Temperature dependence of the elastic constants

The following two equations are proposed for the temperature dependence of the elastic stiffness constants: c(ij) = c(ij)(0) - s/(e(t/T) - 1) and c(ij) = a - bT(2)/(T + c), where c(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 (less than or similar to circle minus(D)/50). A new melting criterion is also examined.