First-principles prediction of high-entropy-alloy stability

Abstract

High entropy alloys (HEAs) are multicomponent compounds whose high configurational entropy allows them to solidify into a single phase, with a simple crystal lattice structure. Some HEAs exhibit desirable properties, such as high specific strength, ductility, and corrosion resistance, while challenging the scientist to make confident predictions in the face of multiple competing phases. We demonstrate phase stability in the multicomponent alloy system of Cr-Mo-Nb-V, for which some of its binary subsystems are subject to phase separation and complex intermetallic-phase formation. Our first-principles calculation of free energy predicts that the configurational entropy stabilizes a single body-centered cubic (BCC) phase from T = 1700 K up to melting, while precipitation of a complex intermetallic is favored at lower temperatures. We form the compound experimentally and confirm that it develops as a single BCC phase from the melt, but that it transforms reversibly at lower temperatures. INTRODUCTIONExploring new materials with outstanding properties is an eternal pursuit of scientists and engineers. High entropy alloys (HEAs) constitute a newly-emerging class of materials that offer enhanced mechanical and corrosion properties for practical applications, while presenting challenges to the scientist making predictions in the face of compositional complexity.1-13 Alloys of two or three species often phase-separate, and when they form a compound, it is often a complex ordered structure with multiple Wyckoff positions. Thus, HEAs are remarkable for forming single phases that are, moreover, simple lattice structures in which all atomic positions are equivalent. Trial-and-error experimental approaches to test the phase stability of HEAs are costly and time-consuming, while previously-reported phase-formation rules are empirical and susceptible to the alloy, systems 14,15 motivating a first-principles theoretical approach to accelerate the design of HEAs through the prediction of phase stability and microstructure.Here we illustrate these ideas by demonstrating phase stability in the quaternary Cr-Mo-Nb-V alloy system. Some of its binary and ternary subsystems are subject to phase separation and complex intermetallic phase formation. Utilizing fully firstprinciples calculations of the free energies of the full quaternary and its competing binary and ternary phases, we predict that the configurational entropy stabilizes a single body-centered cubic (BCC) solid solution at high temperatures, but that it will precipitate a complex intermetallic Laves phase at lower temperatures. Experimentally, we verify the formation of the single-phase BCC solid solution from the melt, confirm the precipitation of the Laves phase at low temperatures, and observe that it reverts to a single BCC phase upon annealing at high temperatures, thus illustrating the entropic stabilization principle of HEAs.

Modeling the structure and thermodynamics of high-entropy alloys

“…(1). In the event of chemical ordering onto sublattices 65,66 such as B2 order, [67][68][69] one sums the sublattice entropies weighted by the fractions of atoms {f i } on each sublattice i,…”

“…84 Hybrid MC/MD has been extensively applied to refractory alloys. 4,65,75,85,86 Figure 4(a) shows the structure of Al 1.33 CoCrFeNi at T 5 300 K simulated using hybrid MC/MD with replica exchange. The basic structure is BCC, but lattice distortion is evident in the displacement of atoms from their ideal positions.…”

“…Beyond the CPA, Feng et al 65 calculated the free energy of a previously unknown quaternary, CrMoNbV, through explicit inclusion of configurational, vibrational, and electronic free energies (see Fig. 7).…”

“…Cluster expansions are effective Hamiltonians that efficiently describe the ground state energy of a given distribution of chemical constituents. They have been applied to several refractory element HEA-forming compounds based on BCC lattices, including the quinary Mo-Nb-Ta-V-W, 88 and three quaternaries, Cr-Mo-Nb-V, 65,75,85 Nb-Ti-V-Zr, 75,85 and Mo-Nb-Ta-W. 69,85,109 Given an effective Hamiltonian, rapid search can reveal ground states exhibiting a wide variety of differing patterns of chemical order in alloy ground states. They can also be utilized in Monte Carlo simulation to reveal temperature-driven order-disorder phase transitions.…”

Robust cluster expansion of multicomponent systems using structured sparsity

“…Initially, CE was largely applied to binary alloys 2, [13][14][15][16][17][18][19][20][21][22][23][24][25][26] . Thereafter, it has been applied to more complex systems, including ternary to quinary alloys 5,6,12,[27][28][29] , semiconductors 7,30 , battery materials 31,32 , clathrates 33,34 , magnetic alloys [35][36][37] , and nanoscale alloys 3,4,11,[38][39][40][41][42] . In complex systems, the reduced symmetry increases the number of symmetrically distinct clusters, exacerbating the cluster selection problem.…”