Application of Neumann–Kopp rule for the estimation of heat capacity of mixed oxides

The empirical Neumann–Kopp rule (NKR) for the estimation of temperature dependence of heat capacity of mixed oxide is analyzed. NKR gives a reasonable estimate of Cpm for most mixed oxides around room temperature, but at both low and high temperatures the accuracy of the estimate is substantially lowered. At very low temperatures, the validity of NKR is shown to be predominantly determined by the relation between the characteristic Debye and Einstein temperatures of a mixed oxide and its constituents. At high temperatures, the correlation between their molar volumes, volume expansion coefficients and compressibilities takes the dominance. In cases where the formation of a mixed oxide is not accompanied by any volume change, the difference between dilatation contributions to heat capacity of a mixed oxide and its constituents is exclusively negative. It turns out that in the high-temperature range, where the contribution of harmonic lattice vibrations approached the 3NR limit, ΔoxCp assumes negative values. For more complex oxides whose heat capacity has contributions from terms such as magnetic ordering, electronic excitations, the applicability of NKR is only restricted to lattice and dilatation terms.