Temperature Dependence of the Elastic Constants

TLDR: In this article, the temperature dependence of the elastic stiffness constants was investigated for 57 elastic constants of 22 substances and the applicability of these two equations and that of Wachtman's equation was examined.

Abstract: The following two equations are proposed for the temperature dependence of the elastic stiffness constants: ${c}_{\mathrm{ij}}={c}_{\mathrm{ij}}^{0}\ensuremath{-}\frac{s}{({e}^{\frac{t}{T}}\ensuremath{-}1)}$ and ${c}_{\mathrm{ij}}=a\ensuremath{-}\frac{b{T}^{2}}{(T+c)}$, where ${c}_{\mathrm{ij}}^{0}$, $s$, $t$, $a$, $b$, and $c$ are constants. The applicability of these two equations and that of Wachtman's equation is examined for 57 elastic constants of 22 substances. The first equation has a theoretical justification and gives the best over-all results. Neither of the three equations give the theoretically expected ${T}^{4}$ dependence at low temperatures, and therefore they are not expected to give very accurate results at very low temperatures ($\ensuremath{\lesssim}\frac{{\ensuremath{\Theta}}_{D}}{50}$). A new melting criterion is also examined.