Correlation and prediction of thermodynamic data for oxide and silicate minerals

Often one needs to estimate heat capacities and related properties such as the entropy for a particular material through interpolation, extrapolation, or comparison with data for related materials. A scheme is discussed to perform such estimates, focusing on the vibrational entropy. At intermediate and high temperatures, the entropy depends only on the logarithmic average over the phonon frequencies. This average can be factorized, so that the atomic masses separate from the interatomic force constants. Thus, one can account for the mass effect in the vibrational entropy and get a remaining quantity which depends only on the force constants, i.e., on the electronic structure, and shows a strong regularity when chemically similar materials are compared. In the framework of these ideas, estimates based on an additivity rule for the entropy of a complex system in terms of the entropies of the constituents. and also relations between the vibrational entropy and sound velocities, are discussed. Oxide and silicate minerals are used as examples.