Specific Heats of Cu, GaAs, GaSb, InAs, and InSb from 1 to 30°K

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

“…This limiting ℎ ( ) behaviour is the automatic consequence of the well-known fact that the low-energy (TA phonon) tails of PDOS spectra for three-dimensional crystals are generally given by Taylor series [13,16,18,23,35,39,64,65] of exclusively even-order power terms, (cont.) ( ) = 2 2 + 4 4 + ⋅ ⋅ ⋅ , of the phonon energy.…”

“…), are quantifying the material-specific weights of contributions of the individual, anharmonicityrelated power terms [15,21,54,57]. Furthermore we have still included into (5) an additional linear term, ( ) ( ) = 1 , which has to represent possible contributions of a degenerate electronic system [4,6,13,23,[60][61][62][63] to the measured heat capacities. Such electronic contributions ("Sommerfeld terms" [4,6,60]) are known to be rather strong (tending to become even the dominant ones, at sufficiently low temperatures) in metals, due to large concentrations of conduction electrons.…”

“…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]…”

“…Consequently, it is as a rule possible to realize rather good fittings of available ( ) data on the basis of relatively simple theoretical model functions for PDOS spectra [64], provided that the latter are sufficiently general and flexible for reasonable reproductions of various prominent features, at least. This concerns above all the liquid-helium-hydrogen region [13,64], where the lattice heat capacities are known to be represented in good approximation by Taylor series of odd-order terms [13,16,18,23,35,39,65] (…”

“…Furthermore, towards higher temperatures, many Θ ( ) curves show a more or less pronounced increase up to certain material-specific maxima, Θ max , the actual magnitudes of which are in many cases significantly higher than the respective Θ min levels. Such typical nonmonotonic behaviours of Θ ( ) curves in the cryogenic region have been found in particular for Si and Ge [18][19][20][21] as well as for a large variety of III-V [11,12,15,[22][23][24][25][26][27][28][29][30], II-VI [14,[31][32][33][34][35][36][37][38], and I-VII [16,39,40] materials.…”