The structures of the β-cristobalite phases of SiO₂ and AlPO₄

Abstract

The crystal structures of the ‘cristobalite’ phases of SiO₄ and AlPO₄ have been determined from X-ray data collected at high temperatures. A model is suggested which gives a much better fit to the data than previously published structures. In this model, the 16 oxygen atoms of the unit cell are statistically distributed over the 96 positions (h) of the space group Fd3m. This averaged structure is interpreted as comprising domains of ‘ideal’ cristobalite (space group 142d) joined together in six different orientations as a kind of micro-twinning. In this way the structure retains a short-range order similar to low cristobalite, but loses part of the long-range order of the oxygen atoms. From the results of least-squares refinements at several temperatures, a static disordering is calculated, equal to (U _x ² )^1/2=0·18 Å for the silicon atoms. The β-cristobalite phase of AlPO₄ is similarly disordered, with a short-range structure isomorphous with BPO₄.