The crystal chemistry of a natural, birefringent garnet of composition (Fe1.88Ca0.75Mg0.24Mn0.10)Σ = 2.97(Al1.96Fe0.03Ti0.01)Σ = 2.00Si3.01O12 (approximately pyralspite75-grandite25), produced by subduction-zone metamorphism, has been investigated by single-crystal X-ray diffraction, electron microprobe analysis, Mössbauer spectroscopy, and Fourier-transform infrared spectroscopy. By FTIR the garnet is apparently indistinguishable from synthetic garnets of similar compositions and is anhydrous. The crystal structure has been refined in space group I41/acd, using 592 unique, observed reflections measured with an automated four-circle X-ray diffractometer. Dimensions of the tetragonal unit cell are a = 11.6207(7), c = 11.6230(8) Å. The final conventional residuals are R = 0.033 and Rw = 0.024. X-ray site refinement indicates a slight difference in electron density at the two unique X sites, and this is apparently the cause of birefringence (~0.001). It is proposed that the difference in electron density arises from slight ordering between the pyralspite X components (Fe2+, Mg, and Mn) and the grandite X component (Ca). The high pressure of the geologic environment evidently favored substantial solid solution between pyralspite and grandite end-members, whereas comparatively low temperatures prevented complete disorder.

A group theoretical analysis based on the Landau formalism and including the theory of induced representations shows that the observed space group could have arisen by phase transformation from a parent cubic garnet (space group Ia3d), driven by a single order parameter in each case. Such transitions may occur (1) by the T2g, irreducible representation (IR), leading to possible space groups R3c, Fddd, C2/c, or I1; (2) by the T1g IR, leading to possible space groups R3, I41/a, C2/c, or I1; or (3) by the Eg IR, leading to possible space groups I41/acd or lbca. The first two ordering paths (T2g and T1g) yield octahedral ordering; if the sizes of the octahedral cations are similar (as with Al and Fe3+ in grandites), ordering occurs by T2g, and if they are very different (as in MgSiO3 and MnSiO3 garnets), ordering occurs by T1g. Garnets that possess cations ordered in the eightfold-coordinated sites (for example, some with both significant pyralspite and grossular components) order by Eg. Thus far, the noncubic garnets with refined crystal structures possess space groups Fddd and I1 (T2g), I41/a (T1g), and I41/acd (Eg).

The approach presented is based on the assumption that phase transitions may have occurred to produce garnets of noncubic symmetry. The mathematical treatment used, however, yields the same predictions about possible space groups if ordering is assumed to have arisen as a crystal-growth phenomenon rather than by phase transformation. The experimental and field evidence accumulated so far does not provide clear evidence in favor ofone or the other, and it is possible that each plays a role under different circumstances.

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