Representative hybrid model used for analyses of heat capacities of group‐IV, III–V, and II–VI materials

Abstract

Characteristic non-Debye features inherent to the dispersionrelated hybrid model, which had been devised for the sake of physically adequate representations of isobaric heat capacities of semiconductor and wide band gap materials, are demonstrated and discussed in some detail. We perform least-meansquare fittings of low-and high-temperature C p (T) data sets that are available for group-IV materials (diamond, Si, Ge, 3C-SiC), III-V materials (BN, BP, BAs, AlN, AlP, AlAs, AlSb, GaN, GaP, GaAs, GaSb, InP, InAs, InSb), and II-VI materials (ZnO, ZnS, ZnSe, ZnTe, CdO, CdS, CdSe, CdTe). The simulations of the C p (T) data sets under study, particularly with respect to the cryogenic region, are graphically represented, and existing data deficiencies are discussed. Important by-products of the fittings are presented within the frame of Supporting Information (online at: www.pss-b.com). There are given in tabulated form the characteristic phonon energies, e P (m), for integral orders, m ¼ À2, À1, 0, 1, 2, and 4, including further dispersion-related parameters like average phonon temperatures, Q P , dispersion coefficients, D P , and high-temperature limiting values of Debye temperatures, Q Dh (1). Furthermore, basing on comprehensive calculations of the C p (T) dependences from absolute zero up to room temperature, we provide representative values of entropies, S p (T), enthalpies, H p (T) À H p (0), and Gibbs free energies, G p (T) À G p (0), for the frequently considered reference point, T r ¼ 298.15 K, the accurate knowledge of which is indispensable for possible high-temperature continuations of these standard thermodynamic functions within the frame of the commonly used thermo-chemical formalism.

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

“…Within the frame of numerical analyses of experimental heat capacity data, however, one is continually concerned with a basic theoretical complication due to the inherent differences between the temperature dependencies of theoretical ℎ ( ) functions, on the one hand, and those of measured (isobaric) heat capacities, ( ), on the other hand. The latter are well known to be throughout somewhat higher, ( ) > ℎ ( ), than their theoretical (isochoric) counterparts pertaining to the harmonic lattice regime [4,50,54]. The respective differences, ( ) − ℎ ( ) > 0, are usually found to be very small from 0 up to temperatures of order ℎ , where the heat capacity amounts to about 50% of the Delong-Petit limiting value, ( ℎ ) ≅ ℎ ( ℎ ) = ℎ (∞)/2.…”

“…Within the frame of the harmonic lattice regime, the temperature dependencies of the isochoric heat capacities, ℎ ( ), are well known to be given by corresponding heat capacity shape functions, ℎ ( ), of the general form [4,6,45,[50][51][52][53][54][55] ℎ ( ) ℎ (∞)…”

“…On the other hand, one is usually concerned with a relatively strong monotonic increase of these differences, ( ( ) − ℎ ( ))/ > 0, at higher temperatures ( > ℎ ). These differences are generally ascribed to cumulative effects of lattice expansion and lattice anharmonicities [3,11,18,21,23,39,50,54,56,57]. We have repeatedly found within a larger series of heat capacity studies [14,15,21,50,54] that, within regions from ℎ up to temperatures of order 5 ℎ (at least), the rapid increase of these differences can be simulated in good approximation by a proportionality of type ( ) − ℎ ( ) ∝ × ( ℎ ( )) 2 ∝ × ( ℎ ( )) 2 (note that the structure of the latter is analogous to the known Nernst-Lindemann formula [2,3,58]…”

“…Admitting, furthermore, that at sufficiently high temperatures (up to melting points, if necessary) some additional higher-order power terms of may come into play, it appeared reasonable to simulate the -dependencies of isobaric heat capacities by a duly general algebraic expression of the form [14,15,21,50,54,59] ( ) = ℎ (∞) [ ℎ ( ) + ( ℎ ( )) 2 (∞)…”

“…In Section 3 we display a reformulated, integral-free version of the multioscillator hybrid model [14,21,50]. This is based mainly on the usage of novel, unprecedented analytical formulas (derived in Appendix A) for the contributions of the continuous, longwavelength sections of transverse acoustical (TA) phonons to Advances in Condensed Matter Physics 3 the resulting lattice heat capacities.…”