PARAMETERIZATION OF ENERGY AND INTERACTIONS IN GARNETS: END-MEMBER PROPERTIES

Abstract

We present results of static lattice energy and vibrational energy calculations for the 12 garnet end-members in the system (Ca,Mg,Mn,FeMAl,Cr,Fe)2Si3012' The structure of the end-member phases was first simulated with the aid of expressions of the Novak-Gibbs type followed by a distance least-squares treatment (DLS), with an appropriate choice of the ionic radii of the cations in the crystal structure. The high-P garnet structure was simulated with the assumption that cation-to-O distances obey the generalizations of Ha- zen and Finger (1979, 1982). Polyhedral compressibilities were modified to account for the P dependency of bulk modulus. The resulting bulk moduli are in satisfactory agreement with experimental observations and are internally consistent. The thermal expansion of the various end-members was derived from linear polyhedral expansivities, in a fashion analogous to that used to determine compressibility, by structural simulation and DLS refinements. Compressibilities of garnet end-members are shown to be consistent with the usual exponential form of short-range pair potentials, with a hardness factor ranging from 0.45 to 0.51 A and averaging approximately 0.48 A. Adopting the Huggins-Mayer formulation of repulsive terms (constant hardness factor p = 0.48 for the family ofisostructural com- pounds) and assuming initially repulsive radii to be equal to the crystal radii, it is shown that the preexponential b factors closely obey the Born-Mayer generalization (repulsive factor, b, constant in the same family of compounds). Static energies of the common compounds were then solved with the assumption offull ideality (i.e., p and b constant in the family ofisostructural salts) and for the appropriate repulsive radii. Because the static energies of the 12 garnet end-members are rigorously coplanar in the chemical space of interest, in light of the Born-Haber-Fayans thermochemical cycle, the repulsive energies of the six uncommon end-members (hence the bulk static energy and the corresponding enthalpy at reference state) were readily obtained by application of the combined Huggins- Mayer and Born-Mayer approach. Heat capacities and entropies for all end-members were determined by following the guidelines of the Kieffer model, adjusting the lower cut-off frequency of the optical continuum Wl,Kmu such that the calorimetric third-law entropy (after correction for anharmonicity and magnetic spin) is reproduced and at the same time conforming to the low-T Cp calorimetric data. A complete set of thermodynamic param- eters is given for all 12 garnet end-member components.