TIME DEPENDENT FREEZING OF WATER UNDER MULTIPLE SHOCK WAVE
COMPRESSION
By
DANIEL H. DOLAN III
A dissertation submitted in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
WASHINGTON STATE UNIVERSITY Department of Physics
MAY 2003
°c Copyright by DANIEL H. DOLAN III, 2003 All Rights Reserved °c Copyright by DANIEL H. DOLAN III, 2003 All Rights Reserved To the Faculty of Washington State University:
The members of the Committee appointed to examine the dissertation of DANIEL H. DOLAN III find it satisfactory and recommend that it be accepted.
ii ACKNOWLEDGEMENTS
I would like to thank my advisor, Dr. Yogendra Gupta, for suggesting, supporting, and guiding this project. I am also grateful for the assistance and insight of Dr. James John- son in developing the mixed phase water model. Many thanks go to Dr. Philip Marston for providing the water purification system and serving on the thesis committee. Dr. Matthew
McCluskey and Dr. Jow-Lian Ding are also thanked for serving on the committee.
The wave code calculations in this work were aided by numerous discussions with
Dr. Michael Winey. I thank Dr. Oleg Fat’yanov and Dr. Scott Jones for their assis- tance in the VISAR experiments. Kurt Zimmerman played a large role in the constructing the optical imaging system and other instrumentation for this work. Dave Savage, Steve
Thompson, John Rutherford, and Gary Chantler assisted in building and performing the experiments. Finally, I wish to acknowledge the support and understanding of my wife,
Elizabeth.
Funding for this research was provided by DOE Grant DE-FG03-97SF21388.
iii TIME DEPENDENT FREEZING OF WATER UNDER MULTIPLE SHOCK WAVE
COMPRESSION
Abstract
by Daniel H. Dolan III, Ph.D. Washington State University May 2003
Chair: Y.M. Gupta
Multiple shock wave compression experiments were performed to examine the time dependence of freezing in compressed water. These experiments produced quasi-isentropic compression, generating pressures and temperatures where liquid water is metastable with respect to the ice VII phase. Time resolved optical and wave profile measurements were used in conjunction with a thermodynamically consistent equation of state and a phe- nomenological transition rate to demonstrate that water can freeze on nanosecond time scales.
Single pass optical transmission measurements (ns resolution) indicated that com- pressed water loses its transparency in a time dependent manner. This change is consistent with the formation of ice regions that scatter light and reduce sample transparency. The on- set of freezing and subsequent transition were accelerated as water was compressed further past the ice VII phase boundary. Freezing was always observed when water was in contact with a silica window; the transition did not occur if only sapphire windows were present.
iv These observations suggest that freezing on nanosecond time scales begins through hetero- geneous nucleation at water-window interfaces.
Optical imaging measurements (0.01 mm spatial resolution, 20 ns exposures) re- vealed that freezing in compressed water is heterogeneous on 0.01-0.1 mm length scales and begins at several independent sites. As freezing progressed over time, the water sample became a complex network of opaque material separated by transparent regions of unfrozen liquid. The transition growth morphology was consistent with freezing, which is limited by the diffusion of latent heat.
Laser interferometry was used to measure particle velocity histories in compressed water. The results were compared to calculated wave profiles to show that water remains a pure liquid during the initial compression stages. As compression approached a steady state, the measured particle velocity decreased when a silica window was present. This decrease suggests that the frozen material is denser than the compressed liquid. Similar particle velocity decreases were observed in the calculated wave profiles when water was allowed to remain a metastable liquid for some time. These results are consistent with the transparency loss described above, demonstrating that water can freeze on nanosecond time scales.
v TABLE OF CONTENTS Page
ACKNOWLEDGEMENTS iii
ABSTRACT iv
LIST OF TABLES xii
LIST OF FIGURES xvii
CHAPTER
1. Introduction ...... 1 1.1 Objectives and approach ...... 2 1.2 Organization of Subsequent Chapters ...... 3 References for Chapter 1 ...... 5
2. Background ...... 7 2.1 Liquid water ...... 7 2.1.1 Microscopic structure ...... 8 2.1.2 Thermodynamic and transport properties ...... 10 2.1.3 Optical transmission properties ...... 15 2.2 Solid water ...... 17 2.2.1 The phase diagram of water ...... 19 2.2.2 Solid nucleation from the liquid phase ...... 20 2.2.3 Freezing time scales in water ...... 26 2.3 Previous shock wave experiments on water ...... 28 2.3.1 Shock wave experiments in liquid water ...... 29 2.3.2 Shock induced freezing ...... 30 2.4 Unresolved questions and approach ...... 34 2.5 Multiple shock wave compression ...... 35 2.5.1 Multiple shock compression and plate impact ...... 36 2.5.2 Temperature advantages of multiple shock compression . . . . 38
vi References for Chapter 2 ...... 41
3. Experimental Methods ...... 53 3.1 Optical transmission experiments ...... 53 3.1.1 Overall configuration ...... 53 3.1.2 Mechanical components and assembly ...... 55 3.1.3 Instrumentation and optical components ...... 61 3.1.4 Experimental setup ...... 63 3.2 Optical imaging experiments ...... 71 3.2.1 Overall configuration ...... 71 3.2.2 Mechanical components and assembly ...... 75 3.2.3 Instrumentation and optical components ...... 77 3.2.4 Experimental setup ...... 80 3.3 Wave profile experiments ...... 88 3.3.1 Overall configuration ...... 88 3.3.2 Mechanical components and assembly ...... 88 3.3.3 Instrumentation and optical components ...... 92 3.3.4 Experimental setup ...... 92 References for Chapter 3 ...... 95
4. Experimental Results ...... 97 4.1 Optical transmission measurements ...... 97 4.1.1 Determining sample transmission ...... 99 4.1.2 Experimental results ...... 102 4.1.3 Summary ...... 117 4.2 Optical imaging measurements ...... 117 4.2.1 Determining sample transmission ...... 119 4.2.2 Experimental results ...... 121 4.2.3 Summary ...... 129 4.3 Wave profile measurements ...... 132 4.3.1 Particle velocity determination ...... 132 4.3.2 Experimental results ...... 135
vii 4.3.3 Summary ...... 142 References for Chapter 4 ...... 144
5. Time Dependent Continuum Model for Water ...... 145 5.1 EOS development ...... 145 5.1.1 Thermodynamic consistency ...... 146
5.1.2 The form of f (T,v) for constant cv ...... 146 5.2 Liquid water model ...... 147 5.2.1 Choice of EOS ...... 147 5.2.2 EOS formulation ...... 148
5.2.3 Isentropic freezing and the value of cv ...... 154 5.3 Solid water model ...... 157 5.3.1 Assumptions ...... 157 5.3.2 EOS formulation ...... 157 5.4 Mixed phase modelling ...... 160 5.4.1 Mixture rules ...... 160 5.4.2 Time dependence of the freezing transition ...... 161 5.4.3 Limiting cases for isentropic compression ...... 162 5.5 Wave propagation calculations ...... 167 5.5.1 Calculation outline ...... 167 5.5.2 Enforcing the mixture rules ...... 168 5.5.3 Mixed phase calculations ...... 171 References for Chapter 5 ...... 182
6. Analysis and Discussion ...... 187 6.1 First order phase transition ...... 187 6.1.1 Latent heat ...... 188 6.1.2 Volume change ...... 188 6.2 The importance of surface effects ...... 190 6.2.1 Evidence for surface effects ...... 192 6.2.2 Surface initiated freezing ...... 197 6.2.3 Ice nucleation at window surfaces ...... 206
viii 6.3 Freezing time scales ...... 209 6.3.1 Apparent time scales ...... 209 6.3.2 Incubation time analysis ...... 213 6.3.3 Transition time analysis ...... 218 6.4 Transition length scales ...... 220 6.4.1 Domains of the water sample ...... 220 6.4.2 Lateral freezing variations ...... 222 6.4.3 Composition of the transformed material ...... 228 References for Chapter 6 ...... 231
7. Summary and Conclusions ...... 235 7.1 Summary ...... 235 7.2 Conclusions ...... 238 7.3 Recommendations for future work ...... 239 References for Chapter 7 ...... 240
APPENDIX
A. Mechanical Drawings ...... 243 References for Appendix A ...... 268
B. Window Materials ...... 269 B.1 Soda lime glass ...... 269 B.2 Fused silica ...... 270 B.3 z-cut quartz ...... 271 B.4 a-cut Sapphire ...... 272 References for Appendix B ...... 273
C. Water Sample Preparation ...... 275 C.1 Contamination and treatment methods ...... 275 C.2 Sample purification ...... 277 C.3 Filling the liquid cell ...... 284 References for Appendix C ...... 285
ix D. Supplemental Data ...... 287 D.1 Soda lime glass experiments ...... 287 D.1.1 Water experiments ...... 287 D.1.2 Transparency of shocked soda lime glass ...... 289 D.1.3 Summary ...... 292 D.2 Supplemental photodiode records ...... 292 D.2.1 Imacon 200 demonstration experiments ...... 292 D.2.2 Summary ...... 295 References for Appendix D ...... 297
E. Optical Extinction in a Scattering Medium ...... 299 E.1 Single particle scattering ...... 299 E.2 Multiple scatterers and optical extinction ...... 302 E.3 Limitations of optical transmission measurements ...... 305 E.4 Transmission interpretation ...... 306 References for Appendix E ...... 309
F. Details of the VISAR Calculations ...... 311 F.1 Apparent velocity ...... 311 F.2 Window corrections ...... 315 References for Appendix F ...... 319
G. Details of the Mixed Phase Water Model ...... 321 G.1 Numerical stability of the mixed phase model ...... 321 G.2 Mixed phase model subroutines ...... 323 G.2.1 Alterations of the COPS source code ...... 323 G.2.2 Source code for mixed phase water model ...... 324 G.2.3 Material list ...... 332 References for Appendix G ...... 333
H. Heat Dissipation in Solidification Processes ...... 335 H.1 Planar solidification of a supercooled liquid ...... 335 H.1.1 The Stefan problem ...... 335
x H.1.2 Solid growth in reverberated water ...... 339 H.2 Growth stability in a supercooled liquid ...... 341 References for Appendix H ...... 346
xi LIST OF TABLES Page
2.1 Physical properties of liquid water ...... 11
4.1 Summary of optical transmission experiments ...... 98 4.2 Summary of optical imaging experiments ...... 118 4.3 Summary of wave profile experiments ...... 133
5.1 b(v) fit parameters for liquid water ...... 153
6.1 Measured incubation and transition times ...... 212
C.1 Classes of water contaminants ...... 276 C.2 Standard water purification techniques ...... 276 C.3 Summary of water testing ...... 282
D.1 Summary of soda lime glass experiments ...... 288 D.2 Supplemental photodiode measurements ...... 293
G.1 Summary of single phase EOS parameters ...... 322
H.1 Summary of Stefan problem solutions ...... 340
xii LIST OF FIGURES Page
2.1 Hydrogen bonding in water ...... 9 2.2 Crystal structure of ice Ih ...... 9 2.3 Dielectric functions of liquid water ...... 16 2.4 Equilibrium phase diagram of water ...... 18 2.5 Formation of a solid nucleus in a liquid ...... 21 2.6 Stability of a solid nucleus ...... 21
2.7 Variation of nucleation time and rate with gL − gS ...... 24 2.8 Calculated P,T states of shocked liquid water ...... 31 2.9 Multiple shock compression ...... 37 2.10 Temperature advantages of multiple shock compression ...... 40
3.1 Setup for optical transmission measurements ...... 54 3.2 Transmission experiment projectile ...... 56 3.3 Liquid cell assembly ...... 58 3.4 Transmission experiment target ...... 60 3.5 Rear view of transmission setup ...... 64 3.6 Electronic setup for transmission measurements ...... 66 3.7 Timing calibration ...... 68 3.8 Wavelength calibration ...... 70 3.9 General setup of optical imaging experiments ...... 72 3.10 Telescope based image relay system ...... 73 3.11 Lens based image relay system ...... 76 3.12 Cross section of the DRS Hadland 8 way beam splitter ...... 78 3.13 Imaging experiment target chamber setup ...... 81 3.14 Imaging experiment external optics setup ...... 82 3.15 Calibration with 1951 USAF resolution chart ...... 85 3.16 Linearity of the optical imaging system ...... 87 3.17 General setup of VISAR measurement ...... 89
xiii 3.18 Mirror configurations for VISAR experiments ...... 90 3.19 Electronic setup for VISAR measurements ...... 94
4.1 Transmission losses in a non-absorbing sample ...... 100 4.2 Measured photodiode outputs ...... 100 4.3 Photodiode transmission for experiments T1, T2, and T3 ...... 103 4.4 Photodiode transmission for experiments T4 ...... 106 4.5 Photodiode transmission records for experiments T5 and T6 ...... 108 4.6 Spectrally resolved transmission for experiment T5 ...... 109 4.7 Photodiode transmission records for experiments T7 and T8 ...... 111 4.8 Loading history in quartz, sapphire, and hybrid liquid cells ...... 113 4.9 Photodiode transmission records for experiments T9 and T10 ...... 114 4.10 Photodiode transmission records for experiments T11 and T12 ...... 116 4.11 Raw images from experiment I1 ...... 120 4.12 Measured transmission for experiment I1 ...... 122 4.13 Images obtained in experiment I1 ...... 123 4.14 Measured transmission for experiment I2 ...... 126 4.15 Images obtained in experiment I2 ...... 127 4.16 Images obtained in experiment I3 ...... 128 4.17 Photodiode transmission record for experiment I4 ...... 130 4.18 Images obtained in experiment I4 ...... 131 4.19 Raw signals of the VISAR measurement ...... 134 4.20 Particle velocity history for experiment V1 ...... 137 4.21 Particle velocity history for experiment V2 ...... 138 4.22 VISAR measurement for experiment V3 ...... 140 4.23 VISAR measurements long after compression ...... 141 4.24 Particle velocity history for experiment V4 ...... 143
5.1 25◦ C isotherm for liquid water ...... 150 5.2 P − v Hugoniot for liquid water ...... 152 5.3 b(v) for liquid water ...... 153
5.4 The value of cv and adiabatic freezing ...... 155
xiv 5.5 300 K isotherm for ice VII ...... 158 5.6 Liquid-ice VII coexistence curve ...... 159 5.7 Limits of isentropic compression ...... 164 5.8 Mixed phase compression in the P − v plane ...... 165 5.9 Multiple shock compression temperatures for various liquid cells ...... 172 5.10 Thermodynamic histories under multiple shock compression ...... 173 5.11 Multiple shock loading path in the T − P plane ...... 175 5.12 Multiple shock compression loading path in the P − v plane ...... 177 5.13 Simulated particle velocity profiles ...... 178 5.14 Incubation and transition time effects ...... 180
6.1 Latent heat and growth morphology ...... 189 6.2 Volume change and wave profiles ...... 191 6.3 Extinction histories for different window configurations ...... 194 6.4 Surface effects in wave profile measurements ...... 196 6.5 Temperature of the water-window interface ...... 199 6.6 Optical transmission in surface initiated freezing ...... 203 6.7 Increasing extinction with sample thickness ...... 205 6.8 Time scales and peak pressure ...... 210 6.9 Comparisons of the quartz cell photodiode experiments ...... 211 6.10 Fit of the T5 photodiode record ...... 212 6.11 Incubation time and the metastable history ...... 215 6.12 Incubation time and sample thickness ...... 217 6.13 Transition time and sample thickness ...... 219 6.14 Longitudinal length scales of the freezing of water ...... 221 6.15 Consistency of the optical transmission measurements ...... 223 6.16 Initiation and growth in imaging measurements ...... 225 6.17 Nucleation rate and lateral freezing ...... 227 6.18 Measured transmission profile and the Rayleigh scattering limit ...... 229
A.1 4” standard projectile ...... 244 A.2 4” monkey’s fist projectile ...... 245
xv A.3 2.5” projectile ...... 246 A.4 Projectile modifications ...... 247 A.5 Alignment projectile ...... 248 A.6 Soda lime glass impactor mount ...... 249 A.7 Universal impactor mount ...... 250 A.8 Projectile turning mirror mounts (glass) ...... 251 A.9 Projectile turning mirror mounts (standard)) ...... 252 A.10 Impactor apertures ...... 253 A.11 Soda lime glass liquid cell ...... 254 A.12 Silica window liquid cell ...... 255 A.13 Sapphire window liquid cell ...... 256 A.14 Quartz liquid cell (VISAR without buffer) ...... 257 A.15 Standoff target ring ...... 258 A.16 Soda lime glass cell target plate ...... 259 A.17 Quartz/fused silica cell target plate ...... 260 A.18 Sapphire cell target plate ...... 261 A.19 Unbuffered VISAR target plate ...... 262 A.20 Lens bracket for glass target plate ...... 263 A.21 Lens bracket for quartz/fused silica target plate ...... 264 A.22 Lens bracket for sapphire target plate ...... 265 A.23 Transmission lens unit ...... 266 A.24 VISAR lens unit ...... 267
C.1 Water purification stages ...... 278 C.2 High-Q 103S still ...... 279
D.1 Photodiode transmission for experiments G1 and G2 ...... 290 D.2 Transparency of shocked soda lime glass ...... 291 D.3 Photodiode transmission of experiment IS1 ...... 294 D.4 Photodiode transmission of experiment IS2 and IS3 ...... 296
E.1 Single scattering setup ...... 300
xvi E.2 Optical extinction from a collection of scattering particles ...... 303 E.3 Extinction complications in a scattering system ...... 307
F.1 Simplified view of the VISAR measurement ...... 312 F.2 True versus apparent velocity in the VISAR system ...... 316
H.1 Layout of the Stefan problem ...... 336 H.2 Numerical solutions to Stefan problem ...... 342 H.3 Uniform solid size limits in freezing water ...... 343 H.4 Instabilities in supercooled solidification ...... 345
xvii Chapter 1
Introduction A material at thermodynamic equilibrium assumes the structure or phase that is most favorable under the applied conditions [1]. At a fixed temperature T and pressure P, the stable phase is one that has the minimum specific Gibb’s free energy g(T,P); all other phases present under such conditions will eventually convert to the stable phase. The time required for this conversion varies greatly depending on the nature of the transition and the conditions of interest. For example, polymorphic phase transitions in shocked cadmium sulfide [2] occur on 10−10 s times scales, while the transition from graphite to diamond at ambient conditions takes much longer than hundreds of years (À 109 s) [3]. There is a broad interest in understanding and controlling the time scales of phase transitions in numerous system, such as atmospheric clouds [4] and biological tissues [5]. The study of phase transition dynamics requires that thermodynamic changes be made on time scales less than or equal to the transformation time. Shock waves provide a useful approach for generating rapid thermodynamic changes, and as such have been used to study polymorphic and melting transitions [6]. In contrast, shock induced freezing presents several fundamental difficulties. Shock compression in liquids leads to significant temperature increases, often producing states that are too hot for freezing. Even when freezing is thermodynamically possible, there is some time required for the transition to take place. This time may be on the order of many seconds [7], which is much longer than the typical 10−6 s duration of a shock wave experiment. Whether freezing actually occurs in shock wave loading is an issue that has not been resolved [6] and is the subject of the present study.
1 1.1 Objectives and approach The general objective of this work was to examine and understand shock wave induced freezing in liquid water on nanosecond time scales. Liquid water was chosen for a variety of reasons. Not only is water a material of general scientific interest [8], it has an unusually large specific heat, which reduces the temperature rise caused by shock compression. There has also been a long standing controversy regarding shock induced freezing in liquid water [6]. The specific objectives of this work were:
1. To generate P,T states such that water may freeze using shock wave techniques.
2. To perform optical and wave profile measurements in shocked water to examine and characterize changes due to freezing.
3. To construct a model that describes liquid and solid water under shock compression as well as the mixed phase state.
4. To study the nucleation mechanism (i.e. homogeneous versus heterogeneous) gov-
erning shock induced freezing.
5. To assess the characteristic time and length scales for freezing.
High pressure states were generated in liquid water using multiple shock wave com- pression, a method that has been applied to other liquids [9, 10]. In this technique, a thin water sample confined between two optical windows is subjected to multiple shock com- pression using plate impact. This process approximates isentropic compression and results in substantially lower temperatures than those in single shock compression. With this tech- nique, water can be compressed to a state where ice VII [11] is more stable than the liquid phase.
2 Time resolved optical transmission measurements [9] were performed to detect the presence of scattering caused by liquid-solid coexistence. Optical imaging experiments were also performed to examine and characterize morphological features during freezing. Wave profiles were measured using laser interferometry [12] to obtain time-resolved me- chanical changes resulting from freezing. A mixed phase water model was constructed to simulate reverberation loading and to investigate time dependent changes caused by freezing. Complete equations of state for the liquid and solid phases were constructed using published data and thermodynamic consistency requirements [10]. Rules governing the mixed phase state and a time depen- dent transformation law were incorporated in the water model to examine phase transition dynamics [13–16]. The water model was incorporated into a one dimensional wave propa- gation code [17] for modelling the reverberation experiments.
1.2 Organization of Subsequent Chapters Chapter 2 presents a general overview of the relevant properties of liquid and solid water. A discussion of the freezing process is also given with a review of previous stud- ies on rapid freezing in water. The specific scientific questions relevant to this work are summarized with a discussion of the overall experimental approach. Chapter 3 describes the experimental details of the optical transmission, optical imaging, and wave profile measurements made in this work. Construction, setup, and calibration procedures are given for each type of experiment. Chapter 4 presents the results from these experiments.
Chapter 5 discusses a method for constructing the complete equation of state for a single phase. This method is used to develop models for liquid and solid water. Rules for treating a mixed phase system are postulated along with a time dependent transition rate to model the freezing process. The use of this model in a one dimensional wave propagation
3 code is also discussed. In Chapter 6, the experimental results are analyzed to show that freezing can occur on nanosecond time scales if suitable nucleation sites are present. The relevant time and length scales of the transition are also discussed. An overall summary of this work and the resulting conclusions are given in Chapter 7. Appendix A contains mechanical drawings for all components used in this work. Appendix B presents specifications and mechanical models for all window materials used in the experiments. Appendix C describes the preparation and characterization of water samples. Appendix D contains supplemental data not presented in Chapter 4. A brief review of optical scattering theory and its application to the transmission experiments is presented in Appendix E. The calculation of particle velocity from laser interferometry measurements is discussed in Appendix F. Details of the mixed phase water model are contained in Appendix G. The effects of heat dissipation during the solidification of a liquid are discussed in Appendix H.
4 References for Chapter 1 [1] H.B. Callen. Thermodynamics and an introduction to statistical mechanics. Wiley, New York, 2nd edition, (1985).
[2] M.D. Knudson. Picosecond electronic spectroscopy to understand the shock-induced phase transition in cadmium sulfide. Ph.D. thesis, Washington State University, (1998).
[3] H.T. Hall. The synthesis of diamond. J. Chem. Ed. 38, 484 (1961).
[4] B.J. Mason. Clouds, Rain, and Rainmaking. Cambridge University Press, London, (1962).
[5] R.E. Lee, G.J. Warren and L.V. Gusta, editor. Biological Ice Nucleation and Its Ap- plications. American Phytopathological Society Press, St. Paul, (1995).
[6] G.E. Duvall and R.A. Graham. Phase transitions under shock wave loading. Rev. Mod. Phys. 49, 523 (1977).
[7] P.G. Debenedetti. Metastable Liquids. Princeton University Press, Princeton, (1996).
[8] D. Eisenberg and W. Kauzmann. The Structure and Properties of Water. Oxford Press, New York, (1969).
[9] G.E. Duvall, K.M. Ogilvie, R. Wilson, P.M. Bellmany and P.S.P Wei. Optical spec- troscopy in a shocked liquid. Nature 296, 846 (1982).
[10] J.M. Winey. Time-resolved optical spectroscopy to examine shock-induced decompo- sition in liquid nitromethane. Ph.D. thesis, Washington State University, (1995).
[11] P.W. Bridgman. Phase diagram of water to 45,000 kg/cm2. J. Chem. Phys. 5, 964 (1937).
[12] L.M. Barker and R.E. Hollenbach. Laser interferometer for measuring high velocities of any reflecting surface. J. Appl. Phys. 43, 4669 (1972).
[13] Y. Horie. The kinetics of phase change in solids by shock wave compression. Ph.D. thesis, Washington State University, (1966).
[14] D.J. Andrews. Equation of state of the alpha and epsilon phases of iron. Ph.D. thesis, Washington State University, (1970).
[15] D.B. Hayes. Experimental determination of phase transition rates in shocked potas- sium chloride. Ph.D. thesis, Washington State University, (1972).
[16] J.N. Johnson, D.B. Hayes and J.R. Asay. Equations of state and shock-induced trans- formations in solid I-solid II-liquid bismuth. J. Phys. Chem. Solids 35, 501 (1974).
5 [17] Y.M. Gupta. COPS wave propagation code (Stanford Research Institute, Menlo Park, CA, 1978), unpublished.
6 Chapter 2
Background This chapter presents background information relevant to the present work. The structure and properties of liquid water are discussed in Section 2.1. Solid phases of water and the freezing transition are discussed in Section 2.2. Previous shock wave research on liquid water and shock induced freezing are reviewed in Section 2.3. Unresolved questions regarding the freezing of water on nanosecond time scales are summarized in Section 2.4. The multiple shock wave compression technique used in this work is described in Section 2.5.
2.1 Liquid water “Of all known liquids, water is probably the most studied and least under- stood...” –Felix Franks [1]
Although water is among the most familiar substances on Earth, the complete de- scription of liquid water continues to be an outstanding problem in modern science. A brief overview of the microscopic structure of liquid water is presented here to summarize the challenges that make water so difficult to understand. The remainder of this section discusses the thermodynamic, transport, and optical transmission properties of liquid wa- ter. This discussion focuses on a small subset of past water research. Extensive reviews of water may be found in the ongoing series by Franks [2]; more concise reviews are given in References 3 and 4.
7 2.1.1 Microscopic structure
Ordinary water, H2O, has a molecular mass of 18.015 g/mol. Two hydrogens are covalently bonded to an oxygen atom with a mean O-H distance of 0.957 A˚ and an H-O-H bond angle of 104.52◦ [5,6]. Electrons are not distributed equally in these bonds, leaving a residual negative charge on the oxygen atom and partial positive charges on the hydrogens. Water molecules may form hydrogen bonds with one another, which link a hydrogen from one molecule to the oxygen of another molecule with a mean O-O separation of 2.74-2.76
A˚ [5, 6]. These bonds occur in a nearly tetrahedral fashion as shown Figure 2.1. In the normal solid phase, these bonds lead to the open crystal structure shown in Figure 2.2.
When ice melts, water molecules infiltrate the open volume of the crystal, which leads to a higher density in the liquid phase. Liquid water has no permanent microscopic structure, although local molecular positions are correlated at each instant through hydrogen bonding. The average local struc- ture is well known from diffraction studies [9], but such information does not reveal the temporal fluctuations of molecules in the liquid. Numerous models have been proposed during the last century to describe the structural dynamics and understand water’s macro- scopic properties. These models generally fall into one of two classes– mixture models and the uniformist viewpoint [10]. Mixture models can be traced back to Rontgen¨ [11], who proposed that liquid water is composed of ice-like molecular clusters of various sizes. Although this approach can be used to empirically model various thermodynamic proper- ties [12], the presence of small ice clusters is inconsistent with the observed vibrational spectra and x-ray diffraction data [5]. Other mixture models treat liquid water as a hydro- gen bonded structure containing numerous unbonded molecules in the interstitial volume. Interstitial models are generally consistent with vibrational spectra and x-ray diffraction measurements [5], but there is some opposition to the concept of distinguishable bonded
8 Figure 2.1: Hydrogen bonding in water (from Ref. 7) Oxygen atoms are shown in red, hydrogen atoms in white. Hydrogen bonds are indicated with dashed lines; covalent O-H bonds are represented with solid rods.
Figure 2.2: Crystal structure of ice Ih (from page 26 of Ref. 8) Oxygen positions are shown as open circles; hydrogen locations have been omitted.
9 and unbonded molecules. The uniformist description, first suggested by Pople [13], views liquid water as a perturbed form of ice Ih, where hydrogen bonds are severely distorted but not broken. Recent mixture models have begun to incorporate aspects of the uniformist viewpoint by treating liquid water as a combination of bonding structures from different ice polymorphs [14]. Molecular dynamics and Monte Carlo simulations [15] have also been performed to study the instantaneous structure of liquid water. Such studies typically assume an empirical potential for water [16–19] to numerically simulate an ensemble of molecules; first principles molecular dynamics have also been applied recently to liquid water [20]. Although numerical simulations can generate reasonable radial distribution functions [9], the results have been inconclusive since competing interpretations can been applied [21]. To date, there is no single description of liquid water that can account for all of its known properties. It is generally accepted that the instantaneous structure of liquid water is similar to ice and has a lifetime of 1-5 ps [3]; beyond that are many competing theories and unanswered questions. Since this work focused primarily on the macroscopic properties of liquid water, an exact description of the microscopic structure was not needed.
A qualitative understanding of macroscopic properties of liquid water can be formulated in terms of the presence or absence of hydrogen bonding. When these bonds are present, liquid water shows a number of anomalous properties. As the bonds are destroyed and/or distorted, water loses its anomalous behavior.
2.1.2 Thermodynamic and transport properties
Standard conditions The distinction between liquid water and water vapor persists up to the critical point at 22.064 MPa and 647.096 K [25]. At atmospheric pressure, liquid water is stable for temperatures ranging from 0 to 100◦ C. Near the freezing point, liquid water is anomalous
10 Table 2.1: Physical properties of liquid water at 1 bar and 298.15 K
Specific heat cp [22] 4.18 J/g·K
Density [22] 0.997049 g/cc
Sound speed [23] 1.496687 km/s
Self diffusivity [24] 2.26×10−9m2/s
Thermal conductivity∗ 0.610 W/m·K
Viscosity∗ 1.0016×10−7 N·s
Surface tension∗ 0.07198 J/m2
Electrical resistivity∗ 18.182 MΩ · cm
∗ Technical reports from the International Association for the Properties of Water and Steam (IAPWS) given in Refs. 25–28.
11 ∂ ∂ in that the density increases with temperature, so ( v/ T)P< 0. This trend continues ◦ ∂ ∂ to about 4 C, above which ( v/ T)P> 0. Table 2.1 summarizes the general properties of water at ambient conditions. The specific heat of liquid water is considerably higher than most materials and nearly twice that of ice or water vapor. This anomaly is tied to the configurational energy of the fluctuating hydrogen bond network [4]. The density and sound speed of water are comparable to other liquids, as are the self diffusivity, thermal conductivity, and viscosity. The surface tension, however, is 3-5 times larger in water than most liquids [29] due to extensive hydrogen bonding. Pure liquid water has a resistivity of 18.182 MΩ · cm; for comparison, the resistivity of tap water is on the order of 10−3 MΩ · cm [30].
Static high pressure compression There are several practical difficulties to studying liquid water at elevated pressures.
Water at room temperature solidifies at pressures above 1 GPa, limiting the range that can be studied under static conditions. Hot, compressed water becomes quite corrosive, and is known to attack the gaskets and ruby pressure standards used in diamond anvil cell experiments above 200◦ C [31]. There is evidence that water can etch diamond at 5 GPa for temperatures near 1300◦ C [32], completely dissolving diamond at 1500◦ C. It is generally accepted that the application of high pressure disrupts the hydrogen bonding network in water, eliminating many of the anomalies observed at atmospheric pressure [33]. An extensive compilation of thermodynamic measurements of liquid water prior to 1990 may be found in Ref 34. Much of that work focused on measuring specific volume as a function of temperature and pressure. High pressure volumetric studies of liquid water date back to the pioneering work of Bridgman [35], who measured the specific volume of liquid water up to 3.5 GPa and 175◦ C [36]. Numerous other measurements of specific volume have been reported, mostly restricted to pressures below 1 GPa. Aside from v(T,P),
12 the thermodynamic properties of liquid water at high pressure are not well known beyond 1 GPa. Many thermodynamic response functions, such as specific heat, are difficult to measure under high pressure and have not been extensively studied beyond 0.1-0.2 GPa. One exception to this is the acoustic sound speed, which has been measured directly in liquid water for pressures up to 1 GPa [37,38]. Optical measurements of sound speed have been made in diamond anvil cell studies up to 3.5 GPa [31, 39]. The transport properties of liquid water are largely unknown for pressures beyond 1 GPa. Measurements of the transport properties below 1 GPa show a number of extrema that are not observed in other
liquids [33]. Overall, the viscosity and thermal conductivity of liquid water increase with pressure, while the self diffusivity decreases with pressure. Recent measurements indicate that the thermal conductivity of water increases with pressure up to 3.5 GPa. The thermal conductivity of water at elevated temperatures is known to increase with pressure up to 3 GPa [40]. Numerical simulations have been used to estimate the thermodynamic properties of liquid water at high pressures. Madura et al. [41] applied Monte Carlo techniques to calculate the room temperature density to within 2% of the experimental measurements up ∂ ∂ ∂ ∂ to 1 GPa; the correct qualitative pressure trends for cP, ( v/ T)P, and ( v/ P)T were also obtained. Tse and Klein [42] used molecular dynamics to simulate liquid water over the same range and were able to reproduce v(T,P) within a few percent. Molecular dynamics studies of liquid water above 1 GPa have been reported by Brodholt and Wood [43] and Belonoshko and Saxena [44]. The former study covered the 300-2300 K and 0.05-4 GPa range, while the latter dealt with the 700-4000 K and 0.5-100 GPa range. The validity of these simulations is difficult to determine given the limited experimental data. Wiryana et al. [39] used high pressure sound speed measurements to argue that the intermolecular potential in numerical simulations must be refined to account for increased density of water at high pressures. Since these potentials are typically optimized to match the properties of
13 liquid water at ambient conditions, it is not clear that numerical simulations can provide accurate high pressure thermodynamic information.
Thermodynamic models of liquid water Several thermodynamic tabulations are available for temperatures up to 1023 K and pressures of 1 GPa [45, 46], although these are of limited use outside the tabulated range. For temperatures much higher than 100◦ C, water has been modelled as a Redlich-
Kwong fluid [47, 48], an extension of the van der Waals fluid [49]. A variety of water models have been constructed by assuming constant isobaric or constant isochoric specific heats [50–53]. Thermodynamic properties of water may also be found by integrating the thermodynamic consistency relationships involving the acoustic sound speed (c) and the
isobaric specific heat capacity (cP). µ ¶ µ ¶ ∂v v2 T ∂v 2 = − 2 − (2.1) ∂P c cP ∂T µ ¶T µ ¶ P ∂c ∂ 2v P = −T (2.2) ∂ ∂ 2 P T T P
Vedam and Holton [54] first applied this method to liquid water at pressures below 1 GPa and temperatures of 0-100◦ C. Similar constructions have been made for the 1 atm-0.1 GPa pressure range and temperatures of 0-150◦ C [22, 55, 56]. Wiryana et al. [31, 39] extended this calculation to pressures of 3.5 GPa and temperatures of 200◦ C. Another approach to modelling liquid water is to construct a functional form for the specific Helmholtz free energy f (T,v) with a set of adjustable parameters. The model parameters can then be adjusted to optimally match published thermodynamic measure- ments. This approach was used by Saul and Wagner [57] to create an equation of state for water containing 58 adjustable parameters; an updated version of this model has since been published [58, 59]. The model is reported to be valid for temperatures up to 1273 K and pressures of 25 GPa. Within its intended range, this model is probably the most accurate
14 thermodynamic description of water. The accuracy and stability outside that range are not immediately clear.
2.1.3 Optical transmission properties
Standard conditions Light transmission through liquid water is determined by the absorption coefficient
−αx α, where I = I0e . This coefficient is related to the complex dielectric function ε = ε0 + iε00 [60]. Ã µ ¶ !1/2 8π2ε0 ε00 2 α2 = 1 + − 1 (2.3) λ 2 ε0
Light absorption occurs for nonzero values of ε00. Figure 2.3 shows the functions ε0(λ) and
ε00(λ) for liquid water. In the range of 0.2-1 µm, the value of ε00 is much small than ε0, so Equation 2.3 can be simplified.
2π ε00 α ≈ √ (2.4) λ ε0
In this region, α is on the order of 10−3 − 10−4 cm−1, which means that water samples √ less than about 100 cm are effectively transparent. The refractive index of water n ≈ ε0 is about 1.33-1.34 in the visible range (λ = 400 − 700 nm) [61, 62]. Water strongly absorbs light on either side of the visible spectrum. Below 180 nm, the optical response is dominated by electronic excitations [64]. The optical properties in the 1-100 µm range are determined by motions of the water molecule [63]. Vibrational modes, which consist of a symmetric OH stretch, an anti-symmetric OH stretch, and a bending mode and their overtones, contribute to optical absorption in the 1-10 µm region.
Molecular rotations contribute to absorption at 17 µm; at 62 µm, translational vibrations are active. At very long wavelengths (λ > 100 µm), dissipation occurs due to thermal randomization of the permanent molecular dipoles. Ice thus absorbs far less light at long
15 Figure 2.3: Dielectric functions of liquid water (from pg. 275 of Ref. 63) Dotted lines mark the 400-700 nm visible range.
16 wavelengths due to the restricted dipole motion in the crystal lattice. The optical properties
of liquid and solid water are fairly similar at wavelengths shorter than about 10 µm. In the visible region, normal ice has a refractive index of about 1.30-1.32 [65], which is slightly lower than that of liquid water. This difference results from lower density of ice, which leads to a lower refractive index through the Clausius-Mossotti relation [60].
Static high pressure conditions
All available experimental evidence suggests that water retains its transparency un- der static high pressure. Optical microscopy studies of water have verified transparency for pressures of 0.1-3 GPa [66–68]. Careful studies of the refractive index of liquid water under high pressure are more limited. Several empirical formulations have been developed for the refractive index below 0.1 GPa [14, 62]. Vedam et al. [69–71] measured the refrac- tive index of liquid water up to 1.1 GPa and found a linear relationship with the Eulerian
strain ε. · ¸ 1 ³v ´2/3 n(v) = n(v ) − Aε where ε ≡ 1 − 0 (2.5) 0 2 v
The value of A is approximately 1.01 for λ=546.1 nm.
2.2 Solid water Water exists in many different solid phases at different pressures and temperatures. A brief overview of these phases is presented here; more general reviews are given in Refs. 65 and 72. Solid nucleation is then discussed to demonstrate that freezing is an activated process, which requires some time to initiate. Previous studies of the limiting time scales of freezing in water are also summarized.
17 800 500 750 450 700 critical 400 point 650 350 600 300 550
250 C) 500 vapor o T (K)
liquid T ( 200
450 18 150 400 100 350 VII ambient 50 V 300 conditions III VI 0 250 VIII Ih II −50 200 −7 −6 −5 −4 −3 −2 −1 0 1 10 10 10 10 10 10 10 10 10 P (GPa) Figure 2.4: Equilibrium phase diagram of water [29, 72–76] 2.2.1 The phase diagram of water Figure 2.4 shows an equilibrium phase diagram for water [29, 72–76]. The term equilibrium is used here to indicate phase stability. At equilibrium, water assumes the most stable phase, which for fixed temperature and pressures is defined by the minimum in Gibbs free energy [49]. The familiar form of ice is properly known as ice Ih due to its hexagonal crystal structure. Ice Ih is less dense than liquid water and melts with the application of pressure. With sufficient compression, water can transform to a number of different ice phases that are denser than the liquid phase. Ices II, III and V, which exist at temperatures below 0◦ C and pressures 0.2-0.5 GPa, were discovered in the early 20th century [35].
Bridgman [35, 77] discovered two phases, ice VI and VII, which are stable above 0◦ C. At ambient temperature, liquid water transforms to ice VI above 0.9 GPa. Ice VII is stable above 2 GPa and for pressures up to at least 50 GPa. When cooled below 0◦ C, ice VII transforms to ice VIII. Ice IX, which is not related to the fictional ice IX of Vonnegut [78], is a form of ice III that exists below -100◦ C [79]. Ice phases X, XI, and XII have also been reported, although there is some skepticism that all of these phases are distinct from ice VII [80]. Computational studies have predicted new ice phases that have not been experimentally observed [81]; such phases are not generally assigned a Roman numeral until their crystal structure is established by diffraction and/or spectroscopy measurements
[72]. High pressure ices are optically transparent like ice Ih, but have larger refractive indices than liquid water due to their higher density [82, 83]. Water may also exist in a number of metastable phases that do not reflect the true energy minimum. For example, liquid water can often be found in the solid domain of P,T space [35], in which case the liquid is said to be in a supercooled state (i.e. below the melting temperature at fixed pressure). Some high pressure ices can exist at atmospheric pressure if cooled in liquid nitrogen prior to decompression [84]. There exist ice structures,
19 such as ice IV [35], which are not stable under any conditions. Ice Ic, a cubic form of ice Ih, can be formed at atmospheric pressure by vapor deposition of water on a substrate cooled to temperatures of ∼133-173 K [65]; this phase is irreversibly converted to ice Ih by heating. A variety of amorphous ice phases may also be produced with different cooling and compression techniques [72, 85]. The existence of metastable phases implies that the equilibrium phase diagram shown in Figure 2.4 is an incomplete description of water. The microscopic structure of a water sample depends on its complete P,T history.
2.2.2 Solid nucleation from the liquid phase Metastable phases are the result of an energetic barrier that prevents the stable phase from forming. Classical nucleation theory relates this barrier to the Gibbs free energy differences between the liquid and solid phases. A brief review of nucleation theory is presented here; more extensive treatments may be found in References 86 and 87.
Classical nucleation theory The following discussion follows the review by Walton [86]. Consider a mass M of liquid water that is metastable with respect to some solid phase at fixed temperature and pressure. The specific Gibbs free energy of the liquid phase (gL) is higher than that of the solid phase (gS), but the entire mass cannot freeze simultaneously because that would require long range, coordinated molecular motion. Solid formation instead begins with small nuclei that form within the liquid. Figure 2.5 shows a system where a nucleus of mass m has formed. The stability of this system is related to the Gibbs free energy difference
∆G = GL+S − GL needed to create the nucleus. This energy is a combination of the bulk energies of each phase and the energy required to maintain the solid-liquid interface, which has an area A and surface tension σ.
∆G = [(mgS + (M − m)gL + σA] − MgL = −m(gL − gS) + σA (2.6)
20 liquid (mass=M-m)
r
solid (mass=m)
Figure 2.5: Formation of a solid nucleus in a liquid
∆ G*
0 G(r) ∆
r*
0 Solid radius r
Figure 2.6: Stability of a solid nucleus as a function of size
21 If the nucleus is treated as a sphere of radius r, ∆G may be written in terms of the solid size. 4π ∆G(r) = − ρ (g − g )r3 + 4πσr2 (2.7) 3 S L S A plot of ∆G(r) is shown in Figure 2.6. Competition between the r2 and r3 terms creates a maximum value of ∆G∗ when r = r∗.
2σ r∗ = (2.8) ρS (gL − gS) 16π σ 3 ∆G∗ = (2.9) ρ2 2 3 S (gL − gS) Nuclei smaller than r∗ are not thermodynamically stable since small fluctuations will tend to force the system back to the pure liquid state. When an embryo larger than r∗ is formed, it will tend to grow larger and cause the entire system to solidify. Freezing begins when a single water molecule adheres to a solid nucleus of size r∗. The equilibrium number density of these nuclei N(r∗) is defined by a Boltzmann distribu- tion related to the magnitude of ∆G∗. µ ¶ ∆G∗ N(r∗) ∝ exp − (2.10) kT
Freezing from any specific nucleus is a random event, but an average nucleation rate per unit volume J can be defined for a large ensemble of metastable water samples. This rate is proportional to N(r∗). µ ¶ −∆G∗ J = J exp 0 kT µ ¶ B 16πσ 3 = J exp − where B ≡ (2.11) 0 2 ρ2 (gL − gS) 3 S kT
22 The characteristic time for a single nucleation event tn is inversely proportional to the nu- cleation rate and volume V of each sample in the ensemble. µ ¶ 1 B tn = exp 2 (2.12) J0V (gL − gS)
J0 is related to microscopic details of the nucleation process and is assumed to be constant here. For simplicity, B is also assumed to be constant. Figure 2.7 shows the variation in nucleation rate and nucleation time as a function of gL − gS. Along the equilibrium phase boundary, gL = gS, so the nucleation rate is zero and an infinite time is required 1 for solid formation. As the liquid moves further into the solid domain, gL − gS increases , resulting in a higher nucleation rate and a shorter nucleation time. The dramatic decrease in nucleation time creates an observational limit on supercooling possible in a liquid sample. For example, water at atmospheric pressure freezes within a fraction of a second below about -40◦ C, so this temperature is considered a lower limit for experiments with times scales ≥ 1 s. However, the value of tn does not go to zero as gL −gS → ∞ because nucleation always requires a finite time, as shown in Figure 2.7. Thus far, it has been assumed that all portions of a metastable liquid are equivalent, a situation known as homogeneous nucleation. Most phase transitions are not actually initiated in this way, but instead rely upon heterogeneous nucleation that occurs in certain regions of the sample [86]. The boundaries of the water sample may have a lower surface tension with the solid phase than the liquid phase, thus reducing the value of ∆G∗ (Equation 2.6) and making freezing more likely. The presence of dispersed foreign material may also assist freezing in the same way. Experimental studies of metastable liquids are typically limited by the most effective heterogeneous nucleator in the system. Only with extensive care can all heterogeneous nucleations sites be removed to allow the system to transform
1 To a first approximation, the value of gL −gS increases linearly with temperature and pressure for isobaric and isothermal (respectively) supercooling [88].
23 Nucleation time
Nucleation rate
g −g L S
Figure 2.7: Variation of nucleation time and rate with gL − gS
24 via homogenous nucleation.
Heterogeneous nucleation in liquid water A variety of substances assist freezing in water through heterogeneous nucleation. Although freezing can occur at any temperature below 0◦ C (at 1 atm), foreign substances typically induce freezing in supercooled water at a specific temperature [88–94]. This temperature is defined by averaging the results from an ensemble of water samples or by repeated freezing of a single sample. Silver iodide, first studied by Vonnegut [95], is the best known freezing agent, inducing solidification at temperatures above -10◦ C (reports vary from -8 to -4◦ C) at atmospheric pressure. Numerous inorganic crystals, particularly iodides and sulfides, and various minerals can nucleate ice at temperatures above -20◦ C [96, 97]. For example, ice nucleation in natural snowflakes commonly occurs around airborne silicate particles [98,99], although pure silica (SiO2) is considered to be a poor ice nucleator unless it is exposed to certain chemical and/or heat treatments [100–102]. Water soluble alcohols tend to inhibit freezing, but alcohol monolayers can be effective freezing nucleators [90, 103]. Amino acid crystals [104] as well as some bacteria, plants, and fungi
[105] have also been found to be suitable freezing agents. Various organic molecules are able to nucleate ice phases II-VI at high pressures [106, 107]. Understanding the actual mechanism for ice nucleation on a substrate is not a sim- ple matter. Traditionally, it has been thought that water freezes effectively on hydrophillic substrates that have crystal structures similar to ice. The nucleating effectiveness of silver iodide and its similarity to ice Ih [95] partially motivates this viewpoint, although silver iodide is largely hydrophobic [100]. Electric field effects are another consideration in nucleator effectiveness. The strong dipole moment [4] of water molecules tend to align with external electric fields, producing a more ordered structure that may assist the freez- ing process. Externally applied fields have been shown to induce ice nucleation in cloud
25 chamber studies [108] as well as bulk water samples [65, 109]. The nucleating effective- ness of silver iodide may also increase in the presence of an external field [110], although some have argued that the highest effectiveness of silver iodide occurs when the surface is uncharged [111, 112]. The latter argument is based on the fact that ice Ih is proton dis- ordered, so the molecular dipoles have no common orientation, whereas an electric field will tend to align these dipoles. This difficulty may be overcome, however, if the field is nonuniform. Nucleation studies with ferroelectric barium titanate [113] and polar amino acid crystals [104] indicate that alternating positive and negative surface charges that exist in microscopic cracks of a solid substrate can promote freezing in supercooled water. For many freezing substrates, there are reports of a “memory effect” [90, 114, 115], which is observed when the nucleation effectiveness increases after previous freezing has occurred. This observation suggests that a monolayer of solid ice resides on the substrate after the water sample is melted. If the temperature is not raised too high above the melting point, the substrate tends to nucleate ice more readily the next time it is exposed to supercooled water.
2.2.3 Freezing time scales in water Several freezing time measurements have been reported for supercooled liquid wa- ter at atmospheric pressure [89,91–93,116]. In these measurements, liquid water is held at a temperature T < 0◦ C until freezing is observed. The time measured for a single freezing event is random, so multiple samples or heating/cooling cycles are performed to find an av- erage time dependence. Measured freezing times in such experiments range from 102 −104 seconds, even in the presence of a silver iodide nucleation seed [91]. The lower limit to the freezing time is the time required to cool the liquid sample, which is on the order of several seconds.
26 While isobaric cooling ultimately leads to freezing in liquid water, heat conduc- tion limits the rate at which temperature can change, and thus governs the freezing time scale. One way to circumvent this difficulty is by using small samples, which reduces the time necessary for thermal diffusion. For example, cooling rates of 107 − 1010 K/s can be
produced by spraying water droplets (1-10 µm diameter) into a cryogenic medium [117]. Molecular water clusters also allow rapid cooling and can show signs of solid structure
(measured by electron diffraction) on 10-30 µs time scales [118]. Mechanical compression is another way to induce freezing in water. It is often observed that mechanical distur-
bances may initiate freezing in water clouds [119], although there is some debate on the mechanism of this process. Vonnegut [119, 120] argued that the adiabatic expansions that follow compression reduce temperatures to the homogeneous nucleation limit. Shock tube measurements by Goyer et al. [121] suggested that rapid compression of supercooled water causes freezing through cavitation in water droplets. Subsequent studies [122, 123] do not support the cavitation conclusion, and suggest instead that supercooled water droplets in shock tubes freeze in the presence of hydrophobic surfaces. Freezing has been reported when bullets of sufficient velocity are fired into liquid water [124]. There are also claims
of freezing from shock waves created during the collapse of a gas bubble in liquid wa- ter. Hickling [125] suggested that this collapse produced pressure states compatible with high pressure ice phases on nanosecond time scales. In that work, it was argued that tran- sient freezing during bubble collapse could explain the enhanced sonoluminescence and the reduced substrate erosion for liquid water cooled near 0◦ C. Ohsaka and Trinh [126] obtained microscope images of bubble collapse with a high speed video camera. These images indicate a solidification process on 10−1 − 10−2 s time scales. The shortcoming of these dynamic cooling and compression experiments is that the thermodynamic history of the water sample is poorly characterized. For example, the peak
pressure generated by bubble collapse is thought to be anywhere from 1-10 GPa, depending
27 on how the collapse is modelled [126]. In the process, water is exposed to a complex series of compression and tension states. Similar uncertainties exist in fast cooling experiments, where direct measurements of temperature have not been made. Real time diagnostics are not employed in most dynamic cooling or compression experiments, so the true time dependence of freezing is not known. Molecular dynamics simulations represent another approach to studying the lower time limits of freezing in liquid water. Svishchev and Kusalik [127,128] demonstrated that water molecules simulated with the TIP4P [16] potential can freeze within 200 ps in the presence of an external electric field; similar results were obtained by Borzsak´ and Cum- mings [129]. Simulations of water confined within a small pore can also solidify on 1-10 ns time scales [130]. Xia and Berkowitz [131] found that freezing occurred in less than 1 ns for water confined between platinum substrates if the substrates carried a sufficient electric charge. Matsumoto et al. [132] reported that water can form stable ice clusters about 200 ns after being cooled to 230 K without an external field or surface perturbations. These clusters grow and cover the entire sample within about 100 ns after their first appearance. Freezing has recently been observed in simulated water on 3-30 ns time scales [133] using the TIP5P potential [19], although there have been some suggestions that this model does not represent water as well as the TIP4P potential [134].
2.3 Previous shock wave experiments on water The term shock wave is used here to denote a rapid, planar compression that trav- els with a constant velocity. Such a compression is described by the velocity of the shock front and the particle velocity, density, longitudinal stress, and internal energy behind the front. These variables are linked to the conditions ahead of the front through the Rankine- Hugoniot jump conditions [135]. States obtained by shock compression lie along the Hugo- niot curve [136], which may be derived from a series of shock wave experiments or from
28 a complete equation of state [137]. The rapid mechanical changes produced by shock compression are useful for studying the dynamics of phase transitions [138]. Two types of shock wave experiments are reviewed in this section. First, general shock wave ex- periments on liquid water are summarized. A review of previous shock induced freezing studies is then presented.
2.3.1 Shock wave experiments in liquid water Numerous shock wave experiments have been performed on liquid water. The most
notable of these is the work of Walsh and Rice [139], who reported the first Hugoniot measurements for liquid water. Those measurements showed a smooth Hugoniot in the 3-42 GPa range. Al’tshuler et al. [140] disputed this conclusion and claimed that there was break in the Hugoniot near 11 GPa. Subsequent Hugoniot measurements [141–146] generally agree with the Walsh and Rice data and do not suggest any such discontinuity. Hugoniot measurements provide a mechanical description of the shocked state, but do not provide information about the temperature in that state. Very few tempera- ture measurements have been reported for shocked water. Optical pyrometry was used by
Kormer [147] to infer shock temperatures in water in the 30-40 GPa range. This method was also used by Lyzenga et al. [148] for water shocked to pressures of 50-80 GPa. Flu- orescence thermometry [149] results have been reported for water shocked below 1 GPa. No measurements have been reported for intermediate pressures (1-30 GPa), where shock temperatures must be calculated from a complete equation of state. These calculations can be constrained using the results of double shock compression experiments. Walsh and ∂ ∂ Rice [139] used this method to determine the quantity ( h/ v)p, where h is the specific enthalpy, from double shock compressions and calculated shock temperatures for pressures in the 0-45 GPa range [50]. A similar method was used by Mitchell and Nellis [145] to ∂ ∂ specify ( P/ e)v in the 30-230 GPa range.
29 Shock temperatures of water compressed beyond 10 GPa are on the order of 103 K, so it is possible for water molecules to decompose into ionic species. The presence of these ions can be detected by their contribution to the electrical conductivity of the water sample. Conductivity measurements [145, 150–152] demonstrate that the conductivity of liquid water increases dramatically for shock pressures in the 10-20 GPa range. Raman spectroscopy of shocked water [153, 154] indicates that this conductivity arises from a decomposition of water into ionic hydrogen H+ and hydroxol OH−. That work also found significant hydrogen bonding in water compressed to 12 GPa, whereas these bonds are largely destroyed at 26 GPa.
2.3.2 Shock induced freezing There has been a long standing debate as to whether it is possible for water to freeze under shock compression. Snay and Rosenbaum [155] calculated a T − P Hugoniot curve that suggests that shock compression crosses the ice VII phase boundary at roughly 2.7 GPa. Figure 2.8 shows this curve along with the calculations of Rice and Walsh [50], which showed that the Hugoniot might access the ice VII phase near 3.5-4.2 GPa. The differences between these curves lead to some uncertainty about the possibility of freezing under shock wave compression. Even if the proper P,T conditions could be attained, it does not immediately follow that freezing will be observed in a shock experiment. Freezing is preceded by a metastable period, which may be on the order of seconds (Section 2.2.3), un- til stable ice nuclei form. Since time durations in shock experiments are limited to the order of microseconds, it is quite possible that only the metastable liquid state can be observed in these experiments. The first experimental study of shock induced freezing in water was made by Walsh and Rice [139]. In their experiments, light was passed through the shocked liquid and reflected from the metal driver plate, which was covered with a rectangular grid. The
30 1200
1100
1000
900 Rice and Walsh
800
Liquid T (K) 700
Snay and 600 Rosenbaum
500 Ice VII
400
300 VI 0 2 4 6 8 10 12 14 P (GPa)
Figure 2.8: Calculated P,T states of shocked liquid water Dark lines indicate the equilibrium phase boundaries of water [74, 75].
31 image of this grid was used to determine the state of the water sample. Clear images of the grid were expected while the sample remained a pure liquid, while image quality degradation would suggest freezing in the sample. No loss in image clarity was detected
for water shocked to 3-10 GPa over 20 µs time scales, suggesting that either the Hugoniot does not access the ice VII region or that the metastable lifetime is much longer than 20
µs. These results were challenged by Al’tshuler et al. [140], who reported a loss in optical transparency and a discontinuity in the Hugoniot slope near 11 GPa. These observations have been used to argue that liquid water coexists with ice VII at pressures above 10 GPa,
which is consistent with reports of unusually large viscosity for shock states near 15 GPa [156]. Revised Hugoniot calculations [157] predict that shock loading crosses the ice VII phase boundary somewhere between 4 and 8 GPa, creating a mixed phase state to 13 GPa. Rybakov [158] has suggested that the Hugoniot of liquid water is composed of three distinct regions: a liquid region below 3 GPa, a mixed liquid-ice VII region between 3 and 10 GPa, and another pure liquid region above 10 GPa. The difficulty with the shock freezing discussion above is that it assumes that single shock loading crosses the ice VII boundary near 3 GPa. However, such a crossing has
never been observed in optical studies. Furthermore, the arguments for freezing have relied
on a piecewise linear Us − up Hugoniot, but it is well established that most liquids have nonlinear Hugoniots [159]. Hamann and Linton [151] have made an alternate suggestion that the observed changes are the result of increasing ionization in water rather than a phase transition. Furthermore, shock wave studies of water saturated porous rocks do not show signs of freezing, although freezing in such systems is readily observed under hydrostatic compression [160]. The argument for freezing under shock compression is further weakened by the fact that the optical changes reported by Al’tshuler et al. [140] have never been repro-
duced [161]. Zel’dovich et al. [162] found no change in optical transparency for water
32 shocked to 4-14 GPa. A similar conclusion was reached by Kormer et al. [147, 163], who found that optical changes could only be observed when water was exposed to two shock compressions. In measurements by Kormer et al. [147,163], a change from specular reflec- tions to diffuse scattering was observed 10−7 − 10−6 s after double shock compression to the ice VII region. Experiments by Yakushev et al. [164] also showed that light reflected from the metal drive plate was attenuated in doubly shocked water, but only when a bare lithium fluoride window was exposed to the water. If this window was covered with a pro- tective lacquer, the reflection change was not observed. Those results were interpreted as an indication of heterogeneous ice nucleation or dissolution at the lithium fluoride-water interface2. Both Kormer et al. [147, 163] and Yakushev et al. [164] reported that optical changes observed in liquid water were not seen in other doubly shocked materials such as alcohol, glycerine, nitrobenzene, and Plexiglas. Overall, there is little evidence to suggest that water or any other liquid freezes under shock compression [138]. In the case of liquid water, it is not clear that single shock loading from ambient conditions is even thermodynamically possible; the water model developed in Chapter 5 suggests that it is not. The strongest support to date for freezing is from the double shock experiments of Kormer et al. [147,163], although the optical results are crude and somewhat ambiguous. These results are also unclear on the nature of surface effects, which Yakushev et al. [164] suggest are necessary for optical changes to occur. Even if one accepts that freezing can happen in double shock loading, no indication of a first order phase transition has been reported. Sheffield [166] measured particle velocity in a doubly shocked water sample, but did not find any evidence of a volume change. There is some evidence that shock wave loading of ice Ih can cause melting and refreezing to a high pressure ice phase. Using embedded electromagnetic particle velocity gauges, Larson [167] found that plate impact experiments with single and polycrystalline
2LiF dissolves in water at ambient conditions [165].
33 ice samples produced time dependent wave profiles. Using a Lagrangian analysis [168] of the data, he argued that these changes were caused by the melting of ice Ih and subsequent refreezing to ices VI and VII. Tchijov [169] performed wave propagation calculations with a water model containing the liquid phase as well as ices Ih, II, III, V, and VI; this model has since been extended to include ice VII [170]. Those calculations predict that shock loading in ice Ih produces a dynamic mixture of all of these phases over several microsec- onds. Given the complexity of the problem and the extremely limited experimental mea- surements, it is difficult to support or deny these claims. A key difference between shocked ice research and the issue of shock induced freezing in liquid water is that solid ice phases are always present in the former case, which can provide nucleation sites for the refreezing process. Based on an independent examination of all relevant data, it may be concluded that freezing in shock compressed water is an open question. This is similar to the conclusions reached by Duvall and Graham [138], who stated that “The case for freezing in shock is not a strong one...”.
2.4 Unresolved questions and approach The fundamental purpose of this thesis is to examine the lower time limits of freez- ing in liquid water. The discussion in Sections 2.2.3 and 2.3.2 indicate that there is no conclusive evidence for freezing on time scales less than 10−7 s, and that there are cer- tain obstacles in producing the proper conditions for freezing on such time scales. The following questions were posed in this work.
1. Using shock wave techniques, is it possible to create a state where liquid water can freeze?
2. Do consistent signs of freezing occur on 10−9 − 10−6 s time scales? Are these
34 changes consistent with a first order phase transition?
3. Does freezing occur through heterogeneous or homogeneous nucleation on these times scales?
Question #1 is addressed with quasi-isentropic compression obtained through mul- tiple shock compression, a technique described in Section 2.5. With the development of a complete equation of state for water, it is demonstrated that multiple shock compression can produce states of possible freezing while single shock loading cannot. Question #2 is addressed with the use of optical transmission, optical imaging, and wave profile measurements during multiple shock compression experiments. The optical diagnostics show that water changes from a clear liquid to a complex liquid-solid mixture. Wave profile measurements indicate that water initially remains a pure liquid, but then transforms into a material that is denser than the compressed liquid. Question #3 is addressed with multiple shock compression experiments for water confined in different types of windows. It is shown that heterogeneous nucleation occurs at the water-window surfaces, but that the transformation is not confined to these surfaces.
2.5 Multiple shock wave compression As discussed in Section 2.3.2, it is unclear whether shock compression can produce temperatures where freezing is thermodynamically possible. The difficulty arises from the fact that shock compression is an irreversible, adiabatic process [137], which leads to sig- nificant temperature increases. Multiple shock wave compression can be used to minimize the entropy produced during rapid compression, leading to considerably lower tempera- tures than single or double shock compression. This technique has been applied in other high pressure liquid studies [171–175] and was used in this work to generate thermody- namics states compatible with freezing. The following discussion explains how multiple
35 shock wave compression loading is obtained in a plate impact experiment. The temperature differences between multiple and single shock compression are also discussed.
2.5.1 Multiple shock compression and plate impact Figure 2.9(a) shows a schematic configuration for a multiple shock experiment, where a liquid sample is confined by two solid windows. A light gas gun [176] accelerates an impactor that strikes the front window of the liquid cell, generating an impact longitudi- nal stress Pi and particle velocity ui. The values of Pi and ui are defined by the intersection of the impactor and front window Hugoniots, which maintains continuity of stress and par- ticle velocity at the impact interface [137]. This construction is shown in Figure 2.9(b) for the case where the impactor, front window, and rear window are all composed of the same material. After impact, a right going shock wave propagates through the front window and reaches the liquid sample as shown in Figure 2.9(c). This creates a new state (u1,P1) at the intersection of the front window unloading curve and the liquid Hugoniot. The new shock wave propagates through the water sample and reaches the rear window, generating a re-
flected shock (u2,P2). This shock wave travels back to the front window, creating another reflected shock (u3,P3). The process continues as shown in Figures 2.9(b) and 2.9(c) until a peak state is reached, which is identical to the original impact state (ui,Pi). Pressure in the liquid sample increases in stages to Pi as shown in Figure 2.9(d). The number and timing of loading stages in this history depends upon the thickness and properties of the liquid sample, but the peak pressure depends only upon the impact velocity and window/impactor materials. The steady state particle velocity is also independent of the liquid sample and equals half of the original impact velocity. Should the sample undergo some time depen- dent transition that leads it away from (ui,Pi), subsequent wave reflections from the front and rear windows will lead the system back to the original steady state.
With multiple shock wave compression, it is possible to generate peak pressures
36 (a) sample (b) impact/peak state midpoint v
6 5
4 s
s e
r 3 t s
l a n i 2 IM loading/ d
u FW unloading t i
impactor g front liquid rear n
(IM) o
window sample window L 1 (FW) (LS) (RW) FW/RW loading
v/2 v Particle velocity
(c) impactor FW LS RW (d)
6 peak state 6 5 5 4 t n i 3 4 o p d i e m
m 3 i
e 2 l T p
m
2 a s
t a
1 s
1 s e
shock arrival r t
at sample S
i i 0 impact 0 Lagrangian position Time
Figure 2.9: Multiple shock compression (a) Plate impact experiment setup (b) Loading path for a symmetric impact (c) Shock waves generated in multiple shock compression (d) Stress history at the liquid sample midpoint.
37 from 1 GPa to more than 10 GPa with a single stage gas gun (v = 0.2−1 km/s). The use of
plate impact generates a state of uniaxial strain (εi j = 0 for i, j 6= 1) throughout the system for a short time due to inertial confinement [137]. This state is preserved until the arrival of release waves from the free edges of the impactor. Estimates of the edge wave arrival can be made by assuming that these waves travel at an angle of 45◦ from the impact direction. For an impactor diameter D, an experimental probe diameter of d, and a edge wave velocity c (which is the sound speed in the shocked state), the maximum duration of uniaxial strain is given by tmax. D − d tmax ≈ √ (2.13) 2 c More precise estimates of the uniaxial strain duration can be made using two dimensional wave calculations [175, 177].
2.5.2 Temperature advantages of multiple shock compression At this point, it is important to distinguish an adiabatic process, which occurs in the absence of heat flow, from an isentropic process, which occurs at fixed entropy. All reversible adiabatic processes are isentropic, but there are adiabatic process which are irre- versible. Shock wave compression is an example of such a process, where the magnitude of the entropy increase is related to the change in specific volume change [137]. µ ¶ 1 d2P ∆s = A(v − v)3 where A ≡ (2.14) single 0 12T dv2 0 v=v0 Multiple shock compression is simply a sequence of individual shock waves, so entropy is also generated in the process. For a series of N shocks of equal volume increment, the total entropy change is equal to a sum of terms similar to Equation 2.14
N−1 µ ¶3 N−1 3 v0 − v ∆sreverb = ∑ Ai(vi − vi+1) = ∑ Ai (2.15) i=0 N i=0
38 The sum in this relation scales with the number of shocks N, so the overall entropy change scales with 1/N2. In the limit N → ∞, the total entropy change goes to zero. In reality, some entropy is produced because the first few compressions have a nonzero magnitude, but the total entropy production is substantially lower than in single shock compression. Multiple shock compression is therefore a quasi-isentropic process. The difference in entropy production for multiple and single shock leads to very different temperatures for the same peak pressure. To demonstrate this difference, consider T = T(s,P). µ ¶ · µ ¶ ¸ ∂T ∂v dT = ∂ ds + ∂ dP (2.16) s P T P ∂ ∂ ∂ ∂ 3 ( T/ s)P and ( v/ T)P are positive , so temperature increases with both pressure and entropy. In multiple shock loading, ds ≈ 0, so only the right term contributes to the temper- ature. However, ds > 0 in shock compression, so both terms contribute to the temperature increases. Thus isentropic and quasi-isentropic compression lead to lower temperatures than single shock compression to the same pressure. Figure 2.10 shows calculated Hugo- niot and isentrope states for liquid water based on a model presented in Chapter 5. Single shock loading does not enter the ice VII domain at any pressure in this range, while isen- tropic compression produces states of possible freezing for pressures above 2 GPa. There is no indication that isentropic loading will reenter the liquid domain at high pressures, so pressure can be increased as necessary to reduce the metastable lifetime of the liquid phase. Since isentropic loading produces the lowest possible temperatures for an adiabatic compression, it provides a limit on the possibility of freezing on short time scales. In other words, if freezing does not occur under isentropic loading, one can conclude that it will not occur in any other kind of adiabatic compression.
3 ∂ ∂ It is possible for ( v/ T)P to be negative in liquid water, but not at temperatures relevant to this work.
39 800
750 single shock loading 700
650
600 Liquid
550
isentropic 500 loading Temperature (K)
450
400
Ice VII 350
300 VII 0 1 2 3 4 5 6 7 8 9 10 Pressure (GPa)
Figure 2.10: Temperature advantages of multiple shock compression Dark lines indicate the equilibrium phase boundaries of water [75,178]. The Hugoniot and isentrope curves are calculated from an equation of state presented in Chapter 5.
40 References for Chapter 2 [1] F. Franks. Introduction– Water, The Unique Chemical. In Water: A Comprehensive Treatise, F. Franks, editor, v. 1, pg. 18. Plenum Press, New York (1972).
[2] F. Franks. Water: A Comprehensive Treatise, v. 1-7. Plenum Press, New York, (1972).
[3] F. Franks. Water. Royal Society of Chemistry, London, 2nd edition, (2000).
[4] D. Eisenberg and W. Kauzmann. The Structure and Properties of Water. Oxford Press, New York, (1969).
[5] H.S. Frank. The structure of ordinary water. Science 169, 635 (1970).
[6] F.H. Stillinger. Water revisted. Science 209, 451 (1980).
[7] R. Cotterill. The Cambridge Guide to the Material World. Cambridge University Press, Cambridge, (1985).
[8] N.H. Fletcher. The Chemical Physics of Ice. Cambridge University Press, London, (1970).
[9] T. Head-Gordon and G. Hura. Water structure from scattering experiments and sim- ulation. Chem. Rev. 102, 2651 (2002).
[10] N.H. Fletcher. Structural aspects of the ice-water system. Rep. Prog. Phys. 34, 913 (1971).
[11] Rontgen.¨ Ann. phys. chim. (Wied.) 45, 91 (1892).
[12] H.M. Chadwell. The molecular structure of water. Chem. Rev. 4, 375 (1927).
[13] J.A. Pople. Proc. R. Soc. Lond. A 205, 163 (1951).
[14] C.H. Cho. Mixture model description of the T-, P dependence of the refactive index of water. J. Chem. Phys. 114, 3157 (2001).
[15] M.P. Allen and D.J. Tildesley. Computer Simulation of Liquids. Clarendon Press, New York, (1987).
[16] W.L. Jorgensen, J. Chandrasekhar, J.D. Madura, R.W. Impey and M.L. Klein. Com- parison of simple potential functions for simulating liquid water. J. Chem. Phys. 79, 926 (1983).
[17] A. Wallqvist and B.J. Berne. Effective potentials for liquid water using polarizable and nonpolarizable models. J. Phys. Chem 97, 13841 (1993).
41 [18] Y. Liu and T. Ichyie. Soft sticky dipole potential for liquid water: a new model. J. Phys. Chem 100, 2723 (1996).
[19] M.W. Mahoney and W.L. Jorgensen. A five-site model for liquid water and the reproduction of the density anomaly by rigid, nonpolarizable potential functions. J. Chem. Phys. 112, 8910 (2000).
[20] E. Schwegler, G. Galli and F. Gygi. Water under pressure. Phys. Rev. Lett. 84, 2429 (2000).
[21] M.F. Chaplin. A proposal for the structuring of water. Biophys. Chem. 83, 211 (1999).
[22] G.S. Kell. Density, thermal expansivity, and compressibility of liquid water from 0 to 150◦ C: correlations and tables for atmospheric pressure and saturation reviewed and expressed on 1968 temperature scale. J. Chem. Eng. Data 20, 97 (1975).
[23] V.A. Del Grosso and C. W. Mader. Speed of sound in pure water. J. Acous. Soc. Am. 52, 1442 (1972).
[24] P. Atkins. Physical Chemistry. W.H. Freeman, New York, 6th edition, (1998).
[25] B. Rukes and R.B. Dooley. Guideline on the use of fundamental physical constants and basic constants of water. Technical report, IAPWS, September 2001 (2001).
[26] R. Fernandez-Prini and R.B. Dooley. Revised release on the IAPWS formulation 1985 for the thermal conductivity of ordinary water substance. Technical report, IAPWS, September 1998 (1998).
[27] J.R. Cooper and R.B. Dooley. IAPWS release on surface tension of ordinary water substance. Technical report, IAPWS, September 1994 (1994).
[28] P.M. Pichal and R.B. Dooley. Electrolytical conductivity (specific conductance) of liquid and dense supercritical water from 0◦ C to 800◦ C and pressures up to 1000 MPa. Technical report, IAPWS, (1990).
[29] D.E. Gray, editor. American Institute of Physics Handbook. McGraw-Hill, New York, 3rd edition, (1972).
[30] V.C. Smith. Preparation of Ultrapure Water. In Ultrapurity: Methods and Tech- niques, M. Zief and R. Speights, editors. Marcel Dekker, New York (1972).
[31] S. Wiryana, L.J. Slutsky and J.M. Brown. The equation of state of water to 200◦ C and 3.5 GPa: model potentials and the experimental pressure scale. Earth Planet. Sci. Lett. 163, 123 (1995).
42 [32] H. Kanda, S. Yamaoka, N. Setaka and H. Komatsu. Etching of diamond octahedrons by high pressure water. J. Crys. Grow. 38, 1 (1977).
[33] K. Todheide. Water at high temperatures and pressures. In Water: A Comprehensive Treatise, F. Franks, editor, v. 1. Plenum Press, New York (1972).
[34] H. Sato, K. Watannabe, J.M.H. Levelt Sengers, J.S. Gallagher, P.G. Hill, J. Straub and W. Wagner. Sixteen thousand evaluated experimental thermodynamic property data for water and steam. J. Phys. Chem. Ref. Data 20, 1023 (1991).
[35] P.W. Bridgman. Water, in the liquid and five solid forms, under pressure. Proc. Am. Acad. Arts. Sci. 47, 441 (1911).
[36] P.W. Bridgman. Freezing parameters and compressions of twenty-one substances to 50,000 kg/cm2. Proc. Am. Acad. Arts. Sci. 74, 399 (1942).
[37] A.H. Smith and A.W. Lawson. The velocity of sound in water as a function of temperature and pressure. J. Chem. Phys. 22, 351 (1954).
[38] G Holton, M.P. Hagelberg, S Kao and W. H. Johnson Jr. Ultrasonic velocity mea- surements in water at pressures to 10,000 kg/cm2. J. Acous. Soc. Am. 43, 102 (1968).
[39] S. Wiryana. Physical properties of aqueous solutions under high pressures and temperatures. Phd, University of Washington, (1998).
[40] E.H. Abramson, J.M. Brown and L.J. Slutsky. The thermal diffusivity of water at high pressures and temperatures. J. Chem. Phys. 115, 10461 (2001).
[41] J.D. Madura, B.M. Pettitt and D.F. Calef. Water under high pressure. Mol. Phys. 64, 325 (1988).
[42] J.S. Tse and M.L. Klein. A molecular dynamics study of the effect of pressure on the properties of water and ice. J. Phys. Chem 92, 315 (1988).
[43] J. Brodholt and B. Wood. Molecular dynamics of water at high temperatures and pressures. Geochim. Cosmochim. Acta 54, 2611 (1990).
[44] A. Belonoshko and S.K. Saxena. A molecular dynamics study of the pressure- volume-temperature properties of super-critical fluids. I. H2O. Geochim. Cos- mochim. Acta 55, 381 (1991).
[45] L. Haar, J.S. Gallagher and G.S. Kell. NBS/NRC Steam Tables. Hemisphere, (1984).
[46] H. Sato, M. Uematsu, K. Watanbe, A. Saul and W. Wagner. New international skeleton tables for the thermodynamic properties of ordinary water substance. J. Phys. Chem. Ref. Data 17, 1439 (1988).
43 [47] H. Halbach and N.D. Chatterjee. An emprical Redlich-Kwong type equation of state for water to 1000◦ C and 200 kbar. Contrib. Mineral. Petrol. 79, 337345 (1982).
[48] T. Holland and R. Powell. A compensated (CORK) equation for volumes and fu- ◦ gacities for CO2 and H2O in the range 1 bar to 50 kbar and 100-1500 C. Contrib. Mineral. Petrol. 109 (1991).
[49] H.B. Callen. Thermodynamics and an introduction to statistical mechanics. Wiley, New York, 2nd edition, (1985).
[50] M.H. Rice and J.M. Walsh. Equation of state of water to 250 kilobars. J. Chem. Phys. 26, 824 (1957).
[51] M. Cowperthwaite. Significance of some equations of state obtained from shock wave data. Am. J. Phys. 34, 1025 (1966).
[52] M. Cowperthwaite and R. Shaw. cv(T) equation of state for liquids. J. Chem. Phys. 53, 555 (1970).
[53] G.A. Gurtman, J.W. Kirsch and C.R. Hastings. Analytical equation of state for water compressed to 300 kbar. J. Appl. Phys. 42, 851 (1971).
[54] R. Vedam and G. Holton. Specific volumes of water at high pressures, obtained from ultrasonic-propagation measurements. J. Acous. Soc. Am. 43, 108 (1968).
[55] D.P. Wang and F.J. Millero. Precise representation of the PVT properties of water and seawater determined from sound speeds. J. Geophys. Res. 78, 7122 (1973).
[56] R.A. Fine and F.J. Millero. Compressibility of water as a function of temperature and pressure. J. Chem. Phys. 59, 5529 (1973).
[57] A. Saul and W. Wagner. A fundamental equation for water covering the range from the melting line to 1273 K at pressures up to 25,000 MPa. J. Phys. Chem. Ref. Data 18, 1537 (1989).
[58] K. Watanabe and R.B. Dooley. Release on the IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. Technical report, IAPWS, September 1996 (1996).
[59] W. Wagner and A. Pruss. The IAWPS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 31, 387 (2002).
[60] J.D. Jackson. Classical Electrodynamics. John Wiley & Sons, New York, 2nd edi- tion, (1975).
44 [61] L.W. Tilton and J.K. Taylor. Refractive index and dispersion of distilled water for visible radiation, at temperatures 0 to 60◦. J. Res. Nat. Bureau Stand. 20, 419 (1938).
[62] A.H. Harvey, J.S. Gallagher and J.M.H.L Sengers. Revised formulation for the re- fractive index of water and steam as a function of wavelength, temperature, and density. J. Phys. Chem. Ref. Data 27, 761 (1998).
[63] C.F. Bohren and D.R. Huffman. Absorption and Scattering of Light by Small Parti- cles. John Wiley & Sons, New York, (1983).
[64] G.D. Kerr and R.N. Hamm. Optical and dielectric properties of water in the vacuum ultraviolet. Phys. Rev. A 5, 2523 (1972).
[65] P.V. Hobbs. Ice Physics. Claredon Press, Oxford, (1974).
[66] K. Yamamoto. Supercooling of the coexisting state of ice VII and water withing ice VI region observed in diamond anvil pressure cells. Japanese J. Appl. Phys. 19, 1841 (1980).
[67] S.N. Tkachev, R.M. Nasimov and V.A. Kalinin. Phase diagram of water in the vicinity of the triple point. J. Chem. Phys. 105, 3722 (1996).
[68] I.M Chou, J.G. Blank, A.F Goncharov, H.K. Mao and R.J. Hemley. In situ observa- tions of a high pressure phase of H2O ice. Science 281, 809 (1998). [69] K. Vedam and P. Limsuwan. Piezo-optic behavior of water and carbon tetrachloride under high pressure. Phys. Rev. Lett. 35, 1014 (1975).
[70] K. Vedam and P. Limsuwan. Piezo- and elasto-optic properties of liquids under high pressure. I. Refractive index vs pressure and strain. J. Chem. Phys. 69, 4762 (1978).
[71] K. Vedam and P. Limsuwan. Piezo- and elasto-optic properties of liquids under high pressure. II. Refractive index vs. density. J. Chem. Phys. 69, 4772 (1978).
[72] V.F. Petrenko and R.W. Whitworth. Physics of Ice. Oxford University Press, Oxford, (1999).
[73] E. Whalley, D.W. Davidson and J.B.R. Heath. Dielectric properties of ice VII. Ice VIII: a new phase of ice. J. Chem. Phys. 45, 3976 (1966).
[74] C.W. Pistorius, M.C. Pistorius, J.P. Blakey and L.J. Admiraal. Melting curve of ice VII to 200 kbar. J. Chem. Phys. 38, 600 (1963).
[75] C.W. Pistorius, E. Rapoport and J.B. Clark. Phase diagrams of H2O and D2O at high pressures. J. Chem. Phys. 48, 5509 (1968).
45 [76] W. Wagner, A. Saul and A. Pruss. International equations for the presure along the melting and along the sublimation curve of ordinary water substance. J. Phys. Chem. Ref. Data 23, 515 (1994). [77] P.W. Bridgman. Phase diagram of water to 45,000 kg/cm2. J. Chem. Phys. 5, 964 (1937). [78] K. Vonnegut. Cat’s cradle. Delacorte Press, New York, (1963). [79] E. Whalley, J.B.R. Heath and D.W. Davidson. Ice IX: an antiferroelectric phase related to ice III. J. Chem. Phys. 48, 2362 (1968). [80] W.B. Holzapfel. Evasive ice X and heavy fermion ice XII: facts and fiction about high-pressure ices. Physica B 265, 113 (1999). [81] I.M. Svishchev and P.G. Kusalik. Quartzlike polymorph of ice. Phys. Rev. B 53, R8815 (1996).
[82] A. Polian and M. Grimsditch. Brillouin scattering from H2O: Liquid, ice VI, and ice VII. Phys. Rev. B 27, 6409 (1983). [83] H. Shimizu, T. Nabetani, T Nishiba and S. Sasaki. High pressure elastic properties of the VI and VII phase of ice in dense H2O and D2O. Phys. Rev. B 53, 6107 (1996). [84] B. Kamb. Structural studies of the high-pressure forms of ice. Trans. Am. Crysallo- graph. Soc. 5, 61 (1969). [85] C.A. Tulk, C.J. Benmore, J. Urquidi, D.D. Klug, J. Neuefeind, B. Tomberli and P.A. Egelstaff. Structural studies of several distinct metastable forms of amorphous ice. Science 297, 1320 (2002). [86] A.G. Walton. Nucleation in liquids and solutions. In Nucleation, A.C. Zettlemoyer, editor. Marcel Dekker, New York (1969). [87] P.G. Debenedetti. Metastable Liquids. Princeton University Press, Princeton, (1996). [88] L.H. Seeley. Heterogeneous nucleation of ice from supercooled water. Ph.D. thesis, Unversity of Washington, (2001). [89] L.H. Seeley, G.T. Seidler and J.G. Dash. Apparatus for statistical studies of hetero- geneous nucleation. Rev. Sci. Instrum. 70, 3664 (1999). [90] L.H. Seeley and G.T. Seidler. Preactivation in the nucleation of ice by Languir films of aliphatic alcohols. J. Chem. Phys. 114, 10464 (2001). [91] A.F. Heneghan, P.W. Wilson, G. Wang and A.D.J. Haymet. Liquid-to-crystal nucle- ation: automated lag-time apparatus to study supercooled liquids. J. Chem. Phys. 115, 7599 (2001).
46 [92] A.F. Heneghan and A.D.J. Haymet. Liquid-to-crystal nucleation: a new generation lag-time apparatus. J. Chem. Phys. 117, 5319 (2002).
[93] A.F. Heneghan, P.W. Wilson and A.D.J. Haymet. Heterogeneous nucleation of su- percooled water, and the effect of an added catalyst. PNAS 99, 9631 (2002).
[94] A.F. Heneghan and A.D.J. Haymet. Liquid-to-crystal heterogeneous nucleation: bubble accelerated nucleation of pure supercooled water. Chem. Phys. Lett. 368, 177 (2003).
[95] B. Vonnegut. The nucleation of ice formation by silver iodide. J. Appl. Phys. 18, 593 (1947).
[96] R. Smith-Johansen. Some experiments in the freezing of water. Science 108, 652 (1948).
[97] G.W. Bryant, J. Hallett and B.J. Mason. The epitaxial growth of ice on single crys- talline substrates. J. Phys. Chem. Solids 12, 189 (1959).
[98] M. Kumai. Snow crystals and the identification of the nuclei in the northern United States of America. J. Meterology 18, 139 (1961).
[99] M. Kumai and K.E. Francis. Nuclei in snow and ice crystals on the Greenland ice cap under natural and artificially stimulated conditions. J. Atmos. Sci. 19, 474 (1962).
[100] A.C. Zettlemoyer, N. Tcheurekdjian and C.L. Hosler. Ice nucleation by hydrophobic surfaces. Z. Angew. Math. Phys. 14, 496 (1963).
[101] A.C. Zettlemoyer, J.J. Chessick and N. Tcheurekdjian. Nucleating process, (1966). U.S. Patent 3,272,434.
[102] D.R. Bassett, A.A. Boucher and A.C. Zettlemoyer. Adsorption studies on ice- nucleating substrates. Hydrophobed silicas and silver iodide. J. Colloid Interface Sci. 34, 436 (1970).
[103] M. Gavish, R. Popovitz-Biro, M. Lahav and L. Leiserowitz. Ice nucleation by alco- hols arragned in monolayers at the surface of water drops. Science 250, 973 (1990).
[104] M. Gavish, J.L. Wang, M. Eisenstein, M. Lahav and L. Leiserowitz. The role of crystal polarity in alpha amino acid crystals for induced nucleation of ice. Science 256, 815 (1992).
[105] R.E. Lee, G.J. Warren and L.V. Gusta, editor. Biological Ice Nucleation and Its Applications. American Phytopathological Society Press, St. Paul, (1995).
[106] L.F. Evans. Selective nucleation of the high-pressure ices. J. Appl. Phys. 38, 4930 (1967).
47 [107] L.F. Evans. Ice nucleation under pressure and in salt solution. Trans. Faraday Soc. 63, 3060 (1967).
[108] M. Roulleau. The influence of an electric field on the freezing of water. In Physics of Ice, N. Riehl, editor (Plenum Press, Munich, Germany, 1968).
[109] R.W. Salt. Effect of electrostatic field on freezing of supercooled water and insects. Science 133, 458 (1961).
[110] R.G. Layton. Ice nucleation by silver iodide: influence of an electric field. J. Colloid Interface Sci. 42, 214 (1972).
[111] N.H. Fletcher. Size effect in heterogeneous nucleation. J. Chem. Phys. 28, 572 (1958).
[112] G.R. Edwards and L.F. Evans. Effect of surface charge on ice nucleation by silver iodide. Trans. Faraday Soc. 58, 1649 (1962).
[113] H.R. Pruppacher and J.C. Pflaum. Some characteristics of ice-nucleation active sites derived from experiments with a ferroelectric substrate. J. Colloid Interface Sci. 52, 543 (1975).
[114] L.F. Evans. Two dimensional nucleation of ice. Nature 213, 384 (1967).
[115] G.R. Edwards, L.F. Evans and A.F. Zipper. Two-dimensional phase changes in water adsorbed on ice-nucleating substrates. Trans. Faraday Soc. 66, 220 (1970).
[116] G. Vali. Freezing rate due to heterogeneous nucleation. J. Atmos. Sci. 51, 1843 (1994).
[117] E. Mayer and P. Bruggeller. Vitrification of pure liquid water by high pressure jet freezing. Nature 298, 715 (1982).
[118] L.S. Bartell. Nucleation rates in freezing and solid-state transitions. Molecular clus- ters as model systems. J. Phys. Chem 99, 1080 (1995).
[119] B. Vonnegut. Production of ice crystals by the adiabatic expansion of gas. J. Appl. Phys. 19, 959 (1948).
[120] B. Vonnegut and C.B. Moore. Nucleation of ice formation in supercooled clouds as the result of lightning. J. Appl. Meteorology 4, 640 (1965).
[121] G.G. Goyer, T.C. Bhadra and S. Gitlin. Shock induced freezing of supercooled water. J. Appl. Meteorology 4, 156 (1964).
[122] G.R. Edwards, L.F. Evans and S.D. Hamann. Nucleation of ice by mechanical shock. Nature 223, 390 (1969).
48 [123] S.N. Gitlin. Shock waves and freezing. J. Appl. Meteorology 9, 716 (1970). [124] H. Schardin. Jahrbuch Der Deutsche Akademie Der Luftahrtforschung , 314 (1941). [125] R. Hickling. Transient, high-pressure solidification associated with cavitation in water. Phys. Rev. Lett. 73, 2853 (1994). [126] K. Ohsaka and E.H. Trinh. Dynamic nucleation of ice induced by a single stable cavitation bubble. Appl. Phys. Lett. 73, 129 (1998). [127] I.M. Svishchev and P.G. Kusalik. Crystallization in liquid water in a molecular dynamics simulation. Phys. Rev. Lett. 73, 975 (1994). [128] I.M. Svishchev and P.G. Kusalik. Electrofreezing of liquid water: a microscopic perspective. J. Am. Chem. Soc. 118, 649 (1996). [129] I. Borzsak´ and P.T. Cummings. Electrofreezing of water in molecular dynamics simulations accelarated by oscillatory shear. Phys. Rev. E 56, 6279 (1997). [130] K. Koga, X.C. Zeng and H. Tanaka. Freezing of confined water: a bilayer ice phase in hydrophobic nanopores. Phys. Rev. Lett. 79, 5262 (1997). [131] X. Xia and M.L. Berkowitz. Electric-field induced restructuring of water at a platinum-water interface: a molecular dynamics computer simulation. Phys. Rev. Lett. 74, 3193 (1995). [132] M. Matsumoto, S. Saito and I. Ohmine. Molecular dynamics simulation of the ice nucleation and growth processes leading to water freezing. Nature 416 (2002). [133] M. Yamada, S. Mossa, H.E. Stanley and F. Sciortino. Interplay between time- temperature transformation and the liquid-liquid phase transition in water. Phys. Rev. Lett. 88, 195701 (2002). [134] M. Lisal, J. Kolafa and I. Nezbeda. An examination of the five-site potential (TIP5P) for water. J. Chem. Phys. 117, 8892 (2002). [135] G.E. Duvall and G.R. Fowles. Shock waves. In High pressure physics and chemistry, R.S. Bradley, editor, v. 2. Academic Press, London (1963). [136] W. Band and G.E. Duvall. Physical nature of shock propagation. Am. J. Phys. 29, 780 (1961). [137] Y.M. Gupta. Lecture notes for “Fundamentals of large amplitude plane stress wave propagation in condensed materials”, Physics 592 (Washington State University), (2001). [138] G.E. Duvall and R.A. Graham. Phase transitions under shock wave loading. Rev. Mod. Phys. 49, 523 (1977).
49 [139] J.M. Walsh and M.H. Rice. Dynamic compression of liquids from measurements on strong shock waves. J. Chem. Phys. 26, 815 (1957).
[140] L.V. Al’tshuler, A.A. Bakanova and R.F. Trunin. Phase transformation of water compressed by strong shock waves. Sov. Phys. Doklady 3, 761 (1958).
[141] M.A. Cook, R.T. Keyes and W.O. Ursenbach. Measurements of detonation pressure. J. Appl. Phys. 33, 3413 (1962).
[142] T.J. Ahrens and M.H. Ruderman. Immersed-foil method for measuring shock wave profiles in solids. J. Appl. Phys. 37, 4758 (1966).
[143] P.C. Lysne. A comparison of calculated and measured low-stress hugoniots and release adiabats of dry and water-saturated tuff. J. Geophys. Res. 75, 4375 (1970).
[144] J. Baconin and A. Lascar. Experimental results for extending the Rice-Walsh equa- tion of state of water. J. Appl. Phys. 44, 4583 (1973).
[145] A.C. Mitchell and W.J. Nellis. Equation of state and electrical conductivity of water and ammonia shocked to the 100 GPa pressure range. J. Chem. Phys. 76, 6273 (1982).
[146] K. Nagayama, Y. Mori, K. Shimada and M. Nakahara. Shock Hugoniot compression curve for water up to 1 GPa by using a compressed gas gun. J. Appl. Phys. 91, 476 (2002).
[147] S.B. Kormer. Optical study of the characteristics of shock-compressed condensed dielectrics. Sov. Phys. Uspekhi 11, 229 (1968).
[148] G.A. Lyzenga, T.J. Ahrens, W.J. Nellis and A.C. Mitchell. The temperature of shock- compressed water. J. Chem. Phys. 76, 6282 (1982).
[149] B.L. Justus, A.L. Huston and A.J. Campillo. Fluorescence thermometry of shocked water. Appl. Phys. Lett. 47, 1159 (1985).
[150] S.D. Hamann and M. Linton. Electrical conductivity of water in shock compression. Trans. Faraday Soc. 62, 2234 (1966).
[151] S.D. Hamann and M. Linton. Electrical conductivities of aqueous solutions of KCl, KOH, and HCl, and the ionizations of water at high shock pressures. Trans. Faraday Soc. 65, 2186 (1969).
[152] K. Hollenberg. The electrical conductivity of water at dynamic pressures from 5 to 40 GPa. J. Phys. D 16, 385 (1983).
[153] N.C. Holmes, W.J. Nellis, W.B. Graham and G.E. Walrafen. Spontaneous Raman scattering from shocked water. Phys. Rev. Lett. 55, 2433 (1985).
50 [154] N.C. Holmes, W.J. Nellis, W.B. Graham and G.E. Walrafen. Raman spectroscopy of shocked water. In Shock Waves in Condensed Matter, Y.M. Gupta, editor, v. A24, 191 (Plenum, Spokane, WA, 1986).
[155] H.G. Snay and J.H. Rosenbaum. Shockwave parameters in fresh water for pressures up to 95 kilobars. Technical Report NAVORD Report 2383, U.S. Naval Ordinance Laboratory, (1952).
[156] G.H. Miller and T.J. Ahrens. Shock-wave viscosity measurement. Rev. Mod. Phys. 63, 919 (1991).
[157] R.C. Schroeder and W.h. McMaster. Shock-compression freezing and melting of water and ice. J. Appl. Phys. 44, 2591 (1973).
[158] A.P. Rybakov. Phase transformation of water under shock compression. J. Appl. Mech. Tech. Phys. 37, 629 (1996).
[159] R.W. Woolfolk, M. Cowperthwaithe and R. Shaw. A “universal” Hugoniot for liq- uids. Thermochim. Acta 5, 409 (1973).
[160] D.B. Larson and G.D. Anderson. Plane shock wave studies of porous geologic me- dia. J. Geophys. Res. 84, 4592 (1979).
[161] L V Al’tshuler, R F Trunin, V D Urlin, V E Fortov and A I Funtikov. Development of dynamic high-pressure techniques in Russia. Physics-Uspekhi 42, 261 (1999).
[162] Ya.B. Zel’dovich, S.B. Kormer, M.V. Sinitsyn and K.B. Yushko. A study of the optical properties of transparent materials under high pressure. Sov. Phys. Doklady 6, 494 (1961).
[163] S.B. Kormer, K.B. Yushko and G.V. Krishkevich. Phase transformation of water into ice VII by shock compression. Sov. Phys. JETP 27, 879 (1968).
[164] V.V. Yakushev, V. Yu. Klimenko, S.S. Nabatov and A.N. Dremin. On the issue of water freezing in dynamic compression. In Detonation. Critical Phenomena. Physicochemical Conversions in Shock Waves, F. I. Dubovitskii, editor, 116, (1978). English translation provided by O. Fat’yanov (Insititute for Shock Physics, Pullman, WA, 2002).
[165] J.J. Gilman, W.G. Johnston and G.W. Sears. Dislocation etch pit formation in lithium fluoride. J. Appl. Phys. 29, 747 (1958).
[166] S.A. Sheffield. Shock-induced reaction in carbon disulfide. Ph.D. thesis, Washington State University, (1978).
[167] D.B Larson. Shock wave studies of ice under uniaxial strain conditions. J. Glaciol- ogy , 235 (1983).
51 [168] J.B. Aidun. Study of shear and compression waves in shocked calcium carbonate. Ph.D. thesis, Wasington State University, (1989).
[169] V Tchijov, J Keller, S.R. Romo and O Nagornov. Kinetics of phase transitions induced by shock wave loading in ice. J. Phys. Chem. B 101, 6215 (1997).
[170] G.C. Leon, S.R. Romo and V. Tchijov. A kinetic model of multiple phase transitions in ice. In Shock Compression in Condensed Matter, M.D. Furnish, editor (American Institute of Physics, Atlanta, GA, 2001).
[171] G.E. Duvall, K.M. Ogilvie, R. Wilson, P.M. Bellmany and P.S.P Wei. Optical spec- troscopy in a shocked liquid. Nature 296, 846 (1982).
[172] C.S. Yoo and Y.M. Gupta. Time-resolved absorption changes of thin CS2 samples under shock compression: electronic and chemical implications. J. Phys. Chem 94, 2857 (1990).
[173] R.L. Gustavsen. Time resolved reflection spectroscopy on shock compressed liquid carbon disulfide. Ph.D. thesis, Washington State Univesity, (1989).
[174] G.I. Pangilinan and Y.M.Gupta. Use of time-resolved Raman scattering to determine temperatures in shocked carbon tetrachloride. J. Appl. Phys. 81, 6662 (1997).
[175] J.M. Winey. Time-resolved optical spectroscopy to examine shock-induced decom- position in liquid nitromethane. Ph.D. thesis, Washington State University, (1995).
[176] G.R. Fowles, G.E. Duvall, J. Asay, P. Bellamy, F. Feistmann, D. Grady, T. Michaels and R. Mitchell. Gas gun for impact studies. Rev. Sci. Instrum. 41, 984 (1970).
[177] J.M. Winey, (2002). Private communication regarding edge wave arrival estimates.
[178] Carl W.F.T. Pistorius and W.E. Sharp. Properties of water. Part VI. Entropy and Gibbs free energy of water in the range 10-1000◦ C and 1-250,000 bars. American Journal of Science 258, 757 (1960).
52 Chapter 3
Experimental Methods This chapter describes the experimental techniques and instrumentation used in the present study. Optical transmission experiments are discussed in Section 3.1. Optical imag- ing experiments are covered in Section 3.2. Wave profile experiments are described in Sec- tion 3.3. Technical drawings for all parts used in this study are presented in Appendix A. Specifications and mechanical models for the window materials used in this work are sum- marized in Appendix B. Water treatment, testing, and handling is described in Appendix C.
3.1 Optical transmission experiments
3.1.1 Overall configuration Optical transmission studies have been used to probe material response in plate im- pact experiments for some time [1]. Optical transmission may be reduced due to either absorption or scattering [2]; such changes can indicate shock induced chemical [3] reac- tions, phase transitions [4], or inelastic deformation [5]. Since there is no optical absorption in water for the pressures of interest (Section 2.1.3), a decrease in optical transparency in shocked liquid water can be attributed to light scattering from liquid-solid coexistence. Figure 3.1 shows the experimental configuration [6] used for optical transmission measurements in the present work. Reverberation loading (Section 2.5) was obtained by impacting a transparent window onto a liquid cell containing water. The impactor was at- tached to a projectile, which was accelerated to the desired impact velocity using a 4” gas gun [7]. Visible light, generated by a xenon flashlamp, was collimated with a parabolic
53 streak CCD camera spectrometer
projectile transmission photodiode target chamber impactor liquid sample port
optical collection fiber
collimating lens 45° turning mirrors 45° turning mirror windows
target chamber port
flashlamp pulsed Xe flashlamp monitor photodiode
parabolic turning mirror
Figure 3.1: Setup for optical transmission measurements Collimated light from a pulsed xenon flashlamp was directed through the liquid sample with a series of mirrors. Light exiting the sample was collected with an optical fiber and recorded. The transmission measured with this technique was constant while the water sample remains a pure liquid. The formation of ice regions created scattering and reduced light transmission.
54 turning mirror and directed through the impactor with a series of planar turning mirrors. This light passed through the liquid cell and was focused into an optic fiber. The optical signal in this fiber was split into two fibers, each connected to a detection system. A photo- diode detector provided a wavelength integrated measurement of transmitted light. Wave- length dispersed light from the spectrometer was coupled to a streak camera and recorded on a CCD to provide a time resolved measurement of the transmitted light spectrum. Op- tical transmission was calculated by comparing light levels during the impact experiment with levels measured at ambient conditions.
3.1.2 Mechanical components and assembly
Projectile construction
Two different projectile designs were used in this study. Impact velocities above 0.3 km/s were obtained using a standard 4” projectile (Figure A.1); below 0.3 km/s, a modified projectile was used (Figure A.2). Mounting holes (Figure A.4) were drilled into the projectile face, which was lapped perpindicular (≤ 0.1 mrad) to the projectile axis. Figure 3.2(a) shows a cross section view of a projectile used in transmission exper- iments. Two 45◦ mirrors were positioned on the projectile with aluminum mounts (Figures A.6-A.9). The central mount also had a brass aperture (Figure A.10) and the impactor win- dow. This aperture was spray painted black to minimize stray light reflections. The mirrors, aperture, and impactor were bonded to the mounts with Shell 815 epoxy. After the epoxy had set, the aluminum base of the impactor mount was machined parallel to the impactor surface and attached to the projectile with screws. Impactor surface tilt (with respect to the projectile axis) was checked using an autocollimator. If significant tilt was measured, the impactor mount was removed and preferentially sanded to correct the problem. The impactor was reattached to the projectile and checked again. Corrections to the impactor mount were made until the measured tilt was about 0.1 mrad. Next, the turning mirror
55 (a) (b)
aperture mirrors impactor mirror mount
impactor mount 56
projectile body
Figure 3.2: Transmission experiment projectile (a) Schematic cross section. The impactor and turning mounts are fixed to the projectile with screws (not shown). (b) Completed projectile mount was fixed to the projectile. Epoxy was applied around all screws to completely seal the projectile face. An assembled projectile is shown in Figure 3.2(b).
Liquid cells Water samples were confined in liquid cells to provide a well defined thickness and to seal the sample from the evacuated target chamber. Two different cell designs were used in this study. The first configuration, cell design #1, used a press fit to hold the rear window in the cell. Cell design #2 was used in experiments where the rear window could not be press fitted. Figure 3.3(a) shows a cross-sectional view of cell design #1. Cell assembly was started by soldering 1/16” stainless steel fill tubes to the brass cell. To prevent strain on these joints, each tube was soldered to two points on the brass body. Oxidized brass formed during soldering was abrasively cleaned from the cell. The inside diameter of the cell was then machined for press fitting of the rear window. For sapphire windows, the undersizing was 0.0002-0.0003” from the actual window diameter. Undersizing for fused silica and quartz windows was 0.0001-0.0002” to prevent damage during press fitting. Liquid fill channels (∼0.050” wide × 0.025” deep) were cut in the cell interior from the fill tubes to the top of the brass step. After machining, the cell was cleaned with alcohol and fitted with a Viton O-ring. The rear window was then slowly pressed into the cell from the rear. Final sample sizing was done by machining the brass step of the cell with respect to interior rear window surface. The front O-ring groove was also machined with respect to brass step (0.061” deep). 1/16” stainless steel Swagelocks connectors were added to the fill tubes. The cell was flushed with alcohol and cleaned in an ultrasonic alcohol bath. To ensure a good seal on the rear window, a bead of epoxy was run around the window/cell edge. The front O-ring (Viton) and window were cleaned with alcohol and held in the cell using a brass lock ring.
57 (a) lock ring
brass step front window machined to control sample thickness second O-ring fill first tube O-ring fill channels
rear window (press fit)
fill tube
(b) front window
brass O-ring cell fill channel body cut in brass step
rear window Teflon pad 0.03" thick lock ring
Figure 3.3: Liquid cell assembly (a) In design # 1, the rear window is held in place with a press fit, while the front window fastened with a lock ring. (b) In design # 2, the front window is epoxied to the liquid cell, and the rear window held in place with a lock ring.
58 Figure 3.3(b) shows the cross-sectional view construction for cell design #2. In this configuration, 1/16” stainless steel tubing was soldered to the front of the cell rather than the side. Fill channels were cut perpendicular to the fill tubes. After the cell was abrasively roughened and cleaned, the front window was set in place using Shell 815 or Epotech 301 epoxy. Care was taken to ensure that epoxy did not flow up the sides of the window and into the sample region. Once the window was set in place, a bead of epoxy was applied to the front side for additional strength and better sealing. Sample sizing was done by machining the interior brass step with respect to the interior surface of the front window.
1/16” stainless steel Swagelocks were added to the fill tubes, and the cell was cleaned with alcohol. A single nitrile O-ring was held in place with the rear window and a lock ring. A Teflon pad was placed between the lock ring and the glass window to avoid chipping and cracking. All liquid cells were leak tested by applying 1 atm of overpressure for at least 12 hours. If the cell successfully maintained overpressure, the assembled cell thickness was measured with a supermicrometer1. Sample thickness was determined from the difference in assembled cell thickness and individual window thicknesses (measured when cell is disassembled). Water was injected into the cell following the procedures given in Appendix C. Once filled with water, the cell was placed in a vacuum chamber for 5-10 minutes. If no visible changes occurred in the cell, final sample thickness measurements were made. The liquid cell was then mounted to the target as described below.
Target construction Figure 3.4(a) shows a schematic view of a target used in transmission experiments. The standoff ring (Figure A.15) was used to mount the entire assembly to the muzzle of the 4” gas gun. Both surfaces of this ring were rough lapped; the front surface was also
1Soda lime glass cells were measured when filled with liquid and sealed to minimize bowing of the 1/16” front window.
59 (a) (b) standoff liquid ring cell
aperture target plate
lens collimating 60 bracket lens tube
optic fiber
Figure 3.4: Transmission experiment target (a) Schematic cross section. Screws (not shown) are used to mount the liquid cell and lens bracket to target plate. The target plate is attached to the standoff ring with Belville washers (not shown) for alignment purposes. (b) Completed target (cell design 1) viewed from the impact side. A rear view of the target is shown in Figure 3.5. fine lapped. A rough lapped target plate (Figures A.16 - A.18) was separated from the ring by flexible Belville washers (120◦ apart). The liquid cell and the lens bracket (Fig- ures A.20-A.21) were held on opposite sides of the target plate with screws. The Belville washers were used to align the front window surface of the liquid cell to within 0.1 mrad of the standoff ring surface. A collimating lens unit (Figure A.23) was held within the lens bracket. This unit located the tip of an optical fiber at the focal plane of a converging lens, so that collimated light incident on the unit was focused into the fiber. A completed target is shown in Figure 3.4(b).
Just before the experiment was performed, two shorting pins were mounted within the target plate for triggering and diagnostic purposes. These pins were constructed from RG 174A/U coaxial cable mounted within a 3/32” brass tubing. The outer conductor was soldered to the tube; the inner conductor was separated from the tube with epoxy. The 3/32” tube was soldered into a larger brass tube with a threaded exterior, which was used to control the pin height with respect to impact surface of the liquid cell. The striking surface of the pins were lapped with respect the axis of the threaded section. Surface variations of
the pin tips were on the order of 5 µm or less.
3.1.3 Instrumentation and optical components
Flashlamp
A pulsed xenon flashlamp (Xenon Corporation model 457) provided illumination for transmission measurements in this work. The xenon filled flashtube (Xenon Corp #S- 1156D) was powered by a 0.5 µF capacitor, charged to about 11 kV, generating a peak pulse energy of 30 J. This discharge generated light over approximately 10 µs; peak output occured 4-5 µs after the lamp was triggered. The arc within the flashtube was about 3” long and 3 mm wide. The lamp produced broad spectral output covering the ultraviolet and visible ranges.
61 Mirrors, lenses and fibers A 35×35 mm plane turning mirror (Edmund Scientific #45519, 4-6 waves flatness) was used to direct collimated light toward the projectile. Two 12.5×12.5 mm turning mir- rors (Edmund Scientific #43790, 4-6 waves flatness) were mounted on the projectile. These mirrors were made from aluminum plated glass and optimized for visible light reflection. The collection lens was plano-convex, 12 mm in diameter, and had a 24 mm focal length (Edmund Scientific #32011). The lens was made from uncoated BK-7 glass. The collection fiber (3M FT-1.0-UMN) had a 1 mm core and numerical aperture of 0.39. Smaller fibers
(Mitsubishi #STU400E-SY, 400 µm core, 0.2 NA) were used to carry light to the detectors.
Photodiode detector THOR photodiodes (Models DET200 and DET210) were used to record provide a wavelength integrated transmission profile. The detector was sensitive to light in the 185-1100 nm range with peak sensitivity around 950 nm. Sensitivity at 600 nm was ap-
proximately twice that at 400 nm. Light from the 400 µm optical fiber was either directly incident on the detector or coupled with a 1:1 lens imaging system. This light was typically
attenuated by a factor of 10 using neutral density filters to maintain detector linearity.
Digitizers Tektronix TDS 654C or 684C models were used to digitize electronic data and diagnostic signals. Both digitizers collected 15000 sample points. The diagnostic digitizer
sweep was 15 µs, much longer than the useful experiment duration, to acquire the entire sequence of events (trigger pulses, flashlamp pulse, etc). The data digitizer operated for a shorter duration (3-6 µs) near the time of impact.
62 Spectrometer Initially, a SPEX 1681C spectrometer was used to disperse light in a horizontal plane. This was later changed to an imaging spectrometer (Spectra Pro 150, Acton Re- search Corp). Vertical spot size was controlled by the input fiber (∼400 µm); horizontal spot size was set by an adjustable slit (∼50 µm). The 300 lines/mm diffraction grating (600 nm blaze) was oriented to center the 350-650 nm range on the CCD.
Streak camera and CCD
Horizontally dispersed spectrometer output was directed onto the photocathode (S- 20 with Corning 9823 UV transmitting glass) of a Cordin 160-5B streak camera. To protect the photocathode, a mechanical shutter was placed between the spectrometer and streak camera. This shutter was manually opened just before each acquisition and closed immedi- ately afterwards. The photocathode output was swept vertically and converted to an optical image output. The streak rate of the camera was adjusted to cover the desired experimental duration (1-3 µs) on the CCD. The two dimensional optical output from the streak camera was imaged onto an air cooled Princeton Instruments TE/CCD-512-TKBM detector. A mechanical shutter cover- ing the CCD was opened just prior to each acquisition and is closed approximately 1 ms after the CCD was triggered. The detector was oriented so that wavelength varies horizon- tally and time vertically. The CCD had a 16 bit dynamic range and was binned to produce a 256×512 (vertical×horizontal) image.
3.1.4 Experimental setup
Optical alignment Setup of the optical transmission experiment (Figure 3.1) required that the projectile be located near its impact position. The target was centered with respect to the projectile
63 Figure 3.5: Rear view of transmission setup The mirror mounted to the brass rod directs light from the xenon flashlamp towards the projectile, which has been removed here. Transmitted light from the sample is collected by the brass lens unit and carried to the detectors through optical fiber. Two shorting pins (right side) are used for triggering and impact diagnostics.
64 and secured to the muzzle of the gas gun. Continuous laser light was coupled into an optic fiber and sent into the collimating lens unit. This light travelled opposite to the light path shown in Figure 3.1, passing through the sample, striking the projectile mirrors, and emerging off-center from the gun barrel axis. The remaining planar and parabolic mirrors were adjusted to focus this light upon the filament of the xenon flashlamp. When the flashlamp was fired, collimated light emerged from the parabolic mirror, passed through the sample, and was collected by the lens unit. Sample illumination was restricted to the central 1/4” diameter by the aperture mounted behind the impactor. A second aperture on the lens unit restricted light collection to the same region. Transmitted light collected by the lens unit was taken out of the target chamber by 1 mm core fiber and split into two 400 µm fibers coupled to the optical detection systems. Figure 3.5 shows the target prior to impact. Although the impact tilt magnitude is quite small (∼0.5 mrad), the projectile can rotate in the 4” gun barrel. If the rotation is large enough (>45◦), light will not strike the projectile turning mirror and no measurement is obtained. Typically, rotation angles are on the order of 10-15◦. In each experiment, the projectile was rotated through this range to determine if adequate light intensity was obtained. If these minor rotations resulted in insufficient light intensity, the optical system was realigned. After the liquid cell was filled, mounted, and aligned with the target ring, it was placed in the target chamber for final testing. All movable joints in the optical system are epoxied and reference signals recorded. The projectile was then removed from the barrel and loaded in its firing position.
Timing synchronization
The electronic setup shown schematically in Figure 3.6 permitted the following sequence of events during the optical transmission experiments.
65 v
projectile impacting surfaces h h+D h trigger impact pin pin D1