Yunfeng Shi and Donald W. Brenner- Simulated thermal decomposition and detonation of nitrogen cubane by molecular dynamics

8/3/2019 Yunfeng Shi and Donald W. Brenner- Simulated thermal decomposition and detonation of nitrogen cubane by molec

1/7

Simulated thermal decomposition and detonation of nitrogen cubaneby molecular dynamics

Yunfeng Shia and Donald W. BrennerDepartment of Materials Science and Engineering, North Carolina State University,Raleigh, North Carolina 27587-7907, USA

Received 11 July 2007; accepted 14 August 2007; published online 2 October 2007

We present simulations of a model molecular solid of nitrogen cubane subject to thermal agitationand mechanical shock. A new approach, a reactive state summation potential, has been used tomodel nitrogen cubane dissociation. At elevated temperatures, the system decomposes to N2 mixedwith a small amount of oligomeric nitrogen. When subject to shock loading the system detonatesabove some critical threshold after which a shock front is self-sustained by the energy release fromchemical reactions at a constant intrinsic speed. This is the first example of a fully three-dimensionalatomic simulation of a chemically-sustained detonation. The spatial confinement of the shock frontresults in longer chain intermediates than in the case of thermal decomposition, suggesting thatshock intermediates can be structurally very different from the same material subject to comparabletemperatures and pressures. 2007 American Institute of Physics. DOI: 10.1063/1.2779877

I. INTRODUCTION

Solids under shock loading can exhibit various phenom-ena such as phase transformation,1 plastic deformation,2 andchemical reaction,3 which are crucial in discovering newphases, studying dynamical mechanical responses, and un-derstanding condensed phase chemistry. However, it is verydifficult to achieve those extreme conditions experimentallyand measuring various physical values is even harder. In par-ticular, the motion of detonation fronts in solid explosivesoccurs on the spatial scale of tens of nanometers within atime scale of picoseconds. Although advances in experimen-tal techniques such as high resolution transmission electronmicroscopy and time-resolved molecular spectroscopy areproviding the capability to probe subnanometer features orphysical processes with nanosecond resolution,4 it is still im-practical to achieve both spatial and temporal resolutions si-multaneously. Theoretical frameworks such as the classicZeldovich, von-Neumann, and Doering continuum theoryconcerns the conservation of mass, balance of momentum,and energy in the case of planar shocks, but contains nodescription of atomic-scale defects or anisotropy of the mo-lecular crystal. More importantly, the material inside the re-action zone is far from equilibrium; thus the assumption thatthermodynamic variables other than chemical compositionare in equilibrium may not hold.

While the spatial and temporal scales associated withshock dynamics are difficult to probe experimentally, thesescales are ideal for molecular dynamics MD simulations.5

One of the challenges to using MD simulation in modelingphysical processes involving chemical reactions is the designof an appropriate interatomic potential.6 A range of inter-atomic potential forms have been developed over the last 20yrs that have incorporated chemical reactivity into simula-tions of shock and related phenomena, including chemically-

sustained detonations. Examples include predissociativemodels,7 a London-Eyring-Polanyi-Sato LEPS potential,8

bond-order based potentials,915 tight bindingHamiltonians,1618 and first principles methods.1921 The firstpotentials to demonstrate intrinsic detonation velocities in anatomic simulation in one and two dimensions were the LEPSRef. 8 and the A-B model,9 respectively. The lattermodel, which is based on a bond-order formalism,22 is com-putationally efficient such that large-scale two- and three-dimensional simulations can be carried out, yet still capturesgeneric but essential features of chemical reactivity. Otherrelated analytic potentials have been developed since, most

notably the ReaxFF potentials developed by Goddardet al.,12,14,15 that attempt to model the details of specific sys-tems rather than generic chemistry, but at the cost of compu-tational efficiency.

Each of these approaches to modeling interatomic forcesfor shock simulations have their relative merits, and in somecases severe limitations. In predissociative models, for ex-ample, chemical energy is released through bond breakage,instead of bond formation. This can lead to the nonphysicalpartitioning of the energy such that no energy goes initiallyinto intramolecular vibration.23 Generic studies such as theA-B model, which emphasize computational efficiency, have

focused primarily on energetic materials of small moleculeswhere all energy release comes from bond formation. Thesesmall molecule simulations, while providing critical ex-amples of self-sustaining shock chemistry, may have behav-ior that is very different from energetic materials composedof relatively large molecules. For example, vibrational relax-ation in large molecules will be significantly different fromsmall molecules, and for large molecules a high fraction ofthe energy release can come from dissociation into frag-ments. It should also be noted that a simulated atomic-scaleaElectronic mail: [email protected]

THE JOURNAL OF CHEMICAL PHYSICS 127, 134503 2007

0021-9606/2007/12713 /134503/7/$23.00 2007 American Institute of Physics127, 134503-1

Downloaded 03 Oct 2007 to 152.14.69.2. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
http://dx.doi.org/10.1063/1.2779877http://dx.doi.org/10.1063/1.2779877http://dx.doi.org/10.1063/1.2779877http://dx.doi.org/10.1063/1.2779877http://dx.doi.org/10.1063/1.2779877http://dx.doi.org/10.1063/1.2779877http://dx.doi.org/10.1063/1.2779877


2/7

shock front sustained by chemical reaction with an intrinsicvelocity has only been demonstrated in one and twodimensions.8,9

Reported in this article are the results of simulations of amodel molecular solid of nitrogen cubane subject to thermalagitation and mechanical shock. These simulations use a newapproach to modeling large-scale reactivity in a covalent sys-tem that retains computational efficiency while still allowing

a physical treatment of chemical reactions and intermediatestates. This relatively simple potential used to describe con-densed phase reaction of a large molecule is intended to pro-vide a bridge between generic treatments such as the A-Bmodel and the detailed but more complicated descriptive po-tentials such as ReaxFF. As discussed below the simulationsshow the formation of N2 and short-chain nitrogen clustersas products of both thermal and shock decomposition. In thecase of shocks, decomposition of multiple molecules is spa-tially confined to the shock front as opposed to thermal de-composition that occurs randomly throughout the simulation.The former conditions result in longer chain intermediatesthan in the case of thermal decomposition, suggesting that

shock intermediates can be structurally very different fromthe same material subject to the comparable temperaturesand pressures.

II. REACTIVE STATE SUMMATION POTENTIAL

The reactive state summation potential is an extension ofa concept that was originally implemented to control angular

terms in modeling silica24 and boron oxide.25 During achemical reaction, the system starts from the state of thereactant in the potential energy landscape. Driven by thermalagitation at high temperature or mechanical agitation undershock, the system evolves over the chemical reaction barriertoward a product state. The state of the reactant, the finalproducts, and other possible intermediates, which we refer toas reactive states, determines the thermodynamics and kinet-

ics of the chemical reaction. Each of these reactive states canbe quantified and distinguished by a reaction coordinate. Thecentral idea of this formulation is to model each state sepa-rately, then combine them together through a reaction-coordinate-dependent weighting function. Therefore, indi-vidual force fields can be turned on or off depending on thereaction coordinate. If each reactive state is modeled by aconventional two-body interatomic potential, the total poten-tial energy is the sum of those potentials modulated by aweighting function

PE =

1

2 iN jNs wis

E

srij

,

1

where i, j loops over N atoms, s loops over a number ofreactive states including any number of reactants, productsand intermediates and Esrij is the pair potential for reactivestate s. The weighting function wi is written as

wi = eACNi CN

2, 2

CNi = j=NfCNrij, 3

fCNrij = 1 rij = rij

c 2w

1

2+

1

2cos

2rij rijc + w

w+ 1 rijc 2wrijrijc

0 rij = rijc

. 4

The parameter A controls the width of the weighting func-

tion. CN is the coordination number, which is the sum of aneighbor-counting function fCN. fCN is a smooth functionchanging from 1 to 0 in a transition region of width 2w fromrij

c 2w to rijc as the interatomic distance increases. CN is the

coordination number for a specific reactive state that has tobe unique among all states. Therefore, the reaction coordi-nate is represented by the coordination number for its sim-plicity computationally, although there are many alternativeways to define such a quantity.

Here a nitrogen RSS force field is given that considersthe chemical reaction of N8 nitrogen cubane as it decom-poses in the solid state into N2 molecules. Therefore thereactant r is chosen to be N8 nitrogen cubane and the prod-

ucts p are N2 nitrogen molecules. The total energy is the

weighted sum of two reactive states plus a Van der WaalsVDW term as well as a hard sphere HS repulsion term

PE =1

2 iN

jN

wrErrij + wpE

prij

+ EHSrij + EVDWrij . 5

It should be noted that there is no explicit angular constraintsfor N8. Instead, the constraint on the coordination ensures thecubic shape of the molecule. To accurately describe the en-ergetics of other threefold-coordinated phases such as theblack phosphorous or cubic gauche structures, angular con-straints would have to be included. Inclusion of these terms,

134503-2 Y. Shi and D. W. Brenner J. Chem. Phys. 127, 134503 2007



3/7

however, would reduce the computational efficiency of themodel. As stated above, because our intent is to produce apotential that is intermediate in complexity between the A-Band more descriptive potentials, these terms are neglected.Both reactive states are modeled by a pair-wise Morse-typepotential

Erij = e2rij 2erijfcutoffrij, 6

fcutoffrij = fCNrijB, 7

EHSrij =

eA/rij rij ,

0 rij

,8

EVDWrij = 4 rij

12 rij

6 1 fCNrij . 9The cutoff function ensures the finite range of the cova-

lent bonding as well as the computational efficiency. Thepotential parameters can be readily obtained from the bondlength, bond strength, and bond vibration frequency fromexperiments or first principles calculations, which are listedin Table I.26,27 The hard sphere repulsion term is to ensurethat no atoms overlap for coordination states other than thosetwo reactive states considered in this simple potential model.The intermolecular interaction is a conventional 126Lennard-Jones potential. Because the inter- or intra-molecular interactions are calculated for all atoms in thisRSS formalism, the short covalent bond distance betweenatoms within one molecule would result in a large positivepotential energy due to the repulsive regime of the Lennard-Jones interaction. Therefore, the Lennard-Jones potential ismodulated to zero within the covalent bonding distance as inEq. 9. This approach is similar to the treatments of otherreactive force fields.28 Because no data is available for thenitrogen cubane-cubane Van der Waals interaction experi-mentally or computationally, a relatively weak potential en-ergy depth has been chosen to keep the dominance of the

intramolecular force in the cubane-cubane interaction. Theequilibrium distance of this Van der Waals interaction is also

set to be small for computational efficiency. There are alsono reports on the crystalline state of nitrogen cubane. Similarcubic shaped molecules, such as C8H8 cubane,

29 normallyhave a rhombohedral crystalline state. However, the ratio ofcube-cube distance over the cube size for C8H8 cubane isabout 3.5, which is larger than the ratio 2.9 for the currentmodel nitrogen cubane. It is conceivable that as the cube-cube separation decreases, simple cubic will eventually be-come the choice for the densest packing. Therefore, wechoose an apparent simple cubic packing to construct thenitrogen cubane crystal. The lattice constant is 0.4313 nm.This yields a density of 2.32 g/cm3 that is within the range

of 2.292.65 g/cm3

estimated from empirical methods.30

The physical values for N8 and N2 are given in Table II forthis model along with comparable literature values.

The advantage of this RSS formulism is its simplicityand flexibility. Due to the absence of long-range interactionsand a simple switching between inter- and intra-molecularinteractions, the computing time for the force calculation forRSS nitrogen potential scales linearly with system size. It isalso straight forward to include multiple species, angular de-pendency and multiple products. Furthermore, it is also pos-sible to combine two sets of parameters for the same poten-tial or totally different force fields in a multiscale simulationapproach.

III. THERMAL DECOMPOSITION

A series of thermal decomposition simulations were per-formed using the RSS potential. Simulations were carried outwith N8 cubane crystals within an NVT ensemble. The initialsystem consists of 216 N8 cubane molecules or 1728 nitro-gen atoms with a fixed density of 2.32 g/cm3.

For a reactive system that has a single reactant and onepossible product, the chemical reaction is accomplished byindividual molecules going through a thermally activated re-

action path. The extent of the reaction can be monitored bythe average potential energy

TABLE I. Parameters for the RSS potential for nitrogen.

CN A B rijc w eV 1 Cutoff

Reactant 3 1.15 1.15 2.05 0.1 1.6 1.5 0.90 2.05Product 1 1.30 1.30 2.05 0.1 9.8 1.1 3.82 2.05VDW 2.05 0.1 0.0005 2.55 3.75HS 0.1 20 0.95 0.95

TABLE II. Physical values for N8 and .N2

Bond length

Bondangle

Vibrationperiod

fs

Atomization energyper atom

eV

N8 N2 N8 N2 N8 N2

RSS model 1.52 1.10 90.0 14.14 2.41 4.91Literature values 1.52

261.1027

90.026

14.1326

2.3826

4.9027

134503-3 Thermal decomposition of nitrogen cubane J. Chem. Phys. 127, 134503 2007



4/7

PE = PEp + PEr PEpeRt , 10

where PE is the average potential energy per atom, PE r and

PEp are the potential energy for the reactant and productrespectively, R is the reaction rate at the given temperature,and t is the time. By monitoring the average potential energyevolution of the system, R, PEr, and PEp can be obtained atvarious temperatures through nonlinear fitting procedures asplotted in Fig. 1. The reaction rate follows the Arrhenius ratelaw, as demonstrated by Fig. 2, which is characterized by anactivation energy barrier of 1.0 eV. We found that there is noneed to include an equilibration-induction time in Eq. 10,as was done in Ref. 15, because the reaction rate is wellbehaved without the addition of a fitting parameter.

The product at the end of the reaction is composed ofmostly N2 nitrogen molecules onefold coordinated with a

small percentage of nitrogen oligomers twofold coordi-nated. The nitrogen chains are quasi-one-dimensional with amaximum cluster size of 6 as shown in Fig. 3a. The prod-uct after reacting at 2030 K for 380 ps consists of about 56%N2 and 44% oligomeric nitrogen in terms of atomic percent-age as shown in Fig. 4. As the cookoff temperature increases,there is less oligomeric nitrogen in the final product. Theaverage potential energy per atom for twofold-coordinated

nitrogen is approximately 3.0 eV, which is much higher

than the onefold-coordinated nitrogen which is about4.9 eV. Therefore, chainlike polymer clusters are meta-stable energetically and tend to overcome the dissociationbarrier and turn into smaller segments at higher temperature.

Although there is no explicit term for twofold-coordinated oligomeric nitrogen in Eq. 5, its energetics isdetermined by the weighted sum of one- and threefold coor-dinated states. Moreover, the twofold-coordinated state is a

FIG. 1. Average potential energy evolution gray dots as a function of timeat temperatures 2030, 2320, 2901, 3481, 4062, and 4642 K, from right toleft. Solid lines are nonlinear fitting to Eq. 10 assuming a constant reactionrate for each temperature.

FIG. 2. Reaction rates from nonlinear fitting of the average potential energyevolution according to Eq. 10 as a function of reaction temperature from2030 to 4642 K. The slope of this Arrhenius plot is 1.0 eV.

FIG. 3. Color Cluster analyses for the reaction product a a nitrogencubane system at 2030 K after 380 ps. Clusters with four or more nitrogenatoms are shown; b a nitrogen cubane system that is subject to a shockinitiated by a flyer plate 10.5 km/s after 5 ps. Clusters with eight or morenitrogen atoms are shown. For both figures, two atoms are considered con-nected if the separation distance is smaller than 0.135 nm, which is theupper bound of the first peak of the pair correlation function. Atoms in thesame cluster have the same color. The size of the box in a and the heightof the box in b are both approximately 2.6 nm. The right end of the box inb indicates the shock front position. The shock propagates from left toright as shown by the arrow.

FIG. 4. Cluster size distributions in terms of atomic weight for thermaldecomposition simulations at different temperatures for 380 ps. Clusterswith cluster size 2 are diatomic nitrogen N2.




5/7

natural intermediate state in the transition from threefold-coordinated to onefold-coordinated state, given that simulta-neous bond breaking is less likely than bond breaking one by

one. Such metastable polymeric form for nitrogen has alsobeen predicted previously by first principles methods.31 Thepresence of oligomeric nitrogen may also be due to the shorttime scale of the system with such a high temperature andhigh pressure. We note that the fit in Fig. 1 deviates from thefunction at low temperatures and long times, which suggeststhat there may be multiple reaction barriers. Nonetheless, theoverall chemical reaction can be characterized by a singlereaction barrier as shown in Fig. 2. This may be because: 1the secondary reaction from N8 cubane to oligomeric nitro-gen has a similar reaction barrier; 2 the amount of twofold-coordinated nitrogen is small, especially in the high tempera-ture regime.

IV. SHOCK SIMULATIONS OF NITROGEN CUBANE

To simulate chemical reactions caused by mechanicalshock waves, both moving pistons and flyer plates are usedto initiate shock waves. A simple cubic N8 cubane crystalwith 4320 molecules 34560 atoms in a box of 2.62.652 nm3 is subject to shock. The system is periodic in thetwo directions perpendicular to the shock propagation direc-tion Z direction. The initial system rests at 0 K. There is nothermostat or barostat coupled to the shock simulations. Tosimulate shocks formed by a moving piston, the left nega-

tive Z direction most layer of material consisting of 36 mol-ecules are held rigid while moving to the right positive Zdirection with a constant piston speed. To simulate shocksformed by a flyer plate, the same left most layer is given aninitial velocity without restricting their dynamics thereafter.

The shock velocity scales approximately linearly withthe piston velocity as plotted in Fig. 5. The longitudinalsound velocity is about 1.3 km/s as determined by extrapo-lating the shock velocity to a zero piston velocity. For apiston velocity less than 1.58 km/s, no chemical reaction isobserved during the course of the simulation 3.8 ps. Forpiston velocities greater than about 1.84 km/s, chemical re-action occurs behind the shock front and propagates quickly,

eventually overtaking the preceding shock front. Similarly,shocks by flyer plate will not initiate chemical reactions forflyer plate speeds lower than a threshold value. Figure 6shows the average potential energy along the shock directionat different times, which demonstrates that the shock frontmoves at a constant speed and is followed by a very narrowreaction zone about 2 nm at the beginning of the shock andabout 15 nm at the end of the simulation. The reaction prod-ucts at the end of the simulation are a mixture of N2, chain-like nitrogen and single nitrogen atoms. For example, with aflyer plate speed of 10.5 km/s, the product at 5 ps after theshock consists of 63% N2 molecules, 23% chainlike nitrogenand about 14% isolated nitrogen atoms, all in terms ofweight percentage. A connectivity analysis Fig. 7 shows

that the dominant oligomeric nitrogen is N3 trimer, which issimilar to the product of thermal decomposition at high tem-peratures. However, as depicted in Fig. 7, the difference isthat the size of the oligomeric nitrogen clusters can wellexceed 10 with the maximum size of 24. These large clustersare metastable energetically and quickly dissociate to smallersegments, thus they are only concentrated in the reactionzone immediately trailing the shock front as shown in Fig.3b. This is in clear contrast to the maximum nitrogen clus-

FIG. 5. Shock front speeds plotted as a function of piston speeds. The soundvelocity is about 1.3 km/s, which is extrapolated as the shock front speed atzero piston speed. A smaller system that spans 2.62.652 nm3 is used toobtain this data.

FIG. 6. Average potential energy profiles at different times for a shocksimulation initiated by a 10.5 km/s flyer plate. The horizontal line corre-sponds to 0 ps and the right-most line corresponds to 5.3 ps. The timeinterval between adjacent lines is 0.23 ps. The shock propagates from left toright.

FIG. 7. The cluster size distribution for the shock simulation product, sameas Fig. 3b, in terms of atomic weight.




6/7

ter, which is 6, during the whole simulation process for ther-mal decomposition. This is because at the shock front the

chemical reaction occurs almost simultaneously in neighbor-ing nitrogen cubane molecules; thus smaller chains can belinked together before being further decomposed into N2molecules. In the case of thermal decomposition, the chemi-cal reaction occurs randomly both spatially and temporallyso that large polymeric clusters are less likely to form.

Plotted in Fig. 8 are the positions of the shock front as afunction of time as determined by the position of the rightmost atom that deviates from the initial crystal structure. Forfour different flyer plate speeds, the final shock fronts propa-gate at a common detonation speed of about 11.0 km/s, asindicated by Fig. 9. For flyer plate speeds higher than thefinal detonation speed, the shock front slows down, while forflyer plate speeds lower than the final detonation speed, theshock front speeds up. For even lower flyer plate speeds, noreaction occurs. Therefore, a threshold flyer plate speed toinitiate chemical reaction can be identified. Note that thisvalue can be affected by the thickness of the flyer plate, theduration of the simulation, and the presence of defects in thelattice. For the current simulation with one layer of nitrogen

cubane molecules as a flyer plate and a shock simulation for7.6 ps, this threshold value resides between 4.05.3 km/s.

V. CONCLUSIONS

The thermal decomposition and shock loading of an en-ergetic molecular solid of nitrogen cubane has been simu-lated at the atomic scale. The interatomic interactions aremodeled with a new RSS formalism that yields an activation

energy barrier for thermal decomposition of 1.0 eV. Undershock loading with a rigid piston, the simulations show athreshold piston velocity above which a fully three-dimensional chemically sustained detonation with an intrin-sic velocity of 11.0 km/s is initiated. Structural analysisshows that chainlike nitrogen forms during reaction, and thatthe maximum chain length in the shock simulations is muchlarger than that in thermal decomposition simulations. Thisobservation is mainly due to the fact that, unlike thermalcook-off conditions, reactions occur instantaneously in a co-operative manner in shocks. Therefore, the shocked materialis structurally different from the system subject to similartemperatures and pressures.

ACKNOWLEDGMENTS

We thank stimulating discussions with L. P. Huang forpotential development and D. Thompson, T. Sewell, Y. Hu,L. Sun, and B. Broom regarding shock simulations. Molecu-lar dynamics simulations were carried out in LAMMPS.3234

The North Carolina State University High-PerformanceComputing Facility is also thanked for providing computa-tional resources. This work was supported by a Multi-University Research Initiative from the U.S. Army ResearchOffice.

1 C. S. Yoo and W. J. Nellis, Science 254, 1489 1991.2 M. W. Chen, J. W. McCauley, D. P. Dandekar, and N. K. Bourne, Nat.Mater. 5, 614 2006.

3 W. Fickett and W. C. Davis, Detonation University of California Press,Berkeley, 1979.

4 D. D. Dlott, Annu. Rev. Phys. Chem. 50, 251 1999.5 B. L. Holian, Shock Waves 13, 489 2004.6 D. W. Brenner, O. A. Shenderova, and D. A. Areshkin, in Quantum-Based Analytic Interatomic Forces and Materials Simulation, Reviews in

Computational Chemistry, edited by K. B. Lipkowitz and D. B. BoydVCH Publishers, New York, 1998, pp. 213245.

7 M. Peyrard, S. Odiot, E. Lavenir, and J. M. Schnur, J. Appl. Phys. 57,2626 1985.

8 M. L. Elert, D. M. Deaven, D. W. Brenner, and C. T. White, Phys. Rev.B 39, 1453 1989.

9 D. W. Brenner, D. H. Robertson, M. L. Elert, and C. T. White, Phys. Rev.

Lett. 70, 2174 1993.10 D. H. Robertson, D. W. Brenner, and C. T. White, Phys. Rev. Lett. 67,3132 1991.

11J. J. C. Barrett, D. H. Robertson, and C. T. White, Chem. Phys. Rep. 18,1969 2000.

12 B. M. Rice, W. Mattson, and S. F. Trevino, Phys. Rev. E 57, 5106 1998.13 A. Strachan, A. C. T. van Duin, D. Chakraborty, S. Dasgupta, and W. A.

Goddard, Phys. Rev. Lett. 91, 098301 2003.14 A. C. T. van Duin, Y. Zeiri, F. Dubnikova, R. Kosloff, and W. A. God-

dard, J. Am. Chem. Soc. 127, 11053 2005.15 A. Strachan, E. M. Kober, A. C. T. van Duin, J. Oxgaard, and W. A.

Goddard, J. Chem. Phys. 122, 054502 2005.16 J. D. Kress, S. R. Bickham, L. A. Collins, B. L. Holian, and S.

Goedecker, Phys. Rev. Lett. 83, 3896 1999.17 S. R. Bickham, J. D. Kress, and L. A. Collins, J. Chem. Phys. 112, 9695

2000.

FIG. 8. Shock front positions as a function of time for various flyer platespeeds: 9.2 triangle up, 10.5 circle, and 15.8 square and 21.0 km/striangle down. The black lines are a linear fit to obtain a steady shockpropagation speed that is sustained by chemical reaction.

FIG. 9. Steady shock propagation speeds for shocks that initiate chemicalreaction as a function of flyer plate speed. The shock front speed is set tozero to represent shocks that do not initiate chemical reaction.




7/7

18M. R. Manaa, L. E. Fried, C. F. Melius, M. Elstner, and T. Frauenheim, J.Phys. Chem. A 106, 9024 2002.

19M. Riad Manaa, E. J. Reed, L. E. Fried, G. Galli, and F. Gygi, J. Chem.Phys. 120, 10146 2004.

20H. Liu, J. J. Zhao, and D. Q. Wei, and Z. Z. Gong, J. Chem. Phys. 124,124501 2006.

21S. Mazevet, P. Blottiau, J. D. Kress, and L. A. Collins, Phys. Rev. B 69,224207 2004.

22D. W. Brenner, Mater. Res. Bull. 21, 36 1996.23D. W. Brenner, in Shock Compression of Condensed Matter, edited by S.

C. Schmidt, R. D. Dick, J. W. Forbes, and D. G. Tasker North-Holland,Amsterdam, 1992, p. 115.

24L. P. Huang, M. Durandurdu, and J. Kieffer, Nat. Mater. 5, 977 2006.25L. P. Huang and J. Kieffer, Phys. Rev. B 74, 224107 2006.26W. J. Lauderdale, J. F. Stanton, and R. J. Bartlett, J. Phys. Chem. 96,

1173 1992.

27 R. D. Johnson, NIST Computational Chemistry Comparison and Bench-mark Database 2005 http://srdata.nist.gov/cccbdb.

28 S. J. Stuart, A. B. Tutein, and J. A. Harrison, J. Chem. Phys. 112, 64722000.

29 E. B. Fleischer, J. Am. Chem. Soc. 86, 3889 1964.30 R. Engelke and J. R. Stine, J. Phys. Chem. 94, 5689 1990.31 C. Mailhiot, L. H. Yang, and A. K. McMahan, Phys. Rev. B 46, 14419

1992.32 L. A. M. M. P. S. Molecular Dynamics Simulator http://

lammps.sandia.gov.33 S. J. Plimpton and J. Comp, Physica 117, 1 1995.34 S. J. Plimpton, R. Pollock, and M. Stevens, Proceedings of the Eighth

SIAM Conference on Parallel Processing for Scientific Computing, Min-neapolis, MN 1997.


D l d d 03 O t 2007 t 152 14 69 2 R di t ib ti bj t t AIP li i ht htt //j i /j / i ht j

Documents

Yunfeng Shi and Donald W. Brenner- Simulated thermal decomposition and detonation of nitrogen cubane by molecular dynamics