Search

Single crystals of tetragonal [Ca.sub.3][Mn.sub.2][Ge.sub.3][O.sub.12] garnet (space group symmetry [14.sub.1]/a, a = 12.3098(7) [Angstrom], c = 12.3277(9) [Angstrom]) were characterized by X-ray diffraction and transmission electron microscopy. Their structure is topologically isosymmetric to tetragonal high-pressure garnets such as majorite, displaying the same two distinct types of macroscopic twin mechanisms. Twinning occurs as pseudomerohedral ferroelastic twin lamellae with preferred orientation of the twin-domain boundaries parallel to [{101}.sub.tet], whereas merohedral ferrobielastic twin domains occur without any orientational preference. The crystal structure was determined from single-crystal X-ray diffraction data of a crystal fragment completely free of pseudo-merohedral twin domains. It shows two different Jahn-Teller distorted Mn[O.sub.6] octahedra, with a different orientation of the axis of polyhedral elongation. The ordering scheme of these Jahn-Teller distorted octahedra follows in an alternating pattern the densest rod packing, and the cooperative effect of the electronically induced octahedral distortion was found to be responsible for the cubic-to-tetragonal symmetry breaking in [Ca.sub.3][Mn.sub.2][Ge.sub.3][O.sub.12] garnet. The extent of polyhedral distortion indicates a partially dynamic character of the Jahn-Teller effect. The distortion of the tetrahedral T2 sites controls the cooperative effect of the lattice strain induced by the Jahn-Teller distortion of the [Mn.sup.3+] octahedra and thus is responsible for the overall lower symmetry.

The volumes of mixing of six garnet binaries in the four-component system almandine-pyrope-spessartine-grossular have been analyzed and compared. The almandine-pyrope join is thermodynamically ideal and the others show positive deviations from ideality. The magnitude of the excess volume of mixing of a given binary, as described by a symmetric mixing model, is shown to be a function of the volume difference between the two end-member components. The relationship between the magnitude of nonideality and volume difference can be described with a linear or quadratic function, but the latter has a physical basis in strain theory. Positive deviations from ideal thermodynamic mixing are primarily a result of strain resulting from the substitution of dodecahedral X-site cations of different sizes, but second-order chemical effects (e.g., electronic, coulombic) also appear to contribute to thermodynamic properties. XRD and IR spectroscopic measurements show that nonlinear behavior of microscopic properties, such as bond lengths and polyhedral distortions and volumes, across a solid solution is strong for pyrope-grossular garnets and very small to nonexistent for almandine-pyrope solid solutions. The magnitude of the deviations from linearity in the microscopic properties can be related to the excess volume of mixing for a given binary. A good correlation exists between microscopic structural strain and the macroscopic volume of mixing.