Temperature Dependence of the Elastic Constants

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.