Anharmonic thermal vibrations and disorder of atoms in tourmaline

Elbaite (space group R3m), a Li-bearing tounnaline with general fonnula of XY3Z"(B03hSi,,0,,W4, has 5 kinds of cations and 8 kinds 01'0 (including W). Of the structural studies of tourmaline, those of Gabrielle Donnay and hcr group were unique in focusing on the structural aspccts ofthc primary pyroelectricity (Donnay, 1977" etc). Donnay (1977) refined the structure of elbaite, and tound that the magnitudes of u values for 0] and, to a lesser degree for X and O2, point to abnonnalities in the thennal vibrations. From the atomic coordinates at two different temperatures, she noticed that, while neither X nor A, has shifted signiticantly, 0] has. In the present study, we attemptcd least-squares retinement with a generalized structure lactor expression, based on the Gram-Charlicr expansion of atomic probability density fimctions (PO F), to examine the anharmonic characters of atoms in elbaite at room temperature, suggested by Donnay (1977). The chemical formula of a green prismatic crystal from Lahgman (Afghanistan) was X = (Nao52CaoI3Ko.II]().34h.-],Y = (Li]2,,Alo.<JsFeo.,oMno2oMgooITioo,h.-3, Z = AI".oo and W = ([0,(OH)]197FoIJJ)I-4. All the diffraction data werc obtained at room temperature with a spherical specimen of diameter about 0.3 mm. The unitcell dimensions are a = 15.874(3) and c = 7.116(3) A. All the refinement cycles were perfonned using the 306 I Fo without omitting any rellection trom the mcasured. The polarity of our spherical specimcn was dctennined with respect to the structure of Donnay (1977). The ham10nic least-squares relinement with 88 variables, initiated with thc positional paramcters of Donnay (1977), converged at R = 0.0337, showing considerably large thennal parameters for X, Y, 01 and A, atoms (First group) compared to the rest atoms (Second group). The further relinements with additional 63 variables lor the third and fourth order coefficients for the lirst-group atoms converged at R = 0.0294, resulting in significantly anham10nic or multimodal PDFs for the first-group atoms. Thesc PDFs are clearly asymmetric along c with the modcs shifted toward the positive side lor the a atoms and toward the ncgative side lor the cation sites trom the corresponding means. Our result of the single-temperature measurement, particularly tor 0], is just concordant with Donnay (I 977)'s two-temperature measurement of atomic shilt The prcsent study furthcr indicated that 0] was disordered over three potential energy minima in the plane perpcndicular to the 3-fold axis. I) Donnay G. Acta Cryst. A33, 927-932, 1977