Abstract
This article provides a short review on computational modeling on the formation, thermodynamics, and elasticity of single-phase high-entropy alloys (HEAs). Hundreds of predicted single-phase HEAs were re-examined using various empirical thermo-physical parameters. Potential BCC HEAs (CrMoNbTaTiVW, CrMoNbReTaTiVW, and CrFeMoNbReRuTaVW) were suggested based on CALPHAD modeling. The calculated vibrational entropies of mixing are positive for FCC CoCrFeNi, negative for BCC MoNbTaW, and near-zero for HCP CoOsReRu. The total entropies of mixing were observed to trend in descending order: CoCrFeNi > CoOsReRu > MoNbTaW. Calculated lattice parameters agree extremely well with averaged values estimated from the rule of mixtures (ROM) if the same crystal structure is used for the elements and the alloy. The deviation in the calculated elastic properties from ROM for select alloys is small but is susceptible to the choice used for the structures of pure components.
Similar content being viewed by others
References
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. 6, 299 (2004).
B. Cantor, I.T.H. Chang, P. Knight, and A.J.B. Vincent: Microstructural development in equiatomic multicomponent alloys. Mater. Sci. Eng., A 375–377, 213 (2004).
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. 61, 1 (2014).
M.C. Gao, J.W. Yeh, P.K. Liaw, and Y. Zhang: High-Entropy Alloys: Fundamentals and Applications, 1st ed. (Springer International Publishing, Cham, 2016); p. 516.
D.B. Miracle and O.N. Senkov: A critical review of high entropy alloys and related concepts. Acta Mater. 122, 448 (2017).
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. 10, 534 (2008).
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. 4, 57 (2014).
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. 109, 103505 (2011).
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 321, 120 (2003).
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. 104, 53 (2015).
Y.F. Ye, C.T. Liu, and Y. Yang: A geometric model for intrinsic residual strain and phase stability in high entropy alloys. Acta Mater. 94, 152 (2015).
Z.J. Wang, W.F. Qiu, Y. Yang, and C.T. Liu: Atomic-size and lattice-distortion effects in newly developed high-entropy alloys with multiple principal elements. Intermetallics 64, 63 (2015).
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. 104, 172 (2016).
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 5, 011041 (2015).
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. 658, 603 (2016).
M.G. Poletti and L. Battezzati: Electronic and thermodynamic criteria for the occurrence of high entropy alloys in metallic systems. Acta Mater. 75, 297 (2014).
I. Toda-Caraballo and P.E.J. Rivera-Diaz-del-Castillo: A criterion for the formation of high entropy alloys based on lattice distortion. Intermetallics 71, 76 (2016).
S. Guo: Phase selection rules for cast high entropy alloys: An overview. Mater. Sci. Technol. 31, 1223 (2015).
M.C. Gao, C.S. Carney, Ö.N. Doğan, P.D. Jablonksi, J.A. Hawk, and D.E. Alman: Design of refractory high-entropy alloys. JOM 67, 2653 (2015).
B. Zhang, M.C. Gao, Y. Zhang, and S.M. Guo: Senary refractory high-entropy alloy CrxMoNbTaVW. CALPHAD 51, 193 (2015).
M.C. Gao, B. Zhang, S. Yang, and S.M. Guo: Senary refractory high-entropy alloy HfNbTaTiVZr. Metall. Mater. Trans. A 47, 3333 (2016).
H.W. Yao, J.W. Qiao, M.C. Gao, J.A. Hawk, S.G. Ma, H.F. Zhou, and Y. Zhang: NbTaV–(Ti,W) refractory high entropy alloys. Mater. Sci. Eng., A 674, 203 (2016).
H.W. Yao, J.W. Qiao, M.C. Gao, J.A. Hawk, S.G. Ma, and H.F. Zhou: MoNbTaV medium-entropy alloy. Entropy 18, 189 (2016).
C. Zhang, F. Zhang, S.L. Chen, and W.S. Cao: Computational thermodynamics aided high-entropy alloy design. JOM 64, 839 (2012).
M.C. Gao and D.E. Alman: Searching for next single-phase high-entropy alloy compositions. Entropy 15, 4504 (2013).
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 45, 1 (2014).
O.N. Senkov, J.D. Miller, D.B. Miracles, and C. Woodward: Accelerated exploration of multi-principal element alloys for structural applications. CALPHAD 50, 32 (2015).
C. Zhang and M.C. Gao: CALPHAD modeling 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 International Publishing, Cham, 2016); p. 399.
B. Zhang, M.C. Gao, Y. Zhang, S. Yang, and S.M. Guo: Senary refractory high-entropy alloy MoNbTaTiVW. Mater. Sci. Technol. 31, 1207 (2015).
M.C. Gao: Design 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 International Publishing, Cham, 2016); p. 369.
M.C. Gao, B. Zhang, S.M. Guo, J.W. Qiao, and J.A. Hawk: High-entropy alloys in hexagonal close packed structure. Metall. Mater. Trans. A 47, 3322 (2016).
M. Widom, W.P. Huhn, S. Maiti, and W. Steurer: Hybrid Monte Carlo/molecular dynamics simulation of a refractory metal high entropy alloy. Metall. Mater. Trans. A 45, 196 (2014).
M. Widom: Prediction of structure and phase transformations. In High-Entropy Alloys: Fundamentals and Applications, M.C. Gao, J.W. Yeh, P.K. Liaw, and Y. Zhang, eds. (Springer International Publishing, Cham, 2016); p. 267.
F.Y. Tian, L. Delczeg, N.X. Chen, L.K. Varga, J. Shen, and L. Vitos: Structural stability of NiCoFeCrAlx high-entropy alloy from ab initio theory. Phys. Rev. B 88, 085128 (2013).
F.Y. Tian, Y. Wang, D.L. Irving, and L. Vitos: Applications of coherent potential approximation to HEAs. In High-Entropy Alloys: Fundamentals and Applications, M.C. Gao, J.W. Yeh, P.K. Liaw, and Y. Zhang, eds. (Springer International Publishing, Cham, 2016); p. 299.
M.C. Gao, C. Niu, C. Jiang, and D.L. Irving: Applications of special quasi-random structures to high-entropy alloys. In High-Entropy Alloys: Fundamentals and Applications, M.C. Gao, J.W. Yeh, P.K. Liaw, and Y. Zhang, eds. (Springer International Publishing, Cham, 2016); p. 333.
D. Ma, B. Grabowski, F. Kormann, J. Neugebauer, and D. Raabe: Ab initio thermodynamics of the CoCrFeMnNi high entropy alloy: Importance of entropy contributions beyond the configurational one. Acta Mater. 100, 90 (2015).
H. Bei: Multi-component solid solution alloys having high mixing entropy. USPC, No. US20130108502 A1, UT-BATTELLE, LLC, Oak Ridge, TN, Knoxville, 2013.
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. 6, 6529 (2015).
G. Kresse and J. Hafner: Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558 (1993).
G. Kresse and J. Furthmüller: Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).
P.E. Blochl: Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994).
J.P. Perdew, K. Burke, and M. Ernzerhof: Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).
S.H. Wei, L.G. Ferreira, J.E. Bernard, and A. Zunger: Electronic properties of random alloys: Special quasirandom structures. Phys. Rev. B 42, 9622 (1990).
A. Zunger, S.H. Wei, L.G. Ferreira, and J.E. Bernard: Special quasirandom structures. Phys. Rev. Lett. 65, 353 (1990).
H.J. Monkhorst and J.D. Pack: Special points for brillouin-zone integrations. Phys. Rev. B 13, 5188 (1976).
W.P. Huhn and M. Widom: Prediction of A2 to B2 phase transition in the high-entropy alloy Mo–Nb–Ta–W. JOM 65, 1772 (2013).
M.C. Gao, C. Zhang, P. Gao, F. Zhang, L.Z. Ouyang, M. Widom, and J.A. Hawk: Thermodynamics of concentrated solid solution alloys. Curr. Opin. Solid State Mater. Sci. (2017). (in press). doi: https://doi.org/10.1016/j.cossms.2017.08.001.
H. Ackermann, G. Inden, and R. Kikuchi: Tetrahedron approximation of the cluster variation method for bcc alloys. Acta Metall. 37, 1 (1989).
B. Sundman, B. Jansson, and J.O. Andersson: The Thermo-Calc databank system. CALPHAD 9, 153 (1985).
G.H. Gulliver: The quantitative effect of rapid cooling upon the constitution of binary alloys. J. Inst. Met. 9, 120 (1913).
E. Scheil: Comments on the layer crystal formation. Z. Metallkd. 34, 70 (1942).
M.S. Lucas, L. Mauger, J.A. Munoz, Y. Xiao, A.O. Sheets, S.L. Semiatin, J. Horwath, and Z. Turgut: Magnetic and vibrational properties of high-entropy alloys. J. Appl. Phys. 109, 07E307 (2011).
M.S. Lucas, D. Belyea, C. Bauer, N. Bryant, E. Michel, Z. Turgut, S.O. Leontsev, J. Horwath, S.L. Semiatin, M.E. McHenry, and C.W. Miller: Thermomagnetic analysis of FeCoCrxNi alloys: Magnetic entropy of high-entropy alloys. J. Appl. Phys. 113, 17A923 (2013).
Y. Le Page and P. Saxe: Symmetry-general least-squares extraction of elastic data for strained materials from ab initio calculations of stress. Phys. Rev. B 65, 104104 (2002).
M.C. Gao, Y. Suzuki, H. Schweiger, Ö.N. Doğan, J. Hawk, and M. Widom: Phase stability and elastic properties of Cr–V alloys. J. Phys.: Condens. Matter 25, 075402 (2013).
M. Born and K. Huang: Dynamical Theory of Crystal Lattices, 1st ed. (Clarendon Press, Oxford, 1954).
B. Feng and M. Widom: Elastic stability and lattice distortion of refractory high entropy alloys. Mater. Chem. Phys. (2017). (in press). doi: https://doi.org/10.1016/j.matchemphys.2017.06.038.
L.Y. Tian, G. Wang, J.S. Harris, D.L. Irving, J. Zhao, and L. Vitos: Alloying effect on the elastic properties of refractory high-entropy alloys. Mater. Des. 114, 243 (2017).
H.J. Ge, F.Y. Tian, and Y. Wang: Elastic and thermal properties of refractory high-entropy alloys from first-principles calculations. Comput. Mater. Sci. 128, 185 (2017).
F.Y. Tian, L.K. Varga, J. Shen, and L. Vitos: Calculating elastic constants in high-entropy alloys using the coherent potential approximation: Current issues and errors. Comput. Mater. Sci. 111, 350 (2016).
Z. Wang, S. Guo, and C.T. Liu: Phase selection in high-entropy alloys: From nonequilibrium to equilibrium. JOM 66, 1966 (2014).
B.L. Zhang, Y. Mu, M.C. Gao, W.J. Meng, and S.M. Guo: On single-phase status and segregation of an as-solidified septenary refractory high entropy alloy. MRS Commun. 7, 78 (2017).
S.W. Sohn, Y.H. Liu, J.B. Liu, P. Gong, S. Prades-Rodel, A. Blatter, B.E. Scanley, C.C. Broadbridge, and J. Schroers: Noble metal high entropy alloys. Scr. Mater. 126, 29 (2017).
B. Fultz, L. Anthony, J.L. Robertson, R.M. Nicklow, S. Spooner, and M. Mostoller: Phonon modes and vibrational entropy of mixing in Fe–Cr. Phys. Rev. B 52, 3280 (1995).
B. Fultz: Vibrational thermodynamics of materials. Prog. Mater. Sci. 55, 247 (2010).
J.A. Munoz, M.S. Lucas, O. Delaire, M.L. Winterrose, L. Mauger, C.W. Li, A.O. Sheets, M.B. Stone, D.L. Abernathy, Y. Xiao, P. Chow, and B. Fultz: Positive vibrational entropy of chemical ordering in FeV. Phys. Rev. Lett. 107, 115501 (2011).
ACKNOWLEDGMENTS
This work was carried out in support of the Cross-Cutting Technologies Program at the National Energy Technology Laboratory (NETL), managed by Robert Romanosky (Technology Manager). The Research was executed through NETL’s Research and Innovation Center’s Innovative Process Technologies (IPT) Field Work Proposal. Research performed by AECOM Staff was conducted under the RES contract DE-FE-0004000. L.Z. Ouyang acknowledges support by DE-FE-0011549 and DE-NA0002630. Work at Carnegie Mellon was supported under grant DE-SC0014506.
Author information
Authors and Affiliations
Corresponding author
Additional information
This section of Journal of Materials Research is reserved for papers that are reviews of literature in a given area.
Supplementary Materials
Rights and permissions
About this article
Cite this article
Gao, M.C., Gao, P., Hawk, J.A. et al. Computational modeling of high-entropy alloys: Structures, thermodynamics and elasticity. Journal of Materials Research 32, 3627–3641 (2017). https://doi.org/10.1557/jmr.2017.366
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1557/jmr.2017.366