Qualitatively Different Non‐Quartic Low‐Temperature Heat Capacity Behaviors due to Various Non‐Metallic Solids

Abstract

Different non-quartic cryogenic heat capacity dependences can be unambiguously associated with the qualitatively different types of either sub-quartic or super-quartic regimes. The simplest way for a prompt association with one of these two alternative regimes is based on a couple of parameters controlling the straight-line tangents to the material-specific C(T)/T 3 curves in consideration. A representative non-Debye heat capacity formula is used for performing high-accuracy fittings of cryogenic heat capacity data sets, including reliable determinations of the material-specific temperature dependences of effective power function exponents. The cryogenic heat capacity dependences of the exemplary wide bandgap materials AgCl and LiI are found to show pronounced sub-quartic behaviors, whereas germanium and silicon are seen to pertain to the regime of super-quartic behavior. These results are in clear contrast to a hypothetical field-theoretical model published recently by Gusev [R. Soc. Open Sci. 2019, 6, 171285], which suggested an allegedly universal low-temperature behavior of quartic type. An unprecedented graphical distinction tool is introduced here, consisting in alternative C(T)/T 4 data representations, by means of which the qualitative differences between opposite non-quartic heat capacity behaviors for the materials under study have been visualized in rather pronounced form. A brief discussion is given of preliminary assessments of non-quartic cryogenic heat capacity behaviors for a larger variety of III-V, II-VI, and I-VII materials.

Experimental Verification of the Field Theory of Specific Heat With the Scaling in Crystalline Matter

“…The surface heat capacity contribution is present at any temperature, but its relative contribution with respect to the bulk specific heat depends on temperature. The numerical analysis of measured specific heats in [62] supports this idea by finding 'sub-quartic' and 'super-quartic' behaviours. These behaviours may be determined by the full spectrum of acoustic frequencies of a crystal that was not incorporated yet into the field theory of specific heat.…”

“…It is encouraging to see the early interest in these ideas since one of the goals of our publications was to excite the critical revision of existing thermal theories by condensed matter physicists [1], p. 71. Despite its generally negative opinion, the empirical analysis [62] extends the exploration of experimental data we began in [1,2], and its conclusions generally agree with the field theory of specific heat.…”

“…Pässler, summarized in the dedicated paper [62]. It is encouraging to see the early interest in these ideas since one of the goals of our publications was to excite the critical revision of existing thermal theories by condensed matter physicists [1], p. 71.…”

“…The preliminary statistical analysis of [1] was improved in [2]. In fact, the work [62] used the form of the statistical estimate, ( 13) and ( 14) introduced in our second paper [2].…”

“…Regretfully, the work [62] is devoted entirely to mathematical modelling, with the focus on the T 3 vs T 4 problem, and leaves theoretical physics out of consideration. The difference between the two is fundamental.…”