# Energetics of garnets: Computational model of the thermochemical and thermophysical properties

#### Abstract

This study is composed of two parts. The aim of the first part is to understand the behavior of garnet solid solutions in the four-component system Grossular-Pyrope-Almandine-Spessartine. A review on the spinodal decomposition in silicate minerals suggested that this mechanism may cause phase separation in silicate garnets. The literature points to the fact that the introduction of the Ca component into the Pyrope-Almandine-Spessartine system is mostly responsible for its non-ideal behavior and may provoke immiscibilities in this system. This is illustrated here by the theoretical investigations of the stability domaines of this system using the spinodal isotherm method. The anisotropy observed in natural garnets, from South African Kimberlites (representative of this system) is interpreted as resulting from the formation of composition fluctuations during the early stages of spinodal decomposition. A hypothesis was set forth: homogeneous garnets in peridotite fragments were picked up by the rising flow of kimberlites towards the earth's surface. The rapid emplacement of these xenoliths in a low pressure and chilling environment triggered the spinodal decomposition mechanism in these crystals; the kinetics were frozen immediately by this fast quenching effect preventing any noticeable defects from developing in the garnets. The second part is designed as a strategy to gain more information on isostructural end member compounds composing a multicomponent system such as the garnet group. The question examined here is whether the behavior of a solid solution can be predicted from the sole knowledge of the characteristic properties of its end members. The garnet system taken under consideration is constituted by 12 end members and is represented by (Ca,Mg,Mn,Fe)$\rm \sb3(Al,Cr,Fe)\sb2Si\sb3O\sb{12}.$ Systematic refinements of the end member structures are performed and the radii of cations in each structure are optimized with the use of the distance-least-squares (DLS) method. A method based on similar triangles properties is used to determine the thermal expansion and the bulk modulus of each end member. A relationship between the thermophysical and thermochemical properties of the end members and the characteristic properties of the atomic species in the corresponding structure is established. The high level of accuracy with which the published data on some garnets is reproduced (standard deviations between 10$\sp{-3}$ and 10$\sp{-5})$ has given enough confidence to use this relationship to estimate the missing data for other garnet components. Lattice energies, enthalpies of formation, bulk moduli, thermal expansions, heat capacities and entropies are thus tabulated for all 12 end members. A mixing model based on lattice energy calculations and using the Pyrope-Grossular join as an example is proposed.

#### Subject Area

Geology|Geochemistry|Mineralogy

#### Recommended Citation

Bokreta, M'hamed K, "Energetics of garnets: Computational model of the thermochemical and thermophysical properties" (1992). Dissertations available from ProQuest. AAI9235112.
https://repository.upenn.edu/dissertations/AAI9235112

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