Abstract
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.
Highlights
Since the invocation of the concept of apparently characteristic, material-specific temperature parameters, Θ, within Debye’s classical paper [1] on specific heats of solids, one was concerned with a large variety of quotations of corresponding ΘD values within numerous thermophysical research papers, including various representative review articles [2,3,4,5] and books [6,7,8,9,10]
The basic cause of the occurrence of relatively deep minima, ΘDmin, in the cryogenic region had been indicated already many years ago by Schrodinger [2] to be obviously due to the onset of thermal activation of short-wavelength transverse acoustical (TA) phonons, which are quantumtheoretically manifested by pronounced peaks in the respective material-specific phonon density of states (PDOS) spectra (see, e.g., the calculated gP(ε) spectra shown in [45, 46] for ZnSe and ZnTe)
We have repeatedly found within a larger series of heat capacity studies [14, 15, 21, 50, 54] that, within regions from Th up to temperatures of order 5Th, the rapid increase of these differences can be simulated in good approximation by a proportionality of type Cp(T) − CVh(T) ∝ T × (CVh(T))2 ∝ T × (κh(T))2 (note that the structure of the latter is analogous to the known Nernst-Lindemann formula [2, 3, 58], Cp(T) − CV(T) ∝ T × (Cp(T))2, for the differences between isobaric and isochoric heat capacities)
Summary
Since the invocation of the concept of apparently characteristic, material-specific temperature parameters, Θ, within Debye’s classical paper [1] on specific heats of solids, one was concerned with a large variety of quotations of corresponding ΘD values (so-called “Debye temperatures”) within numerous thermophysical research papers, including various representative review articles [2,3,4,5] and books [6,7,8,9,10]. The basic cause of the occurrence of relatively deep minima, ΘDmin, in the cryogenic region had been indicated already many years ago by Schrodinger [2] to be obviously due to the onset of thermal activation of short-wavelength transverse acoustical (TA) phonons, which are quantumtheoretically manifested by pronounced peaks (singularities) in the respective material-specific phonon density of states (PDOS) spectra (see, e.g., the calculated gP(ε) spectra shown in [45, 46] for ZnSe and ZnTe) Such drastic deviations of physically realistic PDOS spectra from Debye’s naıve (quadratic) PDOS model function [1], gD(ε) ∝ ε2, are continually confirmed to be the main cause of the obviously typical, nonmonotonic (non-Debye) behaviours of ΘD(T) curves.
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