Fifth-degree elastic energy for predictive continuum stress–strain relations and elastic instabilities under large strain and complex loading in silicon

Chen, Hao; Zarkevich, Nikolai A.; Levitas, Valery I.; Johnson, Duane D.; Zhang, Xiancheng

doi:10.1038/s41524-020-00382-8

Title: Fifth-degree elastic energy for predictive continuum stress–strain relations and elastic instabilities under large strain and complex loading in silicon

Journal Article · Tue Aug 04 00:00:00 EDT 2020 · npj Computational Materials

DOI:https://doi.org/10.1038/s41524-020-00382-8· OSTI ID:1644704

;

; Zhang, Xiancheng

Materials under complex loading develop large strains and often phase transformation via an elastic instability, as observed in both simple and complex systems. Here, we represent a material (exemplified for Si I) under large Lagrangian strains within a continuum description by a 5th-order elastic energy found by minimizing error relative to density functional theory (DFT) results. The Cauchy stress—Lagrangian strain curves for arbitrary complex loadings are in excellent correspondence with DFT results, including the elastic instability driving the Si I → II phase transformation (PT) and the shear instabilities. PT conditions for Si I → II under action of cubic axial stresses are linear in Cauchy stresses in agreement with DFT predictions. Such continuum elastic energy permits study of elastic instabilities and orientational dependence leading to different PTs, slip, twinning, or fracture, providing a fundamental basis for continuum physics simulations of crystal behavior under extreme loading.

View Journal Article

Cite

Export

Save

Research Organization:: Ames Laboratory (AMES), Ames, IA (United States); Iowa State Univ., Ames, IA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division; National Science Foundation (NSF); US Department of the Navy, Office of Naval Research (ONR); National Key Research and Development Program of China; National Natural Science Foundation of China (NSFC)

Grant/Contract Number:: AC02-07CH11358; N00014-16-1-2079

OSTI ID:: 1644704

Alternate ID(s):: OSTI ID: 1645120

Report Number(s):: IS-J-10,239; 115; PII: 382

Journal Information:: npj Computational Materials, Journal Name: npj Computational Materials Vol. 6 Journal Issue: 1; ISSN 2057-3960

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United Kingdom

Language:: English

Citation Metrics:

Cited by: 12 works

Citation information provided by
Web of Science

References (63)

Generalized Gradient Approximation Made Simple Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868 https://doi.org/10.1103/PhysRevLett.77.3865	journal	October 1996
Crystal thermoelasticity at extreme loading rates and pressures: Analysis of higher-order energy potentials Clayton, J. D. Extreme Mechanics Letters, Vol. 3 https://doi.org/10.1016/j.eml.2015.03.005	journal	June 2015
Surface-Induced Phase Transformations: Multiple Scale and Mechanics Effects and Morphological Transitions Levitas, Valery I.; Javanbakht, Mahdi Physical Review Letters, Vol. 107, Issue 17 https://doi.org/10.1103/PhysRevLett.107.175701	journal	October 2011
Effect of normal stress on the ideal shear strength in covalent crystals Umeno, Yoshitaka; Černý, Miroslav Physical Review B, Vol. 77, Issue 10 https://doi.org/10.1103/PhysRevB.77.100101	journal	March 2008
Lattice instabilities in metallic elements Grimvall, Göran; Magyari-Köpe, Blanka; Ozoliņš, Vidvuds Reviews of Modern Physics, Vol. 84, Issue 2 https://doi.org/10.1103/RevModPhys.84.945	journal	June 2012
Projector augmented-wave method Blöchl, P. E. Physical Review B, Vol. 50, Issue 24, p. 17953-17979 https://doi.org/10.1103/PhysRevB.50.17953	journal	December 1994
Ab initio calculations of mechanical properties: Methods and applications Pokluda, J.; Černý, M.; Šob, M. Progress in Materials Science, Vol. 73 https://doi.org/10.1016/j.pmatsci.2015.04.001	journal	August 2015
Ab initio calculations of third-order elastic constants and related properties for selected semiconductors Łopuszyński, Michał; Majewski, Jacek A. Physical Review B, Vol. 76, Issue 4 https://doi.org/10.1103/PhysRevB.76.045202	journal	July 2007
Triaxial-Stress-Induced Homogeneous Hysteresis-Free First-Order Phase Transformations with Stable Intermediate Phases Levitas, Valery I.; Chen, Hao; Xiong, Liming Physical Review Letters, Vol. 118, Issue 2 https://doi.org/10.1103/PhysRevLett.118.025701	journal	January 2017
Ideal strength and ductility in metals from second- and third-order elastic constants de Jong, Maarten; Winter, Ian; Chrzan, D. C. Physical Review B, Vol. 96, Issue 1 https://doi.org/10.1103/PhysRevB.96.014105	journal	July 2017
Lattice Instability during Solid-Solid Structural Transformations under a General Applied Stress Tensor: Example of $Si I \to Si II$ with Metallization Zarkevich, Nikolai A.; Chen, Hao; Levitas, Valery I. Physical Review Letters, Vol. 121, Issue 16 https://doi.org/10.1103/PhysRevLett.121.165701	journal	October 2018
Pressure-induced amorphization and an amorphous–amorphous transition in densified porous silicon Deb, Sudip K.; Wilding, Martin; Somayazulu, Maddury Nature, Vol. 414, Issue 6863 https://doi.org/10.1038/35107036	journal	November 2001
Elastic instability in α-quartz under pressure Binggeli, N.; Chelikowsky, James R. Physical Review Letters, Vol. 69, Issue 15 https://doi.org/10.1103/PhysRevLett.69.2220	journal	October 1992
Large elastoplasticity under static megabar pressures: Formulation and application to compression of samples in diamond anvil cells Feng, Biao; Levitas, Valery I.; Hemley, Russell J. International Journal of Plasticity, Vol. 84 https://doi.org/10.1016/j.ijplas.2016.04.017	journal	September 2016
From ultrasoft pseudopotentials to the projector augmented-wave method Kresse, G.; Joubert, D. Physical Review B, Vol. 59, Issue 3, p. 1758-1775 https://doi.org/10.1103/PhysRevB.59.1758	journal	January 1999
Microstructural Observations of α-Quartz Amorphization Kingma, Kathleen J.; Meade, Charles; Hemley, Russell J. Science, Vol. 259, Issue 5095 https://doi.org/10.1126/science.259.5095.666	journal	January 1993
Virtual melting as a new mechanism of stress relaxation under high strain rate loading Levitas, V. I.; Ravelo, R. Proceedings of the National Academy of Sciences, Vol. 109, Issue 33 https://doi.org/10.1073/pnas.1203285109	journal	July 2012
Stress-Measure Dependence of Phase Transformation Criterion under Finite Strains: Hierarchy of Crystal Lattice Instabilities for Homogeneous and Heterogeneous Transformations Babaei, Hamed; Levitas, Valery I. Physical Review Letters, Vol. 124, Issue 7 https://doi.org/10.1103/PhysRevLett.124.075701	journal	February 2020
First-principles calculations of second- and third-order elastic constants for single crystals of arbitrary symmetry Zhao, Jijun; Winey, J. M.; Gupta, Y. M. Physical Review B, Vol. 75, Issue 9 https://doi.org/10.1103/PhysRevB.75.094105	journal	March 2007
Phase field approach for stress- and temperature-induced phase transformations that satisfies lattice instability conditions. Part I. General theory Levitas, Valery I. International Journal of Plasticity, Vol. 106 https://doi.org/10.1016/j.ijplas.2018.03.007	journal	July 2018
Inelastic-neutron-scattering study of phonon eigenvectors and frequencies in Si Kulda, Jiří; Strauch, Dieter; Pavone, Pasquale Physical Review B, Vol. 50, Issue 18 https://doi.org/10.1103/PhysRevB.50.13347	journal	November 1994
Shear driven formation of nano-diamonds at sub-gigapascals and 300 K Gao, Yang; Ma, Yanzhang; An, Qi Carbon, Vol. 146 https://doi.org/10.1016/j.carbon.2019.02.012	journal	May 2019
Phase field approach to dislocation evolution at large strains: Computational aspects Javanbakht, Mahdi; Levitas, Valery I. International Journal of Solids and Structures, Vol. 82 https://doi.org/10.1016/j.ijsolstr.2015.10.021	journal	March 2016
Stability and strength of covalent crystals under uniaxial and triaxial loading from first principles Černý, Miroslav; Řehák, Petr; Umeno, Yoshitaka Journal of Physics: Condensed Matter, Vol. 25, Issue 3 https://doi.org/10.1088/0953-8984/25/3/035401	journal	December 2012
X-ray Imaging of Stress and Strain of Diamond, Iron, and Tungsten at Megabar Pressures Hemley, R. J. Science, Vol. 276, Issue 5316 https://doi.org/10.1126/science.276.5316.1242	journal	May 1997
Principles of stability analysis of ideal crystals Hill, Rodney; Milstein, Frederick Physical Review B, Vol. 15, Issue 6 https://doi.org/10.1103/PhysRevB.15.3087	journal	March 1977
Ideal crystal stability and pressure-induced phase transition in silicon Mizushima, Kazuki; Yip, Sidney; Kaxiras, Efthimios Physical Review B, Vol. 50, Issue 20 https://doi.org/10.1103/PhysRevB.50.14952	journal	November 1994
Amorphization induced by 60° shuffle dislocation pileup against different grain boundaries in silicon bicrystal under shear Chen, Hao; Levitas, Valery I.; Xiong, Liming Acta Materialia, Vol. 179 https://doi.org/10.1016/j.actamat.2019.08.023	journal	October 2019
Ab initiomolecular dynamics for liquid metals Kresse, G.; Hafner, J. Physical Review B, Vol. 47, Issue 1, p. 558-561 https://doi.org/10.1103/PhysRevB.47.558	journal	January 1993
Computer simulation of local order in condensed phases of silicon Stillinger, Frank H.; Weber, Thomas A. Physical Review B, Vol. 31, Issue 8 https://doi.org/10.1103/PhysRevB.31.5262	journal	April 1985
Elastic constants of silicon materials calculated as a function of temperature using a parametrization of the second-generation reactive empirical bond-order potential Schall, J. David; Gao, Guangtu; Harrison, Judith A. Physical Review B, Vol. 77, Issue 11 https://doi.org/10.1103/PhysRevB.77.115209	journal	March 2008
Diamond’s third-order elastic constants: ab initio calculations and experimental investigation Telichko, Arsenii V.; Erohin, Sergey V.; Kvashnin, Gennady M. Journal of Materials Science, Vol. 52, Issue 6 https://doi.org/10.1007/s10853-016-0633-x	journal	November 2016
Tensorial stress−strain fields and large elastoplasticity as well as friction in diamond anvil cell up to 400 GPa Levitas, Valery I.; Kamrani, Mehdi; Feng, Biao npj Computational Materials, Vol. 5, Issue 1 https://doi.org/10.1038/s41524-019-0234-8	journal	October 2019
A hierarchy of catastrophes as a succession of stability limits for the crystalline state Tallon, J. L. Nature, Vol. 342, Issue 6250 https://doi.org/10.1038/342658a0	journal	December 1989
Analysis of shock compression of strong single crystals with logarithmic thermoelastic-plastic theory Clayton, J. D. International Journal of Engineering Science, Vol. 79 https://doi.org/10.1016/j.ijengsci.2014.02.016	journal	June 2014
Temperature Dependent Young's Modulus of Si and Ge Vanhellemont, J.; Swarnakar, A. K.; Van der Biest, O. ECS Transactions, Vol. 64, Issue 11 https://doi.org/10.1149/06411.0283ecst	journal	August 2014
Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene Lee, C.; Wei, X.; Kysar, J. W. Science, Vol. 321, Issue 5887, p. 385-388 https://doi.org/10.1126/science.1157996	journal	July 2008
Phase-field approach for stress- and temperature-induced phase transformations that satisfies lattice instability conditions. Part 2. simulations of phase transformations Si I $\leftrightarrow$ Si II Babaei, Hamed; Levitas, Valery I. International Journal of Plasticity, Vol. 107 https://doi.org/10.1016/j.ijplas.2018.04.006	journal	August 2018
Nonlinear Elasticity of Monolayer Graphene Cadelano, Emiliano; Palla, Pier Luca; Giordano, Stefano Physical Review Letters, Vol. 102, Issue 23 https://doi.org/10.1103/PhysRevLett.102.235502	journal	June 2009
Shear-induced phase transition of nanocrystalline hexagonal boron nitride to wurtzitic structure at room temperature and lower pressure Ji, C.; Levitas, V. I.; Zhu, H. Proceedings of the National Academy of Sciences, Vol. 109, Issue 47 https://doi.org/10.1073/pnas.1214976109	journal	November 2012
Ab initio calculations of second-, third-, and fourth-order elastic constants for single crystals Wang, Hao; Li, Mo Physical Review B, Vol. 79, Issue 22 https://doi.org/10.1103/PhysRevB.79.224102	journal	June 2009
Atomistic Explanation of Shear-Induced Amorphous Band Formation in Boron Carbide An, Qi; Goddard, William A.; Cheng, Tao Physical Review Letters, Vol. 113, Issue 9 https://doi.org/10.1103/PhysRevLett.113.095501	journal	August 2014
Nudged-elastic band method with two climbing images: Finding transition states in complex energy landscapes Zarkevich, Nikolai A.; Johnson, Duane D. The Journal of Chemical Physics, Vol. 142, Issue 2 https://doi.org/10.1063/1.4905209	journal	January 2015
Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set Kresse, G.; Furthmüller, J. Computational Materials Science, Vol. 6, Issue 1, p. 15-50 https://doi.org/10.1016/0927-0256(96)00008-0	journal	July 1996
Lattice instability in β‐SiC and simulation of brittle fracture Tang, Meijie; Yip, Sidney Journal of Applied Physics, Vol. 76, Issue 5 https://doi.org/10.1063/1.357575	journal	September 1994
Special points for Brillouin-zone integrations Monkhorst, Hendrik J.; Pack, James D. Physical Review B, Vol. 13, Issue 12, p. 5188-5192 https://doi.org/10.1103/PhysRevB.13.5188	journal	June 1976
Structural database for reducing cost in materials design and complexity of multiscale computations Zarkevich, Nikolai Complexity, Vol. 11, Issue 4 https://doi.org/10.1002/cplx.20117	journal	January 2006
Electronic Effects in the Elastic Constants of $n$ -Type Silicon Hall, John J. Physical Review, Vol. 161, Issue 3 https://doi.org/10.1103/PhysRev.161.756	journal	September 1967
Crystal instabilities at finite strain Wang, Jinghan; Yip, Sidney; Phillpot, S. R. Physical Review Letters, Vol. 71, Issue 25 https://doi.org/10.1103/PhysRevLett.71.4182	journal	December 1993
Shock-induced amorphization in silicon carbide Zhao, S.; Flanagan, R.; Hahn, E. N. Acta Materialia, Vol. 158 https://doi.org/10.1016/j.actamat.2018.07.047	journal	October 2018
Transgranular amorphous shear band formation in polycrystalline boron carbide Guo, Dezhou; An, Qi International Journal of Plasticity, Vol. 121 https://doi.org/10.1016/j.ijplas.2019.06.004	journal	October 2019
Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium Kresse, G.; Hafner, J. Physical Review B, Vol. 49, Issue 20, p. 14251-14269 https://doi.org/10.1103/PhysRevB.49.14251	journal	May 1994
Size and mechanics effects in surface-induced melting of nanoparticles Levitas, Valery I.; Samani, Kamran Nature Communications, Vol. 2, Issue 1 https://doi.org/10.1038/ncomms1275	journal	April 2011
Thermodynamically consistent phase field approach to dislocation evolution at small and large strains Levitas, Valery I.; Javanbakht, Mahdi Journal of the Mechanics and Physics of Solids, Vol. 82 https://doi.org/10.1016/j.jmps.2015.05.009	journal	September 2015
Measurement of Third‐Order Moduli of Silicon and Germanium McSkimin, H. J.; Andreatch, P. Journal of Applied Physics, Vol. 35, Issue 11 https://doi.org/10.1063/1.1713214	journal	November 1964
Phase-field theory for martensitic phase transformations at large strains Levitas, Valery I. International Journal of Plasticity, Vol. 49 https://doi.org/10.1016/j.ijplas.2013.03.002	journal	October 2013
Smooth Flow in Diamond: Atomistic Ductility and Electronic Conductivity Liu, Chang; Song, Xianqi; Li, Quan Physical Review Letters, Vol. 123, Issue 19 https://doi.org/10.1103/PhysRevLett.123.195504	journal	November 2019
Thermodynamically consistent and scale-dependent phase field approach for crack propagation allowing for surface stresses Levitas, Valery I.; Jafarzadeh, Hossein; Farrahi, Gholam Hossein International Journal of Plasticity, Vol. 111 https://doi.org/10.1016/j.ijplas.2018.07.005	journal	December 2018
Lattice instability during phase transformations under multiaxial stress: Modified transformation work criterion Levitas, Valery I.; Chen, Hao; Xiong, Liming Physical Review B, Vol. 96, Issue 5 https://doi.org/10.1103/PhysRevB.96.054118	journal	August 2017
Modified Broyden’s method for accelerating convergence in self-consistent calculations Johnson, D. D. Physical Review B, Vol. 38, Issue 18 https://doi.org/10.1103/PhysRevB.38.12807	journal	December 1988
Lattice instability approach to the problem of high-pressure solid-state amorphization Brazhkin, V. V.; Lyapin, A. G. High Pressure Research, Vol. 15, Issue 1 https://doi.org/10.1080/08957959608240457	journal	January 1996
First-Principles Calculation of Third-Order Elastic Constants via Numerical Differentiation of the Second Piola-Kirchhoff Stress Tensor Cao, Tengfei; Cuffari, David; Bongiorno, Angelo Physical Review Letters, Vol. 121, Issue 21 https://doi.org/10.1103/PhysRevLett.121.216001	journal	November 2018
Ab initio calculations of pressure-dependence of high-order elastic constants using finite deformations approach Mosyagin, I.; Lugovskoy, A. V.; Krasilnikov, O. M. Computer Physics Communications, Vol. 220 https://doi.org/10.1016/j.cpc.2017.06.008	journal	November 2017

Similar Records

Fifth-degree elastic energy for predictive continuum stress-strain relations and elastic instabilities under large strain and complex loading in silicon

Other · Mon Jul 20 00:00:00 EDT 2020 · OSTI ID:1644704

Levitas, Valery; Johnson, Duane; Zarkevich, Nikolai

Lattice Instability during Solid-Solid Structural Transformations under a General Applied Stress Tensor: Example of Si I → Si II with Metallization

Journal Article · Wed Oct 17 00:00:00 EDT 2018 · Physical Review Letters · OSTI ID:1644704

Zarkevich, Nikolai A.; Chen, Hao; Levitas, Valery I.; +1 more

Lattice instability during phase transformations under multiaxial stress: Modified transformation work criterion

Journal Article · Tue Aug 29 00:00:00 EDT 2017 · Physical Review B · OSTI ID:1644704

Levitas, Valery I.; Chen, Hao; Xiong, Liming

Related Subjects

36 MATERIALS SCIENCE
Atomistic models
Mechanical properties

Title: Fifth-degree elastic energy for predictive continuum stress–strain relations and elastic instabilities under large strain and complex loading in silicon

Citation Formats

References (63)

Similar Records

Related Subjects