Some New Interrelations in the Properties of Solids Based on Anharmonic Cohesive Forces

Abstract

The lattice vibration spectrum of a solid can be characterized by one single frequency, which is defined as "the frequency of the center of gravity" of this spectrum or simply "center frequency." From its equality with the characteristic frequency of specific heat we have recently derived the "center law of the lattice vibration spectra." In assuming now that in a lattice, at equilibrium, the hypothetical maximum of vibrational energy (kinetic energy) of an atom (ion) pair equals the total cohesive energy (potential energy), and at the same time considering the anharmonicity of lattice vibrations, we derive a basic interrelation between center frequency and total cohesive energy. It constitutes a substantial extension of the above "center law." Its validity has been illustrated for 26 solid compounds of six different lattice structures which cover almost the entire range of lattice vibration spectra of solids. This interrelation allows a first determination of thus far inaccessible data of cohesive energy for solids of extremely high sublimation temperatures, such as silicon carbide, boron nitride, and the two types of diamond. Detailed study of the anharmonicity of lattice vibrations results in additional interrelations, such as one between exponent of repulsion and "related mass" [=reduced mass of the vibrating atom (ion) pairs related to argon], one between exponent of repulsion and "relative compressibility" (change of compressibility with pressure over compressibility), and thus one between "relative compressibility" and "related mass." In combining the two interrelations of center frequency, namely that with characteristic temperature and that with cohesive energy, we derive an interrelation between characteristic temperature and total cohesive energy. Examination of the relationship between anharmonicity and atomic behavior suggests a classification of solids according to their different anharmonic force characteristics. The solids can have either a soft or linear or hard force characteristic, dependent on the configuration which they resemble in the periodic chart of the atoms. The underlying concept of anharmonicity deduced in this paper helps to understand the physical properties of solids from an atomistic point of view.