Birefringence among the grandite garnets (grossular-andradite solid-solution series) is common and has been found previously to result, at least in some cases, from ordering of A1 and Fe3+ on the octahedral (a) sites of space group Ia3d, lowering the symmetry to Fddd or I1¯; other possible space groups, all of them subgroups of Ia3d, have been suggested. A group theoretical analysis, based on the Landau formalism and including the theory of induced representations, has been carried out for order-parameter transitions from Ia3d to subgroup symmetries, in which the primitive unit cell is preserved. It is found that only one irreducible representation of Ia3d, namely T2g, leads to space group Fddd, and it yields R3¯c, C2/c, and I1¯ as permissible subgroups as well. Elastic strain, domain formation, and domain-wall orientations are discussed for the transitions from Ia3d. Further, a function that transforms under the identity representation of 3¯ and that is associated with the (0,0,0) site of Ia3d induces the T2g representation of Ia3d, and that function is interpreted as an ordering function. Extension to the remaining 15 octahedral (a) sites in the conventional (nonprimitive) cubic unit cell produces ordering functions (i.e., basis functions of T2g) that can be applied to any of the above subgroups. The ordering functions for Fddd and for I1¯ correctly predict the relative ordering of A1 and Fe3+ observed in grandite garnets of those space groups. It is concluded that for birefringent garnets with compositions between grossular and andradite, ordering schemes that have been observed to date could have occurred as homogeneous phase transformations from Ia3d, driven by a singleT2g order parameter, as well as by crystal-growth phenomena as suggested by other authors.

This content is PDF only. Please click on the PDF icon to access.

First Page Preview

First page PDF preview
You do not have access to this content, please speak to your institutional administrator if you feel you should have access.