Straightforward computation of high-pressure elastic constants using Hooke's law: A prototype of metal Ru

In this paper, we did a systematic comparative study on the accuracy of two computational methods of elastic constants combined with the density functional theory (DFT), the stress-strain method and the energy-strain method. We took metal Ru as a prototype to compare its high-pressure elastic constants calculated by our present stress-strain method with the previous energy-strain results by others. Although the two methods yielded almost the same accuracy of high-pressure elastic constants for Ru, our stress-strain method directly based on the Hooke's law of elasticity theory is much straightforward and simple to implement. However, the energy-strain method needs complicated pressure corrections because of the pressure effects on the total energy. Various crystal systems have various pressure correction methods. Hence, the stress-strain method is preferred to calculate the high-pressure elastic constants of materials. Furthermore, we analyzed the variations of the elastic moduli, elastic anisotropy, sound velocities, Debye temperature of Ru with pressure.