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 ² 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 ¹ TS and S = ¹(@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, + i¹j (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.

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“…The present work led to a subsequent report about the formations of HEAs with bcc, hcp, and fcc structures simultaneously in a composition line. 8) Further relevant thermodynamic researches were performed in terms of mixing entropy of single-phase HEAs itself 9) based on CALPHAD (CALculation of PHAse Diagram) scheme to evaluate whether or not the HEAs truly possess a large magnitude of mixing entropy. These achievements with a knowledge of thermodynamics and relevant theoretical aspects assisted by computational approach have offered profound insights into the nature of HEAs.…”

“…Besides, Alloy C annealed at 1273 K for 200 h maintained a single-hcp structure. These achievements combined with a subsequent thermodynamic analysis of mixing entropy of single-phase HEAs itself based on CALPHAD scheme 9) will open the door for the promising fundamental researches of HEA. Silicon (Si) has attracted considerable interest as a negative electrode material for next-generation lithium (Li)ion batteries because of its high capacity density.…”

A Unique Quenching and Deformation Dilatometer for Combined In Situ Neutron Diffraction Analysis of Engineering Materials

“…[43] Unfortunately, previous studies have shown that results from Thermo-Calc calculations, such as, for example, phase compositions, phase transformation temperature, and chemical compositions of phases differ to some extent from experiment results. [44][45][46] However, combining dilatometry measurements with in situ neutron diffraction data, the phase transformation type and transformation temperature of HEAs can be determined conveniently from an analysis of the length change signal from dilatometry, and the integrated peak intensity and peak position change from in situ neutron diffraction measurements. Thus, an approach using thermodynamic calculations with combined neutron diffraction and dilatometry can substantially reduce the efforts in the development of new HEA systems.…”

Ultra-High Mixing Entropy Alloys with Single bcc, hcp, or fcc Structure in Co–Cr–V–Fe–X (X = Al, Ru, or Ni) Systems Designed with Structure-Dependent Mixing Entropy and Mixing Enthalpy of Constituent Binary Equiatomic Alloys

“…36) Followed by these early studies, the present authors adopted a thermodynamic approach and calculated the value of S mix using Thermo-Calc 7,8) and a specially designated database for HEAs (TCHEA4). The present study was motivated by the authors' previous precise thermodynamic calculations, 9) indicating that S mix < S config (= S ideal ) holds for most of the exact equiatomic (EE) HEAs with a single bcc structure; in particular, for Al-containing bcc EE HEAs. Only one exception was reported, 9) for the bcc CrMoNbTaTiVZr HEA 10) at 1300 K, with S mix /S config = 1.004.…”