An X-ray single crystal study of asymmetric thermal vibrations and the positional disorder of atoms in elbaite

摘要

A least squares refinement with a generalized structure factor expression in the Gram-Charlier expansion was applied to the structure of elbaite, XY_3Z_6(BO_3)_3T_6O_(18)A_3~((1))A~((2)) (X = Na_(0.640)Ca_(0.090)K_(0.006)□_(0.264), Y = Al_(0.415)Fe_(0.084)~(2+)Mn_(0.034)~(2+) Mg_(0.005)Ti_(0.003)~(4+)Li_(0.458), Z = Al, T = Si, A~((1))= (OH)_(0.750), and A~((2))= F_(0.179)(O,OH)_(0.071)). Elbaite has space group R3m, and hexagonal cell dimensions of a = 15.874(3) and c = 7.116(3) A. The least squares refinement of the X-ray single-crystal data measured at room temperature converged at R = 0.0221 for 179 variables, including terms up to the fourth order coefficients. The O1 and O2 sites showed multiple split probability density functions (pdfs), and the X site showed a circular ring-like pdf, providing evidence of positional disorder at these sites. The disorder at the O1 and O2 sites was interpreted to be due to substitutional disorder of the Y site cations. The remaining atom sites all showed unimodal pdfs with a more or less asymmetric tendency along the hexagonal caxis. The asymmetry is related to the primary effect of pyroelectricity.