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In this paper, we did a systematic comparative study on the accuracy of twocomputational methods of elastic constants combined with the density functionaltheory (DFT), the stress-strain method and the energy-strain method. We tookmetal Ru as a prototype to compare its high-pressure elastic constantscalculated by our present stress-strain method with the previous energy-strainresults by others. Although the two methods yielded almost the same accuracy ofhigh-pressure elastic constants for Ru, our stress-strain method directly basedon the Hooke's law of elasticity theory is much straightforward and simple toimplement. However, the energy-strain method needs complicated pressurecorrections because of the pressure effects on the total energy. Variouscrystal systems have various pressure correction methods. Hence, thestress-strain method is preferred to calculate the high-pressure elasticconstants of materials. Furthermore, we analyzed the variations of the elasticmoduli, elastic anisotropy, sound velocities, Debye temperature of Ru withpressure.

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