Anisotropic thermal motions

With data averaged in point group m, the first refinements were carried out to estimate the atomic coordinates and anisotropic thermal motion parameters IP s. We have started with the atomic coordinates and equivalent isotropic thermal parameters of Joswig et al. [14] determined by neutron diffraction at room temperature. The high order X-ray data (0.9 < s < 1.28A-1) were used in this case in order not to alter these parameters by the valence electron density contributing to low order structure factors. Hydrogen atoms of the water molecules were refined isotropically with all data and the distance O-H were kept fixed at 0.95 A until the end of the multipolar refinement. The inspection of the residual Fourier maps has revealed anharmonic thermal motion features around the Ca2+ cation. Therefore, the coefficients up to order 6 of the Gram-Charlier expansion [15] were refined for the calcium cation in the scolecite. 

In the closely related compound AgCuS, the sulfur atoms form a slightly distorted hexagonal close-packed array. The Cu+ ions are located in positions within this framework to form layers, while the Ag+ ions lie between the sulfur-copper layers. These Ag+ ions show a progressively greater anisotropic thermal motion as the temperature rises, until, above 93°C, they are essentially completely mobile, leading to extremely high silver ion conductivity. 

Fio. 215. Benzene. Error synthesis maps. Above—Structure Amplitude calculations based on carbon atoms only, and on isotropic thermal motions. Below—After hydrogen atoms and anisotropic thermal motions were included in calculations. (Cox, Cruickshank and... 

Cruickshank, D. W. J. The determination of the anisotropic thermal motion of atoms in crystals. Acta Cryst. 9, 747-753 (1956). 

In their simplest form, these constraints can be used for atomic sites on special positions (e.g. x,x,x positions in cubic space groups) where there are special relationships between the individual atomic coordinates and also among the individual anisotropic thermal motion parameters (e.g. Ui i = U22 = U33 and Ui2 = Ui3 = U23 for cubic x,x,x sites). 

The equivalent isotropic temperature factors, B, are remarkably similar, atom for atom, in the two stmctures, and the equality of the temperature factors for all four tetrahedral cations (0.65, 0.65, 0.62, 0.63) immediately suggests that the aluminum-silicon distribution is identical in all four positions. A careful consideration of the apparent anisotropic thermal motion of the surface oxygens strongly suggests that the arrangement of and Na ions within either stmcture is completely random there is no evidence for segregation either into different layers or to different domains within a layer. 

---