Abstract
The field (geometrical) theory of specific heat is based on the universal thermal sum, a new mathematical tool derived from the evolution equation in the Euclidean four-dimensional spacetime, with the closed time coordinate. This theory made it possible to explain the phenomena of scaling in the heat capacity of condensed matter. The scaling of specific heat of the carbon group elements with a diamond lattice is revisited. The predictions of the scaling characteristics for natural diamond and grey tin are verified with published experimental data. The fourth power in temperature in the quasi-low temperature behaviour of the specific heat of both materials is confirmed. The phenomenon of scaling in the specific heat, previously known only in glassy matter, is demonstrated for some zincblend lattice compounds and diamond lattice elements, with their characteristic temperatures. The nearly identical elastic properties of grey tin and indium antimonide is the cause for similarity of their thermal properties, which makes it possible to make conjectures about thermal properties of grey tin.
Highlights
In the present paper we demonstrate that the following scaling features, predicted by the field theory of specific heat, for the same crystal lattice, are supported by available experimental data for single crystals with the diamond and zincblend lattices: 1. specific heat functions of crystalline materials, with the same crystal lattice, exhibit the scaling, i.e. these rescaled functions coincide; 2. the magnitude of the specific heats at the corresponding characteristic temperatures, i.e. the ‘boson peak’, which indicates the threshold of the quasi-low temperature regime, is the same for materials with the same class of crystal lattice; 3. the slopes of the linear functions, in the quasi-low temperature regime, of the corresponding C/T3 plots, are the same for the same class of crystal lattice
The specific heat function of α-Sn is expected to match the specific heat of InSb, including the melting temperature, when direct measurements would be made with single crystals of pure grey tin
The specific heat of solid state matter reaches at melting temperatures the limiting value of 27–29 J/(K mol), which is different for different materials
Summary
In the present paper we demonstrate that the following scaling features, predicted by the field theory of specific heat, for the same crystal lattice, are supported by available experimental data for single crystals with the diamond and zincblend lattices: 1. New precision measurements of the specific heat of grey tin could deliver more numerical values to check the proposed functional form of C.
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