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

• Published in: Journal of Mineralogical and Petrological Sciences Vol. 102; no. 2; pp. 115 - 126
• Main Authors: KIHARA, Kuniaki, HIRATA, Hikaru, IDA, Akihiro, OKUDERA, Hiroki, MORISHITA, Tomoaki
• Format: Journal Article
• Language: English
• Published: Sendai Japan Association of Mineralogical Sciences 2007; Japan Science and Technology Agency
• Subjects: Asymmetric thermal vibrations; Disorder; Elbaite; Primary pyroelectricity; Probability density function; Tourmaline
• ISSN: 1345-6296; 1349-3825
• DOI: 10.2465/jmps.060802

A least squares refinement with a generalized structure factor expression in the Gram-Charlier expansion was applied to the structure of elbaite, XY3Z6(BO3)3T6O18A3(1)A(2) (X = Na0.640Ca0.090K0.006[]0.264, Y = Al0.415Fe2+0.084Mn2+0.034Mg0.005Ti4+0.003Li0.458, 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.