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 (alpha(p)). The temperature dependences of C-p and alpha(p) are determined by four characteristic parameters of the solid: the Debye temperature theta(D), the Einstein temperature theta(E), and the Gruneisen parameters gamma(G)(ac) and gamma(G)(op) associated with the volume dependences of theta(D) and theta(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 much less than theta(D)) and increases markedly at higher temperatures. In the high-temperature range (T much greater than theta(E)), C-p is almost independent of temperature and is determined by a simple combination of the Gruneisen parameters gamma(G)(ac) and gamma(G)(op). The results obtained for alpha(p), in the low- and high-temperature limits, are in accord with those found for the asymptotic behavior of C-v with temperature.