Accurate Evaluation of the Specific Heat Capacity of Solids and its Application to MgO and ZnO Crystals

Abstract

Using binomial coefficients, new, simple, and efficient algorithms are presented for the accurate and fast calculation of the heat capacity of solids depending on the Debye temperature. As will be seen, the present formulation yields compact, closed-form expressions which enable the straightforward calculation of the heat capacity of solids for arbitrary temperature values. Finally, the algorithm is used to simulate the variation of the specific heat capacity with temperature of MgO and ZnO crystals. The results were compared with those reported in the literature and found to be in close agreement with those of other studies.

Unprecedented Integral-Free Debye Temperature Formulas: Sample Applications to Heat Capacities of ZnSe and ZnTe

“…Table 5) are found again to be in reasonable agreement with their counterparts of about 11.8 meV or 12.1 meV, for ZnSe, and 9.4 meV or 9.6 meV, for ZnTe, which followed immediately via (45) from the couples of TA and LA values for the average TA and LA phonon energies (which had been detected from the theoretically calculated PDOS spectra presented in Figure 3 of [45] or Figure 4 of [46], resp.). Furthermore we observe that the presently estimated (caloric) = TA&LA values are in good agreement with our former estimations [56], which were based on theoretically calculated PDOS spectral functions published in various earlier papers, namely, 11.7 meV due to (44), and the whole acoustic phonon energy sections, TA&LA (45), including a series of equivalent (moment-related) phonon energies, ( ) (due to (46) and (47) [66,89], or 12.5 meV due to [36], for ZnSe, and 9.5 meV or 9.4 meV due to [32,36], for ZnTe. Let us still consider the upper part of the PDOS spectra in consideration, which are consisting of one LO and two TO branches.…”

“…Actually, not a single binary or ternary material could be found hitherto, within a wealth of thermophysical researches, for which it would have been possible to simulate in adequate way the temperature dependence of measured heat capacities, from the liquidhelium region up to the vicinity of room temperature, in terms of a unique Θ value. This means, among other things, that there is hardly a chance to come to appropriate quantitative descriptions of the temperature dependencies of heat capacities mainly via constructions of various, highly elaborate analytical models [41][42][43][44] for integrals of Debye's type and imputing, at the same time, only some fixed ( -independent) values for Debye temperatures (like Θ = 632 K for GaN [43] or Θ = 920 K for ZnO [44] and Θ = 946 K for MgO [44]). …”

Estimation of the Heat Capacity of Some Semiconductor Compounds Using n-Dimensional Debye Functions

“…Recently, a new formula has been suggested for the calculation of n-dimensional Debye functions using the binomial expansion theorem (for details, see [33,39]) in the following form [31]:…”

“…is the binomial coefficient. The detailed derivation of the above mentioned formulae can be found in a previous report by the current authors [31].…”

“…Hence, analytical formulas based on well known models, such as the Debye model, have proved to be extremely simple and efficient for calculating the thermodynamic properties of the compounds of interest and to remove the above-mentioned problems [21,[25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”