Optimizing the heat capacities of sphalerite phases as single system, or how nuclear physics can help physical chemistry

• Published in: Calphad Vol. 85; p. 102687
• Main Authors: Vassiliev, V.P., Leonov, A.S., Kulinich, S.A.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2024
• Subjects: Diamond like phases; Heat capacity; Similarity method; Heat capacity; Similarity method; Diamond like phases
• ISSN: 0364-5916; 1873-2984
• DOI: 10.1016/j.calphad.2024.102687

The correct mathematical description of heat capacities Cp in a wide range of temperatures is still unsolved problem. A fragmental description of some phases is like a vision of one part of a large mosaic picture. A single description of Cp or other property of a phase of any isostructural series does not allow one to see the integrity of the entire ensemble. We propose a special mathematical model to describe Cp in a wide temperature range for a whole large class of isostructural sphalerite phases. In the proposed model, it is believed that an ideal crystal does not have any foreign inclusions, defects, or dislocations. The group IV elements (Si, Ge, α-Sn and diamond-like Pb) were taken as the basis, with flerovium (114Fl) closing this group. There should be no other elements in this group according to the fine structure constant (α) (or the Sommerfeld constant). As a consequence, the limiting value of the heat capacities of phases with a sphalerite structure falls on the element 114 (114Fl) and has a value of Cp = 30.5 ± 0.3 J · mol-at−1 · K−1. This value was obtained as a maximal virtual point Cp of the last element (114Fl) of group IV and corresponds to Ln (Cp/R) = 1.30 ± 0.01 for the isotherms ln (Cp/R) vs Ln(N), where N is an atomic number of an element of group IV or the sum of the atomic numbers of AIIIBV or AIIBVI compounds per mole-atom. The common point of heat capacity attributable to flerovium is obtained from the linear equations Ср/R vs Ln(N) at low temperatures from 25 to 35K. For only pure elements of group IV (Si, Ge, α-Sn and diamond-like Pb), flerovium closes this group, and there are no other elements behind it, according to α. The maximum heat capacity of flerovium can be taken as 30.5 J·mol-at−1·K−1 with an accuracy of 1%. As the temperature decreases, this value slowly decreases (within 1%), and then, when it approaches 0 K, it drops sharply to 0 J·mol-at−1·K−1. To describe the set of the isostructural experimental data Cp(T) for diamond-like phases in solid state as a whole system, here we used a special multi-parameter family of functions. For each substance, the parameters are found by minimizing the discrepancy between the theoretical dependence Cp(T) and corresponding experimental data. The dependence of the heat capacities for elements of group IV (Si, Ge, α-Sn, diamond-like Pb, Fl) at fixed temperatures on Ln(N), where N is the atomic number or the demi sum of the atomic numbers of phases AIIBVI or AIIIBV. In this case, either a break point or an inflection point attributable to germanium is observed for parameter dependencies on Ln(N). •Experimental data Cp(T) of diamond-like phases are described as a single system.•A multi-parameter family of functions (MPFFs) was used to describe Cp(T).•MPFF coefficients are polynomial equations with N (atomic number of group IV element).•For AIIBVI or AIIIBV phases, N was the demi-sum of atomic numbers.•Unknown MPFF coefficients for Al, Ga, In, Tl and Nh nitrides were interpolated.