The thermal properties of alkali halide crystals III. The inversion of the heat capacity

Abstract

This paper discusses further the information that can be obtained about lattice harmonic frequency spectra from the experimental heat capacities reported in part I. A detailed study is made of sodium chloride, for which spectra of different analytic forms are fitted to the heat capacity within experimental error (0.2 %), thus showing how closely the spectrum is determined by the heat capacity. The information obtained agrees with general features of the theoretical spectra of Kellerman, Karo and Hardy; but more important are the following general conclusions drawn from this example. The low-frequency expansions (αv2+βv4+ . . .) and momentsμnderived in part II do not comprise all the information obtainable from the heat capacity, but suffice to determine a rough integral spectrum. This integral spectrum is determined a little more closely by the heat capacity itself, and the approximate shape of the differential spectrum can be determined not only at low but also at intermediate frequencies (hv< ½kΘ∞), provided that it is known from theory that at low frequencies the spectrum has the formαv2+βv4+ . . .; if this expansion cannot be assumed, however, nothing can be deduced about the detailed spectral shape in any frequency range. Greater experimental accuracy would determine the spectrum more closely at low and intermediate frequencies, but (partly because of anharmonic effects) is still not likely to give much information at high frequencies. Further information must therefore be obtained from other types of experiment or from theoretical models. Particularly accurate information is seen to be contained in the negative moments, which are therefore tabulated for the five salts discussed in this series of papers: sodium chloride and iodide, and potassium chloride, bromide and iodide.