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 ( C p ), and linear thermal expansion coefficient (α P ). The temperature dependences of C p and α p are determined by four characteristic parameters of the solid: the Debye temperature θ D , the Einstein temperature θ E , and the Grüneisen parameters γ   G acand γ   G OPassociated with the volume dependences of θ D and θ E , respectively. It is shown that the difference C P − C V between the calculated isobaric and isochoric specific heat capacities is very small at low temperatures ( T ≪ θ D ) and increases markedly at higher temperatures. In the high‐temperature range ( T ≫ θ E ), C P is almost independent of temperature and is determined by a simple combination of the Grüneisen parameters γ   G acand γ   G OP . The results obtained for α P , in the low‐ and high‐temperature limits, are in accord with those found for the asymptotic behavior of C V with temperature.