Equation of state, isobaric specific heat, and thermal expansion of solids with polyatomic basis in the Einstein‐Debye approximation

A theoretical study of the thermodynamic properties in the Einstein-Debye approximation is made for solids with polyatomic basis. Analytical expressions are derived for the equation of state, isobaric specific heat (Cp), and linear thermal expansion coefficient (αP). The temperature dependences of Cp and αp are determined by four characteristic parameters of the solid: the Debye temperature θD, the Einstein temperature θE, and the Gruneisen parameters γ and γ associated with the volume dependences of θD and θE, respectively. It is shown that the difference CP−CV between the calculated isobaric and isochoric specific heat capacities is very small at low temperatures (T ≪ θD) and increases markedly at higher temperatures. In the high-temperature range (T ≫ θE), CP is almost independent of temperature and is determined by a simple combination of the Gruneisen parameters γ and γ. The results obtained for αP, in the low- and high-temperature limits, are in accord with those found for the asymptotic behavior of CV with temperature.