Abstract
This paper presents an investigation aimed at understanding the shock wave propagation response of oriented α-quartz single crystals by using molecular dynamics (MD) simulations. Several orthorhombic unit cells with different crystal orientations converted from an original monoclinic α-quartz crystal were used to construct the supercells with the crystallographic orientations of [100], [120], and [001] aligned with the shock direction. The shock wave propagation responses were analyzed via position-time (x–t) diagrams of several thermal and mechanical properties. Atomic shear strain and radial distribution function (RDF) were used to investigate the shock-induced material deformation and phase change from crystal to disordered fluid-like flow. The MD simulations enabled the construct of the shock Hugoniot, in terms of the shock velocity Us versus the impact/particle speed Up (i.e., Us–Up plane), and the Hugoniot elastic limit \(\left( {\sigma_{{{\text{HEL}}}} } \right)\) response with reference to precursor decay. It was found that the single crystal α-quartz sample exhibits noticeable anisotropic behaviors in terms of kinetic temperature distribution, stress distribution, and Hugoniot shock velocity response. Among the three studied crystal directions at a relatively low Up, the [120] sample showed a non-uniform shock-induced deformation pattern, and the [001] crystal showed the most prominent energy absorption capacity. At a given high impact speed (e.g., Up = 2.5 km/s), the [001] sample showed a relatively longer amorphous shocked region followed by a shorter deformed crystal region, which was very different from the compressed regions behind the shock front in the other two samples. For all oriented crystals, the RDF results predicted an amorphous structure of silica emerging in the compressed region at the higher speed impact, in addition to a few “shear-bands” or crystal sliding in the [120] sample. The shock Hugoniot Us–Up also indicated a noticeable anisotropic behavior of the α-quartz. At a given value of Up above 1.5 km/s, the [001] crystal yielded the largest Us while the [120] crystal yielded the smallest. A “two-wave” structure was evidently found in the [001] sample at Up = 2.5 km/s, while such a structure was not clearly seen for the other two orientations. The precursor decay phenomenon was observed in [001] direction, indicating a strong strain rate effect on \(\sigma_{{{\text{HEL}}}}\); however, the \(\sigma_{{{\text{HEL}}}}\) decay was not easy to identify in [100] and [120] directions due to the instantaneous microstructural sliding/collapse or fast transition to an extensive amorphous structure behind the shock front. In summary, the MD simulation-based studies reported in the present work demonstrate strong orientation-dependent shock responses of the monoclinic single crystal α-quartz.
Graphical abstract
Similar content being viewed by others
References
Wong V (2012), Geomorphology: the mechanics and chemistry of landscapes - By Robert S. Anderson and Suzanne P. Anderson, 68(1). Wiley
Hazen RM, Finger LW, Hemley RJ, Mao HK (1989) High-pressure crystal chemistry and amorphization of α-quartz. Solid State Commun 72(5):507–511. https://doi.org/10.1016/0038-1098(89)90607-8
Molaei F, Siavoshi H (2020) Molecular dynamics studies of thermal conductivity and mechanical properties of single crystalline α-quartz. Solid State Commun 320:114020. https://doi.org/10.1016/j.ssc.2020.114020
Ghashoghchi RA, Hosseini MR, Ahmadi A (2017) Effects of microbial cells and their associated extracellular polymeric substances on the bio-flocculation of kaolin and quartz. Appl Clay Sci 138:81–88. https://doi.org/10.1016/j.clay.2017.01.002
Pervadchuk V, Vladimirova D, and Gordeeva I, Optimal control of distributed systems in problems of quartz optical fiber production, In: AIP conference proceedings, Jan. 2018, 1926, https://doi.org/10.1063/1.5020485.
Danel JS, Delapierre G (1991) Quartz: a material for microdevices. J Micromech Microeng 1(4):187–198. https://doi.org/10.1088/0960-1317/1/4/001
S. Senapati, Ashutosh Rath, Karuna, and K. Nanda (2018), Understanding the unusual photoluminescence properties of SiO x nanoropes prepared by thermal evaporation method, Appl Phys A. https://doi.org/10.1007/s00339-017-1480-6.
Broughton JQ, Meli CA, Vashishta P, Kalia RK (1997) Direct atomistic simulation of quartz crystal oscillators: bulk properties and nanoscale devices. Phys Rev B-Condens Matter Mater Phys 56(2):611–618. https://doi.org/10.1103/PhysRevB.56.611
Wang J, Rajendran AM, Dongare AM (2015) Atomic scale modeling of shock response of fused silica and α-quartz. J Mater Sci. https://doi.org/10.1007/s10853-015-9386-1
Park J, Kirane K (2021) Transitional flaw size sensitivity of amorphous silica nanostructures analyzed by ReaxFF/SiO based molecular dynamics. J Appl Phys 129(17):175103. https://doi.org/10.1063/5.0044840
Wright AF, Lehmann MS (1981) The structure of quartz at 25 and 590°C determined by neutron diffraction. J Solid State Chem 36(3):371–380. https://doi.org/10.1016/0022-4596(81)90449-7
Demuth T, Jeanvoine Y, Hafner J, Ángyán JG (1999) Polymorphism in silica studied in the local density and generalized-gradient approximations. J Phys Condens Matter 11(19):3833–3874. https://doi.org/10.1088/0953-8984/11/19/306
Ohno I, Harada K, Yoshitomi C (2006) Temperature variation of elastic constants of quartz across the α–β transition. Phys Chem Miner 33(1):1–9. https://doi.org/10.1007/s00269-005-0008-3
Derakhshani SM, Schott DL, Lodewijks G (2015) Micro-macro properties of quartz sand: experimental investigation and DEM simulation. Powder Technol 269:127–138. https://doi.org/10.1016/j.powtec.2014.08.072
Van Beest BWH, Kramer GJ, Van Santen RA (1990) Force fields for silicas and aluminophosphates based on ab initio calculations. Phys Rev Lett. https://doi.org/10.1103/PhysRevLett.64.1955
Van Duin ACT, Strachan A, Stewman S, Zhang Q, Xu X, Goddard WA (2003) ReaxFFSiO reactive force field for silicon and silicon oxide systems. J Phys Chem A 107(19):3803–3811. https://doi.org/10.1021/jp0276303
Guo J (2019) Atomic simulation of basic properties for α-SiO2 Crystal. Mater Sci 09:355–360. https://doi.org/10.12677/MS.2019.94047
Tersoff J (1988) New empirical approach for the structure and energy of covalent systems. Phys Rev B. https://doi.org/10.1103/PhysRevB.37.6991
Farrow MR, Probert MIJ (2011) Atomistic molecular dynamics simulations of shock compressed quartz. J Chem Phys. https://doi.org/10.1063/13615526
Barmes F, Soulard L, Mareschal M (2006) Molecular dynamics of shock-wave induced structural changes in silica glasses. Phys Rev B-Condens Matter Mater Phys 73(22):1–11. https://doi.org/10.1103/PhysRevB.73.224108
Kroonblawd MP, Mathew N, Jiang S, Sewell TD (2016) A generalized crystal-cutting method for modeling arbitrarily oriented crystals in 3D periodic simulation cells with applications to crystal–crystal interfaces. Comput Phys Commun. https://doi.org/10.1016/j.cpc.2016.07.007
Munetoh S, Motooka T, Moriguchi K, Shintani A (2007) Interatomic potential for Si–O systems using Tersoff parameterization. Comput Mater Sci. https://doi.org/10.1016/j.commatsci.2006.06.010
R. Su, M. Xiang, J. Chen, S. Jiang, and H. Wei (2014), Molecular dynamics simulation of shock induced ejection on fused silica surface, J Appl Phys. https://doi.org/10.1063/1.4876742.
He L, Sewell TD, Thompson DL (2011) Molecular dynamics simulations of shock waves in oriented nitromethane single crystals. J Chem Phys. https://doi.org/10.1063/1.3561397
Jiang S, Sewell TD, Thompson DL (2016) Molecular dynamics simulations of shock wave propagation through the crystal-melt interface of (100)-oriented nitromethane. J Phys Chem C. https://doi.org/10.1021/acs.jpcc.6b07002
Tsai DH (1979) The virial theorem and stress calculation in molecular dynamics. J Chem Phys. https://doi.org/10.1063/1.437577
Shen S, Atluri SN (2004) Atomic-level stress calculation and continuum-molecular system equivalence. C–Comput Model Eng Sci. https://doi.org/10.3970/cmes.2004.006.091
Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J Comput Phys. https://doi.org/10.1006/jcph.1995.1039
P. R. Levashov, Shock wave database. http://ihed.ras.ru/rusbank/.
Wackerle J (1962) Shock-wave compression of quartz. J Appl Phys 33(3):922–937. https://doi.org/10.1063/1.1777192
M. van Thiel, J. Shaner, and E. Salinas, Compendium of Shock Wave Data. Volume 2, Revision 1. Section A2. Inorganic Compounds Section B. Hydrocarbons, 1977.
S. P. Marsh, QUARTZ, single-crystal, In: LASL shock Hugoniot data, Univ of California Press, 1980, p. 324.
Badro J, Teter DM (1997) Theoretical study of a five-coordinated silica polymorph. Phys Rev B-Condens Matter Mater Phys 56(10):5797–5806. https://doi.org/10.1103/PhysRevB.56.5797
S. C. Chowdhury, B. Z. Gama. Haque, and J. W. Gillespie (2016), Molecular dynamics simulations of the structure and mechanical properties of silica glass using ReaxFF,J Mater Sci, 51(22), 10139–10159, https://doi.org/10.1007/s10853-016-0242-8.
Belonoshko AB (1994) Molecular dynamics of silica at high pressures: Equation of state, structure, and phase transitions. Geochim Cosmochim Acta 58(6):1557–1566. https://doi.org/10.1016/0016-7037(94)90558-4
Luo S-N, Çaǧin T, Strachan A, Goddard WA, Ahrens TJ (2002) Molecular dynamics modeling of stishovite. Earth Planet Sci Lett 202(1):147–157. https://doi.org/10.1016/S0012-821X(02)00749-5
Yeon J, Chowdhury SC, Daksha CM, Gillespie JW (2021) Development of Mg/Al/Si/O ReaxFF parameters for magnesium aluminosilicate glass using an artificial neural network-assisted genetic algorithm. J Phys Chem C 125(33):18380–18394. https://doi.org/10.1021/acs.jpcc.1c01190
Valisetty R, Rajendran A, Agarwal G, Dongare A, Ianni J, Namburu R (2018) HPC simulations of shock front evolution for a study of the shock precursor decay in a submicron thick nanocrystalline aluminum. Model Simul Mater Sci Eng 26(5):55008. https://doi.org/10.1088/1361-651x/aac1c3
Acknowledgements
The authors acknowledge the support from the U.S. Army Corp of Engineers–Engineering Research and Development Center (W912HZ2020042). S.J. thanks Dr. Tommy Sewell for some helpful discussions.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Additional information
Handling Editor: Avinash Dongare.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zhang, H., Shukla, M.K., Larson, S. et al. Molecular dynamics study of anisotropic shock responses in oriented α-quartz single crystal. J Mater Sci 57, 6688–6705 (2022). https://doi.org/10.1007/s10853-022-07076-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10853-022-07076-0