Unprecedented Integral-Free Debye Temperature Formulas: Sample Applications to Heat Capacities of ZnSe and ZnTe - R. Pässler (Advances in Condensed Matter Physics)
Detailed analytical and numerical analyses are performed for combinations of several complementary sets of measured heat capacities, for ZnSe and ZnTe, from the liquid-helium region up to 600 K. The isochoric (harmonic) parts of heat capacities, CVh(T), are described within the frame of a properly devised four-oscillator hybrid model. Additional anharmonicity-related terms are included for comprehensive numerical fittings of the isobaric heat capacities, Cp(T). The contributions of Debye and non-Debye type due to the low-energy acoustical phonon sections are represented here for the first time by unprecedented, integral-free formulas. Indications for weak electronic contributions to the cryogenic heat capacities are found for both materials. A novel analytical framework has been constructed for high-accuracy evaluations of Debye function integrals via a couple of integral-free formulas, consisting of Debye’s conventional low-temperature series expansion in combination with an unprecedented high-temperature series representation for reciprocal values of the Debye function. The zero-temperature limits of Debye temperatures have been detected from published low-temperature Cp(T) data sets to be significantly lower than previously estimated, namely, 270 (±3) K for ZnSe and 220 (±2) K for ZnTe. The high-temperature limits of the “true” (harmonic lattice) Debye temperatures are found to be 317 K for ZnSe and 262 K for ZnTe.