On the relation of Debye theory and the lattice theory of specific heats

In the Debye theory of the specific heat of solids the value of θ calculated from elastic constants, namely, θD (elastic), should be the same as that found from specific-heat data, θD (specific heat). The ratio of these θ values for crystal lattices is calculated here at a temperature T ~ θD on the basis of lattice theory; it is shown that the ratio is remarkably near unity for crystals of the NaCl type provided the crystals are not very anisotropic. In the case of other crystal types, the agreement is in general less good, the value of unity holding only in isolated cases.