Temperature Dependence of the Elastic Constants

The following two equations are proposed for the temperature dependence of the elastic stiffness constants: c₈₉=c₈₉^0-s ({e^t{T}-1) } and c₈₉=a-bT^{2} (T+c), where c₈₉^0, 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 ({₃}50). A new melting criterion is also examined.