A semi-analytic universal model on elasticity across wide temperatures and pressures

A semi-analytic model is presented universally for the elastic constants and moduli of solid phases in a wide range of temperatures and pressures. We derive in detail the model as a function of temperature and pressure, where the characteristic temperature is clearly associated with the Debye temperature. The abundant experiments of thermal elasticity for Cr-Mn-Fe-Co-Ni high entropy alloys are used to estimate the validity of the characteristic temperature of elasticity. The linear process of the analytical part significantly reduces the high computational and experimental cost of elasticity across a wide range of temperatures and pressures. We take the elastic property of beryllium within the range of up to 6000 K and 500 GPa as a prototype to investigate the accuracy, efficiency and extrapolation of this model. The application to Mg3Al2Si3O12-pyrope and CaSiO3-perovskite in the Earth's mantle further suggests that our model excellently describes the elasticity of different materials across a wide range of temperatures and pressures.