The relationship between atomic displacement factors and structural parameters in silica polymorphs
European Journal of Mineralogy Volume 8 Number 6 (1997), p. 1311 - 1326
published: Jan 8, 1997
manuscript accepted: Jul 30, 1996
manuscript received: Feb 26, 1996
ArtNo. ESP147050806010, Price: 29.00 €
Abstract Multiple linear regression analysis of the equivalent isotropic displacement factor, at room temperature, of oxygen atoms, UeqO, or silicon atoms, UeqSi, as dependent variable, and of numerous structural parameters as independent variables, was applied to a sample of 138 symmetrically independent O atoms and a sample of 71 symmetrically independent Si atoms, from 7 phases with SiO2 chemical composition. UeqO is strongly correlated to: a) the mean value of the negative secant of the four Si-O-Si angles in a tetrahedron averaged over the two tetrahedra bridged by O; b) the average of the distance from the two Si atoms bridged by O; c) the electrostatic site energy of oxygen; and d) the fractional s-character of oxygen, defined as fx(O) = 1/(1-sec(Si-OSi)). UeqO is also correlated to: e) the equivalent displacement factor of the two Si atoms bonded to O; f) the average of the mean distance of O from the six O atoms of the two bridged tetrahedra; g) the electrostatic site energy of the Si atoms bonded to O; h) the fractional s-character of the Si atoms bonded to O, defined as/v(Si) = 2cot23. The "best" regression equation accounts for more than 80% of the UeqO variation. UeqSi is more weakly correlated to structural parameters; its "best" equation significantly correlates UeqSi only to the site energies of the O atoms bonded to Si, but explains only 30% of the UeqSi variation. UeqO correlates strongly with Si-O distances and Si-O-Si angles, even if these parameters are corrected for thermal motion according to the rigid-body model.