Refinement of the structure of a grossularite garnet

Grossularite, a garnet with ideal formula Ca3A1 ~ (SiO4)s, crystallizes in the cubic system, space group Ia3d-O~h with a ----11.8740.004 A and eight formula weights per unit cell. The Ca, A1 and Si atoms are in special positions; the undetermined positional and thermal parameters (except BAI) have been refined by the method of least squares. Only the 101 general structure factors particularly sensitive to the positional coordinates of the oxygen atom were used in this process. The final coordinates x = --0.0389, y ----0.0456, z ----0.1524, correspond to R ----0.126; the Si-O distance is 1.64 A, the nominally-A1-O distance is 1.95 A and the Ca-O distances are 2.33 and 2.49 A. The limits of error in cation-0 distances are +0.02 A, in O-O distances are 0.03 A and in cation-Ocation angles are 1% None of the oxygen polyhedra is regular, although the space group would allow the tetrahedra and octahedra to be regular simultaneously. Unlike the case of yttrium-iron garnet, the octahedra are more nearly regular than the tetrahedra; both of these polyhedra are more regular and the CaO8 dodecahedra less regular than the corresponding oxygen polyhedra in yttrium-iron garnet. These observations lead to a prediction regarding structural relationships in the garnets uvarovite, CaaCrg(SiO4)3, and andradite, CaaF%(SiO4) a.