Thermodynamic consistencies and anomalies among end-member silicate garnets

Materials with the garnet crystal structure include silicate minerals of importance both in geology, on account of their use in geothermobarometry, and industrially as abrasives. As a consequence of the former, there is considerable published thermodynamic information concerning them. We here examine this thermodynamic information for end-member silicate garnets (some of which are synthetic since not all occur in nature) for consistencies and anomalies, using thermodynamic relations between thermodynamic properties that we have established over recent years. The principal properties of interest are formula volume, heat capacity, entropy, formation enthalpy (from which the Gibbs energy may be obtained), and isothermal compressibility. A significant observation is that the ambient-temperature heat capacities of the silicate garnets are rather similar, whereas their ambient-temperature entropies are roughly proportional to their formula volumes. Evaluation of their Debye temperatures implies that their vibrational contributions to heat capacity are fully excited at ambient temperatures. The relatively small isothermal compressibilities of these garnets is related to the rigidity of their constituent silicate tetrahedra. We here establish additive single-ion values for each of the thermodynamic properties, which may be applied in estimating corresponding values for related materials.