First-principles study of the third-order elastic constants and related anharmonic properties in refractory high-entropy alloys

Abstract

The third-order elastic constants (TOECs) and elastic anharmonic behavior in four body-centered cubic refractory high-entropy alloys (HEAs) based on elements of the fourth, fifth, and sixth groups are investigated using density-functional simulations. We find that the values of the TOECs C111 are the largest in magnitude among the studied six independent TOECs and strongly increase with increasing average valence electron concentration (VEC). Interestingly, the TOEC C456 undergos a sign change as a function of the VEC. Using the obtained TOECs, we investigate the mode Grüneisen constants γi as well as the low temperature limit γ¯, derive the long-wavelength acoustic nonlinearity parameters β, and reveal the pressure derivatives of effective elastic constants and polycrystalline moduli as a function of the VEC. Our results show that β displays a different directional order along the pure mode [100], [110], and [111] directions for the four considered refractory HEAs. Furthermore, we show that the directional order of β is not correlated to the crystal symmetry. With the help of the obtained pressure derivatives of polycrystalline moduli, we predict the low temperature volume expansion coefficient.