Fundamental characteristics of solids from low-temperature heat capacity

Abstract

A new approach to obtaining fundamental characteristics of solids is provided. The key element of this approach is related to solving the inverse problem of how to reconstruct phonon density of states g(ω) from low-temperature heat capacity. The original method for numerical solution of this problem allows to calculate the g(ω) dependence with correct description of its shape and correct proportion of the number of vibrational modes in different frequency intervals. This allows to accurately calculate the moments of the g(ω) and related characteristic temperatures which, being constants, unambiguously describe individual substance. Also this allows to calculate a zero-point energy of crystal with high accuracy. This, in turn, opens up the possibility for calculating the full internal energy of a solid. The knowledge of the g(ω) allows calculating the isochoric thermodynamic functions in the entire region of existence of solid phase. Special attention is paid to the estimation of the accuracy of the characteristics obtained. The capacities of the approach are demonstrated on a model object and a real-world object, the latter is represented by a single-crystal lithium molybdate. The described approach is universal and opens up new possibilities for studying solids. The proposed computer algorithm can be used to numerical solve other types of inverse problems that include the integrated form.