| Abstract | We have measured octahedral Fe3+ and tetrahedral Fe3+ site populations, in annite samples equilibrated at different temperatures under the C-CH4 buffer at 2 kbar, with sufficient accuracy (0.2-1 %total-Fe) to test a lateral constraint model that includes differential thermal expansion of the tetrahedral and octahedral bonds, in addition to previously proposed tetrahedral rotation (a) and octahedral flattening (1Jr). We used Mossbauer spectroscopy with data treatment and spectral analysis methods including: (1) analytic methods for removing spectral distortions associated with the effec ts of absorber thickness; and (2) a Voigt-based fitting method that allows arbitrary-shape quadrupole splitting distributions (QSDs) for each site. The usual constant-temperature crystal chemical models based on regular polyhedral constructions are shown to give correct b lattice parameter predictions at room temperature, if tetrahedral elongation (along c) is taken into account by using effective tetrahedral bond lengths based on basal 0-0 distances. When, in addition, we include thennal expansion coefficients for the tetrahedral and octahedral bonds (a, and a 0 , respectively), we lind that our measured site populations are consistent with reasonable parameter values: "' = 56.8 ± 0.6 degrees, at synthesis, and ao - a, = 32.3-33. I X I 0"6 °C '' where a, is taken to lie in the physical range 0 - 20 x 10·6 °C1 and a (the tetrahedral rotation angle) is assumed to be zero at synthesis. This demonstrates the possibility of undenstanding site populations in annite in terms of such models and suggests that differential thermal expansion plays a key role. We also obtain an accurate lower bound for Fe3~1Fe, .. in annite of9.59(9) %, which represents the limit imposed by lateral misfit structural constraints under highly reducing conditions. Finally, we observe a clear migration from octahedral Fe·'- to tetrahedral Feh as equilibration temperature increases. This feature is not elucidated by our model and is presumably due to more subtle effects. such as the temperature dependence of hydrogen fugacity under a given buffer. |
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