Pressure and temperature dependence of second-order elastic constants from third-order elastic constants in TMC (TM=Nb,Ti, V,Zr)

In this paper, we present an efficient and effective method to predict the pressure dependence and temperature dependence of second-order elastic constants (SOECs) by introducing third-order elastic constants (TOECs) in the monocarbide ultrahigh temperature ceramics. The method is validated by comparing with experiments and previous calculations in four TMCs (TM = Nb, Ti, V, Zr). Using this method, we investigate the derivatives of SOECs against pressure and temperature as well as the anisotropic properties of polycrystalline modulus. In addition, we fit the SOECs with pressure and temperature under the framework of CALPHAD for practice usage.