PARAMETERIZATION OF ENERGY AND INTERACTIONS IN GARNETS: END-MEMBER PROPERTIES
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dc.contributor.author | Ottonello G. | |
dc.contributor.author | Sciuto P.F. | |
dc.contributor.author | Bokreta M. | |
dc.date.accessioned | 2020-12-04T08:50:34Z | |
dc.date.available | 2020-12-04T08:50:34Z | |
dc.date.issued | 1996 | |
dc.identifier | https://elibrary.ru/item.asp?id=31672308 | |
dc.identifier.citation | American Mineralogist, 1996, , 3, 429-447 | |
dc.identifier.issn | 0003-004X | |
dc.identifier.uri | https://repository.geologyscience.ru/handle/123456789/20442 | |
dc.description.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. | |
dc.title | PARAMETERIZATION OF ENERGY AND INTERACTIONS IN GARNETS: END-MEMBER PROPERTIES | |
dc.type | Статья |
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