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 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 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
9501
12.7
9501
9407
SE-1
9407
1
-
E
S
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-
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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,
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Proceedings. 706, 2004 and Presentation at meeting, LA-UR-03-9219, p. 839
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Vol 312, 1st European Conference on Cineradiography with Photons or Particles, Paris,
18–21 May 1983
Hugoniots of Inert/Unreacted Material
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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
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S.S. Batsanov, Effects of Explosion on Materials: Modification and Synthesis Under High-
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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
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J.N. Johnson, R. Cheret (eds.), Classic Papers in Shock Compression Science (Springer,
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Condensed Matter (Springer, New York, 2004)
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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),
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10. Springer Series: Shock Waves and High Pressure Phenomena
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