Site-symmetry restrictions on thermal-motion-tensor coefficients up to rank 8

Abstract

An extension of the tables for the site-symmetry restrictions on the thermal-motion-tensor coefficients to include tensors up to rank 6 (up to rank 8 for cubic, hexagonal, tetragonal and trigonal site symmetries) is presented. The dependence relationships of these symmetric polar tensors are calculated in their natural crystallographic lattice frames using a direct method.

Structural role of copper in the minerals of the pearceite-polybasite group: the case of the new minerals cupropearceite and cupropolybasite

“…With the introduction of anisotropic temperature factors for all the atoms and up to fourth-order nonharmonic Gram-Charlier tensors for the DebyeWaller description (Johnson and Levy, 1974;Kuhs, 1984) of the Ag1/Cu1, Ag3 and S4 positions, to mimic the spread of electrons associated with silver along diffusion paths, the residual R value smoothly converged to the R = 0.0340 value for 578 reflections (I > 2s(I)) and R = 0.0537 for all 906 unique reflections (Table 2).…”

Generalized atomic displacements in crystallographic structure analysis

“…Owing to the tensorial character of cumulants and quasimoments any symmetry restrictions are easily introduced in the least-squares procedure. The constraints have been tabulated by Johnson & Levy (1974) up to fourth order and Kuhs (1984) up to eighth order. The statistical approach is well suited to cope not only with lattice anharmonicity but also with any higher-order static displacements and in fact has been used for a description of a variety of disordered crystallographic structures (Kuhs, 1983).…”

Crystal Structure Study of (Ca, Gd)2(Al, Ti)O4

“…Weights proportional to the number of equivalents for each reflection were allotted. Restrictions for the Gram-Charlier series-expanded anharmonic parameters up to the sixth-rank tensors were taken from ref 7. Details for X-ray diffraction and structure refinement are listed in Table 1.…”