Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-26T02:39:24.992Z Has data issue: false hasContentIssue false
  • English
  • Français

Current and emerging practices of CALPHAD toward the development of high entropy alloys and complex concentrated alloys

Published online by Cambridge University Press:  04 June 2018

Stéphane Gorsse Open the ORCID record for Stéphane Gorsse [Opens in a new window]  and
Franck Tancret
Stéphane Gorsse*
Affiliation:
CNRS, University of Bordeaux, ICMCB, UMR 5026, Pessac F-33600, France; and Bordeaux INP, ENSCBP, Pessac F-33600, France
Franck Tancret
Affiliation:
Université de Nantes, Institut des Matériaux de Nantes – Jean Rouxel (IMN), CNRS UMR 6502, Polytech Nantes, BP 50609, Nantes 44306, France
*
a)Address all correspondence to this author. e-mail: [email protected]
Get access

Abstract

This work presents a critical review of the application of CALPHAD techniques in the development of high entropy alloys (HEAs) and complex concentrated alloys (CCAs). This assessment covers three major themes: thermodynamics of mixtures and stability, retrospective thermodynamics, and predictive thermodynamics. Based on statistical and thermodynamic analysis, we assess the concept of entropic stabilization. A brief description of the major accomplishments of the CALPHAD technique applied to explain the stability and microstructure of HEAs and CCAs is presented. We describe the role of CALPHAD and its integration with other design tools, such as physicochemical criteria, data mining, and optimization techniques, to accelerate the discovery of new materials. Finally, we recommend future efforts in the development of the next generation of HEAs and CCAs in connection with the design of their microstructures, with an emphasis on precipitation strengthening and twinning-induced or transformation-induced plasticity (TWIP, TRIP).

Type
Invited Review
Information
Journal of Materials Research , Volume 33 , Issue 19: Focus Issue: Fundamental Understanding and Applications of High-Entropy Alloys , 14 October 2018 , pp. 2899 - 2923
Copyright
Copyright © Materials Research Society 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This section of Journal of Materials Research is reserved for papers that are reviews of literature in a given area.

References

REFERENCES

Kaufman, L. and Cohen, M.: The martensitic transformation in the iron-nickel system. Trans. AIME J. Metals 206, 1393 (1956).Google Scholar
Kaufman, L. and Bernstein, H.: Computer Calculation of Phase Diagrams (Academic Press, New York, 1970).Google Scholar
Saunders, N. and Miodownik, A.P.: CALPHAD—A Comprehensive Guide (Pergamon Press, Oxford, 1998).Google Scholar
Kaufman, L. and Agren, J.: CALPHAD, first and second generation—Birth of the materials genome. Scripta Mater. 70, 3 (2014).CrossRefGoogle Scholar
Gibbs, J.W.: The Collected Works of J. Willard Gibbs (Yale University Press, New Haven, 1957).Google Scholar
Sundman, B., Jansson, B., and Andersson, J.O.: The thermo-calc databank system. Calphad 9, 153 (1985).CrossRefGoogle Scholar
Dinsdale, A.T., Hodson, S.M., and Taylor, J.R.: Proceedings of the 3rd International Conference on Molten Slags and Fluxes, 27–29 June (University of Strathclyde, Glasgow, 1988); p. 246.Google Scholar
Chen, S.L., Daniel, S., Zhang, F., Chang, Y.A., Yan, X.Y., Xie, F.Y., Schmid-Fetzer, R., and Oates, W.A.: The PANDAT software package and its applications. Calphad 26, 175 (2002).CrossRefGoogle Scholar
Cantor, B., Chang, I.T.H., Knight, P., and Vincent, A.J.B.: Microstructure development in equiatomic multicomponent alloys. Mater. Sci. Eng., A 375–377, 213 (2004).CrossRefGoogle Scholar
Yeh, J.W., Chen, S.K., Lin, S.J., Gan, J.Y., Chin, T.S., and Shun, T.T.: Nanostructured high-entropy alloys with multiple principal elements: Novel alloy design concepts and outcomes. Adv. Eng. Mater. 6, 299 (2004).CrossRefGoogle Scholar
Yeh, J-W.: Recent progress in high entropy alloys. Ann. Chimie Sci. Matériaux 31, 633 (2006).CrossRefGoogle Scholar
Pickering, E.J. and Jones, N.G.: High-entropy alloys: A critical assessment of their founding principles and future prospects. Int. Mater. Rev. 61, 183 (2016).CrossRefGoogle Scholar
Miracle, D.: Critical assessment 14: High entropy alloys and their development as structural materials. Mater. Sci. Eng. 31, 1142 (2015).Google Scholar
Varalakshmi, S., Kamaraj, M., and Murty, B.S.: Processing and properties of nanocrystalline CuNiCoZnAlTi high entropy alloys by mechanical alloying. Mater. Sci. Eng., A 527, 1027 (2010).CrossRefGoogle Scholar
Chen, H.Y., Tsai, C.W., Tung, C.C., Yeh, J.W., Shun, T.T., Yang, C.C., and Chen, S.K.: Effect of the substitution of Co by Mn in Al–Cr–Cu–Fe–Co–Ni high-entropy alloys. Ann. Chim. Sci. Mater 31, 685 (2006).CrossRefGoogle Scholar
Yang, X., Zhang, Y., and Liaw, P.K.: Microstructure and compressive properties of NbTiVTaAlx high entropy alloys. Procedia Eng. 36, 292 (2012).CrossRefGoogle Scholar
Zhang, Y., Zhou, Y.J., Lin, J.P., Chen, G.L., and Liaw, P.K.: Solid-solution phase formation rules for multi-component alloys. Adv. Eng. Mater. 10, 534 (2008).CrossRefGoogle Scholar
Li, C., Li, J.C., Zhao, M., and Jiang, Q.: Effect of alloying elements on microstructure and properties of multiprincipal elements high-entropy alloys. J. Alloys Compd. 475, 752 (2009).CrossRefGoogle Scholar
Feuerbacher, M., Heidelmann, M., and Thomas, C.: Hexagonal high-entropy alloys. Mater. Res. Lett. 3, 1 (2014).CrossRefGoogle Scholar
Takeuchi, A., Amiya, K., Wada, T., Yubuta, K., and Zhang, W.: Monocrystalline elastic constants of fcc-CrMnFeCoNi high entropy alloy. JOM 66, 1984 (2014).CrossRefGoogle Scholar
Guo, N.N., Wang, L., Luo, L.S., Li, X.Z., Su, Y.Q., Guo, J.J., and Fu, H.Z.: Microstructure and mechanical properties of refractory MoNbHfZrTi high-entropy alloy. Mater. Des. 81, 87 (2015).CrossRefGoogle Scholar
Senkov, O.N., Scotta, J.M., Senkova, S.V., Miracle, D.B., and Woodward, C.F.: Microstructure and room temperature properties of a high-entropy TaNbHfZrTi alloy. J. Alloys Compd. 509, 6043 (2011).CrossRefGoogle Scholar
Senkov, O.N., Wilks, G.B., Miracle, D.B., Chuang, C.P., and Liaw, P.K.: Refractory high-entropy alloys. Intermetallics 18, 1758 (2010).CrossRefGoogle Scholar
Zhang, Y., Yang, X., and Liaw, P.K.: Alloy design and properties optimization of high-entropy alloys. JOM 64, 830 (2012).CrossRefGoogle Scholar
Mroz, M.: Design et optimisation structurale d'un alliage a forte entropie (HEA) de la famille CoCrFeMnNi à haute résistance mécanique. Ph.D. thesis, École des Mines de Saint-Étienne, France, 2018.Google Scholar
Gorsse, S., Miracle, D.B., and Senkov, O.N.: Mapping the world of complex concentrated alloys. Acta Mater. 135, 177 (2017).CrossRefGoogle Scholar
Toda-Caraballo, I. and Rivera-Díaz-del-Castillo, P.E.J.: A criterion for the formation of high entropy alloys based on lattice distortion. Intermetallics 71, 76 (2016).CrossRefGoogle Scholar
Miracle, D. and Senkov, O.N.: A critical review of high entropy alloys and related concepts,. Acta Mater. 122, 448 (2017).CrossRefGoogle Scholar
Crepain, T.: Boosting crystal discovery in quaternary space: From brute force to intelligent screening. Master’s thesis, Universiteit Gent, Belgium, 2016.Google Scholar
Wang, W.Y., Wang, J., Lin, D., Zou, C., Wu, Y., Hu, Y., Shang, S-L., Darling, K.A., Wang, Y., and Hui, X.: Revealing the microstates of body-centered-cubic (bcc) equiatomic high entropy alloys. J. Phase Equilibria Diffusion 38, 404 (2017).CrossRefGoogle Scholar
Tong, Y., Velisa, G., Yang, T., Jin, K., Lu, C., Bei, H., Ko, J., Pagan, D., Huang, R., and Zhang, Y.: Probing local lattice distortion in medium-and high-entropy alloys. arXiv preprint arXiv:1707.07745 (2017).Google Scholar
Widom, M.: Entropy and diffuse scattering: Comparison of NbTiVZr and CrMoNbV. Metall. Mater. Trans. 47, 3306 (2016).CrossRefGoogle Scholar
Sundman, B. and Ågren, J.: A regular solution model for phases with several components and sublattices, suitable for computer applications. J. Phys. Chem. Solids 42, 297 (1981).CrossRefGoogle Scholar
Guggenheim, E.A.: Mixtures (Clarendon Press, Oxford, 1952).Google Scholar
Kikuchi, R.: A theory of cooperative phenomena. Phys. Rev. 81, 988 (1951).CrossRefGoogle Scholar
Ma, D., Grabowski, B., Körmann, F., Neugebauer, J., and Raabe, D.: Ab initio thermodynamics of the CoCrFeMnNi high entropy alloy: Importance of entropy contributions beyond the configurational one. Acta Mater. 100, 90 (2015).CrossRefGoogle Scholar
Zhang, F., Zhang, C., Chen, S.L., Zhu, J., Cao, W.S., and Kattner, U.R.: An understanding of high entropy alloys from phase diagram calculations. Calphad 45, 1 (2014).CrossRefGoogle Scholar
Morral, J.E. and Chen, S.: A regular solution model for a single-phase high entropy and enthalpy alloy. J. Phase Equilib. Diffus. 38, 382 (2017).CrossRefGoogle Scholar
Otto, F., Yang, Y., Bei, H., and George, E.P.: Relative effects of enthalpy and entropy on the phase stability of equiatomic high-entropy alloys. Acta Mater. 61, 2628 (2013).CrossRefGoogle Scholar
Schön, C.G., Duong, T., Wang, Y., and Arroyave, R.: Probing the entropy hypothesis in highly concentrated alloys. Acta Mater. 148, 263 (2018).CrossRefGoogle Scholar
Zhang, C., Zhang, F., Chen, S., and Cao, W.S.: Computational thermodynamics aided high-entropy alloy design. JOM 64, 839 (2012).CrossRefGoogle Scholar
Senkov, O.N., Zhang, F., and Miller, J.D.: Phase composition of a CrMo0.5NbTa0.5TiZr high entropy alloy: Comparison of experimental and simulated data. Entropy 15, 3796 (2013).CrossRefGoogle Scholar
Hsieh, K-C., Yu, C-F., Hsieh, W-T., Chiang, W-R., Ku, J.S., Lai, J-H., Tu, C-P., and Yang, C.C.: The microstructure and phase equilibrium of new high performance high entropy alloys. J. Alloy. Comp. 483, 209 (2009).CrossRefGoogle Scholar
Liu, S., Gao, M.C., Liaw, P.K., and Zhang, Y.: Microstructure and mechanical properties of AlxCrFeNiTi0.25 alloys. J. Alloy. Comp. 619, 610 (2013).CrossRefGoogle Scholar
Gao, M.C., Yeh, J-W., Liaw, P.K., and Zhang, Y.: High Entropy Alloys: Fundamentals and Applications (Spinger International Publishing, Basel, Switzerland, 2016).CrossRefGoogle Scholar
Scheil, E.: Bemerkungen zur schichtkristallbildung. Z. Metallkd. 34, 70 (1942).Google Scholar
Gulliver, G.: The quantitative effect of rapid cooling upon the constitution of binary alloys. J. Inst. Eng. 9, 120 (1913).Google Scholar
Zhang, B., Gao, M.C., Zhang, Y., Yang, S., and Guo, S.M.: Senary refractory high entropy alloy MoNbTaTiVW. Mater. Sci. Technol. 31, 1207 (2015).CrossRefGoogle Scholar
Zhang, B., Gao, M.C., Zhang, Y., and Guo, S.M.: Senary refractory high-entropy alloy CrxMoNbTaVW. Calphad 51, 193 (2015).CrossRefGoogle Scholar
Haase, C., Tang, F., Wilms, M.B., Weisheit, A., and Hallstedt, B.: Combining thermodynamic modeling and 3D printing of elemental powder blends for high-throughput investigation of high-entropy alloys—Towards rapid alloy screening and design. Mater. Sci. Eng., A 688, 180 (2017).CrossRefGoogle Scholar
Raghavan, R., Hari Kumar, K.C., and Murty, B.S.: Analysis of phase formation in multi-component alloys. J. Alloy. Comp. 544, 152 (2012).CrossRefGoogle Scholar
Senkov, O., Miller, J., Miracle, D.B., and Woodward, C.: Accelerated exploration of multi-principal element alloys for structural applications. Calphad 50, 32 (2015).CrossRefGoogle Scholar
Senkov, O., Miller, J., Miracle, D.B., and Woodward, C.: Accelerated exploration of multi-principal element alloys with solid solution phases. Nat. Commun. 6, 6529 (2015).CrossRefGoogle ScholarPubMed
Tancret, F., Toda-Caraballo, I., Menou, E., and Rivera-Díaz-Del-Castillo, P.E.J.: Designing high entropy alloys employing thermodynamics and Gaussian process statistical analysis. Mater. Des. 115, 486 (2017).CrossRefGoogle Scholar
Gao, M.C., Zhang, C., Gao, P., Zhang, F., Ouyang, L.Z., Widom, M., and Hawk, J.A.: Thermodynamics of concentrated solid solution alloys. Curr. Opin. Solid State Mater. Sci. 21, 238 (2017).CrossRefGoogle Scholar
Hume-Rothery, W.: Atomic Theory for Students of Metallurgy (The Institute of Metals, London, 1969). (5th reprint).Google Scholar
Yeh, J.W., Lin, S.J., Chin, T.S., Gan, J.Y., Chen, S.K., Shun, T.T., Tsau, C.H., and Chou, S.Y.: Formation of simple crystal structures in Cu–Co–Ni–Cr–Al–Fe–Ti–V alloys with multiprincipal metallic elements. Metall. Mater. Trans. A 35, 2533 (2004).CrossRefGoogle Scholar
Fang, S., Xiao, X., Xia, L., Li, W., and Dong, Y.: Relationship between the widths of supercooled liquid regions and bond parameters of Mg-based bulk metallic glasses. J. Non-Cryst. Solids 321, 120 (2003).CrossRefGoogle Scholar
Poletti, M.G. and Battezzati, L.: Electronic and thermodynamic criteria for the occurrence of high entropy alloys in metallic systems. Acta Mater. 75, 297 (2014).CrossRefGoogle Scholar
Guo, S. and Liu, C.T.: Phase stability in high entropy alloys: Formation of solid-solution phase or amorphous phase. Prog. Nat. Sci.: Mater. Int. 21, 433 (2011).CrossRefGoogle Scholar
Guo, S., Ng, C., Lu, J., and Liu, C.T.: Effect of valence electron concentration on stability of fcc or bcc phase in high entropy alloys. J. Appl. Phys. 109, 103505 (2011).CrossRefGoogle Scholar
Miedema, A.R., de Châtel, P.F., and de Boer, F.R.: Cohesion in alloys—Fundamentals of a semi-empirical model. Physica B 100, 1 (1980).CrossRefGoogle Scholar
Yang, X. and Zhang, Y.: Prediction of high-entropy stabilized solid-solution in multi-component alloys. Mater. Chem. Phys. 132, 233 (2012).CrossRefGoogle Scholar
Sheikh, S., Shafeie, S., Hu, Q., Ahlström, J., Persson, C., Veselý, J., Zýka, J., Klement, U., and Guo, S.: Alloy design for intrinsically ductile refractory high-entropy alloys. J. Appl. Phys. 120, 164902 (2016).CrossRefGoogle Scholar
Chen, Y., Li, Y., Cheng, X., Wu, C., Cheng, B., and Xu, Z.: The microstructure and mechanical properties of refractory high-entropy alloys with high plasticity. Materials 11, 208 (2018).CrossRefGoogle ScholarPubMed
Fraczkiewicz, : French Patent No. FR-1459567, 2016.Google Scholar
Yao, H.W., Qiao, J.W., Hawk, J.A., Zhou, H.F., Chen, M.W., and Gao, M.C.: Mechanical properties of refractory high-entropy alloys: Experiments and modeling. J. Alloy. Comp. 696, 1139 (2017).CrossRefGoogle Scholar
Tazuddin, , Gurao, N.P., and Biswas, K.: In the quest of single phase multi-component multiprincipal high entropy alloys. J. Alloy. Comp. 697, 434 (2017).CrossRefGoogle Scholar
Choi, W.M., Jung, S., Jo, Y.H., Lee, S., and Lee, B.J.: Design of new face-centered cubic high entropy alloys by thermodynamic calculation. Met. Mater. Int. 23, 839 (2017).CrossRefGoogle Scholar
Domínguez, L.A., Goodall, R., and Todd, I.: Prediction and validation of quaternary high entropy alloys using statistical approaches. Mater. Sci. Technol. 31, 1201 (2015).CrossRefGoogle Scholar
Nong, Z.S., Zhu, J.C., Cao, Y., Yang, X.W., Lai, Z.H., and Liu, Y.: Stability and structure prediction of cubic phase in as cast high entropy alloys. Mater. Sci. Technol. 30, 363 (2014).CrossRefGoogle Scholar
Raghavan, R., Hari Kumar, K.C., and Murty, B.S.: Analysis of phase formation in multi-component alloys. J. Alloys Compd. 544, 152 (2014).CrossRefGoogle Scholar
Gao, M.C., Carney, C.S., Dogan, O.N., Jablonksi, P.D., Hawk, J.A., and Alman, D.E.: Design of refractory high entropy alloys. JOM 67, 2653 (2015).CrossRefGoogle Scholar
Gao, M.C. and Alman, D.E.: Searching for next single-phase high entropy alloy compositions. Entropy 15, 4504 (2015).CrossRefGoogle Scholar
Miracle, D., Miller, J.D., Senkov, O.N., Woodward, C., Uchic, M.D., and Tiley, J.: Exploration and development of high entropy alloys for structural applications. Entropy 16, 494 (2014).CrossRefGoogle Scholar
King, D.J.M., Middleburgh, S.C., McGregor, A.G., and Cortie, M.B.: Predicting the formation and stability of single phase high-entropy alloys. Acta Mater. 104, 172 (2016).CrossRefGoogle Scholar
Sharma, A., Singh, R., Liaw, P.K., and Balasubramanian, G.: Cuckoo searching optimal composition of multicomponent alloys by molecular simulations. Scr. Mater. 130, 292 (2017).CrossRefGoogle Scholar
Abu-Odeh, A., Galvan, E., Kirk, T., Mao, H., Chen, Q., Mason, P., Malak, R., and Arroyave, R.: Efficient exploration of the high entropy alloy composition-phase space. Acta Mater. 152, 41 (2018).Google Scholar
Menou, E., Toda-Caraballo, I., Rivera-Díaz-del-Castillo, P.E.J., Pineau, C., Bertrand, E., Ramstein, G., and Tancret, F.: Evolutionary design of strong and stable high entropy alloys using multi-objective optimisation based on physical models, statistics and thermodynamics. Mater. Des. 143, 185 (2018).CrossRefGoogle Scholar
Toda-Caraballo, I. and Rivera-Díaz-del-Castillo, P.E.J.: Modelling solid solution hardening in high entropy alloys. Acta Mater. 85, 14 (2015).CrossRefGoogle Scholar
Li, Z., Pradeep, K.G., Deng, Y., Raabe, D., and Tasan, C.C.: Metastable high-entropy dual-phase alloys overcome the strength-ductility trade-off. Nature 534, 227 (2016).CrossRefGoogle ScholarPubMed
He, J.Y., Wang, H., Huang, H.L., Xu, X.D., Chen, M.W., Wu, Y., Liu, X.J., Nieh, T.G., An, K., and Lu, Z.P.: A precipitation-hardened high-entropy alloy with outstanding tensile properties. Acta Mater. 102, 187 (2016).CrossRefGoogle Scholar
Deschamps, A. and Brechet, Y.: Influence of predeformation and agEing of an Al–Zn–Mg alloy—II. Modeling of precipitation kinetics and yield stress. Acta Mater. 47, 293 (1999).CrossRefGoogle Scholar
Hutchinson, C.R., Nie, J.F., and Gorsse, S.: Modeling the precipitation processes and strengthening mechanisms in a Mg–Al–(Zn) AZ91 alloy. Metall. Mater. Trans. A 36, 2093 (2005).CrossRefGoogle Scholar
Aaronson, H.I. and Lee, J.K.: The kinetic equations of solid: Solid nucleation theory and comparisons with experimental observations. In Lectures on the Theory of Phase Transformations, Aaronson, H.I., ed. (TMS, Warrendale, PA, 1999); pp. 165–225.Google Scholar
Russell, K.C.: Nucleation in solids: The induction and steady state effects. Adv. Colloid Interface Sci. 13, 205 (1980).CrossRefGoogle Scholar
Zener, C.: Theory of growth of spherical precipitates from solid solution. J. Appl. Phys. 20, 950 (1949).CrossRefGoogle Scholar
Bouaziz, O., Allain, S., Scott, C.P., Cugy, P., and Barbier, D.: High manganese austenitic twinning induced plasticity steels: A review of the microstructure properties relationships. Curr. Opin. Solid State Mater. Sci. 15, 141 (2011).CrossRefGoogle Scholar
Allain, S., Chateau, J.P., and Bouaziz, O.: A physical model of the twinning-induced plasticity effect in a high manganese austenitic steel. Mater. Sci. Eng., A 387–389, 143 (2004).CrossRefGoogle Scholar
Hadfield, R.A.: Hadfield’s manganese steel. Science 12, 284 (1888).Google Scholar
Rémy, L.: Kinetics of f.c.c. deformation twinning and its relationship to stress-strain behavior. Acta Metall. 26, 443 (1978).CrossRefGoogle Scholar
Otto, F., Dlouhy, A., Somsen, C., Bei, H., Eggeler, G., and George, E.P.: The influences of temperature and microstructure on the tensile properties of a CoCrFeMnNi high-entropy alloy. Acta Mater. 61, 5743 (2013).CrossRefGoogle Scholar
Gludovatz, B., Hohenwarter, A., Catoor, D., Chang, E.H., George, E.P., and Ritchie, R.O.: A fracture-resistant high-entropy alloy for cryogenic applications. Science 345, 1153 (2014).CrossRefGoogle ScholarPubMed
Deng, Y., Tasan, C.C., Pradeep, K.G., Springer, H., Kostka, A., and Raabe, D.: Design of a twinning-induced plasticity high entropy alloy. Acta Mater. 94, 124 (2015).CrossRefGoogle Scholar
Beyramali Kivy, M. and Asle Zaee, M.: Generalized stacking fault energies, ductilities, and twinnabilities of CoCrFeNi-based face-centered cubic high entropy alloys. Scr. Mater. 139, 83 (2017).CrossRefGoogle Scholar
Olson, G.B. and Cohen, M.: A general mechanism of martensitic nucleation: Part I. General concepts and the fcc → HCP transformation. Metall. Trans. A 7, 1897 (1976).Google Scholar