近年發現，即使在低溫下，面心立方（FCC）系列高熵合金（HEA）仍顯示出高強度和高延展性，顛覆了常規合金的概念。但是，到目前為止，還沒有足夠的參考資料可以提供它們在HEA中優異的機械性能和晶格扭曲之間的明確關聯。因此，我們進行了幾種由1、2、3和5種原子類型組成的FCC金屬研究，包括Ni，NiW，FeCrNi，CoNiCrFeMn和Lennard-Jones（LJ）系統，有系統地研究晶格扭曲對彈性各向異性及交叉滑移活動上肢影響，並透過分子動力學/靜態模擬（MD / MS）進行探討。結果發現，在彈性區域中，經過精心設計的LJ模型表明，理論上晶格畸變會增強FCC晶體中的彈性各向異性，但對於HEA這類多組成系統中，因電子密度的不一致性嚴重，使晶格扭曲對彈性異向性的影響變得不顯著。NiW的稀固溶合金以及FeCrNi和CoNiCrFeMn的等原子合金也證實了這一結論。另一方面，在塑性區域中，當變形程度達到一定程度時，FCC系統的交叉滑動過程中將存在多平面劈裂螺旋差排（MSS）。我們發現，僅因原子尺寸失配而導致的幾何畸變才能使MSS發揮作用。通過對這些MD仿真的比較，我們可以知道，MSS的交叉滑動比單平面分裂螺旋差排（SSS）容易得多。此外，我們的研究為交叉滑動機制的解釋提供了額外的支持，並解釋在低疊差能的情況下，HEA在臨場TEM之觀察。

The face-centered cubic (FCC) series of high entropy alloys (HEAs) have been found to exhibit both high strength and high ductility even under cryogenic-temperature, subverting the concept of conventional alloys. However, there is no sufficient reference so far that it can provide a clear correlation between their superior mechanical properties and lattice distortion in HEAs. Therefore, we conduct several FCC metals composed of 1, 2 3, and 5 atomic types, including Ni, NiW, FeCrNi, CoNiCrFeMn, and Lennard-Jones (LJ) systems to systematically investigate the lattice distortion effect on elastic anisotropy, and cross-slip activity by molecular dynamics/static simulations (MD/MS). As a result, in the elastic region, the well-designed LJ model demonstrates that the lattice distortion theoretically will enhance elastic anisotropy in the FCC crystal, but for HEAs, the electron density inconsistency in multicomponent systems will be more dominant than the lattice distortion effect. This conclusion is also confirmed in dilute solid-solution alloys of NiW, and equiatomic alloys of FeCrNi and CoNiCrFeMn. On the other hand, in the plastic region, as the degree of distortion reaches a certain level, Multi-plane Splitting Screw (MSS) will exist in the cross-slip process for FCC systems. We find that just the geometric distortion resulting from the atomic size misfit will be able to make the MSS work. Through the comparison of these MD simulations, we can know that the MSS is much easier to cross-slip than Single-plane Splitting Screw (SSS). Besides, our research provides additional support for the cross-slip mechanism to explain the observation of in-situ TEM in HEAs with low stacking fault energy.

Abstract i
摘要 iii
Acknowledgments v
List of Tables ix
List of Figures xi
Chapter 1: Introduction and Motivation 1
Chapter 2: Background and Literature Review of High Entropy Alloys 7
2.1 The introduction of HEAs 7
2.1.1 The origin of HEAs 7
2.1.2 Four core effects of HEAs 10
2.1.2.1 High configurational entropy 10
2.1.2.2 Sluggish diffusion 13
2.1.2.3 Severe lattice distortion 14
2.1.2.4 Cocktail effect 15
2.1.3 Special properties and applications 16
2.2 Analysis of lattice distortion effects on mechanical properties 20
2.2.1 Atomic size difference parameter 21
2.2.2 Experiments (X-ray and Neutron diffraction/scattering) 22
2.2.3 Simulations (Density Functional Theory, Molecular Dynamics) 24
2.3 Elastic properties 28
2.3.1 Polycrystalline elastic parameters (E, v, and G) 28
2.3.2 Single-crystal elastic constants (C11, C12, and C44) 30
2.4 Deformation mechanisms and behavior 35
2.4.1 TWIP and TRIP mechanisms 35
2.4.2 Cross-slip activity in CrCoNi-based HEAs 40
2.4.3 Local concentration fluctuation effects on dislocation behavior 48
Chapter 3: Background of Molecular Dynamics Simulation 52
3.1 The equations of motion 52
3.2 Time scale 53
3.3 Potential function 54
3.3.1 Pair potential function 54
3.3.2 Multi-body potential function 56
3.4 Truncated distance 57
3.5 Neighbor list 57
3.6 Periodic boundary 59
3.7 Temperature control 60
Chapter 4: Simulation Methodology 63
4.1 Selection and assumption of potential 63
4.2 Measurement of lattice distortion 65
4.2.1 Atomic size difference (δ) 65
4.2.2 von Mises atomic shear strain (η) 65
4.2.3 Radial distribution function (RDF) 67
4.3 Elastic anisotropy 67
4.3.1 Setup of the simulation model to calculate Young’s modulus 67
4.3.2 Setup of the simulation model to calculate Poisson's ratio 68
4.4 Cross-slip activities 69
4.4.1 Molecular statics (MS) for activation energy of cross-slip 69
4.4.2 The internal stress of Escaig and Schmid 72
4.4.3 Molecular dynamics (MD) for SSS and MSS 73
4.5 The software of calculating and analysis 74
Chapter 5: Results, Discussions, and Conclusions 75
5.1 Degree of lattice distortion 75
5.2 Lattice distortion effect on elastic anisotropy 78
5.2.1 Young's modulus 78
5.2.2 Poisson's ratio 85
5.2.3 Influence of elements on the overall Young's modulus and anisotropy 90
5.2.4 Conclusions 98
5.3 Lattice distortion effect on cross-slip activity 99
5.3.1 Peierls stress (τp) 99
5.3.2 MEP calculations for the activation energy of cross-slip 101
5.3.3 Multi-plane Splitting Screw (MSS) 106
5.3.4 Internal Schmid and Escaig stress 110
5.3.5 Comparison of MD calculations for SSS and MSS in CoNiCrFeMn 117
5.3.6 Conclusions 122
References 125

[1] D.B. Miracle, O.N. Senkov, A critical review of high entropy alloys and related concepts, Acta Mater., 122 (2017) 448-511.
[2] M.C. Gao, J.-W. Yeh, P.K. Liaw, Y. Zhang, High-Entropy Alloys, (2016).
[3] Y. Zhang, T.T. Zuo, Z. Tang, M.C. Gao, K.A. Dahmen, P.K. Liaw, Z.P. Lu, Microstructures and properties of high-entropy alloys, Prog. Mater. Sci., 61 (2014) 1-93.
[4] X.Z. Lim, Mixed-up metals make for stronger, tougher, stretchier alloys, Nature, 533 (2016) 306-307.
[5] J.W. Yeh, S.K. Chen, S.J. Lin, J.Y. Gan, T.S. Chin, T.T. Shun, C.H. Tsau, S.Y. Chang, Nanostructured High-Entropy Alloys with Multiple Principal Elements: Novel Alloy Design Concepts and Outcomes, Adv. Eng. Mater., 6 (2004) 299-303.
[6] B. Gludovatz, A. Hohenwarter, D. Catoor, E.H. Chang, E.P. George, R.O. Ritchie, A fracture-resistant high-entropy alloy for cryogenic applications, Science, 345 (2014) 1153-1158.
[7] K.G.P, Z. Li, Y. Deng, D. Raabe, C.C. Tasan, Metastable high-entropy dual-phase alloys overcome the strength-ductility trade-off, Nature, 534 (2016) 227-230.
[8] W.L.S. Huang, S. Lu, F. Tian, J. Shen, E. Holmström, L. Vitos, Temperature dependent stacking fault energy of FeCrCoNiMn high entropy alloy, Scripta Mater., 108 (2015) 44-47.
[9] Z.J. Zhang, M.M. Mao, J. Wang, B. Gludovatz, Z. Zhang, S.X. Mao, E.P. George, Q. Yu, R.O. Ritchie, Nanoscale origins of the damage tolerance of the high-entropy alloy CrMnFeCoNi, Nat. Commun., 6 (2015) 10143.
[10] J.W. Yeh, Alloy Design Strategies and Future Trends in High-Entropy Alloys, JOM, 65 (2013) 1759-1771.
[11] S. Huang, F. Tian, L. Vitos, Elasticity of high-entropy alloys from ab initio theory, J. Mater. Res., 33 (2018) 2938-2953.
[12] Y.X. L. Zhang, J. Han, D.J. Srolovitz, The effect of randomness on the strength of high-entropy alloys, Acta Mater., 166 (2019) 424-434.
[13] S.I. Rao, C. Woodward, T.A. Parthasarathy, O. Senkov, Atomistic simulations of dislocations in a model BCC multicomponent concentrated solid solution alloy, Acta Mater., 134 (2017) 311-320.
[14] C. Varvenne, A. Luque, W.A. Curtin, Theory of strengthening in fcc high entropy alloys, Acta Mater., 118 (2016) 164-176.
[15] C. Varvenne, G.P.M. Leyson, M. Ghazisaeidi, W.A. Curtin, Solute strengthening in random alloys, Acta Mater., 124 (2017) 660-683.
[16] S.I. Rao, C. Woodward, T.A. Parthasarathy, O. Senkov, Atomistic simulations of dislocation behavior in a model FCC multicomponent concentrated solid solution alloy, Acta Mater., 134 (2017) 188-194.
[17] W.G. N€ohring, W.A. Curtin, Correlation of microdistortions with misfit volumes in High Entropy Alloys, Scripta Mater., 168 (2019) 119-123.
[18] G. Laplanche, P. Gadaud, C. Bärsch, K. Demtröder, C. Reinhart, J. Schreuer, E.P. George, Elastic moduli and thermal expansion coefficients of medium-entropy subsystems of the CrMnFeCoNi high-entropy alloy, J. Alloy. Compd., 746 (2018) 244-255.
[19] E.W. Huang, D. Yu, J.W. Yeh, C. Lee, K. An, S.Y. Tu, A study of lattice elasticity from low entropy metals to medium and high entropy alloys, Scripta Mater., 101 (2015) 32-35.
[20] L.Y. Tian, G. Wang, J.S. Harris, D.L. Irving, J. Zhao, L. Vitos, Alloying effect on the elastic properties of refractory high-entropy alloys, Mater. Des., 114 (2017) 243-252.
[21] H. Zhang, X. Sun, S. Lu, Z. Dong, X. Ding, Y. Wang, L. Vitos, Elastic properties of Al CrMnFeCoNi (0 ≤ x ≤ 5) high-entropy alloys from ab initio theory, Acta Mater., 155 (2018) 12-22.
[22] X. Li, D.L. Irving, L. Vitos, First-principles investigation of the micromechanical properties of fcc-hcp polymorphic high-entropy alloys, Sci. Rep., 8 (2018) 11196.
[23] T. Teramoto, K. Yamada, R. Ito, K. Tanaka, Monocrystalline elastic constants and their temperature dependences for equi-atomic Cr-Mn-Fe-Co-Ni high-entropy alloy with the face-centered cubic structure, J. Alloy. Compd., 777 (2019) 1313-1318.
[24] B. Feng, M. Widom, Elastic stability and lattice distortion of refractory high entropy alloys, Chem. Phys., 210 (2018) 309-314.
[25] J.G. Berryman, Long-wave elastic anisotropy in transversely isotropic media, Explor. Geophys., 44 (1979) 896-917.
[26] L. Thomsen, Weak elastic anisotropy, Explor. Geophys., 51 (1986) 1954-1966.
[27] I. Tsvankin, Anisotropic parameters and P-wave velocity for orthorhombic media, Explor. Geophys., 62 (1997) 1292-1309.
[28] H.-R. Wenk, I. Lonardelli, H. Franz, K. Nihei, S. Nakagawa, Preferred orientation and elastic anisotropy of illite-rich shale, Explor. Geophys., 72 (2007) 69–75.
[29] J. Li, K.J.V. Vliet, T. Zhu, S. Yip, S. Suresh, Atomistic mechanisms governing elastic limit and incipient plasticity in crystals, Nature, 418 (2002) 307-310.
[30] J. Brugue, J. Igne-Mullol, J. Casademunt, F. Sagues, Probing elastic anisotropy from defect dynamics in Langmuir monolayers, Phys. Rev. Lett., 100 (2008) 037801.
[31] V. TVERGAARD, J.W. HUTCHINSON, Microcracking in Ceramics Induced by Thermal Expansion or Elastic Anisotropy, J Am Ceram Soc., 71 (1988) 157-166.
[32] Q.X. Pei, C. Lu, Y.Y. Wang, Effect of elastic anisotropy on the elastic fields and vertical alignment of quantum dots, Journal of Applied Physics, 93 (2003) 1487-1492.
[33] M.H. Yoo, ON THE THEORY OF ANOMALOUS YIELD BEHAVIOR OF Ni3AI-- EFFECT OF ELASTIC ANISOTROPY, Scripta Mater., 20 (1986) 915-920.
[34] J.M. Rickman, The role of elastic anisotropy in poroelastic transport, Journal of Applied Physics, 106 (2009).
[35] B. Taylor, H.J. Maris, C. Elbaum, Focusing of Phonons in Crystalline Solids due to Elastic Anisotropy, Phys. Rev. B, 3 (1971) 1462-1472.
[36] C.H. TURNER, A. CHANDRAN, R.M.V. PIDAPARTI, The Anisotropy of Osteonal Bone and Its Ultrastructural Implications, Bone, 17 (1995) 85-89.
[37] P. Lloveras, T. Castan, M. Porta, A. Planes, A. Saxena, Influence of elastic anisotropy on structural nanoscale textures, Phys. Rev. Lett., 100 (2008) 165707.
[38] S. Groh, B. Devincre, L.P. Kubin, A. Roos, F. Feyel, J.-L. Chaboche, Dislocations and elastic anisotropy in heteroepitaxial metallic thin films, Philos. Mag. Lett., 83 (2010) 303-313.
[39] C.M. Kube, Elastic anisotropy of crystals, AIP Advances, 6 (2016) 095209.
[40] F. Tian, L.K. Varga, N. Chen, L. Delczeg, L. Vitos, Ab initioinvestigation of high-entropy alloys of 3delements, Phys. Rev. B, 87 (2013) 075144.
[41] S. Gangireddya, L. Kaimiao, B. Gwalani, R. Mishra, Microstructural dependence of strain rate sensitivity in thermomechanically processed Al0.1CoCrFeNi high entropy alloy, Mater. Sci. Eng. A, 727 (2018) 148-159.
[42] R. Agarwal, R. Sonkusare, S.R. Jha, N.P.Gurao, K. Biswas, N. Nayan, Understanding the deformation behavior of CoCuFeMnNi high entropy alloy by investigating mechanical properties of binary ternary and quaternary alloy subsets, Mater. Des., 157 (2018) 539-550.
[43] J. Li, B. Gao, S. Tang, B. Liu, Y. Liu, Y. Wang, J. Wang, High temperature deformation behavior of carbon-containing FeCoCrNiMn high entropy alloy, J. Alloy. Compd., 747 (2018) 571-579.
[44] Z. Wang, W. Lu, D. Raabe, Z. Li, On the mechanism of extraordinary strain hardening in an interstitial high-entropy alloy under cryogenic conditions, J. Alloy. Compd., 781 (2019) 734-743.
[45] Q. Wang, Y. Lu, Q. Yu, Z. Zhang, The Exceptional Strong Face-centered Cubic Phase and Semi-coherent Phase Boundary in a Eutectic Dual-phase High Entropy Alloy AlCoCrFeNi, Sci. Rep., 8 (2018) 14910.
[46] Q. Ding, X. Fu, D. Chen, H. Bei, B. Gludovatz, J. Li, Z. Zhang, E.P. George, Q. Yu, T. Zhu, R.O. Ritchie, Real-time nanoscale observation of deformation mechanisms in CrCoNi-based medium- to high-entropy alloys at cryogenic temperatures, Materials Today, 25 (2019) 21-27.
[47] J. Liu, C. Chen, Y. Xu, S. Wu, G. Wang, H. Wang, Y. Fang, L. Meng, Deformation twinning behaviors of the low stacking fault energy high-entropy alloy: An in-situ TEM study, Scripta Mater., 137 (2017) 9-12.
[48] R.L. Fleischer, Cross slip of extended dislocations, Acta Metall., 7 (1959) 134-135.
[49] Friedel, J. 1957. “Regarding Seeger's paper on work hardening”. In Dislocations and Mechanical Properties of Crystals, Edited by: Fisher, JC, Johnston, WG, Thomson, T and Vreeland Jr, T. 330New York: John Wiley.
[50] Escaig, B. 1968. “Cross-slipping process in the f.c.c. structure”. In Proceedings of the Battelle Colloquium in Dislocation Dynamics, Edited by: Rosenfield, AR, Hahn, GT, Bement Jr, AL and Jaffee, RI. 655New York: McGraw-Hill.
[51] J. Miao, C.E. Slone, T.M. Smith, C. Niu, H. Bei, M. Ghazisaeidi, G.M. Pharr, M.J. Mills, The evolution of the deformation substructure in a Ni-Co-Cr equiatomic solid solution alloy, Acta Mater., 132 (2017) 35-48.
[52] H. FUJITAT, S. UEDA, STACKING FAULTS AND F.C.C. (y) --f H.C.P. (E) TRANSFORMATION IN 18/8-TYPE STAINLESS STEEL*, Acta Metall., 20 (1972) 759-767.
[53] S. MAHAJAN, M.L. GREEN, D. Brasen, A model for the FCC→HCP transformation, its applications, and experimental evidence, MTA, 8 (1977) 283-293.
[54] W. Püschl, Models for dislocation cross-slip in close-packed crystal structures: a critical review, Prog. Mater. Sci., 47 (2002) 415-461.
[55] P.J. Jackson, Dislocation modelling of shear in f.c.c. crystals, Prog. Mater. Sci., 29 (1985) 139-175.
[56] M. Sudmanns, M. Stricker, D. Weygand, T. Hochrainer, K. Schulz, Dislocation multiplication by cross-slip and glissile reaction in a dislocation based continuum formulation of crystal plasticity, Journal of the Mechanics and Physics of Solids, 132 (2019).
[57] S. Suresh, FatigueofMaterials,seconded.CambridgeUniversityPress., (2004).
[58] K. Kang, J. Yin, W. Cai, Stress dependence of cross slip energy barrier for face-centered cubic nickel, Journal of the Mechanics and Physics of Solids, 62 (2014) 181-193.
[59] S. Saroukhani, D.H. Warner, Investigating dislocation motion through a field of solutes with atomistic simulations and reaction rate theory, Acta Mater., 128 (2017) 77-86.
[60] F.X. Zhang, S. Zhao, K. Jin, H. Xue, G. Velisa, H. Bei, R. Huang, J.Y.P. Ko, D.C. Pagan, J.C. Neuefeind, W.J. Weber, Y. Zhang, Local Structure and Short-Range Order in a NiCoCr Solid Solution Alloy, Phys. Rev. Lett., 118 (2017) 205501.
[61] W.G. N€ohring, W.A. Curtin, Dislocation cross-slip in fcc solid solution alloys, Acta Mater., 128 (2017) 135-148.
[62] W.G. N€ohring, W.A. Curtin, Cross-slip of long dislocations in FCC solid solutions, Acta Mater., 158 (2018) 95-117.
[63] D.B. Miracle, A structural model for metallic glasses, Nat. Mater., 3 (2004) 697-702.
[64] L. Verlet, Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules, Phys. Rev., 159 (1967) 98-103.
[65] H. Hansen-Goos, R. Roth, A new generalization of the Carnahan-Starling equation of state to additive mixtures of hard spheres, J Chem Phys, 124 (2006) 154506.
[66] C. Suryanarayana, Mechanical alloying and milling, Prog. Mater. Sci., 46 (2001) 1-184.
[67] A. Inoue, T. Zhang, S.G. Kim, T. Masumoto, Mg–Cu–Y amorphous alloys with high mechanical strengths produced by a metallic mold casting method, Mater. Trans., 32 (1991) 609-616.
[68] A. Inoue, A. Takeuchi, Recent Progress in Bulk Glassy Alloys, Mater. Trans., 43 (2002) 1892-1906.
[69] Y. Yokoyama, Y. Akeno, T. Yamasaki, P.K. Liaw, R.A. Buchanan, A. Inoue, Evolution of Mechanical Properties of Cast Zr50Cu40Al10 Glassy Alloys by Structural Relaxation, Mater. Trans., 46 (2005) 2755-2761.
[70] A. Inoue, High Strength Bulk Amorphous Alloys with Low Critical Cooling Rates, Mater. Trans., 36 (1995) 866-875.
[71] W.L. Johnson, Bulk Glass-Forming Metallic Alloys: Science and Technology, MRS Bull., 24 (2013) 42-56.
[72] A. Inoue, Bulk amorphous and nanocrystalline alloys with high functional properties, Mater. Sci. Eng., 304 (2001) 1-10.
[73] H.Y. Diao, R. Feng, K.A. Dahmen, P.K. Liaw, Fundamental deformation behavior in high-entropy alloys: An overview, Current Opinion in Solid State and Materials Science, 21 (2017) 252-266.
[74] J. Gild, Y. Zhang, T. Harrington, S. Jiang, T. Hu, M.C. Quinn, W.M. Mellor, N. Zhou, K. Vecchio, J. Luo, High-Entropy Metal Diborides: A New Class of High-Entropy Materials and a New Type of Ultrahigh Temperature Ceramics, Sci. Rep., 6 (2016) 37946.
[75] X. Yan, L. Constantin, Y. Lu, J.-F. Silvain, M. Nastasi, B. Cui, (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)C high-entropy ceramics with low thermal conductivity, Journal of the American Ceramic Society, 101 (2018) 4486-4491.
[76] C.-F. Wu, D.E.S. Arifin, C.-A. Wang, J. Ruan, Coalescence and split of high-entropy polymer lamellar cocrystals, Polymer, 138 (2018) 188-202.
[77] K.Y. Tsai, M.H. Tsai, J.W. Yeh, Sluggish diffusion in Co–Cr–Fe–Mn–Ni high-entropy alloys, Acta Mater., 61 (2013) 4887-4897.
[78] S. Ranganathan, Alloyed pleasures: Multimetallic cocktails, CURRENT SCIENCE, 85 (2003) 1404-1406.
[79] O.N. Senkov, G.B. Wilks, J.M. Scott, D.B. Miracle, Mechanical properties of Nb25Mo25Ta25W25 and V20Nb20Mo20Ta20W20 refractory high entropy alloys, Intermetallics, 19 (2011) 698-706.
[80] O.N. Senkov, J.M. Scott, S.V. Senkova, F. Meisenkothen, D.B. Miracle, C.F. Woodward, Microstructure and elevated temperature properties of a refractory TaNbHfZrTi alloy, J. Mater. Sci., 47 (2012) 4062-4074.
[81] Y. Yuan, Y. Wu, X. Tong, H. Zhang, H. Wang, X.J. Liu, L. Ma, H.L. Suo, Z.P. Lu, Rare-earth high-entropy alloys with giant magnetocaloric effect, Acta Mater., 125 (2017) 481-489.
[82] Y. Lu, Y. Dong, S. Guo, L. Jiang, H. Kang, T. Wang, B. Wen, Z. Wang, J. Jie, Z. Cao, H. Ruan, T. Li, A promising new class of high-temperature alloys: eutectic high-entropy alloys, Sci. Rep., 4 (2014) 6200.
[83] Y. Lu, X. Gao, L. Jiang, Z. Chen, T. Wang, J. Jie, H. Kang, Y. Zhang, S. Guo, H. Ruan, Y. Zhao, Z. Cao, T. Li, Directly cast bulk eutectic and near-eutectic high entropy alloys with balanced strength and ductility in a wide temperature range, Acta Mater., 124 (2017) 143-150.
[84] C. Lu, K. Jin, L.K. Béland, F. Zhang, T. Yang, L. Qiao, Y. Zhang, H. Bei, H.M. Christen, R.E. Stoller, L. Wang, Direct Observation of Defect Range and Evolution in Ion-Irradiated Single Crystalline Ni and Ni Binary Alloys, Sci. Rep., 6 (2016) 19994.
[85] C. Lu, T.Yang, K. Jin, N. Gao, P. Xiu, Y. Zhang, F. Gao, H. Bei, W.J. Weber, K. Sun, Y. Dong, L. Wang, Radiation-induced segregation on defect clusters in single-phase concentrated solid-solution alloys, Acta Mater., 127 (2017) 98-107.
[86] T. Yang, S. Xia, S. Liu, C. Wang, S. Liu, Y. Fang, Y. Zhang, J. Xue, S. Yan, Y. Wang, Precipitation behavior of AlxCoCrFeNi high entropy alloys under ion irradiation, Sci. Rep., 6 (2016) 32146.
[87] O.N. Senkov, S.V. Senkova, D.M. Dimiduk, C. Woodward, D.B. Miracle, Oxidation behavior of a refractory NbCrMo0.5Ta0.5TiZr alloy, J. Mater. Sci., 47 (2012) 6522-6534.
[88] V. Chaudhary, R.V. Ramanujan, Magnetocaloric Properties of Fe-Ni-Cr Nanoparticles for Active Cooling, Sci. Rep., 6 (2016) 35156.
[89] M. Sahlberg, D. Karlsson, C. Zlotea, U. Jansson, Superior hydrogen storage in high entropy alloys, Sci. Rep., 6 (2016) 36770.
[90] S.I. Rao, C. Varvenne, C. Woodward, T.A. Parthasarathy, D. Miracle, O.N. Senkov, W.A. Curtin, Atomistic simulations of dislocations in a model BCC multicomponent concentrated solid solution alloy, Acta Mater., 125 (2017) 311-320.
[91] Y. Zhang, Y.J. Zhou, J.P. Lin, G.L. Chen, P.K. Liaw, Solid-Solution Phase Formation Rules for Multi-component Alloys, Adv. Eng. Mater., 10 (2008) 534-538.
[92] O.N. Senkov, G.B.Wilks, D.B. Miracle, C.P. Chuang, P.K. Liaw, Refractory high-entropy alloys, Intermetallics, 18 (2010) 1758-1765.
[93] S. Guo, Q. Hu, C. Ng, C.T. Liu, More than entropy in high-entropy alloys: Forming solid solutions or amorphous phase, Intermetallics, 41 (2013) 96-103.
[94] Z. Wang, Y. Huang, Y. Yang, J. Wang, C.T. Liu, Atomic-size effect and solid solubility of multicomponent alloys, Scripta Mater., 94 (2015) 28-31.
[95] Y.F. Ye, C.T. Liu, Y. Yang, A geometric model for intrinsic residual strain and phase stability in high entropy alloys, Acta Mater., 94 (2015) 152-161.
[96] Y.F. Ye, X.D. Liu, S. Wang, C.T. Liu, Y. Yang, The general effect of atomic size misfit on glass formation in conventional and high-entropy alloys, Intermetallics, 78 (2016) 30-41.
[97] L.R. Owen, E.J. Pickering, H.Y. Playford, H.J. Stone, M.G. Tucker, N.G. Jones, An assessment of the lattice strain in the CrMnFeCoNi high-entropy alloy, Acta Mater., 122 (2017) 11-18.
[98] Y. Wu, W.H. Liu, X.L. Wang, D. Ma, A.D. Stoica, T.G. Nieh, Z.B. He, Z.P. Lu, In-situ neutron diffraction study of deformation behavior of a multi-component high-entropy alloy, Appl. Phys. Lett., 104 (2014).
[99] W. GUO, W. DMOWSKI, J.-Y. NOH, P. RACK, P.K. LIAW, T. EGAMI, Local Atomic Structure of a High-Entropy Alloy: An X-Ray and Neutron Scattering Study, Metall. Mater. Trans. A, 44 (2012) 1994-1997.
[100] C.-C. Yen, G.-R.H., Y.-C. Tan, H.-W. Yeh, D.-J. Luo, K.-T. Hsieh, E.-W. Huang, J.-W. Yeh, S.-J. Lin, C.-C. Wang, C.-L. Kuo, S.-Y. Chang, Y.-C. Lo, Lattice distortion effect on elastic anisotropy of high entropy alloys, J. Alloy. Compd., 818 (2020) 152876.
[101] T. Ungár, Microstructural parameters from X-ray diffraction peak broadening, Scripta Mater., 51 (2004) 777-781.
[102] S. Guo, C. Ng, Z. Wang, C.T. Liu, Solid solutioning in equiatomic alloys: Limit set by topological instability, J. Alloy. Compd., 583 (2014) 410-413.
[103] L. Lilensten, J.-P. Couzini, L. Perriere, A. Hocini, C. Keller, G. Dirras, I. Guillot, Study of a bcc multi-principal element alloy: Tensile and simple shear properties and underlying deformation mechanisms, Acta Mater., 142 (2018) 131-141.
[104] T. Egami, M. Ojha, O. Khorgolkhuu, D.M. Nicholson, G.M. Stocks, Local Electronic Effects and Irradiation Resistance in High-Entropy Alloys, JOM, 67 (2015) 2345-2349.
[105] H.S. Oh, S.J. Kim, K. Odbadrakh, W.H. Ryu, K.N. Yoon, S. Mu, F. Kormann, Y. Ikeda, C.C. Tasan, D. Raabe, T. Egami, E.S. Park, Engineering atomic-level complexity in high-entropy and complex concentrated alloys, Nat. Commun., 10 (2019) 2090.
[106] I. Toda-Caraballo, J.S. Wróbel, S.L. Dudarev, D. Nguyen-Manh, P.E.J. Rivera-Díaz-del-Castillo, Interatomic spacing distribution in multicomponent alloys, Acta Mater., 97 (2015) 156-169.
[107] M. Widom, Modeling the structure and thermodynamics of high-entropy alloys, J. Mater. Res., 33 (2018) 2881-2898.
[108] H. Song, F. Tian, Q.M. Hu, L. Vitos, Y. Wang, J. Shen, N. Chen, Local lattice distortion in high-entropy alloys, Phys. Rev. Mater., 1 (2017) 023404.
[109] A.v.d. Walle, P. Tiwary, M.d. Jong, D.L. Olmsted, M. Asta, A. Dick, D. Shin, Y. Wang, L.Q. Chen, Z.K. Liu, Efficient stochastic generation of special quasirandom structures, CALPHAD, 42 (2013) 13-18.
[110] S. Zhao, Y.N. Osetsky, Y. Zhang, Atomic-scale dynamics of edge dislocations in Ni and concentrated solid solution NiFe alloys, J. Alloy. Compd., 701 (2017) 1003-1008.
[111] M.A. Meyers, A. Mishra, D.J. Benson, Mechanical properties of nanocrystalline materials, Prog. Mater. Sci., 51 (2006) 427-556.
[112] Z. Wu, W.A. Curtin, Mechanism and energetics of dislocation cross-slip in hcp metals, Proc. Natl. Acad. Sci. U. S. A., 113 (2016) 11137-11142.
[113] T.M. Smith, M.S. Hooshmand, B.D. Esser, F. Otto, D.W. McComb, E.P. George, M. Ghazisaeidi, M.J. Mills, Atomic-scale characterization and modeling of 60° dislocations in a high-entropy alloy, Acta Mater., 110 (2016) 352-363.
[114] Z. Wanga, J. Li, Q. Fang, B. Liu, L. Zhang, Investigation into nanoscratching mechanical response of AlCrCuFeNi high-entropy alloys using atomic simulations, Appl. Surf. Sci., 416 (2017) 470-481.
[115] A.M. Giwa, Z.H. Aitken, P.K. Liaw, Y.-W. Zhang, J.R. Greer, Effect of temperature on small-scale deformation of individual face-centered-cubic and body-centered-cubic phases of an Al0.7CoCrFeNi high-entropy alloy, Mater. Des., 191 (2020) 108611.
[116] I.A. Alhafez, C.J. Ruestes, E.M. Bringa, H.M. Urbassek, Nanoindentation into a high-entropy alloy – An atomistic study, J. Alloy. Compd., 803 (2019) 618-624.
[117] M.J. Demkowicz, Plurality of inherent states in equiatomic solid solutions, Phys. Rev. B, 95 (2017) 094108.
[118] J.H. Li, X.D. Dai, T.L. Wang, B.X. Liu, A binomial truncation function proposed for the second-moment approximation of tight-binding potential and application in the ternary Ni–Hf–Ti system, J. Phys.: Condens. Matter, 19 (2007).
[119] S. Zhao, J.H. Li, S.M. An, S.N. Li, B.X. Liu, Computational assisted design of the favored composition for metallic glass formation in a Ca–Mg–Cu system, RSC Adv., 7 (2017) 39082-39088.
[120] G. Bonny, N. Castin, D. Terentyev, Interatomic potential for studying ageing under irradiation in stainless steels: the FeNiCr model alloy, Model. Simul. Mater. Sci. Eng., 21 (2013) 1-15.
[121] S. Sengul, M. Celtek, U. Domekeli, Molecular dynamics simulations of glass formation and atomic structures in Zr60Cu20Fe20 ternary bulk metallic alloy, Vacuum, 136 (2017) 20-27.
[122] G. Bonny, R.C. Pasianot, N. Castin, L. Malerba, Ternary Fe–Cu–Ni many-body potential to model reactor pressure vessel steels: First validation by simulated thermal annealing, Philos. Mag., 89 (2009) 3531-3546.
[123] S.M. Foiles, M. I. Baskes, M.S. Daw, Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys, Phys. Rev. B, 33 (1986) 7983-7991.
[124] X.W. ZHOU, H.N.G. WADLEY, R.A. Johnsona, D.J. Larsonb, N. Tabatb, A. Cerezoc, A. K.Petford-Longc, G.D.W. Smithc, P.H. Cliftond, R.L. Martense, T.F. Kellye, ATOMIC SCALE STRUCTURE OF SPUTTERED METAL MULTILA, Acta Mater., 49 (2001) 4005–4015.
[125] M. Meraj, S. Pal, Deformation of Ni20W20Cu20Fe20Mo20high entropy alloy for tensile followed by compressive and compressive followed by tensile loading: A molecular dynamics simulation based study, IOP Conf. Ser., 115 (2016) 012019.
[126] G. Anand, R. Goodall, C.L. Freeman, Role of configurational entropy in body-centred cubic or face-centred cubic phase formation in high entropy alloys, Scripta Mater., 124 (2016) 90-94.
[127] A. Sharma, P. Singh, D.D. Johnson, P.K. Liaw, G. Balasubramanian, Atomistic clustering-ordering and high-strain deformation of an Al0.1CrCoFeNi high-entropy alloy, Sci. Rep., 6 (2016) 31028.
[128] L. Xie, P. Brault, A.-L. Thomann, X. Yang, Y. Zhang, G.Y. Shang, Molecular dynamics simulation of Al–Co–Cr–Cu–Fe–Ni high entropy alloy thin film growth, Intermetallics, 68 (2016) 78-86.
[129] L. Xie, P. Brault, A.L. Thomann, J.-M. Bauchire, AlCoCrCuFeNi high entropy alloy cluster growth and annealing on silicon: A classical molecular dynamics simulation study, Appl. Surf. Sci., 285 (2013) 810-816.
[130] F. Maresca, W.A. Curtin, Mechanistic origin of high strength in refractory BCC high entropy alloys up to 1900K, Acta Mater., 182 (2020) 235-249.
[131] W.-M. Choi, Y.H. Jo, S.S. Sohn, S. Lee, B.-J. Lee, Understanding the physical metallurgy of the CoCrFeMnNi high-entropy alloy: an atomistic simulation study, npj Computational Materials, 4 (2018) 1-9.
[132] S.F. Pugh, XCII. Relations between the elastic moduli and the plastic properties of polycrystalline pure metals, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 45 (2009) 823-843.
[133] K. Jin, Y.F. Gao, H. Bei, Intrinsic properties and strengthening mechanism of monocrystalline Ni-containing ternary concentrated solid solutions, Mater. Sci. Eng. A, 695 (2017) 74-79.
[134] Y.L. Hu, L.H. Bai, Y.G. Tong, D.Y. Deng, X.B. Liang, J. Zhang, Y.J. Li, Y.X. Chen, First-principle calculation investigation of NbMoTaW based refractory high entropy alloys, J. Alloy. Compd., 827 (2020).
[135] J.F.L. Nye, R.B., Physical Properties of Crystals: Their Representation by Tensors and Matrices; Clarendon Press: Oxford, UK, (1985).
[136] J.M. Zhang, Y. Zhang, K.W. Xu, V. Ji, Young's modulus surface and Poisson's ratio curve for cubic metals, J. Phys. Chem. Solids, 68 (2007) 503-510.
[137] C. ZENER, Contributions to the Theory of Beta-Phase Alloys, Phys. Rev., 71 (1947) 846-851.
[138] X. Li, D. Wei, L. Vitos, R. Lizarraga, Micro-mechanical properties of new alternative binders for cemented carbides: CoCrFeNiW high-entropy alloys, J. Alloy. Compd., 820 (2020) 153141.
[139] J. Li, Q.H. Fang, B. Liu, Y.W. Liua, Y. Liu, Mechanical behaviors of AlCrFeCuNi high-entropy alloys under uniaxial tension via molecular dynamics simulation, RSC Adv., 6 (2016) 76409-76419.
[140] J. Li, Q. Fang, B. Liu, Y.W. Liu, Y. Liu, Atomic-scale analysis of nanoindentation behavior of high-entropy alloy, Journal of Micromechanics and Molecular Physics, 01 (2016) 1650001.
[141] F. Otto, A. Dlouhy, C. Somsen, H. Bei, G. Eggeler, E.P. George, The influences of temperature and microstructure on the tensile properties of a CoCrFeMnNi high-entropy alloy, Acta Mater., 61 (2013) 5743-5755.
[142] B. Gludovatz, A. Hohenwarter, K.V.S. Thurston, H. Bei, Z. Wu, E.P. George, R.O. Ritchie, Exceptional damage-tolerance of a medium-entropy alloy CrCoNi at cryogenic temperatures, Nat. Commun., 7 (2016) 10602.
[143] A.H. B. Gludovatz, D. Catoor, E.H. Chang, E.P. George, R.O. Ritchie, A fracture-resistant high-entropy alloy for cryogenic applications, SCIENCE, 345 (2014) 1153-1158.
[144] Y. Deng, C.C. Tasan, K.G. Pradeep, H. Springer, A. Kostkaa, D. Raabea, Design of a twinning-induced plasticity high entropy alloy, Acta Mater., 94 (2015) 124-133.
[145] S. Liu, Y. Wei, The Gaussian distribution of lattice size and atomic level heterogeneity in high entropy alloys, Extreme Mechanics Letters, 11 (2017) 84-88.
[146] Y.H. Zhang, Y. Zhuang, A. Hu, J.J.Kai, C.T.Liu, The origin of negative stacking fault energies and nano-twin formation in face-centered cubic high entropy alloys, Scripta Mater., 130 (2017) 96-99.
[147] C. Jin, Y. Xiang, G. Lu, Dislocation cross-slip mechanisms in aluminum, Philos. Mag., 91 (2011) 4109-4125.
[148] R. Hill, R. Ellis, Deformation Twinning: Proceedings of a Conference Sponsored by the Metallurgical Society, American Institute of Mining, Metallurgical and Petroleum Engineers, New York : Gordon and Breach, (1964).
[149] B.E. Warren, A dislocation model for twinning in f.c.c. metals, Acta Mater., 11 (1963) 996-998.
[150] H. Fujita, T. Mori, A Formation Mechanism of Mechanical Twins in F.C.C. Metals, Scripta Metallurgica, 9 (1975) 631-636.
[151] S. Mahajan, G.Y. Chin, COMMENTS ON DEFORMATION TWINNING IN SILVER- AND COPPER-ALLOY CRYSTALS, Scripta Metallurgica, 9 (1975) 815-817.
[152] S. Miura, J.-I. Takamura, N. Narita, Orientation dependence of flow stress for twinning in silver crystals, Trans. Jpn. Inst. Met., 9 (1968) 555-561.
[153] T.S. Byun, On the stress dependence of partial dislocation separation and deformation microstructure in austenitic stainless steels, Acta Mater., 51 (2003) 3063-3071.
[154] S.M. Copley, B.H. Keat, THE DEPENDENCE OF THE WIDTH OF A DISSOCIATED VELOCITY DISLOCATION, Acta Mater., 16 (1968) 227-231.
[155] K.P.D. Lagerloef, J. Castaingy, P. Pirouz, A.H. Heuer, Nucleation and growth of deformation twins: a perspective based on the double-cross-slip mechanism of deformation twinning, Philos. Mag. A, 82 (2002) 2841-2854.
[156] B.C.D. Cooman, Y. Estrin, S.K. Kim, Twinning-induced plasticity (TWIP) steels, Acta Mater., 142 (2018) 283-362.
[157] Q. Ding, Y. Zhang, X. Chen, X. Fu, D. Chen, S. Chen, L. Gu, F. Wei, H. Bei, Y. Gao, M. Wen, J. Li, Z. Zhang, T. Zhu, R.O. Ritchie, Q. Yu, Tuning element distribution, structure and properties by composition in high-entropy alloys, Nature, 574 (2019) 223-227.
[158] C. Varvenne, A. Luque, W.G. Nohring, W.A. Curtin, Average-atom interatomic potential for random alloys, Phys. Rev. B, 93 (2016).
[159] F. Maresca, W.A. Curtin, Theory of screw dislocation strengthening in random BCC alloys from dilute to “High-Entropy” alloys, Acta Mater., 182 (2020) 144-162.
[160] W.F.V. Gunsteren, H.J.C. Berendsen, A Leap-frog Algorithm for Stochastic Dynamics, Molecular Simulation, 1 (2007) 173-185.
[161] J.E. Jones, On the determination of molecular fields. —II. From the equation of state of a gas, Proc. R. Soc. London, 106 (1924) 463-477.
[162] M.S. Daw, M.I. Baskes, Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals, Phys. Rev. B, 29 (1984) 6443-6453.
[163] M.S. Daw, S.M. Foiles, M.I. Baskes, The embedded-atom method: a review of theory and applications, NORTH-HOLLAND AMSTERDAM-LONDON NEW YORK-TOKYO, (1993).
[164] M.W. Finnis, J.E. Sinclair, A simple empirical N-body potential for transition metals, Philos. Mag. A, 50 (2006) 45-55.
[165] L. Verlet, Computer "Experiments" on Classical Fluids. II. Equilibrium Correlation Functions, Phys. Rev., 165 (1968) 201-214.
[166] W. Mattson, B.M. Rice, Near-neighbor calculations using a modified cell-linked list method, Comput. Phys. Commun., 119 (1999) 135-148.
[167] V.A. Kuzkin, On angular momentum balance for particle systems with periodic boundary conditions, J. Appl. Math. Mech., 95 (2014) 1290-1295.
[168] W.G. Hoover, B.L. Holian, Kinetic moments method for the canonical ensemble distribution, Phys. Lett. A, 211 (1996) 253-257.
[169] H.A. Posch, V.G. Hoover, F.J. Vesely, Canonical dynamics of the Nose oscillator: Stability, order, and chaos, Phys. Rev. A, 33 (1986) 4253-4265.
[170] Y. Mishin, D. Farkas, M.J. Mehl, D.A. Papaconstantopoulos, Papaconstantopoulos, Interatomic potentials for monoatomic metals from experimental data and ab initio calculations, Phys. Rev. B, 59 (1999) 3393-3407.
[171] X.W. Zhou, R.A. Johnson, H.N.G. Wadley, Misfit-energy-increasing dislocations in vapor-deposited CoFe/NiFe multilayers, Phys. Rev. B, 69 (2004).
[172] H. Hansen-Goosa, R. Roth, A new generalization of the Carnahan-Starling equation of state to additive mixtures of hard spheres, J Chem Phys, 124 (2006) 154506.
[173] H. Heinz, R.A. Vaia, B.L. Farmer, R.R. Naik, Accurate Simulation of Surfaces and Interfaces of Face-Centered Cubic Metals Using 12-6 and 9-6 Lennard-Jones Potentials, J. Phys. Chem., 112 (2008) 17281–17290.
[174] W.B. Pearson, The crystal chemistry and physics of metals and alloys, Wiley, 1972., 76 (1972) 1286.
[175] F. Shimizu, S. Ogata, J. Li, Theory of Shear Banding in Metallic Glasses and Molecular Dynamics Calculations, Mater. Trans., 48 (2007) 2923-2927.
[176] M.L. Falk, J.S. Langer, Dynamics of viscoplastic deformation in amorphous solids, Phys. Rev. E, 57 (1998) 7192-7205.
[177] M. Sprik, R.W. Impey, M.L. Klein, Second-order elastic constants for the Lennard-Jones solid, Phys. Rev. B, 29 (1984) 4368-4374.
[178] N.L. Okamoto, S. Fujimoto, Y. Kambara, M. Kawamura, Z.M. Chen, H. Matsunoshita, K. Tanaka, H. Inui, E.P. George, Size effect, critical resolved shear stress, stacking fault energy, and solid solution strengthening in the CrMnFeCoNi high-entropy alloy, Sci. Rep., 6 (2016) 35863.
[179] H.J.G. Mills, Quantum and thermal effects in H2 dissociative adsorption: Evaluation of free energy barriers in multidimensional quantum systems, Phys. Rev. Lett., 72 (1994) 1124-1127.
[180] H. Graeme, U.B. P., J. Hannes, A climbing image nudged elastic band method for finding saddle points and minimum energy paths, J. Chem. Phys., 113 (2000) 9901-9904.
[181] V.V.B. W. Cai, J. Chang, J. Li, S. Yip, Dislocation Core Effects on Mobility, (2004), 1-117.
[182] E. Oren, E. Yahel, G. Makov, Kinetics of dislocation cross-slip: A molecular dynamics study, Comp. Mater. Sci., 138 (2017) 246-254.
[183] S. PLIMPTON, Fast Parallel Algorithms for Short-Range Molecular Dynamics, J. Comput. Phys., 117 (1995) 1-19.
[184] A. Stukowski, Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool, Model. Simul. Mater. Sci. Eng., 18 (2010).
[185] A. Stukowski, K. Albe, Extracting dislocations and non-dislocation crystal defects from atomistic simulation data, Model. Simul. Mater. Sci. Eng., 18 (2010).
[186] J.D. Honeycutt, H.C. Andemen, Molecular Dynamics Study of Melting and Freezing of Small Lennard- Jones Clusters, J. Phys. Chem., 91 (1987) 4950-4963.
[187] F. Mouhat, F.-X. Coudert, Necessary and sufficient elastic stability conditions in various crystal systems, Phys. Rev. B, 90 (2014) 224104.
[188] M.G. Zuluaga, F.L. Dri, P.D. Zavattieri, R.J. Moon, Anisotropy Calculator - 3D Visualization Toolkit, (2014).
[189] A.R. Miedema, The electronegativity parameter for transition metals heat of formation and charge transfer in alloys, J. Less-Common Met., 32 (1973) 117–136.
[190] Y. Wu, W.H. Liu, X.L. Wang, D. Ma, A.D. Stoica, T.G. Nieh, Z.B. He, Z.P. Lu, In-situ neutron diffraction study of deformation behavior of a multi-component high-entropy alloy, Appl. Phys. Lett., 104 (2014) 051910.
[191] A.J. Zaddach, C. Niu, C.C. Koch, D.L. Irving, Mechanical Properties and Stacking Fault Energies of NiFeCrCoMn High-Entropy Alloy, JOM-US, 65 (2013) 1780-1789.
[192] F. Tian, L.K. Varga, J. Shen, L. Vitos, Calculating elastic constants in high-entropy alloys using the coherent potential approximation: Current issues and errors, Comp. Mater. Sci., 111 (2016) 350-358.
[193] H. Ge, H. Song, J. Shen, F. Tian, Effect of alloying on the thermal-elastic properties of 3d high-entropy alloys, Mater. Chem. Phys., 210 (2018) 320-326.
[194] J.M. Zhang, Y. Zhang, K.W. Xu, V. Ji, Young’s Modulus Surface and Poisson’s Ratio Curve for Orthorhombic Crystals, J. Chem. Crystallogr., 38 (2008) 733-741.
[195] F. MILSTEIN, J. MARSCHALL, STRUCTURAL BONDING CONTRIBUTIONS AND THE ELASTIC RESPONSE OF B.C.C. AND F.C.C. CRYSTALS, Acta Mater., 40 (1992) 1229-1235.
[196] K. KITAGAWA, M. UEDA, H. MIYAMOTO, THE NEGATIVE CONTRACTION RATIOS OF CUBIC TYPES OF CRYSTALS, Acta Mater., 28 (1980) 1505-1511.
[197] F. Milstein, K. Huang, Existence of a negative Poisson ratio in fcc crystals, Phys. Rev. B, 19 (1979) 2030-2033.
[198] K.W. Wojciechowski, Poisson’s ratio of anisotropic systems, CMST, 11 (2005) 73-79.
[199] Z.A.D. Lethbridge, R.I. Walton, A.S.H. Marmier, C.W. Smith, K.E. Evans, Elastic anisotropy and extreme Poisson’s ratios in single crystals, Acta Mater., 58 (2010) 6444-6451.
[200] G. Laplanche, P. Gadaud, O. Horst, F. Otto, G. Eggeler, E.P. George, Temperature dependencies of the elastic moduli and thermal expansion coefficient of an equiatomic, single-phase CoCrFeMnNi high-entropy alloy, J. Alloy. Compd., 799 (2019) 538-545.
[201] Z. Wu, H. Bei, F. Otto, G.M. Pharr, E.P. George, Recovery, recrystallization, grain growth and phase stability of a family of FCC-structured multi-component equiatomic solid solution alloys, Intermetallics, 46 (2014) 131-140.
[202] Z. Wu, H. Bei, G.M. Pharr, E.P. George, Temperature dependence of the mechanical properties of equiatomic solid solution alloys with face-centered cubic crystal structures, Acta Mater., 81 (2014) 428-441.
[203] W.T. Sanders, Peierls Stress for an Idealized Crystal Model, Phys. Rev., 128 (1962) 1540-1549.
[204] Y. Kamimura, K. Edagawa, A. M.Iskandarov, M. Osawa, Y. Umeno, S. Takeuchi, Peierls stresses estimated via the Peierls-Nabarro model using ab-initio γ-surface and their comparison with experiments, Acta Mater., 148 (2018) 355-362.
[205] S.I. Ranganathan, M. Ostoja-Starzewski, Universal elastic anisotropy index, Phys. Rev. Lett., 101 (2008) 055504.
[206] Y. S, S. X, I.J. Beyerlein, Ab initio-informed phase-field modeling of dislocation core structures in equal-molar CoNiRu multi-principal element alloys, Model. Simul. Mater. Sci. Eng., 27 (2019) 084001.
[207] P. Coulomb, Comment on graphs relating some property to stacking fault energy, Scripta Metallurgica, 15 (1981) 769-770.
[208] A. Malka-Markovitz, D. Mordehai, Cross-slip in face centred cubic metals: a general full stress-field dependent activation energy line-tension model, Philos. Mag. Lett., 99 (2019) 1460-1480.
[209] H. Liu, X. Zhou, D. Hu, J. Song, R. Wang, J. Mao, A new variational line tension model for accurate evaluation of the stress effect on cross-slip energy barrier in face-centered cubic metals, Scripta Mater., 166 (2019) 24-28.