Thermal Expansion of Solids and the Temperature Dependence of Lattice Vibration Frequencies

It is shown that a close relation exists between the temperature coefficient of lattice vibration frequencies and the thermal expansion coefficient. The basic equations[Formula: see text](ν i being the frequency of the ith mode of vibration, T the temperature, C i the Einstein function of frequency ν i , γ the Grueneisen parameter, and β the volume thermal expansion coefficient) are derived and discussed for various temperature ranges.