Other| April 01, 1996 Parameterization of energy and interactions in garnets; end-member properties G. Ottonello; G. Ottonello University of Genoa, Department of Earth Sciences, Genoa, Italy Search for other works by this author on: GSW Google Scholar M. Bokreta; M. Bokreta Search for other works by this author on: GSW Google Scholar P. F. Sciuto P. F. Sciuto Search for other works by this author on: GSW Google Scholar American Mineralogist (1996) 81 (3-4): 429–447. https://doi.org/10.2138/am-1996-3-417 Article history first online: 02 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share Twitter LinkedIn Tools Icon Tools Get Permissions Search Site Citation G. Ottonello, M. Bokreta, P. F. Sciuto; Parameterization of energy and interactions in garnets; end-member properties. American Mineralogist 1996;; 81 (3-4): 429–447. doi: https://doi.org/10.2138/am-1996-3-417 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu nav search search input Search input auto suggest search filter All ContentBy SocietyAmerican Mineralogist Search Advanced Search Abstract We present results of static lattice energy and vibrational energy calculations for the 12 garnet end-members in the system (Ca,Mg,Mn,Fe)3(Al,Cr,Fe)2Si3O12. 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 Å and averaging approximately 0.48 Å. Adopting the Huggins-Mayer formulation of repulsive terms (constant hardness factor ρ = 0.48 for the family of isostructural compounds) and assuming initially repulsive radii to be equal to the crystal radii, it is shown that the preexponential b factors closely obey the Bom-Mayer generalization (repulsive factor, b, constant in the same family of compounds). Static energies of the common compounds were then solved with the assumption of full ideality (i.e., p and b constant in the family of isostructural 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 Bom-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 Bom-Mayer approach. Heat capacities and entropies for all end-members were determined by following the guidelines of the Kieffer model, adjusting the lower cut-oif frequency of the optical continuum ω1,Kmax 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 parameters is given for all 12 garnet end-member components. This content is PDF only. Please click on the PDF icon to access. First Page Preview Close Modal You do not currently have access to this article.