphology of the selected material, using the ‘Erode’, ‘Dilate’, ‘Open’ and ‘Close’ functions. These functions were not used for these analyses. The user can also remove any unwanted bodies   103 from the highlighted material, such as air outside the core, by right-clicking. It’s also possible to select individual bodies by left-clicking on them. Using this function the user can check the connectivity of materials. Selecting or unselecting bodies within a core relies on the segmentation criteria defined by the user in the ‘Process’ tab. For these analyses I picked conservative greyscale values in the ‘Processed’ histogram to define bubbles in the cores. This means the greyscale selected would eliminate some necks between bubbles without applying morphology changes. The result should be a less connected mass of bubbles. I also removed the air outside the samples by right-clicking.  To define a set of greyscale values as a material highlight an appropriate greyscale range using the 3 histograms. A preview of the material will appear in the box on the right. Label the material in the box beneath the drop-down menu on the lower right side, then hit ‘Define’. A progress bar will appear and fill when the process is complete. To define another material use the drop-down menu in the lower right to pick another material label (e.g. ‘Material #2’). Complete the same greyscale-selection process and hit ‘Define’ again. Repeat for any other materials. For these analyses I defined greyscale ranges for bubbles in the cores (i.e. Material #1) and for the total volume of the core (i.e. Material #2). Using these two sets of data I could compute sample porosity by image analysis.   In the ‘Analysis’ tab the user can render movies or figures of different materials, plot the surface area of a specified greyscale within the sample, fit ellipses to a material, and export volume data for a given material. Most of these functions take a lot of time and memory to run so I did not fully explore their capabilities. When exporting volume data, the ‘Tomoview’ program counts the number of individual entities that fall into the greyscale range defined in the   104 ‘Materials’ tab and gives the volume occupied by each entity found, in addition to the greyscale and centroid.   To export volume data in m3 for a given material select it from the drop-down menu on the upper left side. On the lower left side select ‘Table’ from the drop-down menu on the far left and ‘[m]’ from the second drop-down menu. To get centroid data and a header in the resulting table select those two options, again in the lower left corner. Hit ‘Save Database’ and save the resulting .DAT file in the ‘output’ folder for the sample on the desktop. To export volume data for other materials return to the ‘Analysis’ tab, select another material from the drop-down menu on the upper left side and repeat.  To generate a 3D rendering of the processed volume hit the ‘[V]olume Render’ button in the upper left corner of the ‘Analysis’ tab. A new dialog box will open with two tabs: The ‘Render’ tab allows the user to view and manipulate the position of the 3D image; the ‘Materials’ tab lets the user change the color of the materials of interest. To change the color of a specific material in the ‘Materials’ tab, select it from the drop-down menu on the left side. Various color schemes are available in the lowest drop-down menu and the user can manipulate a given set of colors in the graph at the top of the tab. Moving the points on the line in the graph up or down changes the transparency of the color, and changing or flipping the position of the points on the line relative to the x-axis changes which greyscale value the color is assigned to. Unselecting the ‘Render’ button will remove the given material from the final rendered image. There are a few other features in the ‘Materials’ tab but again they run slowly so I did not take the time to explore them.    105  In the ‘Render’ tab the user can move the 3D image using the arrow keys on the keyboard. The user can create an .AVI file containing a 360° rotation of the 3D image by hitting the ‘Save Movie’ button. The user can also render a static figure using the ‘Figure’ button.   To move data from the LMU Mineralogy server to the user’s own computer files should be uploaded to a cloud or sharing website like Dropbox or docs.google. Disconnect from the LMU Mineralogy server when finished using whatever method is available through the remote connection platform.  F.2 Image Processing Effectiveness While ‘Tomoview’ is a relatively fast and easy program to use, the results provided by the program can be difficult to verify: because it effectively functions as a ‘black box’ it’s almost impossible to analyze the steps taken by the program to produce data without delving in to the advanced MATLAB scripts. Relative to other programs and to SEM images of materials ‘Tomoview’ significantly overestimates the number of single voxel entities (Type I errors; Chapter 3): ‘Tomoview’ identifies 60% of the number of bubbles identified as falling in this range while image analysis programs like ImageJ identify ~12% of bubbles in the same size fraction. SEM images of thin sections of vesicular materials show no bubbles in this size fraction. This is probably related to the image resolution and segmentation process. Additionally, ‘Tomoview’ will frequently misidentify up to 90 volume percent of the core as being one bubble (Type II errors; Chapter 3). However SEM images of thin sections show that even between closely packed bubble thin walls exist, indicating physical coalescnse between juxtaposed bubbles is rare in this melt. Thus the Type II errors associated with   106 Tomoview and several other image processing programs, including ImageJ, are again likely related to the image resolution and segmentation process.   Of all the image processing programs tested for this study (‘3D Object Counter’ plugin in ImageJ (Bolte and Cordelières 2006); ‘Particle Analyzer’ tool in the BoneJ (v 1.3.12) plugin for ImageJ (Doube et al. 2010); ‘Tomoview’ (Flaws et al. 2011)), Avizo® Fire produces the fewest Type I and Type II errors and is ‘transparent’ enough that the user can easily assess the effectiveness of different steps in the program. Additionally it is the fastest of all tested programs to run, requires a moderate amount of memory compared to ImageJ plugins, is easy to use, and produces the best figures.  F.3 Avizo® Fire: Instructions Dr. Andre Phillion in the Solidification Processing and Simulation Laboratory in the School of Engineering at the University of British Columbia Okanagan gave me access to a floating license for Avizo® Fire (v.8) by the FEI Visualization Sciences Group for these analyses.  The following are brief instructions for running Avizo® Fire. They are similar to that provided in Chapter 3 but include specific commands for Avizo® Fire: 1) In ImageJ 1.47v (Abramoff et al. 2004; Schneider et al. 2012) adjust the contrast in XCT images using the same methodology outlined above (to near-binary). Invert the image to isolate bubbles as the entities of interest.  2) Load the optimized and inverted TIFF images in to Avizo® Fire. Use the ‘Interactive Thresholding’ command to isolate the bubbles in Avizo® Fire as material to analyze.   107 3) Use the command ‘Separate Objects’ to effectively reconstruct bubble walls that fall below the imaging resolution. I did not adjust any parameters in the preferences menu for this command. 4) Use ‘Label Analysis’ to get the program to separately label, count and gather statistics for each segmented entity generated by the ‘Separate Objects’ command. Again, I did not adjust any parameters in the preferences menu. 5) After collecting data for the bubbles analyze the glass using the set of optimized TIFF images (prior to inverting) and the ‘Interactive Thresholding’ and ‘Label Analysis’ commands. I did not try to generate sophisticated 3D images or movies for these XCT data, though it could certainly be done. The FEI website (http://www.vsg3d.com/avizo/fire) has video tutorials for optimizing Avizo® Fire and producing images.               108 Appendix G  XCT Images and Histograms    109                   110     111    112                   113                   114 Figure G.1 XCT images, histograms and bubble size distributions for all experimental products, separated by temperature suites. Histograms show total bubble number and non-normalized volume fraction against bubble radius (log scale). Bubble size distribution curves are non-normalized cumulative bubble number curves (ΣBND(>r) - r), like those in Figures 3.7 and 3.8. Samples AR-IK-48, AR-IK-34 and AR-IK-47 are reversed samples (see Section 2.4). They were included in BSDs in Chapter 3 where the T was not considered (Figures 3.4, 3.5, 3.6) and used in some cases as plateau samples in Figures 3.9 and 3.10. The experimental conditions are listed in Tables 2.2 and 3.2.            115 Appendix H  EMP Analysis To assess the chemical homogeneity of the starting material used in this study (natural rhyolitic obsidian from Hraftntinnuhryggur, Krafla, Iceland) and to track any potential changes in the composition of the material with exposure to high temperatures I used electron microprobe (EMP) analysis to image and quantitatively characterize the dense and foamed glass cores. These analyses doubled as coursework for EOSC 521 (Microbeam and Diffraction Methods for the Characterization of Minerals and Materials). Most of the information below has been extracted from the final report for that course.   H.1 Introduction H2O solubility is strongly dependent on the overall chemistry of the silicate melt (Moore et al. 1998; Behrens and Jantos 2001). Dingwell et al. (1997) and Zhang et al. (2007) have previously shown that in rhyolite melts Al, Na and K have the strongest effects on the saturation state of H2O, with an addition of Na and K increasing solubility while the addition of Al decreases it. While this compositional effect may be very small at low pressures and high T, where H2O solubility would be near a minimum (Burnham and Jahns 1962; Holtz et al. 1995; Zhang 1999), it could still be significant especially if there were slight variations between or within individual samples.  Additionally Na and K are volatile elements. If there is a depletion of these elements in the glass of the experimental products this may indicate that Na and K have migrated into the vapor within the bubble population. Though the potential concentration of Na and K in the vapor phase would be quite small, it would effect the calculation of the molar concentration of H2O in the vapor phase. The accuracy of the developed models thus depends in part on the chemical homogeneity of the starting material and experimental products.   116 H.2 Methods  One experimental product (AR-IK-16; heated at 1000°C for 2.5 hours; final porosity 66.7%) and one sample of the starting material (AR-IK-UND) were thin sectioned and prepared for electron microprobe analysis at UBC using an automated Cameca SX50 Scanning Electron Microprobe with 4 vertical wavelength-dispersion X-ray spectrometers. In order to minimize sodium mobility and resulting ‘grow-in’ in other elements (Morgan and London, 1996) the following conditions were selected: 15 kV accelerating voltage, 2 nA beam current and 20 µm spot size. This equates to a beam density of 0.02 nA/µm2, within the range suggested by Morgan and London (2005) to reduce Na mobility. To further reduce the potential for Na ‘loss’ backgrounds were collected prior to analyses and beam exposure was limited to 1 minute per analysis spot, with a 20 second count time for each peak.  Analysis spots were selected along NW-SE transects so as to sample the rims and core of each material.  H.3 Results  Table H.1 is the average composition of the starting material (AR-IK-UND) and an experimental product (AR-IK-16) based on 10 EMP spot analyses per sample. Figure H.1 shows lateral variations in SiO2, Al2O3, Na2O and K2O within each core, as well as the spread of the data between the two samples. Ultimately the average composition of the two samples varies within analytical uncertainty (~0.1 wt%), and there are no systematic lateral changes in oxide concentration within individual cores.       117  AR-IK-UNDa  AR-IK-16b  	   mean σ  mean σ |Δ| samplesc |Δ| publishedd SiO2 75.33 0.43  75.38 0.61 0.05 0.10 TiO2 0.27 0.06  0.23 0.05 0.04 0.04 Al2O3 11.81 0.19  11.71 0.26 0.10 0.19 FeO 3.59 0.21  3.73 0.29 0.14 0.31 MnO 0.11 0.07  0.13 0.09 0.02 0.00 MgO 0.13 0.04  0.12 0.03 0.01 0.03 CaO 1.81 0.09  1.71 0.07 0.11 0.15 Na2O 4.72 0.15  4.70 0.23 0.02 0.57 K2O 2.76 0.07  2.83 0.10 0.07 0.01 Total 100.53   100.53  1.2E-03 	  aUndeformed starting material (n=10). bExperimental product foamed at 1000°C for 2.5 hr (n=10). cAbsolute difference between average oxide wt% from each sample. dAbsolute difference between AR-IK-UND and EMPA results published by Tuffen and Castro (2009).  Table H.1 Average composition of Hrafntinnuhryggur obsidian, Krafla, Iceland by EMPA at UBC (15 kV, 2 nA, 20 µm, 20 s).  H.4 Interpretation Previous studies of obsidian from Hraftntinnuhryggur, Krafla, Iceland have shown the anhydrous composition of the material is remarkably consistent, even between samples of different macroscopic texture (e.g. flow-banded, vesiculated, lithophysae-rich) (Tuffen and Castro 2009). EMP transects across both the starting material and an experimental product show that this chemical homogeneity also exists at a microscopic scale. There are no obvious lateral changes in the composition of the material from the rim to the core in either material, and there is agreement between the samples within analytical error. This shows the vesiculation process has no effect on the composition of the melt. Additionally it indicates Na and K have not exsolved along with H2O so I can assume there is not an appreciable quantity of Na and K in the vapor phase to affect the H2O solubility model developed in Chapter 2.    118  Figure H.1 Lateral variations in (a) SiO2, (b) Al2O3, (c) Na2O and (d) K2O in the starting material (closed symbols) and AR-IK-16 (open symbols). Average values are shown as a black solid line and black dashed line for the starting material and AR-IK-16, respectively. Solid grey lines are the oxide concentrations given by Tuffen and Castro (2009). There are no systematic lateral variations in these oxide concentrations from the NW rim (as shown in Figure 5) though the core to the SE rim of the material. The averaged oxide wt% varies by ~0.1 wt% between samples, which is near the analytical uncertainty.  747576SiO 2 (wt%)  SE RIMNW RIM CORE11.211.612Al 2O 3 (wt%)  SE RIMNW RIM CORE44.44.8Na 2O (wt%)  SE RIMNW RIM CORE2.62.83K 2O (wt%)  SE RIMNW RIM CORE(a) (b) (c) (d)   119 Appendix I  Supplementary Sample Photos and SEM Images I have included a number of supplementary photos here that show how the ‘strength’ of the melt (likely an expression of surface tension) affects the rind of the experimental products (I.1) and bubble interactions within samples (I.2). Additionally I have included XCT images of cores that show signs of partial collapse (I.3).    I.1 Sample Photos Figure I.1 shows the exterior surfaces of two experimental products. The appearance and texture of the rinds of these experimental products are typical. The rinds all show that bubbles do not nucleate on or perforate the surfaces of the cores.   Figure I.1 Rinds on experimental products. (left) Photograph of the smooth exterior surface (or rind) and vesicular interior of failed experiment AR-IK-4. Bubbles, though abundant and closely packed within the core, do not perforate the exterior rind of the core. The bubbly interior is only exposed by cutting or breaking the sample. (middle) Photograph of smooth bubble-free rind of failed experiment AR-IK-4. After exposure to high temperatures the exterior of the glass cores becomes smooth, perhaps slightly uneven (though not scalloped), vitreous and copper in color. Again there is no evidence of bubbles intersecting the surface of the cores. The core is ~1 cm in diameter. (right) Photograph of smooth bubble-free rind of irregularly-shaped experimental product ‘glass 4’. This sample was used to test the effect of machining on the observed mass loss in experimental products (Chapter 2; Appendix B). The rind of this sample is nearly the same as that for AR-IK-4 though perhaps more uneven. Again, bubbles do not nucleate on or intersect the rind of the sample. The experimental product is ~ 2 cm in length. This demonstrates the closed-cell nature of these experimental products. This effect is likely controlled by the surface tension of the melt.  I.2 SEM Images Scanning electron microscopy was used as a tool to assess the textural homogeneity of the starting glass and to assess any changes in the texture of the glass with exposure to high temperatures. These analyses doubled as coursework for EOSC 521 (Microbeam and Diffraction   120 Methods for the Characterization of Minerals and Materials). Some of the information below has been extracted from the final report for that course. The aim was to use the images to infer information about potential nucleation, growth and bubble interaction dynamics. Figure I.2 primarily shows images that relate to bubble interactions and the potential for physical coalescence.  Four polished thin sections were prepared for SEM imaging at UBC: AR-IK-UND (undeformed starting material), AR-IK-10 (heated at 950°C for 1.5 hours; final porosity 18.3%), AR-IK-11 (heated at 950°C for 12.5 hours; final porosity 57.4%) and AR-IK-16 (heated at 1000°C for 2.5 hours; final porosity 66.7%). SEM imaging was completed using a Philips XL-30 Scanning Electron Microscope outfitted with Bruker Quantaz EDX and EOS cathodoluminescence systems with 15kV accelerating voltage, working distance of 10.4-10.8 mm, and spot size of 6.0 µm. Secondary electron (SE) imaging was primarily used to reduce the potential for Na or K migration within the glass during excitation by the electron beam. In some areas backscattered electron (BSE) imaging was used to look for microlites within the glass.  SE and BSE images of the experimental products show a general increase in bubble size and degree of interaction with other bubbles in samples with increasing porosity. In AR-IK-10, the experimental product with the lowest porosity (18.3%), there are both isolated and interacting bubbles, even though there appears to be enough space within the core itself that bubbles should not need to interact (Figure I.2a). As bubbles get closer together the individual bubble shapes deviate from circular and become more polygonal, with at least one flatter surface occurring between it and the nearest neighboring bubble (Figure I.2b). In AR-IK-11 (57.4% porosity) the mean bubble size appears to have increased, as has the degree of interaction between bubbles (Figure I.2c). In AR-IK-16 (66.7% porosity), there are even fewer isolated bubbles, and most   121 bubbles, whether they are interacting with other bubbles immediately nearby or if they are relatively isolated, have polygonal shapes (Figure I.2d).    Between most bubbles there are either thin walls or remnants of thin glass films. Even when bubbles are very closely packed and have been distorted to polygonal shapes, walls between bubbles, in some cases less than 5 µm in width, still exist (Figure I.2e). There are few bubbles that obviously show signs of coalescence (Figure I.2f). This may be an effect of the surface tension of the melt. Where surface tension is relatively high it may be too energy-intensive to create two new surfaces where a melt film ruptures.  I.3 XCT Images There are some experimental products that show signs of partial bulk collapse when the timescale of the experiment approaches the relaxation timescale of the melt (e.g. Figure 2.1d relative to Figure 2.1c). One would expect that in these experimental products bubbles would act as strain markers and show the strain imparted on the core by the stress exerted by gravity. However XCT image sequences of some of these products show that bubbles within the melt are apparently spherical (Figure I.3). This suggests that in this low-stress deformational regime the bubbles are acting as rigid obstructions rather than as readily-deformable void spaces.            122                 Figure I.2 SE and BSE images of bubble shape and distribution in experimental products. (a) SE image of AR-IK-10 showing both isolated (nearly circular) and interacting bubbles. Though there is abundant space for every bubble to be isolated, bubbles are predominately interacting. (b) BSE image of interacting and isolated bubbles in AR-IK-10. Bubbles are both circular and polygonal. (c) BSE image of interacting and isolated bubbles in AR-IK-11. Bubbles are both circular and polygonal. Compared to AR-IK-10 the number of bubbles and mean bubble size has increased. (d) BSE image of interacting bubbles in AR-IK-16. There are no isolated bubbles in this image and every bubble is polygonal. Compared to AR-IK-10 the number of bubbles and the mean bubble size has increased, though these values are qualitatively similar to AR-IK-11. Both AR-IK-11 and AR-IK-16 are heavily cracked, probably as a consequence of sample preparation. (e) BSE image of 7 closely packed polygonal bubbles in AR-IK-10. Red boxes outline areas where bubble walls have broken, probably during sample preparation. Blue boxes outline areas where bubble walls may have natural thinned and broken as a consequence of coalescence during the high-temperature experiment. Coalescence appears to be rare in these samples, even between very closely packed bubbles. (f) SE image of interacting bubbles is AR-IK-11. Same symbols as in (e). In all BSE images the glass is dark grey, oxide microlites are bright white and circles are black or light grey nearly-circular shapes. In SE images light grey epoxy bubbles often appear in or on top of larger black/dark grey bubbles. Magnification, accelerating voltage and working distance are listed in the lower left of each image. (a) (b) (c) (d) (e) (f)   123  Figure I.3 XCT images of bubble populations in 1000°C plateau samples showing partial bulk collapse. (top) TIFF from AR-IK-20 (4 h, 63%). This sample is the first sample to sit on the equilibrium plateau at 1000°C and shows no sign of collapse (little to no ‘barreling’ of the core). Bubbles throughout the sample are apparently spherical or slightly elongate in the z-direction at the base of the core. (middle) TIFF from AR-IK-18 (7.5 h, 66%). 3.5 hours after vesiculation has ceased the core has begun to barrel and is now longer in the x-direction than the z-direction. Bubbles are still apparently spherical or very slightly flattened in a few bubbles. Bubbles elongate in the z-direction are still apparent at the base of the sample. (bottom) TIFF from AR-IK-27 (13 h, 61%). 9 hours after vesiculation has ceased the core has barreled significantly. However bubbles are still apparently spherical throughout the core. These images demonstrate that bulk collapse of an experimental core is not accommodated by the bubbles but by the melt. Scale bar in XCT images is 2 mm. Images are oriented with the base of the core at the bottom of the image and the top of the core at the top of the image. Thus top to bottom in the image is the z-axis of the core. From left to right is the x-axis of the core. 

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