Tetrahedral rigid-body motion in silicates

Abstract

The atomic displacement parameters (ADPs) obtained from published refinements of silicate crystals measured at or below room temperature are examined to determine ifT04 (T = AI,Si) tetrahedra display rigid-body thermal motion. In Inany 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 0 atoms. The libration angle for rigid tetrahedra is quadratically dependent on the difference between the isotropic equivalent displacement parameter of the T and 0 atoms, Beq(T) and Beq(O), respectively. The value of Beq(O) is on average twice that of Beq(T), with an observed maximum value of ,2.0 A2. Variation in the observed Si-O bond lengths of rigid tetrahedra in the silica polymorphs is related only to the fractional s-character of 0, h(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.