TETRAHEDRAL RIGID-BODY MOTION IN SILICATES

The atomic displacement parameters (ADPs) obtained from published refinements of silicate crystals measured at or below room temperature are examined to determine if TO4 (T = A1,SI) tetrahedra display rigid-body thermal motion. In many cases, the correlation found among the ADPs is consistent with the TLS model of rigid-body motion. For these data, the translational motion is described by the ADPs of the central T atom, whereas both librational and translational motion are displayed in those of the surrounding O atoms. The libration angle for rigid tetrahedra is quadratically dependent on the difference between the isotropic equivalent displacement parameter of the T and O atoms, B-eq(T) and B-eq(O), respectively. The value of B-eq(O) is on average twice that of B-eq(T), with an observed maximum value of similar to 2.0 Angstrom(2). Variation in the observed Si-O bond lengths of rigid tetrahedra in the silica polymorphs is related only to the fractional s-character of O, f(s)(O). ADPs that do not indicate rigid-body motion for a given tetrahedron may be used to identify crystals containing disorder or suggest problems with the refinement.