Stability of High Entropy Alloys to Spinodal Decomposition

Abstract

When a high entropy alloy (HEA) system contains a single binary miscibility gap, the gap spreads across the entire composition space of the system. Beneath the miscibility gap is a spinodal hypersurface above which HEAs are stable to a continuous change of phase via spinodal decomposition. When there are additional binary miscibility gaps, the stability limits appear separately at high temperature but combine on cooling to form a continuous surface that may contain a cone point, an important feature for the design of age hardening alloys. In this work, an understanding of how spinodal surfaces form, combine, and develop critical features is obtained by investigating several ternary systems each with three binary miscibility gaps. Because their topology is the same, bisection isopleths and isothermal sections of ternary phase diagrams given in this work will help interpret calculated bisection isopleths and isotherms of 5-and 6-dimensional HEA phase diagrams.

Calculation of Critical Points

“…When a phase becomes locally unstable from a stable or metastable state, its smallest eigenvalue changes from a positive value to negative and others keep positive values unless in some special points such as the cone point of spinodal. [7] After a solvent component is selected, Gibbs energy is a function of compositional variables ðx 1 ; x 2 ; . .…”

“…Since this fact is not obvious, a proof of the gauge invariance of the determinant of Gibbs energy Hessian is given in Appendix. However, since the eigenvalues and eigenvectors of Gibbs energy Hessian are gauge variant outside of spinodal, [7] both V and d 3 G dv 3 are gauge variant outside of critical point. As long as U, V, and d 3 G dv 3 are gauge invariant at a critical point, the methods presented above will uniquely determine the critical points as well as the eigenvectors on spinodal.…”

“…[3][4][5][6] Our previous paper has a short summary on the study of alloy spinodal decomposition. [7] Reference 7 uses a regular solution model to study the effect of spinodal decomposition on the stability of high entropy alloys. It has shown how miscibility gaps and spinodal curves evolve from binary systems to ternary and higher order systems as well as how they change with temperature.…”