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

Figure 9

Exact dependence (—) of the characteristic Debye variable (=) on the relative (normalized) magnitudes of heat capacities, (), in comparison with the low- asymptote, (; see (B.1)), and the characteristic high- approximation, (– – – – –; see (B.3)). Considerable reductions of maximum deviations to ±0.13% (see the upper inset) or ±0.0153% (see the middle inset) are achieved by means of combinations of two more elaborate, qualitatively different versions of low-to-intermediate- approximations, (–⋅–⋅–⋅–; see (B.5a) and (B.5b)) and (– –⋅– –⋅–; see (B.6)), in combination with the complementary high- curve sections, that is, or , respectively. From the lower inset we see that the residual deviations of the complementary high-precision formulas (see (B.8)) and (see (B.9)) are throughout smaller than 0.000016%.