Note on Frequency Spectra of Simple Solids from Specific Heat Data

Abstract

If the specific heat C(T) of a solid is given as a function of temperature from T=0 to ∞ with infinite accuracy, the frequency spectrum f(ν) is uniquely determined. What information about f(ν) can be derived from specific heat data of experimental accuracy? The following conclusions give the answer. (1) Experimental specific heats determine accurately the low frequency part of the frequency spectrum but allow a latitude, wide enought to fit almost any theory, for its high frequency part. (2) In a Debye plot (effective Debye temperature θ versus T) peaks and dips in the region 0<T<θ/10 represent dips and peaks in the low frequency part of the frequency spectrum. The correspondence is so simple that it can be interpreted at a glance. The peaks and dips are superimposed on a simple Debye spectrum and presumably have a direct physical meaning, in terms of lattice irregularities. Only their centers and total weights are obtainable, so that they act effectively as single Einstein frequencies. (3) In the region θ/5<T<∞ all information obtainable about f(ν) consists of the first few even moments (three for specific heat errors of order one percent, five for 0.1 percent). These can be represented respectively by two or three weighted equivalent Einstein functions without direct physical meaning. (4) The region θ/10<T<θ/5 corresponds to the high frequency part of the frequency spectrum, but hardly any information can be derived here.