On the Specific Heat of Solids at Low Temperatures

The temperature dependence of the specific heat of solids at very low temperatures is examined, using theoretical models and certain recent experimental results. The temperature region over which the continuum approximation (C ν = aT 3 ) is strictly reliable is shorter than has often been supposed, and the series expansion C ν = aT 3 + bT 5 + cT 7 + … is needed for the analysis of accurate experimental results. For insulators θ 0 can best be estimated from measured specific heats by plotting C ν /T 3 versus T 2 ; the result is a curve whose intercept at T 2 = 0 gives the coefficient of T 3 (and hence θ 0 ), and whose slopeand curvature give additional information about the vibrational spectrum at low frequencies. For metals the usual plot of C ν /T versus T 2 can be used, but here again neglect of curvature may lead to errors in the estimates of γ and θ 0 . A brief discussion is given of the low temperature specific heats of a number of solids for which suitable data are available: potassium chloride, lithium fluoride, white tin, tungsten, the noble metals, and elements of diamond structure.