Non-Debye heat capacity formula refined and applied to GaP, GaAs, GaSb, InP, InAs, and InSb

Abstract

Characteristic non-Debye behaviors of low-temperature heat capacities of GaP, GaAs, GaSb, InP, InAs, and InSb, which are manifested above all in form of non-monotonic behaviors (local maxima) of the respective Cp(T)/T3 curves in the cryogenic region, are described by means of a refined version of a recently proposed low-to-high-temperature interpolation formula of non-Debye type. Least-mean-square fittings of representative Cp(T) data sets available for these materials from several sources show excellent agreements, from the liquid-helium region up to room temperature. The results of detailed calculations of the respective material-specific Debye temperature curves, ΘD(T), are represented in graphical form. The strong, non-monotonic variations of ΘD(T) values confirm that it is impossible to provide reasonable numerical simulations of measured Cp(T) dependences in terms of fixed Debye temperatures. We show that it is possible to describe in good approximation the complete Debye temperature curves, from the cryogenic region up to their definitive disappearance (dropping to 0) in the high temperature region, by a couple of unprecedented algebraic formulas. The task of constructing physically adequate prolongations of the low-temperature Cp(T) curves up to melting points was strongly impeded by partly rather large differences (up to an order of 10 J/(K·mol)) between the high-temperature data sets presented in different research papers and/or data reviews. Physically plausible criteria are invoked, which enabled an a priori rejection of a series of obviously unrealistic high-temperature data sets. Residual uncertainties for GaAs and InAs could be overcome by re-evaluations of former enthalpy data on the basis of a novel set of properly specified four-parameter polynomial expressions applying to large regions, from moderately low temperatures up to melting points. Detailed analytical and numerical descriptions are given for the anharmonicity-related differences of isobaric vs. isochoric (harmonic) parts of heat capacities. Relevant sets of empirical parameters and representative collections of heat capacity and Debye temperature values for all materials under study are presented in tabulated form.