journal article·2024-06Open access

Exploring Multicomponent Phase Space to Discover New Materials

Brian Cantor

Abstract

Abstract Multicomponent phase space has been shown to consist of an enormous number of materials with different compositions, the vast majority of which have never been made or investigated, with great potential, therefore, for the discovery of exciting new materials with valuable properties. At the same time, however, the enormous size of multicomponent phase space makes it far from straightforward to identify suitable strategies for exploring the plethora of potential material compositions and difficult, therefore, to be successful in discovering desirable new materials. Unfortunately, all our knowhow and understanding has been developed for materials with relatively few components in relatively limited proportions, with most of our scientific theories relying essentially on linear assumptions of component dilution and independence that no longer apply in concentrated multicomponent materials. Trial and error, controlled substitution, parameterisation, thermodynamic modelling, atomistic modelling and machine learning techniques have all been employed as methods of exploring multicomponent phase space, with varying levels of success, but ultimately none of these techniques has proved capable of delivering consistent or guaranteed results. This paper provides an overview of the different techniques that have been used to explore multicomponent phase space, indicates their main advantages and disadvantages, and describes some of their successes and failures.
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Research context

OpenAlex topics: High Entropy Alloys Studies · Chalcogenide Semiconductor Thin Films · Shape Memory Alloy Transformations

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References (100+)

Show source-provided references
1. B. Cantor, The Fundamentals of Multicomponent High-entropy Materials. Oxford University Press, Oxford, 2024. in press10.1093/9780191986710.001.0001 ↗
2. B.S. Murty, J.W. Yeh, S. Ranganathan, and P.P. Bhattacharjee, High-entropy Alloys, 2nd edn. Elsevier, Amsterdam, 2019.
3. B. Cantor, Multicomponent High-entropy Cantor Alloys, Progress Mater. Sci., 2021, 120, p 100754.10.1016/j.pmatsci.2020.100754 ↗
4. B. Cantor. Local Nanostructures in multicomponent high-entropy materials, in High Entropy Alloys and Materials, 2024, in press.10.1007/s44210-024-00040-4 ↗
5. B. Cantor, I.T.H. Chang, P. Knight, and A.J.B. Vincent, Microstructural Development in Equiatomic Multicomponent Alloys, Mater. Sci. Eng., 2004, A375–377, p 213-218.10.1016/j.msea.2003.10.257 ↗
6. B. Cantor, Stable and Metastable Multicomponent Alloys, Annales de Chimie – Science des Matériaux, 2007, 32, p 245–256.10.3166/acsm.32.245-256 ↗
7. B. Cantor, Multicomponent and High Entropy Alloys, Entropy, 2014, 16, p 4749–4768.10.3390/e16094749 ↗
8. J.W. Yeh, S.K. Chen, S.J. Lin, J.Y. Gan, T.S. Chin, T.T. Shun, C.H. Tsau, and S.Y. Chang, Nanostructured High Entropy Alloys with Multiple Principal Elements: Novel Alloy Design Concepts and Outcomes, Adv. Eng. Mater., 2004, 6, p 299–303.10.1002/adem.200300567 ↗
9. P.K. Huang, J.W. Yeh, T.T. Shun, and C.K. Chen, Multi-Principal-Element Alloys with Improved Oxidation and Wear Resistance for Thermal Spray Coating, Adv. Eng. Mater., 2004, 6, p 74–78.10.1002/adem.200300507 ↗
10. J.W. Yeh, Recent Progress in High Entropy Alloys, Annales de Chimie - Science des Matériaux, 2006, 31, p 633–648.10.3166/acsm.31.633-648 ↗
11. K.B. Kim, P.J. Warren, and B. Cantor, Formation of Metallic Glasses in Novel (Ti33Zr33Hf33)100-x-y(Ni50Cu50)xAly Alloys, Mater. Trans., 2003, 44, p 411–413.10.2320/matertrans.44.411 ↗
12. K.B. Kim, P.J. Warren, and B. Cantor, Metallic Glass Formation in Multicomponent (Ti, Zr, Hf, Nb)-(Ni, Cu, Ag)-Al Alloys, J. Non-Cryst. Solids, 2003, 317, p 17–22.10.1016/S0022-3093(02)02002-1 ↗
13. K.B. Kim, P.J. Warren, and B. Cantor, Crystallization Behaviour of Novel (TiZrHf)100-x-y (NiCu)x Aly with x = 48-55, J. Metastab. Nanocryst. Mater., 2005, 24–25, p 657–660.
14. K.B. Kim, P.J. Warren, and B. Cantor, Glass-Forming Ability of Novel Multicomponent (Ti33Zr33Hf33)-(Ni50Cu50)-Al Alloys Developed by Equiatomic Substitution, Mater. Sci. Eng. A, 2004, 375, p 317–321.10.1016/j.msea.2003.10.114 ↗
15. C.M. Rost, E. Sachet, T. Borman, A. Moballegh, E.C. Dickey, D. Hou, J.L. Jones, S. Curtarolo, and J.P. Maria, Entropy-Stabilized Oxides, Nat. Commun., 2015, 6, p 8485.10.1038/ncomms9485 ↗
16. C. Suryanarayana, A. Inoue. Bulk Metallic Glasses. (CRC Press, Taylor and Francis, Boca Raton, 2018), ch 1-4, pp 1-170.
17. R.Z. Zhang, and M.J. Reece, Review of High Entropy Ceramics: Design, Synthesis, Structure and Properties, J. Mater. Chem. A, 2019, 7, p 22148–22162.10.1039/C9TA05698J ↗
18. A. Sarkar, B. Breitung, and H. Hahn, High Entropy Oxides: The Role of Entropy, Enthalpy and Synergy, Scr. Mater., 2020, 187, p 43–48.10.1016/j.scriptamat.2020.05.019 ↗
19. H. Xiang, Y. Xing, F.Z. Dai, H. Wang, L. Su, L. Miao, G. Zhang, Y. Wang, X. Qi, L. Yao, H. Wang, B. Zhao, J. Li, and Y. Zhou, High-entropy Ceramics: Present Status, Challenges, and A Look Forward, J. Adv. Ceram., 2021, 10, p 385–441.10.1007/s40145-021-0477-y ↗
20. Y. Zhang, Y.J. Zhou, J.P. Lin, G.L. Chen, and P.K. Liaw, Solid-Solution Phase Formation Rules for Multi-component Alloys, Adv. Eng. Mater., 2008, 10, p 534–538.10.1002/adem.200700240 ↗
21. X. Yang, and Y. Zhang, Prediction of High-Entropy Stabilized Solid-Solution in Multi-Component Alloys, Mater. Chem. Phys., 2012, 132, p 233–238.10.1016/j.matchemphys.2011.11.021 ↗
22. Y. Zhang, X. Yang, and P.K. Liaw, Alloy Design and Properties Optimization of High-Entropy Alloys, J. Met., 2012, 64, p 830–838.
23. S. Guo, Q. Hu, C. Ng, and C.T. Liu, More Than Entropy in High-Entropy Alloys: Forming Solid Solutions or Amorphous Phase, Intermetallics, 2013, 41, p 96–103.10.1016/j.intermet.2013.05.002 ↗
24. A. Takeuchi, K. Amiya, T. Wada, K. Yubuta, W. Zhanb, and A. Makino, Entropies in Alloy Design for High Entropy and Bulk Glassy Alloys, Entropy, 2013, 15, p 3810–3821.10.3390/e15093810 ↗
25. M.X. Ren, B.X. Li, and H.Z. Fu, Formation Condition of Solid Solution Type High-Entropy Alloy, Trans. Nonferrous Met. Soc. China (Engl. Edn.), 2013, 23, p 991–995.10.1016/S1003-6326(13)62557-1 ↗
26. M.G. Poletti, and L. Battezzati, Electronic and Thermodynamic Criteria for the Occurrence of High Entropy Alloys in Metallic Systems, Acta Mater., 2014, 75, p 297–306.10.1016/j.actamat.2014.04.033 ↗
27. G.A. Salishchev, M.A. Tikhonovsky, D.G. Shaysultanov, N.D. Stepanov, A.V. Kuznetsov, I.V. Kolodiy, A.S. Tortika, and O.N. Senkov, Effect of Mn and V on Structure and Mechanical Properties of High-Entropy Alloys Based on CoCr- FeNi System, J. Alloys Compd., 2014, 591, p 11–21.10.1016/j.jallcom.2013.12.210 ↗
28. N.S. Nong, J.C. Zhu, Y. Cao, X.W. Yang, Z.H. Lai, and Y. Liu, Stability and Structure Prediction of Cubic Phase in as Cast High Entropy Alloys, Mater. Sci. Technol., 2014, 30, p 363–369.10.1179/1743284713Y.0000000368 ↗
29. S. Guo, Phase Selection Rules for Cast High Entropy Alloys: An Overview, Mater. Sci. Technol., 2015, 31, p 1223–1230.10.1179/1743284715Y.0000000018 ↗
30. Z. Wang, Y. Huang, Y. Yang, J. Wang, and C.T. Liu, Atomic Size Effect and Solid Solubility of Multicomponent Alloys, Scr. Mater., 2015, 94, p 28–31.10.1016/j.scriptamat.2014.09.010 ↗
31. Y.F. Ye, Q. Wang, J. Lu, C.T. Liu, and Y. Yang, The Generalized Thermodynamic Rule for Phase Selection in Multicomponent Alloys, Intermetallics, 2015, 59, p 75–80.10.1016/j.intermet.2014.12.011 ↗
32. D.J.M. King, S.C. Middleburgh, A.G. Mc Gregor, and M.B. Cortie, Predicting the Formation and Stability of Single Phase High-Entropy Alloys, Acta Mater., 2016, 104, p 172–179.10.1016/j.actamat.2015.11.040 ↗
33. O.N. Senkov, and D.B. Miracle, A New Thermodynamic Parameter to Predict Formation of Solid Solutions or Intermetallic Phases in High Entropy Alloys, J. Alloy. Compd., 2016, 658, p 603–607.10.1016/j.jallcom.2015.10.279 ↗
34. I.T. Caraballo, and P.E.J. Rivera-Diaz-del-Castillo, A Criterion for the Formation of High Entropy Alloys Based on Lattice Distortion, Intermetallics, 2016, 71, p 76–87.10.1016/j.intermet.2015.12.011 ↗
35. D.B. Miracle, and O.N. Senkov, A Critical Review of High-Entropy Alloys and Related Concepts, Acta Mater., 2017, 122, p 448–511.10.1016/j.actamat.2016.08.081 ↗
36. V.K. Soni, S. Sanyal, K. Raja Rao, and S.K. Sinha, A Review on Phase Prediction in High Entropy Alloys, J. Mech. Eng. Sci., 2021, 235, p 6268–6286.10.1177/09544062211008935 ↗
37. M. Hillert, and M. Phase, equilibria, Phase Diagrams and Phase Transformations, 2nd edn. Cambridge University Press, Cambridge, 2008.
38. N.N. Greenwood, and A. Earnshaw, Chemistry of the Elements, 2nd edn. Butterworth-Heinemann, Oxford, 1997.
39. A.W. Weeber, Application of the Miedema Model to Formation Enthalpies and Crystallisation Temperatures of Amorphous Alloys, J. Phys. F, 1987, 17, p 809–813.10.1088/0305-4608/17/4/008 ↗
40. C. Li, Y. Yuan, F. Li, Q. Wei, and Y. Huang, Modification and Verification of Miedema Model for Predicting Thermodynamic Properties of Binary Precipitates in Multi-element Alloys, Phys. B Condens. Matter., 2022, 627, p 413540.10.1016/j.physb.2021.413540 ↗
41. D.R. Gaskell, and D.E. Laughlin, Introduction to the Thermodynamic of Materials, 6th edn. CRC Press, Boca Raton, 2017.
42. B. Cantor, The Equations of Materials. Oxford University Press, Oxford, 2020.10.1093/oso/9780198851875.001.0001 ↗
43. Z.H. Barber, Ed., Introduction to Materials Modelling Maney, London, 2005
44. F. Giustino, Materials Modelling Using Density Functional Theory. Oxford University Press, Oxford, 2014.
45. P. J. Hasnip. Advanced atomistic modelling, in Barber ZH (ref 81), chapter 3, pp 29-44.
46. L. Kaufman, and H. Bernstein, Computer Calculations of Phase Diagrams. Academic Press, New York, 1970.
47. N. Saunders, and A.P. Miodownik, Calphad: Calculation of Phase Diagrams: A Comprehensive Guide. Pergamon Elsevier, Oxford, 1998.
48. H.L. Lukas, S.G. Fries, and B. Sundman, Computational Thermodynamics: The Calphad Method. Cambridge University Press, Cambridge, 2007.10.1017/CBO9780511804137 ↗
49. K.C. Hsieh, C.F. Yu, W.T. Hsieh, W.R. Chiang, J.S. Ku, J.H. Lai, C.P. Tu, and C.C. Yang, The Microstructure and Phase Equilibrium of New High Performance High-Entropy Alloys, J. Alloy. Compd., 2009, 483, p 209–212.10.1016/j.jallcom.2008.08.118 ↗
50. C. Huang, Y. Zhang, J. Shen, and R. Vilar, Thermal Stability and Oxidation Resistance of Laser Clad TiVCrAlSi High Entropy Alloy Coatings on Ti-6Al-4V Alloy, Surf. Coat. Technol., 2011, 206, p 1389–1395.10.1016/j.surfcoat.2011.08.063 ↗
51. O.N. Senkov, F. Zhang, and J.D. Miller, Phase Composition of a CrMoNbTaTiZr High Entropy Alloy: Comparison of Experimental and Simulated Data, Entropy, 2013, 15, p 3796–3809.10.3390/e15093796 ↗
52. M.C. Gao, and D.E. Alman, Searching for Next Single-Phase High-Entropy Alloy Compositions, Entropy, 2013, 15, p 4504–4519.10.3390/e15104504 ↗
53. J.E. Saal, I.S. Berglund, J.T. Sebastian, P.K. Liaw, and G.B. Olson, Equilibrium High Entropy Alloy Phase Stability from Experiments and Thermodynamic Modeling, Scr. Mater., 2018, 146, p 5–8.10.1016/j.scriptamat.2017.10.027 ↗
54. T.T. Shun, and Y.C. Du, Microstructure and Tensile Behaviors of fcc Al0.3CoCrFeNi High Entropy Alloy, J. Alloys Compd., 2009, 479, p 157–160.10.1016/j.jallcom.2008.12.088 ↗
55. K.F. Kao, S.K. Chen, T.J. Chen, P.C. Chu, J.Y. Yeh, and S.J. Lin, Electrical, Magnetic and Hall Properties of AlxCoCrFeNi High-Entropy Alloys, J. Alloy. Compd., 2011, 509, p 1607–1614.10.1016/j.jallcom.2010.10.210 ↗
56. W.R. Wang, W.L. Wang, and J.W. Yeh, Phases, Microstructure and Mechanical Properties of AlxCoCrFeNi high-Entropy Alloys at Elevated Temperatures, J. Alloy. Compd., 2014, 589, p 143–152.10.1016/j.jallcom.2013.11.084 ↗
57. Q. Tang, Y. Huang, H. Cheng, X. Liao, T.G. Langdon, and P. Dai, The Effect of Grain Size on the Annealing-Induced Phase Transformation in an Al0.3CoCrFeNi High Entropy Alloy, Mater. Des., 2016, 105, p 381–385.10.1016/j.matdes.2016.05.079 ↗
58. F. He, Z. Wang, Q. Wu, J. Li, J. Wang, and C.T. Liu, Phase Separation of Metastable CoCrFeNi High Entropy Alloy at Intermediate Temperatures, Scr. Mater., 2017, 126, p 15–19.10.1016/j.scriptamat.2016.08.008 ↗
59. C. Zhang, and M.C. Gao, CALPHAD modelling of high-entropy alloys, in High Entropy Alloys: Fundamentals and Applications. M.C. Gao, J.W. Yeh, P.K. Liaw, and Y. Zhang, Eds., Springer, Berlin, 2016
60. C. Zhang, F. Zhang, H. Diao, M.C. Gao, Z. Tang, J.D. Poplawsky, and P.K. Liaw, Understanding Phase Stability of AlCoCrFeNi High Entropy Alloys, Mater. Des., 2016, 109, p 425–433.10.1016/j.matdes.2016.07.073 ↗
61. H.R. Sistla, J.W. Newkirk, and F. Liou, Effect of Al/Ni Ratio and Heat Treatment on Phase Transformations and Microstructure of AlxFeCoCrNi2x High Entropy Alloys, Mater. Des., 2015, 81, p 113–121.10.1016/j.matdes.2015.05.027 ↗
62. F. Otto, A. Dlouhý, K.G. Pradeep, M. Kubĕnovà, D. Raabe, G. Eggeler, and E.P. George, Decomposition of the Single-Phase High-Entropy Alloy CrMnFeCoNi After Prolonged Anneals at Intermediate Temprature, Acta Mater., 2016, 112, p 40–52.10.1016/j.actamat.2016.04.005 ↗
63. D. Ma, M. Yao, K.G. Pradeep, C.C. Tasan, H. Springer, and D. Raabe, Phase Stability of Non-equiatomic CoCrFeMnNi High Entropy Alloys, Acta Mater., 2015, 98, p 288–296.10.1016/j.actamat.2015.07.030 ↗
64. F. Otto, Y. Yang, H. Bei, and E.P. George, Relative Effects of Enthalpy and Entropy on the Phase Stability of Equiatomic High-Entropy Alloys, Acta Mater., 2013, 61, p 2628–2638.10.1016/j.actamat.2013.01.042 ↗
65. B. Zhang, M.C. Gao, Y. Zhang, S. Yang, and S.M. Guo, Senary Refractory High Entropy Alloy MoNbTaTiVW, Mater. Sci. Technol., 2015, 31, p 1207–1213.10.1179/1743284715Y.0000000031 ↗
66. R. Car, and M. Parrinello, Unified Approach for Molecular Dynamics and Density Functional Theory, Phys. Rev. Lett., 1985, 55, p 2471–2474.10.1103/PhysRevLett.55.2471 ↗
67. M. Born, and R. Oppenheimer, Zur Quantentheorie der Moleküle [On the quantum theory of molecules], Ann. Phys., 1927, 84, p 457–484.10.1002/andp.19273892002 ↗
68. P. Hohenberg, and W. Kohn, Inhomogeneous electron gas, Phys. Rev. B, 1964, 136, p 864–871.10.1103/PhysRev.136.B864 ↗
69. D. Hartree, The Wave Mechanics of an Atom with a Non-Coulomb Central Field, Proc. Camb. Philos. Soc., 1928, 24, p 89–110.10.1017/S0305004100011919 ↗
70. W. Kohn, and L. Sham, Self-consistent Equations Including Exchange and Correlation Effects, Phys. Rev. A, 1965, 140, p 1133–1138.10.1103/PhysRev.140.A1133 ↗
71. F. Bloch, Über die quantenmechanik der elektronen in kristalgittern, Zeitschrifft für Physik, 1928, 52, p 555–600.10.1007/BF01339455 ↗
72. V. Heine, The Pseudopotential Concept, Solid State Phys., 1970, 24, p 1–36.10.1016/S0081-1947(08)60069-7 ↗
73. S. Alavi. Molecular Simulations. (Wiley, Weinheim, 2020), ch 2, pp 5-3310.1002/9783527699452 ↗
74. A. Satoh, Introduction to the Practice of Molecular Simulation: Molecular Dynamics, Monte Carlo, Brownian Dynamics, Dissipative Particle Dynamics. Elsevier Science, Burlington, 2011.
75. F. Tian, A Review of Solid-Solution Models of High-Entropy Alloys Based on Ab Initio Calculations, Front. Mater., 2017, 4, p 36.10.3389/fmats.2017.00036 ↗
76. F. Tian, Y.Wang, D.L. Irving, L. Vitos. Applications of coherent potential approximations to HEAs, in High-Entropy Alloys: Fundamentals and Applications eds M. C. Gao, J. W. Yeh, P. K. Liaw, Y. Zhang. (Springer International, Switzerland, 2016), ch 9, pp 299-332.10.1007/978-3-319-27013-5_9 ↗
77. M. C. Gao, C. Niu, C. Jiang, D. L. Irving. Applications of special quasi-random structures to high-entropy alloys, in High-Entropy Alloys: Fundamentals and Applications eds M. C. Gao, J. W. Yeh, P. K. Liaw, Y.Zhang. (Springer International, Switzerland, 2016), ch 10, pp 333-368.10.1007/978-3-319-27013-5_10 ↗
78. D. Ma, B. Grabowski, F. Körmann, J. Neugebauer, and D. Raabe, Ab Initio Thermodynamics of the CoCrFeMnNi High Entropy Alloy: Importance of Entropy Contributions Beyond the Configurational One, Acta Mater., 2015, 100, p 90–97.10.1016/j.actamat.2015.08.050 ↗
79. X. Sun, H. Zhang, S. Lu, X. Ding, Y. Wang, and L. Vitos, Phase Selection Rule for Al-Doped CrMnFeCoNi High-Entropy Alloys from First Principles, Acta Mater., 2017, 140, p 366–374.10.1016/j.actamat.2017.08.045 ↗
80. J.Y. He, W.H. Liu, H. Wang, Y. Wu, X.J. Liu, T.G. Nieh, and Z.P. Lu, Effects of Al Addition on Structural Evolution and Tensile Properties of the FeCoNiCrMn High-Entropy Alloy System, Acta Mater., 2014, 62, p 105–113.10.1016/j.actamat.2013.09.037 ↗
81. X. Liu, P. Xu, J. Zhao, W. Lu, M. Li, and G. Wang, Material Machine Learning for Alloys: Applications, Challenges and Perspectives, J. Alloys Compd., 2022, 921, p 165984.10.1016/j.jallcom.2022.165984 ↗
82. A. Burkov. The Hundred Page Machine Learning Book. (Andriy Burkov, 2019).
83. S. Yang, and Y. Zhong, Ab Initio Modeling of fcc FeCoCrNi High Entropy Alloys with Full Composition Range, J. Phase Equilib. Diffus., 2021, 42, p 656–672.10.1007/s11669-021-00905-w ↗
84. F. Tian, L.K. Varga, N. Chen, J. Shen, and L. Vitos, Ab Initio Design of Elastically Isotropic TiZrNbMoVx High-Entropy Alloys, J. Alloy. Compd., 2014, 599, p 19–25.10.1016/j.jallcom.2014.01.237 ↗
85. S. Yang, G. Liu, and Y. Zhong, Revisit the VEC Criterion in High Entropy Alloys (HEAs) with High Throughput Ab Initio Calculations: A Case Study with AlCoCrFeNi System, J. Alloys Compd., 2022, 916, p 165477.10.1016/j.jallcom.2022.165477 ↗
86. S.W. McAlpine, J.V. Logan, and M.P. Short, Predicting Single Phase Stability and Segregation in the NbMoTaTi-(W, V) High Entropy Alloy System with the Vacancy Exchange Potential, Scr. Mater., 2021, 191, p 29–33.10.1016/j.scriptamat.2020.08.043 ↗
87. Q. Zhao, J. Li, Q. Fang, and H. Feng, Effect of Al Solute Concentration on Mechanical Properties of AlxFeCuCrNi High-Entropy Alloys: A First Principles Study, Physica B, 2019, 566, p 30–37.10.1016/j.physb.2019.04.025 ↗
88. C. Niu, A.J. Zaddach, C.C. Koch, and D.L. Irving, First Principles Exploration of Near-Equiatomic NiFeCrCo High Entropy Alloys, J. Alloy. Compd., 2016, 672, p 510–520.10.1016/j.jallcom.2016.02.108 ↗
89. H. Song, F. Tian, Q.M. Hu, L. Vitos, Y. Wang, J. Shen, and N. Chen, Local Lattice Distortion in High-Entropy Alloys, Phys. Rev. Mater., 2017, 1, p 023404.10.1103/PhysRevMaterials.1.023404 ↗
90. M. Karabin, W.R. Mondal, A. Östlin, W.G.D. Ho, V. Dobrosavljevic, K.M. Tam, H. Terletska, L. Chioncel, Y. Wang, and M. Eisenbach, Ab Initio Approaches to High-Entropy Alloys: A Comparison of CPA, SQS and Supercell Methods, J. Mater. Sci., 2022, 57, p 10677–10690.10.1007/s10853-022-07186-9 ↗
91. S.M. Chen, Z.J. Ma, S. Qiu, L.J. Zhang, S.Z. Zhang, R. Yang, and Q.M. Hu, Phase Decomposition and Strengthening in HfNbTaTiZr High Entropy Alloy from First-Principles Calculations, Acta Mater., 2022, 225, p 117582.10.1016/j.actamat.2021.117582 ↗
92. F. Biermair, V.I. Razumovskiy, and G. Ressel, Influence of Alloying on Thermodynamic Properties of AlCoCrFeNiTi High Entropy Alloys from DFT Calculations, Comput. Mater. Sci., 2022, 202, p 110952.10.1016/j.commatsci.2021.110952 ↗
93. S. San, Y. Tong, H. Bei, B. Kombaiah, Y. Zhang, and W.Y. Ching, First-Principles Calculation of Lattice Distortion in Four Single Phase High Entropy Alloys with Experimental Validation, Mater. Des., 2021, 209, p 110071.10.1016/j.matdes.2021.110071 ↗
94. S. Liu, P. Cao, D.Á. Lin, and F. Tian, Stability of L21 (NiM)2TiAl (M=Co, Fe) in High-Entropy Alloys, J. Alloy. Compd., 2018, 764, p 650–655.10.1016/j.jallcom.2018.06.113 ↗
95. S. Wang, S. Chen, Y. Jia, Z. Hu, H. Huang, Û. Yang, A. Dong, G. Zhu, D. Wang, D. Shu, F. Tian, Y. Dai, and B. Sun, Fcc-L12 Ordering Transformation in Equimolar FeCoNiV Multi-Principal Element Alloy, Mater. Des., 2019, 168, p 107648.10.1016/j.matdes.2019.107648 ↗
96. R. Ryitsev, V. Gaviko, S. Estemirova, E. Sterkhov, L. Cherepanova, D. Yagodin, N. Chtchelkatchev, N. Dubinin, and S. Uporov, Laves Formation in High Entropy Alloys, Metals, 2021, 11, p 1962.10.3390/met11121962 ↗
97. L. Qiao, Y. Liu, and J. Zhu, A Focused Review on Machine Learning Aided High-Throughput Methods in High Entropy Alloy, J. Alloys Compd., 2021, 877, p 160295.10.1016/j.jallcom.2021.160295 ↗
98. G.L.W. Hart, T. Mueller, C. Toher, and S. Curtarolo, Machine Learning for Alloys, Nat. Rev. Mater., 2021, 6, p 730–755.10.1038/s41578-021-00340-w ↗
99. P. Flach, Machine Learning: The Art and Science of Algorithms That Make Sense of Data. Cambridge University Press, Cambridge, 2012.10.1017/CBO9780511973000 ↗
100. S. Russell, P. Norvig. Artificial intelligence: a modern approach (4th edn). (Pearson Education, Harlow, 2022), section V: machine learning, pp 669-873.