Mixing Entropy of Exact Equiatomic High-Entropy Alloys Formed into a Single Phase

Abstract

Exact equiatomic high-entropy alloys (EE-HEAs) comprising N elements (N ≥ 5) formed into a single phase with either bcc, fcc or hcp structure were investigated based on sub-regular solution model. The analysis was performed by utilizing relationships among Gibbs energy (G), enthalpy (H), entropy (S), absolute temperature (T) and pressure (P), G = H − TS and S = −(∂G/∂T)_P, for representative EE-HEAs, such as bcc-MoNbTaVW, fcc-CoCrFeMnNi and hcp-EE-HEAs comprising heavy lanthanides with and without Y. Mixing entropy (S^mix) was evaluated as the sum of excess entropy (S^excess) and ideal entropy (S^ideal), the latter of which is equivalent to configuration entropy (S^config). Calculation tools contained commercial software (Thermo-Calc 2020a) using a database for HEAs (TCHEA4) mainly for the bcc- and fcc-EE-HEAs and that for solid solutions (SSOL5) for the hcp-EE-HEAs. The analysis revealed that the bcc-MoNbTaVW and NbTaTiVW HEAs exhibited the greatest decrease in S^mix normalized with gas constant (R) down to approximately 87% of S^ideal/R = ln N due to a positive T dependence of interaction parameter, Ω_i−j(T), of i-j atomic pairs in mixing enthalpy (H^mix). In contrast, S^mix/R of the fcc-CoCrFeMnNi HEA was approximately 9% greater than ln N. The hcp-EE-HEAs from a class of athermal solutions behaved as ideal solutions in practice. The results revealed that a relationship of S^mix/R = ln N does not always hold in EE-HEAs.

Relationships between X = H_m^excess and Y = −S_m^excess/(ln N/ln 2) of EE-HEAs from H_m^excess and S_m^excess consisting of H_m^{excess(Sub-Regular Solution Model)}, together with supplemental Y₁ and Y₂ axes.