We performed molecular dynamics simulations of shock wave propagation in diamond in the [110] crystallographic direction and observed an anomalous response of the material. This regime is characterized by absence of plastic deformation in the intermediate interval of shock wave intensities between shear-deformation and overdriven rehybridization shock wave regimes

Elert, M. L.

McLaughlin, K.

Oleynik, I. I.

White, C. T.

Zybin, S. V.

English

Caltech Authors - Main

CP955, Shock Compression of Condensed Matter - 2007, 
edited by M. Elert, M. D. Furnish, R. Cliau, N. Holmes, and J. Nguyen 
O 2007 American Institute of Pliysics 978-0-7354-0469-4/07/$23.00 
MOLECULAR DYNAMICS SIMULATIONS OF AN ANOMALOUS 
RESPONSE OF DIAMOND TO SHOCK COMPRESSION 
K. McLaughlin\ I.I. 01eynik\ S.V. Zybin^ M. L. Elert^ and C. T. White^ 
Department of Physics, University of South Florida, Tampa, FL 33620 
Materials and Process Simulation Center, California Institute of Technology, Pasadena, CA 91125 
Chemistry Department, U. S. Naval Academy, Annapolis, MD 2140 
Naval Research Laboratory, Washington, DC 203 75 
Abstract. We performed molecular dynamics simulations of shock wave propagation in diamond in 
the [110] crystallographic direction and observed an anomalous response of the material. This regime 
is characterized by absence of plastic deformation in the intermediate interval of shock wave intensities 
between shear-deformation and overdriven rehybridization shock wave regimes. 
Keywords: Shock waves, shear stresses, molecular dynamics, diamond 
PACS: 62.50.+P, 82.40.Fp, 81.30.Hd, 46.40.Cd 
INTRODUCTION 
Shock compression of condensed matter is a 
vital tool in the investigation of the fundamental 
properties of solids at high pressures and 
temperatures. Such conditions are realized in 
geothermal processes, hyper-velocity impacts and 
detonation of energetic materials. However, due to 
the sub-nanometer, sub-picosecond length and time 
scales involved, obtaining atomic-scale information 
remains an experimental challenge. In contrast, 
these are precisely the scales in which atomistic 
simulation becomes invaluable [1-3]. Molecular 
dynamics (MD) simulations of millions of atoms 
over a picosecond time scale may yield valuable 
information on shock velocities, thermodynamic 
variables and the atomic scale structure of the 
shock front, while also providing valuable insight 
concerning plastic deformation, phase transitions 
and materials defects. 
Although much focus has been applied to 
determining the properties of shock compressed 
metals [4-5], interest in other classes of materials 
has been on the rise, such as with covalently 
bonded solids and ceramics [6-8]. Diamond, in 
particular, is striking due to its phenomenal 
mechanical properties, having the highest bulk 
modulus of all elemental solids and superb 
resistance to shear deformations [9]. Experiments 
have provided some insight into the material 
transformations of diamond under dynamical 
loading, but the atomic-scale mechanisms are not 
well understood. 
We present results of MD simulations of shock-
wave propagation in diamond single crystals along 
the [110] crystallographic direction. The MD 
simulations reveal the existence of an anomalous 
response at the intermediate interval of shock wave 
intensities between shear-deformation and 
overdriven rehybridization shock waves regimes. 
Our major goal is to investigate the mechanisms 
that are responsible for this anomalous response 
and their relationship to the underlying constitutive 
materials properties which result in this unforeseen 
behavior. 
321 
Downloaded 20 Dec 2007 to 131.215.225.9. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/proceedings/cpcr.jsp
COMPUTATIONAL DETAILS 
Our MD simulations were performed using the 
reactive empirical bond-order (REBO) interatomic 
potential [10-11] which is widely considered as one 
of the best currently available potentials for carbon. 
Initially a single crystal sample, oriented in the 
[110] crystallographic direction is given an initial 
velocity -Up in the z-direction with Up ranging from 
1.0 to 7.2 km/s with increments of 0.2 km/s. 
Periodic boundary conditions are applied in the x 
and y directions of this crystal, which consists of 
approximately 3.4 million atoms and is 200-300 
angstroms in each dimension. 
As the crystal collides with a piston of infinite 
mass, represented by a repulsive potential barrier, 
as many as two shock waves propagate along the z-
axis. These elastic and shear-deformation shock 
waves may be characterized by substantial changes 
in the local variables, such as temperature, stress, 
mass velocity, density, and local potential energy, 
which are calculated using spatial averaging over 
the direction of shock propagation. 
RESULTS AND DISCUSSION 
The simulations of shock wave propagation 
revealed four regimes of material response. They 
are: (a) a pure elastic shock wave at piston 
velocities Up < 1.8 km/s (b) a split shock wave 
30 
I 20 
> 
10, 
^oo 
° Q ° o ° n n a Q Q a D n Q o g ' 
o OshEardtli)miali(m 
D a elastic 
^ ' i anomalous 
c <>rchvbridizatiiiii 
_!_ 
2 4 6 
Particle Velocity (kiii.'s) 
FIGURE 1. The shock Hugoniot for diamond [110]. 
consisting of an elastic precursor followed by a 
slower shear-deformation shock wave at 2.0 km/s < 
Up < 3.4 km/s; (c) an anomalous shock wave at 3.6 
km/s < Up < 5.0 km/s; and finally (d) an overdriven 
rehybridization shock wave at the highest shock 
intensities, Up > 5.2 km/s. These different regimes 
of materials response are conveniently classified 
using the shock Hugoniot, which gives the 
dependence of shock velocity on the piston 
velocity, see Figure 1. 
The pure elastic regime is observed in 
simulations with piston velocities between 1.0 and 
1.6 km/s, with a constant shock wave velocity of 
about 20.3 km/s. This elastic shock wave is best 
described as a strictly uniaxial compression with no 
K J H U H U U M W M m ^ ^ 
, = 3.8 km/s. The three 
regions above are identified as follows: i) anomalous, ii) elastic and iii) unperturbed diamond crystal. 
322 
Downloaded 20 Dec 2007 to 131.215.225.9. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/proceedings/cpcr.jsp
•60 -30 
Shock Direction [110] Z (A) 
FIGURE 3. Shock wave profiles for the four regimes present in diamond [110], Up = 2.0 to 7.2 km/s. From left to 
right: elastic, plastic, anomalous, and rehybridization. 
evidence of changes in crystal structure, see Figure 
3. For each of these cases, a smooth increase in the 
local variables is seen with a maximum 
longitudinal stress a^ of approximately 120 GPa, 
and shear stresses x^ < 60 GPa and Xŷ  < 40 GPa. 
By increasing the particle velocity to values 
between 1.8 and 3.4 km/s, the critical shear stress 
values are reached, and a shear-deformation shock 
wave appears, which propagates with the velocity 
Usheai, 12.4 km/s < Usheai < 17.5 km/s, along with 
an elastic precursor, which propagates with the 
velocity Ugiastic = 20.3 km/s. Although in our 
simulations the time scales are insufficient to 
observe irreversible plastic deformations in this 
regime, it is believed that such plasticity, in fact, 
will be developed in the course of attaining an 
equilibrium state far behind the shock wave front. 
The local variables behind the elastic shock 
front remain constant, and equal to the values 
observed at the critical particle velocity Up = 1.8 
km/s, see Figure 3. Behind the shear deformation 
wave, a decrease of shear stress Xŷ  is observed. 
with the value dropping from 40 to 15 GPa in the 
Up = 2.0 km/s case. Clearly, these deformations are 
due to the relaxation of the crystal into a lower 
energy state. The shear deformation wave is further 
characterized by a large increase in temperature 
with values reaching 500K, as compared to 350K 
behind elastic fronts. 
For Up = 3.6 to 5.0 km/s an anomalous shock 
wave, 16.7 km/s < Uanomaious < 23.3 km/s, is present. 
At the lower end of this range, the anomalous 
shock wave is coupled with an elastic precursor, 
while only an overdriven anomalous wave is 
present when Up > 4.0 km/s. The key feature of this 
response is a complete disappearance of the shear 
deformations that characterize the second regime, 
see Figure 2. 
In terms of local thermodynamic quantities, the 
anomalous shock wave is characterized by a large 
peak followed by rapid fluctuations immediately 
behind the shock front, see Figure 3. Within this 
regime there is a large increase in temperature 
which peaks at Tyy = 1300 K, T^ = 1000 K, before 
323 
Downloaded 20 Dec 2007 to 131.215.225.9. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/proceedings/cpcr.jsp
thennal equilibrium is attainted at about Txx = Tyy = 
Tzz = 800 K. In addition, the anomalous front is 
also accompanied by a decrease in Xŷ  from 41 to -3 
GPa, while Xxz and a^ increase from 66 and 127 
GPa to 80 and 230 GPa, respectively. 
Finally, the overdriven rehybridization regime 
is realized when Up > 5.0 km/s. Initially, the 
features of this shock wave are identical to those of 
the anomalous waves, with a sudden peak in local 
variables, x^ = 200 GPa, Xŷ  = 140 GPa, p = 4.5 
g/cm^, followed by fluctuations, see Figure 3. 
However, in this case, the large shock wave 
intensity is inevitably transformed into chaotic 
atomic motion within the crystal lattice leading to a 
large increase in temperature. Ultimately, these 
temperatures rise to a point where localized regions 
of graphitization and melting begin to appear, and 
consequently, all of the shear stresses steadily drop 
to zero. 
Taken together, our results suggest that the 
Hugoniot elastic limit, that is, the critical value of a 
shock wave intensity resulting in onset of plastic 
deformations, is not solely related to the 
longitudinal stress. On the contrary, as seen with 
the disappearance of shear-deformations and the 
onset of the anomalous response at intermediate 
shock intensities, the critical shear stresses should 
be considered as well. Moreover, we believe this 
anomalous response has a direct link to the non-
monotonic relationship of these shears with respect 
to uniaxial strain. 
Although the topic of the Hugoniot elastic 
limit, as it relates to these results, will be covered 
in more detail elsewhere [12], we believe that these 
results reveal a need to generalize the notion of the 
Hugoniot elastic limit in such a way as to include 
critical shear stresses. 
SCCM 2007 in Hawaii. 
REFERENCES 
1. B.L. Holian, Shock Waves 13, 489 (2004). 
2. S.V. Zybin, V.V. Zhakhovskii, M.L. Elert, and C.T. 
White, in Shock Compression of Condensed Matter 
- 2003, edited by M.D. Furnish and Y.M. Gupta 
(AIP Press, NY, 2004), pp. 310-313. 
3. D.H. Robertson, D.W. Brenner, and C.T. White, 
Phys. Rev. Lett. 67, 3132 (1991), 
4. K. Kadau, T.C. Germann, P.S. Lomdahl, and B.L. 
Holian, Science 296, 1681 (2002) 
5. K. Kadau, T.C. Germann, P.S. Lomdahl, and B.L. 
Holian, Phys. Rev. B 72, 064120 (2005). 
6. T. Mashimo, R. Chau, Y. Zhang, T. Kobayoshi, T. 
Sekine, K. Fukuoka, Y. Syono, M. Kodama, and 
W.J. Nellis, Phys. Rev. Lett. 96, 105504 (2006). 
7. M. Chen, J.W. McCauley, and K.J. Hemker, 
Science 299, 1563(2003). 
8. M.W. Chen, J.W. McCauley, D.P. Dandekar, and 
N.K. Bourne, Nattire Materials 2006, 814 (2006). 
9. Properties of Natural and Synthetic Diamond, 
edited by J.E. Field (Academic Press, 1992). 
10. D.W. Brenner, Phys. Rev. B 42, 9458 (1990). 
11. D.W. Brenner, O.A. Shenderova, J.A. Harrison, S.J. 
Stuart, B. Ni and S.B. Sinnott J. Phys. Cond. Matt. 
14, 783 (2002). 
12. LI Oleynik, K. McLaughlin, S.V. Zybin, M. Flert, 
and C.T. White, to be published. 
ACKNOWLEDGEMENTS 
The work at USF was supported by the Office of 
Naval Research (ONR) through the Naval 
Research Laboratory (NRL). The work at NRL was 
also supported by ONR both directly and through 
NRL. K. McLaughlin thanks the NSF IGERT 
Program Grant DGE 0221681 (Bernard Batson, the 
manager), USF Office of Undergraduate Research, 
and the organizing committee of SCCM 2007 
(Ricky Chau) for the travel support to attend 
324 
Downloaded 20 Dec 2007 to 131.215.225.9. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/proceedings/cpcr.jsp


Molecular dynamics simulations of an anomalous response of diamond to shock compression

CP955, Shock Compression of Condensed Matter - 2007, 
edited by M. Elert, M. D. Furnish, R. Cliau, N. Holmes, and J. Nguyen 
O 2007 American Institute of Pliysics 978-0-7354-0469-4/07/$23.00 
MOLECULAR DYNAMICS SIMULATIONS OF AN ANOMALOUS 
RESPONSE OF DIAMOND TO SHOCK COMPRESSION 
K. McLaughlin\ I.I. 01eynik\ S.V. Zybin^ M. L. Elert^ and C. T. White^ 
Department of Physics, University of South Florida, Tampa, FL 33620 
Materials and Process Simulation Center, California Institute of Technology, Pasadena, CA 91125 
Chemistry Department, U. S. Naval Academy, Annapolis, MD 2140 
Naval Research Laboratory, Washington, DC 203 75 
Abstract. We performed molecular dynamics simulations of shock wave propagation in diamond in 
the [110] crystallographic direction and observed an anomalous response of the material. This regime 
is characterized by absence of plastic deformation in the intermediate interval of shock wave intensities 
between shear-deformation and overdriven rehybridization shock wave regimes. 
Keywords: Shock waves, shear stresses, molecular dynamics, diamond 
PACS: 62.50.+P, 82.40.Fp, 81.30.Hd, 46.40.Cd 
INTRODUCTION 
Shock compression of condensed matter is a 
vital tool in the investigation of the fundamental 
properties of solids at high pressures and 
temperatures. Such conditions are realized in 
geothermal processes, hyper-velocity impacts and 
detonation of energetic materials. However, due to 
the sub-nanometer, sub-picosecond length and time 
scales involved, obtaining atomic-scale information 
remains an experimental challenge. In contrast, 
these are precisely the scales in which atomistic 
simulation becomes invaluable [1-3]. Molecular 
dynamics (MD) simulations of millions of atoms 
over a picosecond time scale may yield valuable 
information on shock velocities, thermodynamic 
variables and the atomic scale structure of the 
shock front, while also providing valuable insight 
concerning plastic deformation, phase transitions 
and materials defects. 
Although much focus has been applied to 
determining the properties of shock compressed 
metals [4-5], interest in other classes of materials 
has been on the rise, such as with covalently 
bonded solids and ceramics [6-8]. Diamond, in 
particular, is striking due to its phenomenal 
mechanical properties, having the highest bulk 
modulus of all elemental solids and superb 
resistance to shear deformations [9]. Experiments 
have provided some insight into the material 
transformations of diamond under dynamical 
loading, but the atomic-scale mechanisms are not 
well understood. 
We present results of MD simulations of shock-
wave propagation in diamond single crystals along 
the [110] crystallographic direction. The MD 
simulations reveal the existence of an anomalous 
response at the intermediate interval of shock wave 
intensities between shear-deformation and 
overdriven rehybridization shock waves regimes. 
Our major goal is to investigate the mechanisms 
that are responsible for this anomalous response 
and their relationship to the underlying constitutive 
materials properties which result in this unforeseen 
behavior. 
321 
Downloaded 20 Dec 2007 to 131.215.225.9. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/proceedings/cpcr.jsp
COMPUTATIONAL DETAILS 
Our MD simulations were performed using the 
reactive empirical bond-order (REBO) interatomic 
potential [10-11] which is widely considered as one 
of the best currently available potentials for carbon. 
Initially a single crystal sample, oriented in the 
[110] crystallographic direction is given an initial 
velocity -Up in the z-direction with Up ranging from 
1.0 to 7.2 km/s with increments of 0.2 km/s. 
Periodic boundary conditions are applied in the x 
and y directions of this crystal, which consists of 
approximately 3.4 million atoms and is 200-300 
angstroms in each dimension. 
As the crystal collides with a piston of infinite 
mass, represented by a repulsive potential barrier, 
as many as two shock waves propagate along the z-
axis. These elastic and shear-deformation shock 
waves may be characterized by substantial changes 
in the local variables, such as temperature, stress, 
mass velocity, density, and local potential energy, 
which are calculated using spatial averaging over 
the direction of shock propagation. 
RESULTS AND DISCUSSION 
The simulations of shock wave propagation 
revealed four regimes of material response. They 
are: (a) a pure elastic shock wave at piston 
velocities Up < 1.8 km/s (b) a split shock wave 
30 
I 20 
> 
10, 
^oo 
° Q ° o ° n n a Q Q a D n Q o g ' 
o OshEardtli)miali(m 
D a elastic 
^ ' i anomalous 
c <>rchvbridizatiiiii 
_!_ 2 4 6 
Particle Velocity (kiii.'s) 
FIGURE 1. The shock Hugoniot for diamond [110]. 
consisting of an elastic precursor followed by a 
slower shear-deformation shock wave at 2.0 km/s < 
Up < 3.4 km/s; (c) an anomalous shock wave at 3.6 
km/s < Up < 5.0 km/s; and finally (d) an overdriven 
rehybridization shock wave at the highest shock 
intensities, Up > 5.2 km/s. These different regimes 
of materials response are conveniently classified 
using the shock Hugoniot, which gives the 
dependence of shock velocity on the piston 
velocity, see Figure 1. 
The pure elastic regime is observed in 
simulations with piston velocities between 1.0 and 
1.6 km/s, with a constant shock wave velocity of 
about 20.3 km/s. This elastic shock wave is best 
described as a strictly uniaxial compression with no 
K J H U H U U M W M m ^ ^ 
, = 3.8 km/s. The three 
regions above are identified as follows: i) anomalous, ii) elastic and iii) unperturbed diamond crystal. 
322 
Downloaded 20 Dec 2007 to 131.215.225.9. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/proceedings/cpcr.jsp
•60 -30 
Shock Direction [110] Z (A) 
FIGURE 3. Shock wave profiles for the four regimes present in diamond [110], Up = 2.0 to 7.2 km/s. From left to 
right: elastic, plastic, anomalous, and rehybridization. 
evidence of changes in crystal structure, see Figure 
3. For each of these cases, a smooth increase in the 
local variables is seen with a maximum 
longitudinal stress a^ of approximately 120 GPa, 
and shear stresses x^ < 60 GPa and Xy^  < 40 GPa. 
By increasing the particle velocity to values 
between 1.8 and 3.4 km/s, the critical shear stress 
values are reached, and a shear-deformation shock 
wave appears, which propagates with the velocity 
Usheai, 12.4 km/s < Usheai < 17.5 km/s, along with 
an elastic precursor, which propagates with the 
velocity Ugiastic = 20.3 km/s. Although in our 
simulations the time scales are insufficient to 
observe irreversible plastic deformations in this 
regime, it is believed that such plasticity, in fact, 
will be developed in the course of attaining an 
equilibrium state far behind the shock wave front. 
The local variables behind the elastic shock 
front remain constant, and equal to the values 
observed at the critical particle velocity Up = 1.8 
km/s, see Figure 3. Behind the shear deformation 
wave, a decrease of shear stress Xy^  is observed. 
with the value dropping from 40 to 15 GPa in the 
Up = 2.0 km/s case. Clearly, these deformations are 
due to the relaxation of the crystal into a lower 
energy state. The shear deformation wave is further 
characterized by a large increase in temperature 
with values reaching 500K, as compared to 350K 
behind elastic fronts. 
For Up = 3.6 to 5.0 km/s an anomalous shock 
wave, 16.7 km/s < Uanomaious < 23.3 km/s, is present. 
At the lower end of this range, the anomalous 
shock wave is coupled with an elastic precursor, 
while only an overdriven anomalous wave is 
present when Up > 4.0 km/s. The key feature of this 
response is a complete disappearance of the shear 
deformations that characterize the second regime, 
see Figure 2. 
In terms of local thermodynamic quantities, the 
anomalous shock wave is characterized by a large 
peak followed by rapid fluctuations immediately 
behind the shock front, see Figure 3. Within this 
regime there is a large increase in temperature 
which peaks at Tyy = 1300 K, T^ = 1000 K, before 
323 
Downloaded 20 Dec 2007 to 131.215.225.9. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/proceedings/cpcr.jsp
thennal equilibrium is attainted at about Txx = Tyy = 
Tzz = 800 K. In addition, the anomalous front is 
also accompanied by a decrease in Xy^  from 41 to -3 
GPa, while Xxz and a^ increase from 66 and 127 
GPa to 80 and 230 GPa, respectively. 
Finally, the overdriven rehybridization regime 
is realized when Up > 5.0 km/s. Initially, the 
features of this shock wave are identical to those of 
the anomalous waves, with a sudden peak in local 
variables, x^ = 200 GPa, Xy^  = 140 GPa, p = 4.5 
g/cm^, followed by fluctuations, see Figure 3. 
However, in this case, the large shock wave 
intensity is inevitably transformed into chaotic 
atomic motion within the crystal lattice leading to a 
large increase in temperature. Ultimately, these 
temperatures rise to a point where localized regions 
of graphitization and melting begin to appear, and 
consequently, all of the shear stresses steadily drop 
to zero. 
Taken together, our results suggest that the 
Hugoniot elastic limit, that is, the critical value of a 
shock wave intensity resulting in onset of plastic 
deformations, is not solely related to the 
longitudinal stress. On the contrary, as seen with 
the disappearance of shear-deformations and the 
onset of the anomalous response at intermediate 
shock intensities, the critical shear stresses should 
be considered as well. Moreover, we believe this 
anomalous response has a direct link to the non-
monotonic relationship of these shears with respect 
to uniaxial strain. 
Although the topic of the Hugoniot elastic 
limit, as it relates to these results, will be covered 
in more detail elsewhere [12], we believe that these 
results reveal a need to generalize the notion of the 
Hugoniot elastic limit in such a way as to include 
critical shear stresses. 
SCCM 2007 in Hawaii. 
REFERENCES 
1. B.L. Holian, Shock Waves 13, 489 (2004). 
2. S.V. Zybin, V.V. Zhakhovskii, M.L. Elert, and C.T. 
White, in Shock Compression of Condensed Matter 
- 2003, edited by M.D. Furnish and Y.M. Gupta 
(AIP Press, NY, 2004), pp. 310-313. 
3. D.H. Robertson, D.W. Brenner, and C.T. White, 
Phys. Rev. Lett. 67, 3132 (1991), 
4. K. Kadau, T.C. Germann, P.S. Lomdahl, and B.L. 
Holian, Science 296, 1681 (2002) 
5. K. Kadau, T.C. Germann, P.S. Lomdahl, and B.L. 
Holian, Phys. Rev. B 72, 064120 (2005). 
6. T. Mashimo, R. Chau, Y. Zhang, T. Kobayoshi, T. 
Sekine, K. Fukuoka, Y. Syono, M. Kodama, and 
W.J. Nellis, Phys. Rev. Lett. 96, 105504 (2006). 
7. M. Chen, J.W. McCauley, and K.J. Hemker, 
Science 299, 1563(2003). 
8. M.W. Chen, J.W. McCauley, D.P. Dandekar, and 
N.K. Bourne, Nattire Materials 2006, 814 (2006). 
9. Properties of Natural and Synthetic Diamond, 
edited by J.E. Field (Academic Press, 1992). 
10. D.W. Brenner, Phys. Rev. B 42, 9458 (1990). 
11. D.W. Brenner, O.A. Shenderova, J.A. Harrison, S.J. 
Stuart, B. Ni and S.B. Sinnott J. Phys. Cond. Matt. 
14, 783 (2002). 
12. LI Oleynik, K. McLaughlin, S.V. Zybin, M. Flert, 
and C.T. White, to be published. 
ACKNOWLEDGEMENTS 
The work at USF was supported by the Office of 
Naval Research (ONR) through the Naval 
Research Laboratory (NRL). The work at NRL was 
also supported by ONR both directly and through 
NRL. K. McLaughlin thanks the NSF IGERT 
Program Grant DGE 0221681 (Bernard Batson, the 
manager), USF Office of Undergraduate Research, 
and the organizing committee of SCCM 2007 
(Ricky Chau) for the travel support to attend 
324 
Downloaded 20 Dec 2007 to 131.215.225.9. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/proceedings/cpcr.jsp


Properties of Natural and Synthetic Diamond, edited by J.E.

to be published. ACKNOWLEDGEMENTS The work at USF was supported by the Office of Naval Research (ONR) through the Naval Research Laboratory (NRL). The work at NRL was also supported by ONR both directly and through NRL.

https://authors.library.caltech.edu/9415/1/MCLaipcp07.pdf

Molecular dynamics simulations of an anomalous response of diamond to shock compression

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