ANHARMONIC EFFECTS IN THERMODYNAMIC PROPERTIES OF SOLIDS .2. 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 ΔC vanh 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 differentialΔS anh/partial differential ln V)T gives the volume dependence of ΔSanh and, to first order, that of ΔC vanh also. For metals the contribution from the conduction electrons must be considered, and this is of the form Sel = C vel = 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. For both lead and aluminium CV and γ have been analysed but no attempt was made to analyse S because of the lack of internally consistent CP data for the whole available temperature range. For lead the data extend to T similar 6capital theta, Greek and C Vanh is of the form CVanh(T, V 0) = AT+2BT2 with A negative and B positive. For aluminium, with data up to only T similar 2capital theta, Greek, A is also negative but no higher-order contribution is detectable. In both cases A varies by about a factor of 2 depending on whether σ0 or σinfinity is used to compute CVel. Analysis of the Grüneisen function yields values for γ infinityqh and γanh for both metals. Recent calculations of anharmonic effects in closepacked crystals, using simple models, are in surprisingly good agreement with experiment. The description of anharmonic effects in terms of volume and explicitly temperature-dependent frequency distributions is discussed. The volume dependence may be derived from γqh and the temperature dependence from ΔSanh or ΔCVanh. The results obtained for both lead and aluminium are expressed in this way and found to be in excellent agreement with the results of inelastic neutron scattering experiments, provided that σinfinity is used in the thermodynamic analysis to compute CVel.