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

Abstract

A least squares refinement with a generalized structure factor expression in the Gram-Charlier expansion was applied to the structure of elbaite, Xy3Z6 (BO3)3T6 O18 A3(1) A(2) (X = Na0.640 Ca0.90 K0.006□ 0.264, Y = A10.415 Fe0.0842+ Mn0.0342+ Mg0.005 Ti0.0034+ Li0.458, Z = Al, T = Si, A(1) = (OH)0.750, and A(2) = F0.179 (O,OH)0.071). Elbaite has space group R3m, and hexagonal cell dimensions of a = 15.874(3) and c = 7.116(3) Å. 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 c-axis. The asymmetry is related to the primary effect of pyroelectricity.