Anharmonic effects in the thermodynamic properties of solids II. Analysis of data for lead and aluminium

Methods are described for analysing the high-temperature thermodynamic properties of crystals into quasi-harmonic (qh) and explicit anharmonic (anh) contributions. The most useful functions to investigate are the entropy, the constant volume heat capacity and the Grüneisen parameter γ(T,V) = βV/χsCp. ΔSanh and ΔCvanh may be obtained as functions of temperature, both at the equilibrium crystal volume VT, and at a fixed volume, for example V0. The anharmonic Grüneisen parameter γanh = (1/ΔCvanh)(partial differentialΔSanh/partial differential ln V)T gives the volume dependence of ΔSanh and, to first order, that of ΔCvanh also. For metals the contribution from the conduction electrons must be considered, and this is of the form Sel = Cvel = σT. Theory suggests that σ should have the free-electron value σinfinity at high temperatures (T > capital theta, Greek) although this has not yet received direct experimental confirmation. In analysing the data for lead and aluminium the effects of using both the free-electron value σinfinity and the experimentally observable low-temperature value σ0 for the coefficient σ have been investigated.