Violation of the Cauchy–Born rule in multi-principal element alloys

Ghosh, Swarnava

doi:10.1063/5.0204091

Title: Violation of the Cauchy–Born rule in multi-principal element alloys

Journal Article · 23 April 2024 · Applied Physics Letters

DOI: https://doi.org/10.1063/5.0204091 · OSTI ID:2351050

^[1]

Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). National Center for Computational Sciences (NCCS)

Multi-principal element alloys are a novel class of materials that are formed by combining multiple elements in high concentrations and show exceptional properties compared to conventional alloys. These alloys have high configurational entropy due to inherent atomic disorder. The Cauchy–Born rule is a popular homogenization method for linking atomistic to continuum length scales. In this Letter, we use ab initio density functional theory calculations to report that the Cauchy–Born rule, which holds in conventional alloys in the absence of defects, is not valid in multi-principal element alloys. Further, the violation of the Cauchy–Born rule in these alloys is attributed to the presence of atomic disorder due to which the deformations are inhomogeneous. Our results also show the deviations in deformation are related to the magnitude of the stretch and shear by power laws.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 2351050

Journal Information:: Applied Physics Letters, Journal Name: Applied Physics Letters Journal Issue: 17 Vol. 124; ISSN 0003-6951

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (48)

Nanostructured High-Entropy Alloys with Multiple Principal Elements: Novel Alloy Design Concepts and Outcomes Yeh, J.-W.; Chen, S.-K.; Lin, S.-J. Advanced Engineering Materials, Vol. 6, Issue 5, p. 299-303 https://doi.org/10.1002/adem.200300567	journal	May 2004
High‐Entropy Oxides: Fundamental Aspects and Electrochemical Properties Sarkar, Abhishek; Wang, Qingsong; Schiele, Alexander Advanced Materials, Vol. 31, Issue 26 https://doi.org/10.1002/adma.201806236	journal	March 2019
On the material symmetry group of elastic crystals and the Born Rule Zanzotto, Giovanni Archive for Rational Mechanics and Analysis, Vol. 121, Issue 1 https://doi.org/10.1007/BF00375438	journal	January 1992
Cauchy–Born Rule and the Stability of Crystalline Solids: Static Problems E., Weinan; Ming, Pingbing Archive for Rational Mechanics and Analysis, Vol. 183, Issue 2 https://doi.org/10.1007/s00205-006-0031-7	journal	September 2006
Validity and Failure of the Cauchy-Born Hypothesis in a Two-Dimensional Mass-Spring Lattice Journal of Nonlinear Science, Vol. 12, Issue 5 https://doi.org/10.1007/s00332-002-0495-z	journal	October 2002
Higher order Cauchy–Born rule based multiscale cohesive zone model and prediction of fracture toughness of silicon thin films Urata, Shingo; Li, Shaofan International Journal of Fracture, Vol. 203, Issue 1-2 https://doi.org/10.1007/s10704-016-0147-1	journal	August 2016
Alloy Design Strategies and Future Trends in High-Entropy Alloys Yeh, Jien-Wei JOM, Vol. 65, Issue 12 https://doi.org/10.1007/s11837-013-0761-6	journal	October 2013
Exploiting Machine Learning in Multiscale Modelling of Materials Anand, G.; Ghosh, Swarnava; Zhang, Liwei Journal of The Institution of Engineers (India): Series D, Vol. 104, Issue 2 https://doi.org/10.1007/s40033-022-00424-z	journal	November 2022
Order Parameter Engineering for Random Systems Anand, G.; Ghosh, Swarnava; Eisenbach, Markus High Entropy Alloys & Materials, Vol. 1, Issue 2 https://doi.org/10.1007/s44210-023-00015-x	journal	May 2023
Nonlinear elasticity of diatomic crystals Ericksen, J. L. International Journal of Solids and Structures, Vol. 6, Issue 7 https://doi.org/10.1016/0020-7683(70)90006-5	journal	July 1970
Solute strengthening in random alloys Varvenne, C.; Leyson, G. P. M.; Ghazisaeidi, M. Acta Materialia, Vol. 124 https://doi.org/10.1016/j.actamat.2016.09.046	journal	February 2017
High entropy alloys: A focused review of mechanical properties and deformation mechanisms George, E. P.; Curtin, W. A.; Tasan, C. C. Acta Materialia, Vol. 188 https://doi.org/10.1016/j.actamat.2019.12.015	journal	April 2020
A bridging domain method for coupling continua with molecular dynamics Xiao, S. P.; Belytschko, T. Computer Methods in Applied Mechanics and Engineering, Vol. 193, Issue 17-20 https://doi.org/10.1016/j.cma.2003.12.053	journal	May 2004
Bridging scale methods for nanomechanics and materials Liu, Wing Kam; Park, Harold S.; Qian, Dong Computer Methods in Applied Mechanics and Engineering, Vol. 195, Issue 13-16 https://doi.org/10.1016/j.cma.2005.05.042	journal	February 2006
A Surface Cauchy-Born model for silicon nanostructures Park, Harold S.; Klein, Patrick A. Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issue 41-42 https://doi.org/10.1016/j.cma.2007.12.004	journal	July 2008
An investigation on the validity of Cauchy–Born hypothesis using Sutton-Chen many-body potential Khoei, A. R.; Qomi, M. J. Abdolhosseini; Kazemi, M. T. Computational Materials Science, Vol. 44, Issue 3 https://doi.org/10.1016/j.commatsci.2008.07.022	journal	January 2009
SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Extended systems Ghosh, Swarnava; Suryanarayana, Phanish Computer Physics Communications, Vol. 216 https://doi.org/10.1016/j.cpc.2017.02.019	journal	July 2017
Mechanical properties of single-walled carbon nanotubes based on higher order Cauchy–Born rule Guo, X.; Wang, J. B.; Zhang, H. W. International Journal of Solids and Structures, Vol. 43, Issue 5 https://doi.org/10.1016/j.ijsolstr.2005.05.049	journal	March 2006
Stability and size-dependency of Cauchy–Born hypothesis in three-dimensional applications Aghaei, A.; Abdolhosseini Qomi, M. J.; Kazemi, M. T. International Journal of Solids and Structures, Vol. 46, Issue 9 https://doi.org/10.1016/j.ijsolstr.2009.01.013	journal	May 2009
Spectral quadrature for the first principles study of crystal defects: Application to magnesium Ghosh, Swarnava; Bhattacharya, Kaushik Journal of Computational Physics, Vol. 456 https://doi.org/10.1016/j.jcp.2022.111035	journal	May 2022
High-entropy alloy: challenges and prospects Ye, Y. F.; Wang, Q.; Lu, J. Materials Today, Vol. 19, Issue 6 https://doi.org/10.1016/j.mattod.2015.11.026	journal	July 2016
Machine-learned prediction of the electronic fields in a crystal Teh, Ying Shi; Ghosh, Swarnava; Bhattacharya, Kaushik Mechanics of Materials, Vol. 163 https://doi.org/10.1016/j.mechmat.2021.104070	journal	December 2021
Electronic structure study regarding the influence of macroscopic deformations on the vacancy formation energy in aluminum Ghosh, Swarnava; Suryanarayana, Phanish Mechanics Research Communications, Vol. 99 https://doi.org/10.1016/j.mechrescom.2019.06.007	journal	July 2019
Microstructural development in equiatomic multicomponent alloys Cantor, B.; Chang, I. T. H.; Knight, P. Materials Science and Engineering: A, Vol. 375-377 https://doi.org/10.1016/j.msea.2003.10.257	journal	July 2004
A temperature-related boundary Cauchy–Born method for multi-scale modeling of silicon nano-structures Khoei, A. R.; DorMohammadi, H.; Aramoon, A. Physics Letters A, Vol. 378, Issue 5-6 https://doi.org/10.1016/j.physleta.2013.09.048	journal	January 2014
Microstructures and properties of high-entropy alloys Zhang, Yong; Zuo, Ting Ting; Tang, Zhi Progress in Materials Science, Vol. 61 https://doi.org/10.1016/j.pmatsci.2013.10.001	journal	April 2014
Influence of chemical disorder on energy dissipation and defect evolution in concentrated solid solution alloys Zhang, Yanwen; Stocks, G. Malcolm; Jin, Ke Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms9736	journal	October 2015
High-entropy alloys George, Easo P.; Raabe, Dierk; Ritchie, Robert O. Nature Reviews Materials, Vol. 4, Issue 8 https://doi.org/10.1038/s41578-019-0121-4	journal	June 2019
Short-range order and its impact on the CrCoNi medium-entropy alloy Zhang, Ruopeng; Zhao, Shiteng; Ding, Jun Nature, Vol. 581, Issue 7808 https://doi.org/10.1038/s41586-020-2275-z	journal	May 2020
Direct observation of chemical short-range order in a medium-entropy alloy Chen, Xuefei; Wang, Qi; Cheng, Zhiying Nature, Vol. 592, Issue 7856 https://doi.org/10.1038/s41586-021-03428-z	journal	April 2021
High-entropy Alloys with High Saturation Magnetization, Electrical Resistivity and Malleability Zhang, Yong; Zuo, TingTing; Cheng, YongQiang Scientific Reports, Vol. 3, Issue 1 https://doi.org/10.1038/srep01455	journal	March 2013
Thermoelectric high-entropy alloys with low lattice thermal conductivity Fan, Z.; Wang, H.; Wu, Y. RSC Advances, Vol. 6, Issue 57 https://doi.org/10.1039/C5RA28088E	journal	January 2016
Quasicontinuum analysis of defects in solids Tadmor, E. B.; Ortiz, M.; Phillips, R. Philosophical Magazine A, Vol. 73, Issue 6 https://doi.org/10.1080/01418619608243000	journal	June 1996
High-Entropy Alloys: A Critical Review Tsai, Ming-Hung; Yeh, Jien-Wei Materials Research Letters, Vol. 2, Issue 3 https://doi.org/10.1080/21663831.2014.912690	journal	April 2014
QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials Giannozzi, Paolo; Baroni, Stefano; Bonini, Nicola Journal of Physics: Condensed Matter, Vol. 21, Issue 39, Article No. 395502 https://doi.org/10.1088/0953-8984/21/39/395502	journal	September 2009
Atomistic/continuum coupling in computational materials science Curtin, W. A.; Miller, Ronald E. Modelling and Simulation in Materials Science and Engineering, Vol. 11, Issue 3 https://doi.org/10.1088/0965-0393/11/3/201	journal	April 2003
Studies of validity of the Cauchy–Born rule by direct comparison of continuum and atomistic modelling Steinmann, P.; Elizondo, A.; Sunyk, R. Modelling and Simulation in Materials Science and Engineering, Vol. 15, Issue 1 https://doi.org/10.1088/0965-0393/15/1/S21	journal	December 2006
Inhomogeneous Electron Gas Hohenberg, P.; Kohn, W. Physical Review, Vol. 136, Issue 3B, p. B864-B871 https://doi.org/10.1103/PhysRev.136.B864	journal	November 1964
Self-Consistent Equations Including Exchange and Correlation Effects Kohn, W.; Sham, L. J. Physical Review, Vol. 140, Issue 4A, p. A1133-A1138 https://doi.org/10.1103/PhysRev.140.A1133	journal	November 1965
Density-functional approximation for the correlation energy of the inhomogeneous electron gas Perdew, John P. Physical Review B, Vol. 33, Issue 12 https://doi.org/10.1103/PhysRevB.33.8822	journal	June 1986
Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation Perdew, John P.; Chevary, J. A.; Vosko, S. H. Physical Review B, Vol. 46, Issue 11 https://doi.org/10.1103/PhysRevB.46.6671	journal	September 1992
Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy-Born rule Arroyo, M.; Belytschko, T. Physical Review B, Vol. 69, Issue 11 https://doi.org/10.1103/PhysRevB.69.115415	journal	March 2004
Complex magnetism of Ho-Dy-Y-Gd-Tb hexagonal high-entropy alloy Lužnik, J.; Koželj, P.; Vrtnik, S. Physical Review B, Vol. 92, Issue 22 https://doi.org/10.1103/PhysRevB.92.224201	journal	December 2015
Discovery of a Superconducting High-Entropy Alloy Koželj, P.; Vrtnik, S.; Jelen, A. Physical Review Letters, Vol. 113, Issue 10 https://doi.org/10.1103/PhysRevLett.113.107001	journal	September 2014
A Method to Determine Material Length Scale Parameters in Elastic Strain Gradient Theory Song, Jingru; Wei, Yueguang Journal of Applied Mechanics, Vol. 87, Issue 3 https://doi.org/10.1115/1.4045523	journal	December 2019
On the Cauchy—Born Rule Ericksen, J. L. Mathematics and Mechanics of Solids, Vol. 13, Issue 3-4 https://doi.org/10.1177/1081286507086898	journal	May 2008
On Nonessential Descriptions of Crystal Multilattices Ericksen, J. L. Mathematics and Mechanics of Solids, Vol. 3, Issue 4 https://doi.org/10.1177/108128659800300401	journal	December 1998
Geometrically-Compatible Dislocation Pattern and Modeling of Crystal Plasticity in Body-Centered Cubic (BCC) Crystal at Micron Scale Xie, Yuxi; Li, Shaofan Computer Modeling in Engineering & Sciences, Vol. 129, Issue 3 https://doi.org/10.32604/cmes.2021.016756	journal	January 2021

Similar Records

Neural-network model for force prediction in multi-principal-element alloys

Journal Article · 2021 · Computational Materials Science · OSTI ID:1809238

Singh, R.; Singh, P.; Sharma, A.; +6 more

Towards violation of Born's rule: description of a simple experiment

Journal Article · 2011 · AIP Conference Proceedings · OSTI ID:21511512

Khrennikov, Andrei

Elastic behavior of binary and ternary refractory multi-principal-element alloys

Journal Article · 2022 · Materials & Design · OSTI ID:1878694

Feng, Rui; Kim, George; Yu, Dunji; +4 more

Related Subjects

36 MATERIALS SCIENCE
Atomistic simulations
Crystalline solids
Crystallography
Density functional theory
Mechanical properties
Quantum Espresso package

Title: Violation of the Cauchy–Born rule in multi-principal element alloys

Citation Formats

References (48)

Similar Records

Related Subjects