Evaluation of Calphad Approach and Empirical Rules on the Phase Stability of Multi-principal Element Alloys
Source abstract
Abstract
The formation of single disordered solid solution phase in multi-principal element alloys (MPEAs) is crucial for the properties of the alloy, and thus several empirical rules have been proposed to predict the stability of disordered solid solution phase in MPEAs. Compared to these empirical rules, Calphad approach provides a more reliable and quantitative prediction. In the present work, we choose three model systems of Al x CoCrFeNi, CoCr x FeMnNi and Al x LiMgSnZn to evaluate these empirical rules by comparing with the Calphad calculated results. The Calphad calculated temperature-composition sections reveal the effect of composition on the phase formation under equilibrium condition. Corresponding diagrams along these sections illustrate parameter variations from empirical rules associated with alloy compositions and highlight predictions and limitations. The impact of the different sources of atomic size data is also discussed.
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Research context
OpenAlex topics: High Entropy Alloys Studies · High-Temperature Coating Behaviors · High Temperature Alloys and Creep
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References (61)
Show source-provided references
1. B. Cantor, I.T.H. Chang, P. Knight, and A.J.B. Vincent, Microstructural Development in Equiatomic Multicomponent Alloys, Mater. Sci. Eng. A, 2004, 375–377, p 213-21810.1016/j.msea.2003.10.257 ↗
2. 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(5), p 299-30310.1002/adem.200300567 ↗
3. Y. Zhang, T.T. Zuo, Z. Tang, M.C. Gao, K.A. Dahmen, P.K. Liaw, and Z.P. Lu, Microstructures and Properties of High-Entropy Alloys, Prog. Mater Sci., 2014, 61, p 1-9310.1016/j.pmatsci.2013.10.001 ↗
4. Z. Li, K.G. Pradeep, Y. Deng, D. Raabe, and C.C. Tasan, Metastable High-Entropy Dual-Phase Alloys Overcome the Strength–Ductility Trade-Off, Nature, 2016, 534(7606), p 227-23010.1038/nature17981 ↗
5. W.H. Liu, Z.P. Lu, J.Y. He, J.H. Luan, Z.J. Wang, B. Liu, Y. Liu, M.W. Chen, and C.T. Liu, Ductile CoCrFeNiMox High Entropy Alloys Strengthened by Hard Intermetallic Phases, Acta Mater., 2016, 116, p 332-34210.1016/j.actamat.2016.06.063 ↗
6. B. Schuh, F. Mendez-Martin, B. Völker, E.P. George, H. Clemens, R. Pippan, and A. Hohenwarter, Mechanical Properties, Microstructure and Thermal Stability of a Nanocrystalline CoCrFeMnNi High-Entropy Alloy After Severe Plastic Deformation, Acta Mater., 2015, 96, p 258-26810.1016/j.actamat.2015.06.025 ↗
7. D.B. Miracle and O.N. Senkov, A Critical Review of High Entropy Alloys and Related Concepts, Acta Mater., 2017, 122, p 448-51110.1016/j.actamat.2016.08.081 ↗
8. 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(6), p 534-53810.1002/adem.200700240 ↗
9. S. Guo, C. Ng, J. Lu, and C.T. Liu, Effect of Valence Electron Concentration on Stability of FCC or BCC Phase in High Entropy Alloys, J. Appl. Phys., 2011, 109(10), p 10350510.1063/1.3587228 ↗
10. X. Yang and Y. Zhang, Prediction of High-Entropy Stabilized Solid-Solution in Multi-component Alloys, Mater. Chem. Phys., 2012, 132(2–3), p 233-23810.1016/j.matchemphys.2011.11.021 ↗
11. O.N. Senkov and D.B. Miracle, A New Thermodynamic Parameter to Predict Formation of Solid Solution or Intermetallic Phases in High Entropy Alloys, J. Alloys Compd., 2016, 658, p 603-60710.1016/j.jallcom.2015.10.279 ↗
12. S. Guo and C.T. Liu, Phase Selection Rules for Complex Multi-component Alloys with Equiatomic or Close-to-Equiatomic Compositions, Chin. J. Nat., 2013, 35(2), p 85-96
13. Y. Zhang, Z.P. Lu, S.G. Ma, P.K. Liaw, Z. Tang, Y.Q. Cheng, and M.C. Gao, Guidelines in Predicting Phase Formation of High-Entropy Alloys, MRS Commun., 2014, 4(2), p 57-6210.1557/mrc.2014.11 ↗
14. Y. Zhang, X. Yang, and P.K. Liaw, Alloy Design and Properties Optimization of High-Entropy Alloys, JOM, 2012, 64(7), p 830-83810.1007/s11837-012-0366-5 ↗
15. 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 28-3110.1016/j.scriptamat.2014.09.010 ↗
16. X. Yang, S.Y. Chen, J.D. Cotton, and Y. Zhang, Phase Stability of Low-Density, Multiprincipal Component Alloys Containing Aluminum, Magnesium, and Lithium, JOM, 2014, 66(10), p 2009-202010.1007/s11837-014-1059-z ↗
17. M.C. Troparevsky, J.R. Morris, P.R.C. Kent, A.R. Lupini, and G.M. Stocks, Criteria for Predicting the Formation of Single-Phase High-Entropy Alloys, Phys. Rev. X, 2015, 5(1), p 011041
18. 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 75-8010.1016/j.intermet.2014.12.011 ↗
19. Y.F. Ye, Q. Wang, J. Lu, C.T. Liu, and Y. Yang, Design of High Entropy Alloys: A Single-Parameter Thermodynamic Rule, Scr. Mater., 2015, 104, p 53-5510.1016/j.scriptamat.2015.03.023 ↗
20. D.J.M. King, S.C. Middleburgh, A.G. McGregor, and M.B. Cortie, Predicting the Formation and Stability of Single Phase High-Entropy Alloys, Acta Mater., 2016, 104, p 172-17910.1016/j.actamat.2015.11.040 ↗
21. A.K. Singh, N. Kumar, A. Dwivedi, and A. Subramaniam, A Geometrical Parameter for the Formation of Disordered Solid Solutions in Multi-component Alloys, Intermetallics, 2014, 53, p 112-11910.1016/j.intermet.2014.04.019 ↗
22. C. Zhang, F. Zhang, S. Chen, and W. Cao, Computational Thermodynamics Aided High-Entropy Alloy Design, JOM, 2012, 64(7), p 839-84510.1007/s11837-012-0365-6 ↗
23. F. Zhang, C. Zhang, S.L. Chen, J. Zhu, W.S. Cao, and U.R. Kattner, An Understanding of High Entropy Alloys from Phase Diagram Calculations, Calphad, 2014, 45, p 1-1010.1016/j.calphad.2013.10.006 ↗
24. C. Zhang, F. Zhang, H. Diao, M.C. Gao, Z. Tang, J.D. Poplawsky, and P.K. Liaw, Understanding Phase Stability of Al-Co-Cr-Fe-Ni High Entropy Alloys, Mater. Des., 2016, 109, p 425-43310.1016/j.matdes.2016.07.073 ↗
25. C. Zhang and M.C. Gao, CALPHAD Modeling of High-Entropy Alloys, High-Entropy Alloys: Fundamentals and Applications, M.C. Gao, J.-W. Yeh, P.K. Liaw, and Y. Zhang, Ed., Springer, Berlin, 2016, p 399-44410.1007/978-3-319-27013-5_12 ↗
26. M.C. Gao, Design of High-Entropy Alloys, High-Entropy Alloys: Fundamentals and Applications, M.C. Gao, J.-W. Yeh, P.K. Liaw, and Y. Zhang, Ed., Springer, Berlin, 2016, p 369-398
27. O.N. Senkov, J.D. Miller, D.B. Miracle, and C. Woodward, Accelerated Exploration of Multi-principal Element Alloys with Solid Solution Phases, Nat. Commun., 2015, 6, p 652910.1038/ncomms7529 ↗
28. O.N. Senkov, J.D. Miller, D.B. Miracle, and C. Woodward, Accelerated Exploration of Multi-principal Element Alloys for Structural Applications, Calphad, 2015, 50, p 32-4810.1016/j.calphad.2015.04.009 ↗
29. T.B. Massalski, Comments Concerning Some Features of Phase Diagrams and Phase Transformations, Mater. Trans., 2010, 51(4), p 583-59610.2320/matertrans.M2010012 ↗
30. U. Mizutani, Hume-Rothery Rules for Structurally Complex Alloy Phases, CRC Press, Taylor & Francis Group, London, 2011
31. H. Sato, M. Inukai, E.S. Zijlstra, and U. Mizutani, NFE Approximation for the e/a Determination for 3d-Transition Metal Elements and Their Intermetallic Compounds with Al and Zn, Philos. Mag., 2013, 93(22), p 3029-306110.1080/14786435.2013.793855 ↗
32. Y. Zhang, S. Guo, C.T. Liu, and X. Yang, Phase Formation Rules, High-Entropy Alloys: Fundamentals and Applications, M.C. Gao, J.-W. Yeh, P.K. Liaw, and Y. Zhang, Ed., Springer, Berlin, 2016, p 21-4910.1007/978-3-319-27013-5_2 ↗
33. G.A. Mansoori, N.F. Carnahan, K.E. Starling, and T.W. Leland, Equilibrium Thermodynamic Properties of the Mixture of Hard Spheres, J. Chem. Phys., 1971, 54(4), p 1523-152510.1063/1.1675048 ↗
34. F.R. Boer, R. Boom, W.C.M. Mattens, A.R. Miedema, and A.K. Niessen, Cohesion in metals: transition metal alloys, North-Holland, Amsterdam, 1988
35. A.R. Miedema, P.F. de Châtel, and F.R. de Boer, Cohesion in Alloys—Fundamentals of a Semi-empirical Model, Phys. B + C, 1980, 100(1), p 1-28
36. A. Takeuchi and A. Inoue, Classification of Bulk Metallic Glasses by Atomic Size Difference, Heat of Mixing and Period of Constituent Elements and Its Application to Characterization of the Main Alloying Element, Mater. Trans., 2005, 46(12), p 2817-282910.2320/matertrans.46.2817 ↗
37. M. Mihalkovic, M. Widom, Alloy Database. http://alloy.phys.cmu.edu/ . Accessed 22 May 2017
38. S. Curtarolo, W. Setyawan, S. Wang, J. Xue, K. Yang, R.H. Taylor, L.J. Nelson, G.L.W. Hart, S. Sanvito, M. Buongiorno-Nardelli, N. Mingo, and O. Levy, AFLOWLIB.ORG: A Distributed Materials Properties Repository from High-Throughput Ab Initio Calculations, Comput. Mater. Sci., 2012, 58, p 227-23510.1016/j.commatsci.2012.02.002 ↗
39. C. Wolverton, Open Quantum Materials Database. http://oqmd.org/ . Accessed 22 May 2017
40. J. Saal, S. Kirklin, M. Aykol, B. Meredig, and C. Wolverton, Materials Design and Discovery with High-Throughput Density Functional Theory: The Open Quantum Materials Database (OQMD), JOM, 2013, 65(11), p 1501-1509, in English10.1007/s11837-013-0755-4 ↗
41. S. Kirklin, J.E. Saal, B. Meredig, A. Thompson, J.W. Doak, M. Aykol, S. Rühl, and C. Wolverton, The Open Quantum Materials Database (OQMD): Assessing the Accuracy of DFT Formation Energies, Npj Comput. Mater., 2015, 1, p 1501010.1038/npjcompumats.2015.10 ↗
42. A. Jain, S.P. Ong, G. Hautier, W. Chen, W.D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, and K.A. Persson, Commentary: The Materials Project: A Materials Genome Approach to Accelerating Materials Innovation, APL Mater., 2013, 1(1), p 01100210.1063/1.4812323 ↗
43. W. Cao, S.L. Chen, F. Zhang, K. Wu, Y. Yang, Y.A. Chang, R. Schmid-Fetzer, and W.A. Oates, PANDAT Software with PanEngine, PanOptimizer and PanPrecipitation for Multi-component Phase Diagram Calculation and Materials Property Simulation, Calphad, 2009, 33(2), p 328-34210.1016/j.calphad.2008.08.004 ↗
44. R. Schmid-Fetzer, Progress in Thermodynamic Database Development for ICME of Mg Alloys, Magnesium Technology 2015, M.V. Manuel, A. Singh, M. Alderman, and N.R. Neelameggham, Ed., Wiley, London, 2015, p 283-28710.1007/978-3-319-48185-2_53 ↗
45. J.O. Andersson, T. Helander, L. Hoglund, P. Shi, and B. Sundman, Thermo-Calc & DICTRA, Computational Tools for Materials Science, Calphad, 2002, 26(2), p 273-31210.1016/S0364-5916(02)00037-8 ↗
46. M. Winter, The University of Sheffield and WebElements Ltd, UK. www.webelements.com . Accessed 22 May 2017
47. C. Kittel, Introduction to Solid State Physics, 8th ed., John Wiley & Sons Inc, New York, 2005
48. A.T. Dinsdale, SGTE Data for Pure Elements, Calphad, 1991, 15(4), p 317-42510.1016/0364-5916(91)90030-N ↗
49. A.L. Allred, Electronegativity Values from Thermochemical Data, J. Inorg. Nucl. Chem., 1961, 17(3–4), p 215-22110.1016/0022-1902(61)80142-5 ↗
50. D.J.M. King, A.G. McGregor, Alloy Search and Predict. www.alloyASAP.com . Accessed 22 May 2017
51. R. Li, J.C. Gao, and K. Fan, Microstructure and Mechanical Properties of MgMnAlZnCu High Entropy Alloy Cooling in Three Conditions, Mater. Sci. Forum, 2011, 686, p 235-24110.4028/www.scientific.net/MSF.686.235 ↗
52. K.M. Youssef, A.J. Zaddach, C. Niu, D.L. Irving, and C.C. Koch, A Novel Low-Density, High-Hardness, High-Entropy Alloy with Close-packed Single-Phase Nanocrystalline Structures, Mater. Res. Lett., 2015, 3(2), p 95-9910.1080/21663831.2014.985855 ↗
53. E. Doernberg, A. Kozlov, and R. Schmid-Fetzer, Experimental Investigation and Thermodynamic Calculation of Mg-Al-Sn Phase Equilibria and Solidification Microstructures, J. Phase Equilib. Diffus., 2007, 28(6), p 523-53510.1007/s11669-007-9203-x ↗
54. B.P. Alblas, W. van der Lugt, J. Dijkstra, and C. van Dijk, Structure of Liquid Li-Sn Alloys, J. Phys. F Met. Phys., 1984, 14(9), p 1995-200610.1088/0305-4608/14/9/006 ↗
55. D. Li, S. Fürtauer, H. Flandorfer, and D.M. Cupid, Thermodynamic Assessment and Experimental Investigation of the Li–Sn System, Calphad, 2014, 47, p 181-19510.1016/j.calphad.2014.09.002 ↗
56. O.N. Senkov and D.B. Miracle, Effect of the Atomic Size Distribution on Glass Forming Ability of Amorphous Metallic Alloys, Mater. Res. Bull., 2001, 36(12), p 2183-219810.1016/S0025-5408(01)00715-2 ↗
57. F.E. Wang, Bonding Theory for Metals and Alloys, Elsevier, Amsterdam, 2005
58. S. Fang, X. Xiao, L. Xia, W. Li, and Y. Dong, Relationship Between the Widths of Supercooled Liquid Regions and Bond Parameters of Mg-Based Bulk Metallic Glasses, J. Non-Cryst. Solids, 2003, 321(1–2), p 120-12510.1016/S0022-3093(03)00155-8 ↗
59. C. Kittel, Introduction to Solid State Physics, 6th ed., John Wiley & Sons Inc, London, 1980
60. XRD, International Tables for X-Ray Crystallography, Birmingham, England, 1968
61. J.L.C. Daams, P. Villars, and J.H.N. van Vucht, Atlas of Crystal Structure Types for Intermetallic Phases, ASM International, Materials Park, 1991