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  • 1. Chapter 1 Introduction to Shock Wave Physics of Condensed Matter 1.1 Introduction The scientific field of shock wave physics uses information from a number of sub-fields, such as hydrodynamics, continuum mechanics, thermodynamics, electrodynamics, and quantum mechanics. Information is presented from these sub-fields, as needed. The reader is responsible for background reading in these sub-fields for further understanding. 1.2 General Assumptions Unless otherwise stated one-dimensional (1-D) plane shock waves in a continuum fluid will be assumed. Solids will be treated in a separate chapter. Addressing fluids allows the basic physics and hydrodynamics to be illustrated simply. Plane geometry is selected, because cylindrical and spherical waves have a natural geometric attenuation term, which makes the treatment more difficult. In 1-D plane continuum mechanics state parameters such as pressure P, temperature T, and particle velocity u are the same across the entire planar wave front. In other words, at a given x the state parameters are the same for all (y, z) points. The wave propagates only in the + x or À x direction. Only isotropic solids under dynamic loading are treated in this primer book. It is assumed that no external energy source exists. Unless noted, it is assumed that the shocked material is in thermodynamic equilibrium. This implies time is not part of the material’s constitutive relationship. In other words, all material processes in shock waves occur almost instantaneously relative to nanosecond times. Therefore, continuum mechanics and thermodynamic treatments are valid. In fact, material science models and treatments are generally valid for shocked material where equilibrium exists. However, material time dependence and strain rate issues have to be dealt with in some specific materials. J.W. Forbes, Shock Wave Compression of Condensed Matter, Shock Wave and High Pressure Phenomena, DOI 10.1007/978-3-642-32535-9_1, # Springer-Verlag Berlin Heidelberg 2012 1
  • 2. When equilibrium is not achieved in all parameters (stress, volume, temperature, pressure), then a time-dependent material and hydrodynamic flow treatment is required. Time dependent material properties will be discussed near the end of the book. The 1-D differential conservation equations for mass, momentum, and energy are derived early in the book to use in showing the uniqueness and simplicity of steady shock wave conservation laws and the wave front rise-time significance. Knowing a shock wave is steady defines the linear P-v compression path without knowing the physical mechanisms, which is not scientifically satisfying, so efforts continue on revealing these physical mechanisms. 1.3 Brief History of Shock Field in the United States of America Twenty-one papers [1] on shock waves in condensed matter were presented at the 1947 American Physical Society meeting in Washington, DC. A majority of these papers were on the properties of shock waves in water and were presented by Navy scientists including Sigmund Jacobs. Cornell University scientists Hans Bethe, J. G. Kirkwood and S. Brinkley presented theoretical shock wave papers at this meeting. However, the shock wave field did not gain acceptance as a scientific discipline until the mid 1950s after the publication of a paper by Bancroft, Petersen and Minshall [2] from Los Alamos on the phase transformation in iron under shock compression. They observed when iron was shocked above 130 kbar (say 200 kbar) that three shock waves propagated through the iron. The first was the elastic shock about 12 kbar, the second was at 130 kbar, which they suggested was due to the phase transformation in iron seen in static work of Bridgman [3], and the third one a plastic shock taking the material to its final stress. Bridgman’s reported transition pressure was higher than 130 kbar, but it was confirmed later that the phase transition stress actually was the stress measured for the second shock wave. Accurate determination of transition pressures of rapid negative volume phase transformations allowed the shock wave field to accurately determine a high pressure calibration scale. Nobel prize winner and pioneer of high pressure static physics P. Bridgman claimed that this transition did not occur at 130 kbar in his static press [4]. He also reasoned that there just was not enough time for this transformation to occur in shock waves. This comment was based on his static work where it took many hours and sometimes days before iron transformed. The shock wave people also were not sure why the transformation occurred so fast. They suggested that the shear forces in shock waves may dramatically increase the rate of transformation. Bridgman decided to check the pressure scale he was using and found it was incorrect. He then performed an experiment with increased force to his compression cell and found that the transition occurred but took days. Bridgman then conducted an experiment where he added shear stresses to his iron sample at pressures exceeding 130 kbar. To his surprise the iron transformation occurred within seconds. He was then convinced that the shock data was correct. However, the physical mechanism for 2 1 Introduction to Shock Wave Physics of Condensed Matter
  • 3. the transition was not understood, which is still true today. This highly publicized controversy launched the shock field as a true sub-field of high pressure science. The well developed experimental and theoretical science was presented to the physics community at large in the 1958 paper by Los Alamos scientists Rice, Walsh, and McQueen [5]. The experiments were based on a precisely controlled high explosive technology [6]. A review of many shock wave subjects is presented in High-Pressure Shock Compression of Solids [7], eds. Asay and Shahinpoor, Springer-Verlag, 1993. For more details of the history of shock wave physics in the United States, read J. W. Taylor [8], R. A. Graham [4] and J. W. Forbes [1]. 1.4 Practical Value of Shock Field Material equations of state and material constitutive relationships require informa- tion from mechanics, static compression, yield surfaces, shock wave data, etc. The information obtained from shock wave experiments and theory are limited to high strain rates. Information not dependent on strain rates can come from many sources other than shock wave experiments. However, there are some unique things that come from shock wave experiments, such as the very high pressure thermodynamic P-v curve called a Hugoniot, which is relatable to other thermodynamic paths such as isotherms and isentropes. Accuracy of 1-D plane experiments is very good, resulting in P-v data with typical accuracy of Æ 3 %. Stresses greater than 10 Mbar with good accuracy are achievable (three times greater than pressures at the earth’s core). This data is clearly important to material scientists, theorists, geophysicists and astrophysicists. Such data provides a test of accuracy of molecu- lar potentials over large compressions and helps to determine the physical state and chemical makeup of the earth’s core. New experimental techniques are becoming available for the study of materials at extreme states where materials become plasmas. An excellent review [9] was recently done on this field known as High- Energy-Density Physics. This new extreme states technical field offers a window into stellar processes, approaches to obtain fusion as an energy source, and world security by understanding nuclear weapons without testing. Shock wave studies can easily and accurately detect rapid negative volume phase transitions, which has allowed a high pressure standard for static work to be developed. This data is used by condensed matter physicists and material engineers to make metastable materials such as the production of industrial small diamonds, due to very fast temperature quench rates. It is also the basis for understanding explosive detonation waves, which will be treated in some detail in this book. The pressure scale used for static high pressure work was not well developed in the 1950s. With shock wave data, an accurate pressure scale was developed up to tens of Mbar. This was a very important contribution to high pressure science. The establishment of this pressure scale was done by measuring phase transformation 1.4 Practical Value of Shock Field 3
  • 4. stress levels on different shocked materials. To calibrate a static piston press for measuring pressure, the materials known to undergo phase transformations in the shock work were compressed until they transformed in the static press. The changes in volume or compression were measured as a function of piston displacement assuming no deformation of the press parts. This allowed making a calibration curve of pressure versus piston displacement for their particular apparatus. How- ever, at high pressures the piston and sample cell in a static press change volume and diameter in unknown amounts above yield strengths so calculating pressure as force applied over original area of piston was not accurate. Following the shock wave transition pressures of a number of materials, the static calibration was done for each press by finding the displacement that the transition occurred at and mapping out a specific displacement versus pressure relationship for each static press. More recently Raman shifts versus stress in ruby and other crystals have been accurately measured as a function of stress [7]. This allows a small ruby chip to be inserted in the cell filled with fluid material surrounding the test sample. Measure- ment of the ruby’s shift in Raman spectra gives accurate pressure in the fluid of the cell. This is widely used in the small diamond anvil static pressure cells. 1.5 Techniques for Producing 1-D Plane Shock Waves The original experiments (reviewed in Chap. 4) to produce 1-D plane shock waves in test materials used explosive shock driver systems. These experiments consisted of a detonator to initiate an explosive plane wave booster (PWB) that transmitted a strong detonation shock wave into a flat disc of a driver explosive. The driver explosive with a characteristic pressure (C-J pressure) would have an inert buffer (usually metal) against it with the test samples on top of this buffer plate. The detonation shock wave from the PWB thus results in a strong plane 1-D shock wave being transmitted to the test sample. This technique is still used today for select high pressure experiments. Most of the shock wave equation of state data has been generated using such an explosive system. Note also that with proper design the metal buffer plate can become a flying plate, which impacts samples set a distance above the plate. Only a small range of induced stresses is available for any one explosive design, which is a limitation. It is important to note that the physical scale of the produced planar shock wave in a test sample is a few centimeters in diameter for these explosive systems. To overcome the limited control of the range of stress available for experiments, flat ended projectiles propelled by light gas guns or explosive powder driven guns were created. These are devices that accelerate flat plates with sabots on the back into stationary test samples. The selection of impact velocity and therefore impact stress in the test sample is a continuum for the range of the guns capability. This has obvious advantages over the limited stress ranges of the explosive systems, espe- cially at lower stresses. Again the physical scale of the produced shock wave in a test sample is a few centimeters. 4 1 Introduction to Shock Wave Physics of Condensed Matter
  • 5. A high powered pulse laser can create large pressures in samples by ablating the surface of a material, causing a shock wave to be transmitted through it into a test sample. Since pressure/stress is a function of area, lasers can reach high stresses for small areas and short pulse widths. This is an emerging technique in the field of shock wave physics since many experiments can be done on a table top in a research laboratory. To reach very extreme states large laser facilities are being used. There are issues of time and space scale that need to be addressed, and more on this will be given later in this book. 1.6 Dynamic Versus Static Compression Static and dynamic compression are not equivalent due to the high strain rate, viscous forces, energy scattering and shear forces in a 1-D plane shock wave. The strain rate in a steady shock wave is the highest strain rate possible for that material to have in an equilibrium situation. Shock waves compress materials in fractions of a microsecond putting energy directly into atoms and molecules. Shock waves also create defects in materials, which increases entropy. The physical mechanism has not been determined to date for energy scattering that keeps the shock compression path for steady waves on a linear P-v path called the Rayleigh line. It will be shown that just the condition of a wave being steady in a continuum media is all that is required for proving the shock P-v curve is along a straight line without knowing the physical mechanism. A major issue for shock physics is the inability to measure continuum tempera- ture in a shocked solid. So average temperatures are calculated from continuum thermodynamics. Clearly the static data is obtained at known or measurable temperatures. Another issue for shock waves is determining the physical mecha- nism for energy scattering and phase transitions. These issues will be addressed later in the book. 1.7 Select Areas of Shock Wave Research A broad range of topics make up shock wave research. They are broadly based around thermodynamic properties, experimental techniques for dynamic loading, Geophysics and Planetary Science, inelastic deformation, fracture and spall, continuum and multi scale modeling, first principal and molecular dynamics calculations, phase transitions, physics and chemistry at high pressure, spectros- copy and optical studies, nanomaterials, and detonation of explosives. A good example of these areas is given in the Shock Compression of Condensed Matter proceedings of the American Physical Society’s Shock Compression of Condensed Matter Topical Group meetings proceedings that are listed in the references. A select list of references for specific subjects are given in this chapter’s references 1.7 Select Areas of Shock Wave Research 5
  • 6. 1.8 What Does a Shock Wave in Condensed Matter Look Like? One of the advances in the field of shock wave physics has been the use of proton beams to produce radiographs of shocks and detonation waves in condensed matter [10–12]. Visualizing a shock wave propagating in condensed matter has been presented as a wave traveling inside the material with an almost instantaneous rise in pressure. These have typically been depicted by line drawings showing such a wave profile as a function of pressure and time. After getting acclimated to this technical field, these line drawings are adequate to convey the basic properties of a shock wave. However, with the use of accurate proton photography, it is now possible to see in snap shots of density difference in a shocked sample what a shock wave looks like as it travels through a sample. If you send protons through the radial direction of two static cylinders of different density the radiographic films have different image densities. If this density change is along a one-dimensional (1-D) plane due to a shock wave, a similar record will be obtained. If a series of fast exposures occurs the propagation of the 1-D shock down a cylinder in the x direction that is perpendicular to the proton beam then shock velocity and density as a function of x direction can be accurately determined. Figure 1.1 shows a flat flyer plate impacting a stationary flat aluminum plate. These plates have milliradian tilt between them so that 1-D compression occurs due to the shock wave. The shock wave front for different times are clearly seen in this figure. The densities at positions along the axis of the cylinder can be obtained within 1 % accuracy, making this a useful diagnostic for shock wave research. Radiographic images of a detonation shock wave allow the detonation process to be studied. Figure 1.2 shows a special case where two PBX 9502 cylinders of the same size are placed end to end with identical initiation systems of a SE-1 detonator and a booster cylinder of PBX 9501. These two cylinder charges are detonated at the same time, and the wave propagation, density, and interaction of these two detonation waves as they collide near the mid-length of the cylinders are measured. Just after the detonation waves collide the pressure and density in between the two separating wave fronts are very high, because of the non-linearity of the explosive detonation products pressure-volume properties. There are hundreds of x-ray radiographs of shock wave phenomena of solids and detonation characteristics of explosives produced by the previously active pulsed high-energy radiographic machine (PHERMIX) [13, 14]. These radiographs gave information on complicated hydrodynamic flow in various multidimensional shock loading experiments. For detonation waves, pictures of waves turning corners with regions of explosive not reacting, and radiographs showing how explosives can be desensitized by preshocking with a stress below the initiation threshold, and then a second following shock with stress above the initiation threshold was unable to initiate detonation. 6 1 Introduction to Shock Wave Physics of Condensed Matter
  • 7. Fig. 1.1 Proton beam radiographs of shocked aluminum at three different times for an aluminum plate impacting an aluminum sample [10, 11]. The arrows indicate the shock fronts 12.7 50 50 50 50.8 9502 9502 950112.7 9501 9407SE-1 94071-ES Dimensions in mm a b Fig. 1.2 Colliding detonation waves (a) experimental configuration, (b) four proton radiograph pictures before detonation wave collision and after detonation waves collide [12]. State A is ahead of the detonation wave, B and C are behind the detonation front. State D is material that has been detonated, released to state C 1.8 What Does a Shock Wave in Condensed Matter Look Like? 7
  • 8. References 1. J.W. Forbes, The history of the APS topical group on shock compression of condensed matter, in Shock Compression of Condensed Matter – 2001. AIP Conference Proceedings, vol. 620 (American Institute of Physics, Melville, 2002), pp. 11–19 2. D. Bancroft, E.L. Petersen, S. Minshall, Polymorphism of iron at high pressure. J. Appl. Phys. 27(3), 291 (1956) 3. P.W. Bridgman, High pressure polymorphism of iron, Letter to Editor. J. Appl. Phys. 27, 659 (1956) 4. R.A. Graham, Bridgman’s concern, in High-Pressure Science and Technology – 1993. AIP Conference Proceedings, vol. 309 (AIP Press, New York, 1994), pp. 3–12 5. M.H. Rice, R.G. McQueen, J.M. Walsh, Solid State Physics, vol. VI (Academic, New York, 1958), pp. 1–63 6. W.E. Deal Jr., Dynamic high pressure techniques, in Modern High Pressure Techniques, ed. by R.H. Wentorf Jr. (Butterworths, Washington, DC, 1962), pp. 200–227 7. J.R. Asay, S. Mohsen (eds.), High Pressure Shock Compression of Solids (Springer Verlag, New York, 1993) 8. J.W. Taylor, Thunder in the mountains, in Shock Waves in Condensed Matter-1983 (Elsevier Science, New York, 1984), pp. 3–15 9. R.P. Drake, High-energy-density physics. Physics Today June, 28–33 (2010) 10. P.A. Rigg, C.L. Schwartz, R.S. Hixson, G.E. Hogan, K.K. Kwiatkowski, F.G. Mariam, M. Marr-Lyon, F.E. Merrill, C.L. Morris, P. Rightly, A. Saunders, D. Tuba, Proton radiogra- phy and accurate density measurements: A window into shock wave processes. Phys. Rev. B 77, 220101(R) (2008) 11. P.A. Rigg, C.L. Schwartz, R.S. Hixson, F.E. Merrill, C.L. Morris, A. Saunders, pRad Team, Direct shock density measurements using plate impact and proton radiography, LA-UR-07- 1672. Presentation at TMS 2008 Annual Meeting, New Orleans, 9–13 March 2008 12. E.N. Ferm, S. Dennison, R. Lopez, K. Prestridge, J.P. Quintana, C. Espinoza, G. Hogan, N. King, J.D. Lopez, F. Merrill, K. Morley, C.L. Morris, P. Pazuchanis, A. Saunders, S.A. Baker, R. Liljestrand, R.T. Thompson, Proton radiography experiments on shocked high explosive products. in Shock Compression of Condensed Matter-2003, AIP Conference Proceedings. 706, 2004 and Presentation at meeting, LA-UR-03-9219, p. 839 13. C.L. Mader (ed.), LASL PHERMIX, vol. I–III (University of California Press, Berkeley, 1980) 14. R.D. Dick, Pulsed high-energy radiographic machine emitting x-rays (PHERMIX): Applications to study high-pressure flow and detonation waves. in Proceedings of SPIE, Vol 312, 1st European Conference on Cineradiography with Photons or Particles, Paris, 18–21 May 1983 Hugoniots of Inert/Unreacted Material R.A. Kinslow (ed.), High-Velocity Impact Phenomena (Academic, New York, 1970) S.P. Marsh (ed.), LASL Shock Hugoniot Data (University of California Press, Berkeley, 1980) R.G. McQueen, S.P. Marsh, J.W. Taylor, J.N. Fritz, W.J. Carter, The equation of state of solids from shock wave studies, in High-Velocity Impact Phenomena, ed. by R. Kinslow (Academic, New York, 1970). Has thermodynamic parameters in Appendices of many materials M. Van Thiel, Compendium of Shock Wave Data, LLNL report UCRL-50108, June 1971 R.F. Trunin, Experimental Data on Shock Compression and Adiabatic Expansion of Condensed Matter (RFNC-VNIEF, Sarov, 2001) 8 1 Introduction to Shock Wave Physics of Condensed Matter
  • 9. General References L.V. Al’tschuler, Use of shock waves in high-pressure physics. Sov. Phys. Usp. 8(1), 52–91 (1965). July–August 1965 S.S. Batsanov, Effects of Explosion on Materials: Modification and Synthesis Under High- Pressure Shock Compression (Springer, New York, 1994) A.V. Bushman, G.I. Kanel, A.L. Ni, V.E. Fortov, Intense dynamic loading of condensed matter. Institute of Chemical Physics, USSR Academy of Science, 1988, (trans: English by S. Chomet, and English version J. Shaner (ed.)). Taylor and Francis, London (1993) L.C. Chhabildas, L. Davison, Y. Horie (eds.), The Science of High-Velocity Impact (Springer, New York, 2005) R. Courant, K.O. Friedrichs, Supersonic Flow and Shock Waves (Springer, Berlin, 1976) A.N. Dremin, Toward Detonation Theory (Springer, New York, 1999) D.S. Drumheller, Introduction to Wave Propagation in Nonlinear Fluids and Solids (Cambridge University Press, Cambridge, 1998) G.E. Duvall, Bull. Seismol. Soc. Am. 52, 869 (1962) G.E. Duvall, Shock waves in solids, in Shock Metamorphism of Natural Materials, ed. by B.M. French, N.M. Short (Mono Book Corporation, Baltimore, 1968) G.E. Duvall, Shock waves in condensed media, in Physics of High Energy Density (Academic, New York, 1971) G.E. Duvall, G.R. Fowles, in High Pressure Physics and Chemistry, ed. by R.S. Bradley, vol. 2 (Academic, New York, 1963) V.E. Fortov, L.V. Al’tshuler, R.F. Trunin, A.I. Funtikov, Shock Waves and Extreme States of Matter (Springer, New York, 2004) D. Grady, Fragmentation of Rings and Shells: The Legacy of N. F. Mott (Springer, Berlin/New York, 2006) R. Graham, Solids Under High-Pressure Shock Compression Mechanics, Physics, and Chemistry (Springer, New York, 1993) Y. Horie, L. Davison, N. Thadhani, High-Pressure Shock Compression of Solids VI: Old Paradigms and New Challenges (Springer, New York, 2003) J.N. Johnson, R. Cheret (eds.), Classic Papers in Shock Compression Science (Springer, New York, 1998) G.I. Kanel, S.V. Razorenov, V.E. Fortov, Shock-Wave Phenomena and the Properties of Condensed Matter (Springer, New York, 2004) R.G. McQueen, S.P. Marsh, J.W. Taylor, J.N. Fritz, W.J. Carter, The equation of state of solids from shock wave studies, in High-Velocity Impact Phenomena, ed. by R. Kinslow (Academic Press, New York, 1970) M.A. Meyers, Dynamic Behavior of Materials (Wiley, New York, 1994) W.J. Nellis, Encyclopedia of Applied Physics, vol 18, (Wiley, Hoboken, N.J. 1997), p. 541 V.F. Nesterenko, Dynamics of Heterogeneous Materials (Springer, New York, 2001) M.H. Rice, R.G. McQueen, J.M. Walsh, Solid State Physics, vol. VI (Academic, New York, 1958), pp. 1–63 A.B. Sawaoka (ed.), Shock Waves in Material Science (Springer, Tokyo/New York, 1993) I.C. Skidmore, An introduction to shock waves in solids. Appl. Mater. Res. 4, 131–147 (1965) M. Suceska, Test Methods for Explosives (Springer, New York, 1995) R.F. Trunin, Shock Compression of Condensed Materials (Cambridge University Press, Cambridge, 1998) Y.B. Zeldovich, Y.P. Raizer, Physics of Shock Waves and High Temperature Hydrodynamic Phenomena (Academic, New York, 1966) M.V. Zhernokhletov, Methods for Study of Substance Properties under Intensive Dynamic Load- ing (Springer, New York, 2005) J.A. Zukas, W.P. Walters (eds.), Explosive Effects and Applications (Springer, New York, 1998) References 9
  • 10. Springer Series: Shock Waves and High Pressure Phenomena T. Antoun, D.R. Curran, G.I. Kanel, S.V. Razorenov, A. Utikin, Spall Fracture (Springer, New York, 2002) J. Asay, M. Shahinpoor (eds.), High Pressure Shock Compression of Solids (Springer, New York/ Heidelberg, 1993) R. Chere´t, Detonation of Condensed Explosives (Springer, New York, 1993) L. Davison, D. Grady, M. Shahinpoor (eds.), High-Pressure Shock Compression of Solids II (Springer, New York, 1996) L. Davison, Y. Horie, M. Shahinpoor (eds.), High-Pressure Shock Compression of Solids IV (Springer, New York, 1997) L. Davison, M. Shahinpoor (eds.), High-Pressure Shock Compression of Solids III (Springer, New York, 1998) A.N. Dremin, Toward Detonation Theory (Springer, New York, 1999) W.J. Nellis, Dynamic compression of materials: Metallization of fluid hydrogen at high pressures. Rep. Prog. Phys. 69, 1479 (2006) Springer Series: Shock Wave Science and Technology Reference Library B.W. Asay (ed.), Non-Shock Initiation of Explosives, vol. 5 (Springer, Berlin/Heidelberg, 2010) M. van Dongen (ed.), Multiphase Flows I, vol. 1 (Springer, Berlin/Heidelberg, 2007) Y. Horie (ed.), Solids I, vol. 2 (Springer, Berlin, 2007) Y. Horie (ed.), Solids II, vol. 3 (Springer, Berlin, 2009) F. Zhang (ed.), Heterogeneous Detonation, vol. 4 (Springer, Berlin, 2009) F. Zhang (ed.), Detonation Dynamics, vol. 6 (Springer, Berlin/London, 2012) Shock Wave Compression of Condensed Matter Conference Proceedings M. Elert, M.D. Furnish, R. Chau, N. Holmes, J. Nguyen (eds.), Shock Compression of Condensed Matter – 2007, Waikoloa, Hawai’i (AIP #955, New York, 2007) M.L. Elert, W.T. Buttler, M. Furnish, W.W. Anderson, W.G. Proud (eds.), Shock Compression of Condensed Matter – 2009, Nashville (AIP# 1195, New York, 2009) M.L. Elert, W.T. Buttler, J.P. Borg, J.L. Jordan, T.J. Vogler (eds.), Shock Compression of Condensed Matter – 2011. AIP Conference Proceedings, vol. 1426 (American Institute of Physics, Melville, 2012) M.D. Furnish, L.C. Chhabildas, R.S. Hixon (eds.), Shock Compression of Condensed Matter-1999, Snowbird (AIP #505, New York, 2000) M.D. Furnish, N.N. Thadhani (eds.), Shock Compression of Condensed Matter-2001, Atlanta (AIP #620, New York, 2002) M.D. Furnish, Y.M. Gupta, J.W. Forbes (eds.), Shock Compression of Condensed Matter-2003, Portland (AIP #706, New York, 2004) M.D. Furnish, M. Elert, T.P. Russell, C.T. White (eds.), Shock Compression of Condensed Matter – 2003, Baltimore (AIP #845, New York, 2006) Y.M. Gupta (ed.), Shock Waves in Condensed Matter, Spokane (Plenum Press, New York, 1986) 10 1 Introduction to Shock Wave Physics of Condensed Matter
  • 11. Y.M. Gupta ed., Shock Compression of Condensed Matter. in Proceedings of Symposium in Honor of George Duvall, Pullman, (Washington State University, Pullman), 1 Sept 1988 W.J. Nellis, L. Seaman, R.A. Graham (eds.), Shock Waves in Condensed Matter, Menlo Park (American Institute of Physics, New York, 1982) S.C. Schmidt, N.C. Holmes (eds.), Shock Waves in Condensed Matter-1987, Monterey (North- Holland, Amsterdam, 1988) S.C. Schmidt, W.C. Tao (eds.), Shock Compression of Condensed Matter-1995, Seattle (AIP #370, New York, 1996) S.C. Schmidt, R.A. Graham, G.K. Straub (eds.), Shock Waves in Condensed Matter-1983, Sante Fe (North-Holland, Amsterdam, 1984) S.C. Schmidt, J.N. Johnson, L.W. Davison (eds.), Shock Waves in Condensed Matter-1989, Albuquerque (North-Holland, Amsterdam, 1990) S.C. Schmidt, R.D. Dick, J.W. Forbes, D.G. Tasker (eds.), Shock Waves in Condensed Matter-1991, Williamsburg (North-Holland, Amsterdam, 1992) S.C. Schmidt, J.W. Shaner, G.A. Samara, M. Ross (eds.), High-Pressure Science and Technology-1993, Colorado Springs (AIP #309, New York, 1994) S.C. Schmidt, D.P. Dandekar, J.W. Forbes (eds.), Shock Compression of Condensed Matter-1997, Amherst (AIP #429, New York, 1998) References 11