Thermo-elastic behavior of hexagonal Sc–Ti–Zr–Hf high-entropy alloys

Abstract

Recent advance in tuning the long-standing strength-ductility tradeoff draw attention to high-entropy alloys (HEAs), and the appearance of the hexagonal close-packed (hcp) structure is emphasized. However, few studies have explored the elastic moduli of the hcp HEAs, which is of prime importance to improve the understanding of the outstanding mechanical properties. In this work, we focus on a set of equiatomic rare-earth-free HEAs with the hcp structure, i.e., ScTiZr, ScTiHf, ScZrHf, TiZrHf, and ScTiZrHf, and their thermo-elastic properties are studied using quantum mechanical first-principles methods. It is found that for all considered HEAs, the hexagonal axial ratio shows a weak dependence on the temperature effect, and the thermal expansion coefficient remains almost unchanged above room temperature. From the calculated temperature dependent single-crystal elastic constants, we analyzed the mechanical stability, elastic anisotropy, and derived polycrystalline moduli. Results indicate that the present HEAs exhibit rather high elastic isotropy and large elastic softening resistance. The ab initio predicted Young’s modulus, shear modulus, and specific modulus do not obey the rule of mixture, which indicates that there exists a strong intrinsic hardening effect in all of the considered HEAs. The calculated results are in good agreement with the available experimental measurements.

Theoretical Approach to Investigate Temperature Dependent Ultrasonic and Thermophysical Properties of Ti-Zr-Hf Ternary Alloy

“…While all of the elastic moduli decrease significantly with temperature, the Poisson's ratio is 0.2357 at room temperature (300K) and does not change significantly with temperature. The bulk modulus, shear modulus and Young's modulus at room temperature is 88.5 GPa, 56.79 GPa and 140.36 GPa respectively which are in good agreement with the values available in literature [5], [17].…”

“…The SOECs and TOECs in the temperature range of 0K-900K have been computed using lattice parameters available in the literature [17] and presented in Fig. 1 and Fig.…”

“…The Grüneisen constant for thermal conductivity has been calculated with the help of Coefficient of thermal expansion α values available in the literature [17]. The dependence of thermal conductivity on temperature and direction in the crystal is plotted in the Fig.…”

“…Duan et al [5] have studied the second order elastic constants (SOECs), elastic moduli at room temperature of HCP ternary alloy Ti-Zr-Hf using first principles method. Huang et al [17] have investigated HCP ternary and quaternary alloys of Sc-Ti-Zr-Hf for their thermoelastic properties including SOECs, elastic moduli and coefficients of thermal expansion (CTE) at different temperatures. In spite of these studies, temperature dependence of third order elastic constants (TOECs), thermophysical properties such as Debye temperature, heat capacity, thermal conductivity and ultrasonic behaviour of the Ti-Zr-Hf HCP alloy are yet to be studied.…”