Shock-induced consolidation of tungsten nanoparticles—A...

J. Appl. Phys. 127, 025901 (2020); https://doi.org/10.1063/1.5133660 127, 025901

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Shock-induced consolidation of tungstennanoparticles—A molecular dynamicsapproachCite as: J. Appl. Phys. 127, 025901 (2020); https://doi.org/10.1063/1.5133660Submitted: 24 October 2019 . Accepted: 28 December 2019 . Published Online: 13 January 2020

Jianrui Feng, Jing Xie, Mingjian Zhang, Xiaowen Liu, Qiang Zhou, Rongjie Yang, and Pengwan Chen

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Shock-induced consolidation of tungstennanoparticles—A molecular dynamics approach

Cite as: J. Appl. Phys. 127, 025901 (2020); doi: 10.1063/1.5133660

View Online Export Citation CrossMarkSubmitted: 24 October 2019 · Accepted: 28 December 2019 ·Published Online: 13 January 2020

Jianrui Feng,1 Jing Xie,2 Mingjian Zhang,2,3 Xiaowen Liu,2 Qiang Zhou,2 Rongjie Yang,1 and Pengwan Chen2,a)

AFFILIATIONS

1School of Materials Science and Engineering, Beijing Institute of Technology, Beijing 100081, China2State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China3College of Physical Science and Technology, Southwest Jiaotong University, Chengdu 610031, China

a)Author to whom correspondence should be addressed: [email protected]

ABSTRACT

Shock-induced consolidation of tungsten nanoparticles to form a bulk material was modeled using molecular dynamics simulation. Byarranging the nanoparticles in a three-dimensional model of body-centered cubic super-lattice, the calculated shock velocity-particle velocityHugoniot data are in good agreement with the experiments. Three states, including solid-undensified, solid-densified, and liquid-densified,can be sequentially obtained with the increase of the impact velocity. It is due to the flow deformation at the particle surface that densifiesthe cavity, and the high pressure and temperature that join the particles together. Melting is not a necessary factor for shock consolidation.Based on whether or not melting takes place, the consolidation mechanisms are liquid-diffusion welding or solid-pressure welding.

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I. INTRODUCTION

Shock consolidation is a unique method which utilizes ashock wave generated by an explosive or by high-speed collision,in compacting powders to strong bulk materials.1,2 During thepropagation of shock waves, powders experience a high-levelpressure, which causes particle deformation and densification atextremely high strain rates (107–108 s−1). Compared to conventionalconsolidation methods, shock consolidation has some particularadvantages, such as a wide range of pressures and temperatures,high quenching rates, and a much larger sample volume than thestatic high-pressure method.3 Because of the extraordinarily fastconsolidation process within a microsecond time scale, the finestructure of the starting powders retains and no grain growthoccurs. As a result, over the past few decades, many bulk nanoma-terials, including aluminum,4,5 copper,6 silver,7 tungsten-copper,8

and aluminum ceramic9 have been fabricated from nanoparticlesusing this method. Although shock consolidation has beenstudied since the 1950s, it is extraordinarily difficult to experimen-tally obtain complete dynamic microscopic information duringthe process of consolidation, because of the extremely small parti-cles and a very short time span. To optimize the dynamic powdercompaction process, a better understanding of the consolidationbehavior is quite necessary.

So far, some experimental and simulation efforts have beendedicated to shock consolidation for practical applications andunderstanding the mechanisms. By observing the microstructure ofthe samples in experiments, Matsumoto and Kondo10 revealed thatthe consolidation mechanism includes jet ejection, dynamic frictionbetween particles and plastic deformation around a void. Based onthe general theories of shock compaction, Kondo and Sawai11 pro-posed that shock consolidation of ultrafine powders relates to thespatial and temporal partitioning of shock-induced thermal energy.Gao et al.12 concluded that melting welding is the most commonconsolidation mechanism for metal powder with a random arrange-ment. Zhou and Chen13,14 fabricated fine-grained W-Cu compositesand found that the main mechanisms of W particles are void col-lapse and plastic deformation.

Molecular dynamics (MD) simulation, which can revealatomic-scale structure evolution and interpret the relevant experi-ments at the microscopic level, is an effective method to clarify theprocess of shock consolidation. Huang et al.6 performed shock con-solidation of Cu nanoparticles and characterized the dynamic tensileresponse. In their simulations, cylindrical rather than sphericalgrains were adopted for simplicity. Tavakol et al.15 investigated themechanical properties of Al/SiC nanocomposites produced by theHugoniostat method. However, the high temperature generated by

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shock waves was not considered. Mayer et al.16,17 investigated shockconsolidation of nanoparticles into a nanocrystalline coating andstudied the plastic deformation of aluminum nanopowder atdynamic compaction. All their results demonstrated that MD simu-lation is an effective method to investigate shock consolidation.However, the dynamic behavior of nanoparticles still needs furtherinvestigation. What is more, whether melting is a necessary factorfor shock consolidation has not been verified.

Compared with conventional coarse-grained tungsten, nano-crystalline tungsten has significant potential to exhibit superiormechanical properties and irradiation resistance.18–20 However, thesintering of pure tungsten by conventional methods usually needs avery high temperature and a long time, which will induce significantgrain growth. In this work, shock consolidations of tungsten nano-particles were modeled using MD simulation. We explored a body-centered cubic (BCC) super-lattice model nanoparticle system at dif-ferent impact velocities (250–2000m/s) and presented the detailedanalysis of consolidation. Section II of this presentation addressesthe methodology related to MD simulations and the analysismethods. The results and discussion are presented in Sec. III. Basedon the simulation results, the consolidation mechanism is proposedin Sec. IV, followed by conclusions in Sec. V.

II. METHODOLOGY

The Large-scale Atomic/Molecular Massively Parallel Simulator(LAMMPS) was used to simulate the process of shock consolida-tion.21 Crystalline tungsten [body-centered cubic (BCC) structure]was described using an embedded atom method potential developedby Zhou et al.22 At first, a spherical single crystal particle with adiameter of 20 nm was built at 300 K. The lattice constant of tung-sten was 3.157 Å at 300 K. To eliminate the quantity limitation ofthe particles and atoms in MD simulation, the particle was replicatedand arranged as a BCC super-lattice.15 Totally, the initial model con-tained 4 754 322 atoms. In the BCC super-lattice, the atoms in allthe particles arrange with the same crystallographic orientation. Themaximum values of theoretical density for the FCC, BCC, and SCsuper-lattice are, respectively, 74%, 68%, and 52%. The reason wechose the BCC super-lattice is that we can acquire the values 55%and 69% of theoretical density and compare the simulation resultswith experiments. In the experiments, the shock velocity (Us) andparticle velocity (Up) Hugoniot data of tungsten particles with thevalues 55% and 69% of theoretical density have already been con-ducted.23,24 In the initial BCC super-lattice model, the “lattice cons-tant” between the particles was 25 nm, and the density of the systemwas 10.3 g/cm3 (approximately initial value 53.5% of theoreticaldensity). The values 55% and 69% of theoretical density were,respectively, acquired under a constant-pressure-temperature (NPT)ensemble at 300 K and 0.1 GPa pressure for approximately 0.94 psand 5.93 ps, where periodic boundary conditions were employed inall three directions. Then, the particles were equilibrated under theNPT ensemble for 1000 ps at 300 K and at zero pressure. The dimen-sions of the particles were, respectively, 24.7 × 24.7 × 222.3 nm3 and22.9 × 22.9 × 206.1 nm3. In the BCC super-lattice model with thevalue 69% of theoretical density, a little deformation takes place atthe contact surfaces of the particles. A bulk single crystalline tung-sten with a 5 nm thickness was constructed as a flyer plate. A

standoff distance of 1 nm was kept between the flyer plate andparticles. In this tungsten potential, the cutoff distance was about0.79 nm.22 In the initial model, the standoff distance should belonger than the cutoff. The configuration of the initial model ispresented in Fig. 1. To observe the particles’ deformation inshock consolidation, each neighbor particles and blocks weregiven different colors. For all simulations, a constant integrationtime step of 1 fs was used.

Planar shock wave loading simulations were performed follow-ing the methods detailed in Ref. 25. The flyer plate as a rigid pistonwas given a prescribed constant velocity to collide the particles.The impact induced a shock wave propagating along the z axis intothe particles. To investigate the influence of impact velocities onconsolidation, impact velocities (Vz), ranging from 250 to 2000 m/swith an increment of 250 m/s, were, respectively, applied to theflyer plate. Because of the rigid property of the flyer plate, the parti-cle velocity of the shock wave is equal to the applied impact velocityof the flyer plate. The shock simulations were performed with themicrocanonical ensemble. Periodic boundary conditions wereapplied along the x and y directions, and free boundary conditionswere applied to the z direction. It should be mentioned that, due tothe thin flyer plate in our model and without considering theeffects of reflected wave, the cracks generated by the reflected wavecannot be simulated under high impact velocities.

After simulation, the Us−Up Hugoniot data of the tungstenparticles were calculated. For a given particle velocity, the corre-sponding shock velocity was obtained based on the velocity historyat the end free surface.26–28 In our simulations, the influences oflattice directions ({100}, {110}, and {111}), particle sizes (10 nmand 20 nm), and initial theoretical densities (55% and 69%) on theUs−Up Hugoniot were, respectively, investigated. A binning analysismethod, with 0.3 nm in each slice, was used to obtain mass density(ρ) along the shock direction.29 Radial distribution functions(RDFs) were adopted to analyze the atomic structures of the

FIG. 1. The configuration of the initial model. The violet block at the left side isthe flyer plate.


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https://aip.scitation.org/journal/jap

compressed particles. The stress (σ) and temperature (T) of eachatom in the compressed particles were calculated. When calculatingthe stress and temperature, the center-of-mass velocity from thebinning analysis were removed and only the thermal velocities wereused. We used Voronoi analysis to calculate the correspondingvolume for each atom in the compressed particles.30 Then, a sim-plified volume, averaged from the atoms in the inner surface of theparticle, was used to calculate the stress of each atom. Atom visuali-zations were performed using the OVITO software.31

III. RESULTS AND DISCUSSION

A. Us−Up HugoniotDepending on the velocity history at the end free surface, Us

can be directly calculated. Then, we can use the Us and Up data toestablish the Us−Up Hugoniot. The influences of lattice directions,particle sizes, and initial values of theoretical density on the Us−UpHugoniot data were, respectively, considered. As can be seen inFig. 2, Us and Up increase linearly under the impact velocities from0 to 2000 m/s. In the initial value 69% of theoretical density, whenthe shock wave travels along the three lattice directions of {100},{110}, and {111}, the Us−Up Hugoniot data with the particle size of20 nm is almost the same but a little lower in {100}. Changing theparticle size from 20 nm to 10 nm, the Us−Up Hugoniot data arealso nearly identical. However, the Us−Up Hugoniot data with theinitial value 55% of theoretical density are much lower. Figure 2also reveals the experimental results performed by Bakanova et al.23

and Trunin et al.24 In their experiments, the initial values of theo-retical density and particle sizes are, respectively, 69%, 50 μm and55%, 100 μm. As can be seen, our calculated Us−Up Hugoniot dataare in close agreement with their experimental results. By fittingthe Us−Up Hugoniot data, the equation of state with the initialvalues 55% and 69% of theoretical density are, respectively,Us = 1.9 ×Up + 295 and Us = 1.9 ×Up + 936. The simulation resultsindicate that, by using the BCC super-lattice model, this potential

can accurately model the process of shock consolidation. What ismore, the Us−Up Hugoniot of tungsten nanoparticles mainlydepends on the initial value of theoretical density. Then, in the fol-lowing part of Sec. III, the consolidation behaviors of 20 nm parti-cles, with a lattice direction of {100} and an initial value 69% oftheoretical density, were investigated.

B. Density

To detect whether or not the particles are fully compacted, thedensities of the compressed particles were measured. Figure 3(a)shows the density distribution of the compressed particles. In theinitial model, due to the BCC super-lattice arrangement of the

FIG. 2. The Us−Up Hugoniot data of tungsten nanoparticles.

FIG. 3. (a) The density distribution of the compressed particles under theimpact velocities of 0 m/s, 500 m/s, 750 m/s, 1250 m/s, and 2000 m/s. (b) Theaverage densities under the impact velocities from 0 to 2000 m/s, and thedashed line at 19.3 g/cm3 corresponds to the density of bulk single crystal tung-sten at ambient conditions.


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particles, the densities of slices distribute unevenly. In some regions,the densities are lower than 12 g/cm3, which is due to the existence ofcavity. Under the impact velocity of 500m/s, the densities of thecompressed particles are higher than the initial model, but the cavitiesstill exist. However, under the impact velocities of higher than 750m/s,the densities almost distribute uniformly and the cavities vanish.Figure 3(b) shows the average densities of the compressed particlesin each situation. A kink appears at the impact velocity of approxi-mately 620m/s, and the density increases linearly on either side ofthe kink. The corresponding density at the kink is 19.7 g/cm3, whichis a little higher than the density of bulk single crystal tungsten(19.3 g/cm3 at 300 K). The results indicate that the tungsten nanopar-ticles are fully compacted under the impact velocities of higher than620 m/s. By fitting the data of Up and ρ, the relations of Up and ρcan be summarized as ρ = 0.0015 × Up + 13.22 (0 < Up ≤ 620 m/s)and ρ = 0.0026 × Up + 18.06 (620 < Up ≤ 2000 m/s).

C. RDF

To analyze the atomic structures, Fig. 4(a) illustrates the RDFsof the compressed nanoparticles. Before the propagation of shockwaves [0 m/s in Fig. 4(a)], the atoms arrange in the BCC structures,and the positions of the first two peaks sequentially represent thefirst neighbor distance and lattice constant. With the increase ofimpact velocities, the peaks shift to the left gradually. This is due tothe high stress [Fig. 5(b)] that reduces the average distance ineach atom.32 Figure 4(b) shows the first neighbor distance in eachsituation. Under the impact velocities from 0 m/s to 2000 m/s, theaverage distance decreased from 2.75 Å to 2.45 Å. Because of thereduced neighbor distance, when the impact velocities are higherthan 620 m/s, the densities of the compressed particles still tendto increase [Fig. 3(b)]. In Fig. 4(a), it can be also found that, whenUp ≤ 500 m/s, the atoms mainly arrange in the BCC structure.The results indicate that, in this situation, elastic deformationmainly takes place in the particles. When 750≤ Up ≤ 1000 m/s,the second peak (lattice constant) gradually obscure. This is becauseof the high stress that breaks some lattice structures. When1250≤Up≤ 1500m/s, the second peak disappears completely andthe third and fourth peaks form into a split peak. The split peak is acharacteristic only of an amorphous structure.33 However, whenUp≥ 1750m/s, the third and fourth peaks form into one peakwithout split. The results indicate the appearance of the liquidphase in the compressed particles.34,35

D. Stress

To investigate the influence of shock stress on consolidation,Fig. 5(a) shows the compression stress-strain of bulk tungsten, andFig. 5(b) reveals stress (σz) distribution along the shock direction.To model uniaxial compression, cubic bulk tungsten, with dimen-sions of 12.7 × 12.7 × 12.7 nm3, was established. Periodic boundaryconditions were employed in all three directions. In the experi-ments of shock consolidation, the compressive strain rate is higherthan 107 s−1. In our simulations, the strain rates of 1 × 109 s−1,5 × 109 s−1, and 1 × 1010 s−1 were, respectively, applied along thelattice direction of {100}. As can be seen in Fig. 5(a), the stress-strain curves are almost identical under the compressive strain ratefrom 109 to 1010 s−1. Figure 5(a) also shows the evolution of atomic

structures under the strain rate of 1 × 1010 s−1. Plastic flow startsaround 56.0–58.5 GPa, which leads to the rate dependence andrapid decrease in stress to about 12 GPa. Figure 5(b) illustrates thestress distribution in a compressed particle along the shock direc-tion. Under the impact velocities of 250 m/s and 500 m/s, thestresses of almost all atoms are lower than 56 GPa. Obviously, inthese situations, only elastic deformation takes place in the com-pressed particles. Under the impact velocities of 750 m/s and1000 m/s, the stresses in some atoms (approximately 3% and 22%)are higher than 56 GPa. In these conditions, a little plastic deforma-tion near the surface compacts the particles into a densely bulkmaterial. Under the impact velocities of higher than 1250 m/s, thestresses of most atoms are higher than 56 GPa. The high stressbreaks the lattice structures and forms the atoms into the disorderedstates [Fig. 4(a)]. After fully consolidated into a bulk material, the

FIG. 4. The RDFs (a) and the first neighbor distance (b) of the compressedparticles under the impact velocities from 0 to 2000 m/s.


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generated high stress can also bring and keep the atoms at the parti-cle surface together to form a strong bonding. Combined with thedensities of the compressed particles in Fig. 3(b), we can considerthat the occurrence of plastic deformation results in complete com-paction under the impact velocities of higher than 620m/s.

E. Temperature

Figure 6 shows the average temperatures of the compressedparticles in each situation. The temperature tends to increasewith the increase of the impact velocities. By fitting the data ofUp and T, the relations of Up and T can be summarized asT = 0.002 × (Up)

2 + 1.227 × Up + 162.28. The melting temperatureof tungsten at zero pressure is approximately 3685 K, plotted as

the dash line in Fig. 6. Under the impact velocities of lower than1000 m/s, the generated temperature is lower than the meltingpoint of tungsten at zero pressure. As a result, the particles remainin the solid state after the propagation of shock waves. Under theimpact velocities of higher than 1000 m/s, the generated tempera-ture is higher than the melting point of tungsten at zero pressure.In shock conditions, the high stress [Fig. 5(b)] will seriouslyrestrict the atomic migration and increase the melting point.36 Asa result, during the propagation of shock wave, the particlesremain in the solid state under the impact velocities of 1250 m/sand 1500 m/s [Fig. 4(a)]. However, after the propagation of shockwaves, with the disappearance of high stress, the tungsten nano-particles may melt by the accumulated temperature. Under theimpact velocities of higher than 1750 m/s, the generated high tem-perature directly leads to melting in the particles during the propa-gation of shock waves [Fig. 4(a)].

F. Morphologies

Based on the densities, RDFs, stresses, and temperatures ofthe compressed particles, three types of results, including solid-undensified, solid-densified, and liquid-densified, can be sequen-tially obtained in shock consolidation. Figure 7 reveals the threetypical morphologies under the impact velocities of 500 m/s,1000m/s, and 2000m/s. To clearly observe the morphologies, aslice in 1 nm thickness, which is at the x = y surface, were cut fromthe compressed particles. Agreed with the result of densities inFig. 3, the particles are not fully compacted under the impact veloc-ity of 500 m/s. Cavities still exist between the particles and almostall the atoms arrange in the BCC structure [Fig. 7(a)]. Under theimpact velocity of 1000m/s, a bulk material is fully compactedwithout the presence of voids [Fig. 7(b)]. It is due to the plasticdeformation at the particle surface that moves the atoms to fill thecavity.17 In this condition, most atoms still remain in the BCC

FIG. 6. The temperatures in the compressed particles under the impact veloci-ties from 0 to 2000 m/s, and the dashed line at 3685 K corresponds to themelting point of tungsten at ambient conditions.

FIG. 5. (a) The compressive stress-strain curves of bulk single crystal tungstenat the strain rates of 1 × 109 s−1, 5 × 109 s−1, and 1 × 1010 s−1. The inset alsoshows the evolution of atomic structures under strain of 0.10, 0.17, and 0.25. (b)The stress distribution of a compressed particle under the impact velocities from0 to 2000 m/s, and the dashed line at 56 GPa corresponds to the plastic flow.


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structure, but a few arrange in the disordered state at the bondingsurface. Under the impact velocity of 2000m/s, the atoms mainlyarrange in the disordered state, but remain the BCC structure at thecenter of the particle [Fig. 7(c)]. What is more, atomic diffusion canbe observed near the particle surface. We can conclude that, in thissituation, melting mainly occurs at the particle surface and meltingresults in the atomic diffusion. The atomic diffusion offers a strongbonding between the particles.36

IV. CONSOLIDATION MECHANISM

Based on the MD simulation, the process of shock consolida-tion can divide into two steps, including densification process andwelding process. It is due to the plastic deformation that denselyfills the cavities. Then, the high pressure and temperature producedby the shock wave tightly join the particles together.

Depending on the atomic deformation in the particles, threestates of bulk materials, including solid-undensified (Up≤ 620 m/s),solid-densified (620m/s

14Q. Zhou and P. W. Chen, J. Alloys Compd. 657, 215 (2016).15M. Tavakol, M. Mahnama, and R. Naghdabadi, Comp. Mater. Sci. 125, 255(2016).16A. E. Mayer and A. A. Ebel, J. Appl. Phys. 122, 165901 (2017).17A. E. Mayer, A. A. Ebel, and M. K. A. Al-Sandoqachi, Int. J. Plast. 124, 22 (2020).18Q. Wei, H. T. Zhang, B. E. Schuster, K. T. Ramesh, R. Z. Valiev, L. J. Kecskes,R. J. Dowding, L. Magness, and K. Cho, Acta Mater. 54, 4079 (2006).19Q. Zhou and P. W. Chen, Int. J. Refract. Met. Hard Mater. 42, 215 (2014).20R. Sarathi, T. K. Sindhu, S. R. Chakravarthy, A. Sharma, and K. V. Nagesh,J. Alloys Compd. 475, 658 (2009).21S. Plimpton, J. Comput. Phys. 117, 1 (1995).22X. W. Zhou, R. A. Johnson, and H. N. G. Wadley, Phys. Rev. B 69, 144113(2004).23A. A. Bakanova, I. P. Dudoladov, and Y. N. Sutulov, J. Appl. Mech. Tech.Phys. 15, 241 (1974).24R. F. Trunin, G. V. Simakov, Y. N. Sutulov, A. B. Medvedev, B. D. Rogozkin,and Y. E. Fedorov, Sov. Phys. JETP 69, 580 (1989).25B. L. Holian and P. S. Lomdahl, Science 280, 2085 (1998).

26E. M. Bringa, J. U. Cazamias, P. Erhart, J. Stolken, N. Tanushev, B. D. Wirth,R. E. Rudd, and M. J. Caturla, J. Appl. Phys. 96, 3793 (2004).27Q. An, W. Z. Han, S. N. Luo, T. C. Germann, D. L. Tonks, andW. A. Goddard, J. Appl. Phys. 111, 053525 (2012).28S. N. Luo, Q. An, T. C. Germann, and L. B. Han, J. Appl. Phys. 106, 013502(2009).29B. Arman, S. N. Luo, T. C. Germann, and T. Cagin, Phys. Rev. B 81, 144201(2010).30J. R. Feng, P. W. Chen, and M. Li, Phys. Rev. B 98, 024201 (2018).31A. Stukowski, Model. Numer. Simulat. Mater. Sci. 18, 015012 (2010).32J. R. Feng, P. W. Chen, and M. Li, J. Appl. Phys. 124, 165901 (2018).33J. R. Feng, P. W. Chen, and M. Li, J. Phys. Condens. Matter 30, 255402 (2018).34S. P. Pan, J. Y. Qin, W. M. Wang, and T. K. Gu, Phys. Rev. B 84, 092201(2011).35Y. Y. Ju, Q. M. Zhang, Z. Z. Gong, G. F. Ji, and L. Zhou, J. Appl. Phys. 114,093507 (2013).36J. R. Feng, K. D. Dai, Q. Zhou, J. Xie, R. J. Yang, I. A. Bataev, and P. W. Chen,J. Phys. Condens. Matter 31, 415403 (2019).


J. Appl. Phys. 127, 025901 (2020); doi: 10.1063/1.5133660 127, 025901-7


https://doi.org/10.1016/j.jallcom.2015.10.057https://doi.org/10.1016/j.commatsci.2016.08.032https://doi.org/10.1063/1.4996846https://doi.org/10.1016/j.ijplas.2019.08.005https://doi.org/10.1016/j.actamat.2006.05.005https://doi.org/10.1016/j.ijrmhm.2013.09.008https://doi.org/10.1016/j.jallcom.2008.07.092https://doi.org/10.1006/jcph.1995.1039https://doi.org/10.1103/PhysRevB.69.144113https://doi.org/10.1007/BF00850666https://doi.org/10.1007/BF00850666https://doi.org/10.1126/science.280.5372.2085https://doi.org/10.1063/1.1789266https://doi.org/10.1063/1.3692079https://doi.org/10.1063/1.3158062https://doi.org/10.1103/PhysRevB.81.144201https://doi.org/10.1103/PhysRevB.98.024201https://doi.org/10.1088/0965-0393/18/1/015012https://doi.org/10.1063/1.5040512https://doi.org/10.1088/1361-648X/aac45fhttps://doi.org/10.1103/PhysRevB.84.092201https://doi.org/10.1063/1.4819298https://doi.org/10.1088/1361-648X/ab30d7https://aip.scitation.org/journal/jap

Shock-induced consolidation of tungsten nanoparticles—A molecular dynamics approachI. INTRODUCTIONII. METHODOLOGYIII. RESULTS AND DISCUSSIONA. Us−Up HugoniotB. DensityC. RDFD. StressE. TemperatureF. Morphologies

IV. CONSOLIDATION MECHANISMV. CONCLUSIONSReferences

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