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-De bye 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 t emperature dependences of C-p and alpha(p) are determined by four char acteristic parameters of the solid: the Debye temperature theta(D), th e 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 capacitie s is very small at low temperatures (T much less than theta(D)) and in creases markedly at higher temperatures. In the high-temperature range (T much greater than theta(E)), C-p is almost independent of temperat ure and is determined by a simple combination of the Gruneisen paramet ers 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 foun d for the asymptotic behavior of C-v with temperature.