ISOBARIC SPECIFIC-HEAT AND THERMAL-EXPANSION OF SOLIDS IN THE DEBYE APPROXIMATION

A theoretical study in the Debye approximation is made of the isobaric specific heat (C-P) and thermal expansion of solids with a Bravais lattice. Analytical expressions are obtained for the variations of C-P and the linear thermal expansion coefficient (alpha(P)) with temperature. The temperature dependence of C-P is determined by two characteristic parameters of the solid: the Debye temperature theta and the Gruneisen parameter gamma(G). 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) and increases markedly at higher temperatures. In the range T much greater than theta, C-P is almost independent of temperature and is determined solely by gamma(G). This provides a technique to estimate the Gruneisen parameter gamma(G) from the measurements of isobaric specific heat at high temperatures. The results obtained for alpha(P), in the low- and high-temperature limits, are in agreement with those in literature.