Model-free temperature scaling for heat capacity

In treating the experimental data on the heat capacity of solids, the essence of any model application is in the searching for the scaling factors (k _i or 1/Θ_i) which transform a set of independent functions C _P,i(T) for every substance into a function C _P(T·k _i) universal for the particular set of substances. DSC heat capacities of I–III–VI₂ compounds at elevated temperatures exceed the upper limit of 12R (3R per mole of atoms) and make impossible application of any model. Nevertheless, the temperature scaling of heat capacity can be solved as a pure mathematical problem without any physical model (theory). The benefits of the model-free scaling are illustrated with the case of four isostructural chalcogenides (LiInS₂, LiInSe₂, LiGaS₂, and LiGaSe₂) measured recently with DSC in a temperature range from 180 to 460 K. The upper limit of C _P(T·k _i) functions was expanded up to 635 K. Low-temperature heat capacity of LiInSe₂ published in 1995 made it possible to derive the thermodynamic functions (enthalpy and entropy) for LiInS₂ (0–590 K), LiGaS₂ (0–640 K), and LiGaSe₂ (0–490 K) and expand those data for LiInSe₂ from 300 to 460 K.