Estimation of Shear Modulus and Hardness of High-Entropy Alloys Made from Early Transition Metals Based on Bonding Parameters

Abstract

The relationship between the tendencies towards rigidity (measured by shear modulus, G) and hardness (measured by Vickers hardness, HV) of early transition metal (ETM)-based refractory high-entropy alloys (RHEA) and bond parameters (i.e., valence electron concentration (VEC), enthalpy of mixing (ΔHmix)) was investigated. These bond parameters, VEC and ΔHmix, are available from composition and tabulated data, respectively. Based on our own data (9 samples) and those available from the literatures (47 + 27 samples), it seems that for ETM-based RHEAs the G and HV characteristics have a close correlation with the bonding parameters. The room temperature value of G and HV increases with the VEC and with the negative value of ΔHmix. Corresponding equations were deduced for the first time through multiple linear regression analysis, in order to help design the mechanical properties of ETM refractory high-entropy alloys.

Prediction of the Cohesion Energy, Shear Modulus and Hardness of Single-Phase Metals and High-Entropy Alloys

“…In Figure 7, the measured and calculated HV data are represented as a function of VEC. The maximum is approximately VEC = 6-7, which corresponds to the maximal, d = VEC − 2 = 5, uncompensated d electrons and hence to the maximal bonding strength (see Friedel model in [26,27]). The maximal hardness is approximately 600 kgf/mm 2 and decreases both around VEC = 4 (refractory HEAs) and VEC = 8 (derivatives of FCC Cantor alloy).…”