High-temperature specific heat of UO2, ThO2, and AL2O3

The high-temperature specific heat of solid UO2, ThO2, and Al2O3 can be represented by an equation of the form Csub(p(s))=3nRF(THETAsub(D)/T)+dT3 (1), where THETAsub(D) is the Debye temperature, F(THETAsub(D)/T) is the Debye function, d represents contributions of the anharmonic vibrations within the lattice, and n denotes the number of atoms per molecule. In the liquid the corresponding equation is Csub(p(l))=3nRF(THETAsub(D)/T)+h/T2 (2), where h is the anharmonic term. It is shown that for Al2O3 and UO2, where experimental data for the liquid phase are also available, h has the same value, indicating that both materials behave identically. If we compare the thermodynamic relationship Csub(p)-Csub(v)=Vα2KT (3), where V is the volume, α the volume expansion coefficient, and K the bulk modulus, with equation (1), it follows that d must be equal to Vα2K/T2; the value of Vα2K/T2 is calculated in the temperature region where d was obtained; within experimental error they are equal. (orig.)