Mixing entropy of exact equiatomic high-entropy alloys formed into a single phase

Akira Takeuchi

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5 Citations (Scopus)


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 (Smix) was evaluated as the sum of excess entropy (Sexcess) and ideal entropy (Sideal), the latter of which is equivalent to configuration entropy (Sconfig). 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 Smix normalized with gas constant (R) down to approximately 87% of Sideal/R = lnN due to a positive T dependence of interaction parameter, Ωi-j(T), of i-j atomic pairs in mixing enthalpy (Hmix). In contrast, Smix/R of the fcc-CoCrFeMnNi HEA was approximately 9% greater than lnN. The hcp-EE-HEAs from a class of athermal solutions behaved as ideal solutions in practice. The results revealed that a relationship of Smix/R = lnN does not always hold in EE-HEAs.

Original languageEnglish
Pages (from-to)1717-1726
Number of pages10
JournalMaterials Transactions
Issue number9
Publication statusPublished - 2020 Sep 1


  • Excess entropy
  • High-entropy alloy
  • Interaction parameter
  • Mixing entropy
  • Sub-regular solution model

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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