Volume 194, Issue 1-2

For structures with approximate pseudotranslational symmetry the E -values obtained by a renormalizing procedure are investigated. Specially for main reflections the mean scattering power of point-atoms is considered as a function dependent on sin θ / λ and on how far the atoms in the structure deviate from ideal symmetry. For sin θ / λ – ranges in which the scattering power is a constant function classical probabilistic distributions are available. The effects are demonstrated for some real structures which were difficult or not to solve via direct methods procedures because they suffer under weak rational dependencies between their atoms.

For structures with approximate pseudotranslational symmetry a renormalizing procedure is derived specially valid for superstructure reflexions. The E -values are described in such a way that they depend on independent positions of point-atoms which in general are not the centres of the electron density of the real structure and not those of the average structure as well. The scattering power of these point-atoms is calculated using the concept of complement structure after M. Buerger. It reveals to be a function (nearly) constant in a wide sin θ / λ range so that usual probabilistic distributions are available.

Single crystals of Cs 3 Sr[Cu 2 (SCN) 7 ] of optical quality and dimensions up to 10 × 10 × 30 mm 3 have been grown from non-stoichiometric aqueous solutions. The crystal structure has been determined from singlecrystal diffractometer data by Patterson methods and refined to a final R = 0.029 for 1116 unique reflections (tetragonal, I [unk] 2m , a = 10.863(2) Å, c = 19.883(5) Å, Z = 4, D x = 2.888 Mgm −3 , μ (Mo K α ) = 9.17 mm −1 , T = 293 K). The main structural component is the binuclear complex [Cu 2 (SCN) 7 ] 5− , where the copper atoms are tetrahedral coordinated by four sulphur atoms. The linear electro-optic tensor [ r ijk σ ] (undamped) and the tensor of the linear electrostriction [ d ijk ] have been determined to: r 123 σ = + 0.06(2), r 231 σ = +1.21(2); d 312 = + 1.64(4), d 123 = −2.44(5) (unit: 10 −12 m/V, T = 295 K, λ = 633 nm).

The title compound, dimeric [Cu(bipy)(pht)] · 2H 2 O (CBP), has been synthesized by a simple new method and its crystal structure determined by X-ray analysis. The structure was solved by the heavy-atom method and by successive Fourier syntheses. CBP crystallizes in monoclinic space group P 2 1 / n , a = 15.685(11) Å, b = 12.900(9) Å, c = 8.825(3) Å, β = 100.45(3)°, Z = 4; 2983 unique reflections gave a final R = 0.057. The structure consists of centrosymmetric dimeric [Cu 2 (bipy) 2 (pht) 2 ] units together with the water of hydration. Water molecules are arranged in channels parallel to the c -axis. The coordination geometry arround Cu is square pyramidal (the CuN 2 O 2 O′ chromophore).

Three (Ni,Mg) 3 (VO 4 ) 2 solid solutions have been prepared and studied. The crystal structures ( Cmca ; Z = 4) have been refined with the Rietveld profile technique on the basis of accurate X-ray powder diffractometer data. The Ni 2+ /Mg 2+ cation distribution is almost random, but nickel has a slight preference for the smaller but less symmetrical of the two distinct, octahedrally coordinated metal sites (M1 has point symmetry 2/ m , M2 has point symmetry 2 . The results are briefly discussed in relation to Ni 2+ /Mg 2+ partitionings in olivine and three other structure types.

Large single crystals of optical quality of triclinic lithium hydrogen Oxalate monohydrate have been grown from aqueous solutions. Complete sets of pyroelectric, dielectric, piezoelectric, elastic and thermoelastic properties have been determined. The elastic constants were derived from ultrasonic measurements of resonance frequencies including piezoelectric coupling terms. These crystals possess strong pyroelectric and piezoelectric effects (coupling coefficient for thickness modes up to 0.52) which stem from the asymmetric hydrogen bond chains along [101]. These dominant bond chains are also responsible for the extremely large anisotropy of thermal expansion and elasticity. The crystals exhibit unusually large elastooptic effects in specific directions which in combination with the strong piezoelectric effects might be suitable for certain applications.

The basic definitions connected with sphere packings are given. The way in which sphere packings with tetragonal symmetry have been derived and assigned to generation classes and (topological) types is described. The results for tetragonal lattice complexes with zero and one degree of freedom are listed and – in the latter case – the sphere-packing conditions are illustrated by diagrams.

For tetragonal lattice complexes with two degrees of freedom the sphere-packing conditions, the generation classes and the (topological) types of sphere packings are tabulated. The exceptional situation for the lattice complex I 4 1 8/ amd 16 h . m . is discussed and illustrated by diagrams.

Crystal structure refinement was carried out on a defect spinel with composition Mg 0.388 Al 2.408 O 4 synthesized at 2050°C Combining information from site occupancies and bond distances for tetrahedral and octahedral sites, the following cation and vacancy distribution were obtained: (Al 0.653 Mg 0.347 )(Al 1.755 Mg 0.041 □ 0.204 )O 4 . Structural analysis performed after heating the same crystal at 1150°C led to the same result, suggesting that the obtained distribution is stable over a wide range of temperatures.

The crystal structure of HgAl 2 Se 4 was refined to R = 0.0333 ( R w = 0.0325) with the thiogallate structure type of space group I [unk]. Se is located at x = 0.2736(2), y = 0.2635(2) and z = 0.1382(1). The lattice parameters are a 0 = 5.7183(1) Å and c 0 = 10.7643(2) Å.

We wish to point out that papers by Rahman (1988) and Rahman and Weichert (1990) contain a basic error in concept. In these papers, the authors seek to shorten the amount of computation necessary for a simulation of a high-resolution transmission electron microscope (HRTEM) image of a structure containing a defect, using as an example an oxygen vacancy in mullite. Unfortunately, the method used leads to errors in the simulated image. The usual method of computing an image of a non-periodic structure is to construct a “supercell” consisting of a number of perfect unit cells surrounding the cell(s) containing the defect (e. g. Iijima and O'Keefe, 1978). The computation is then carried out using the supercell as the new unit cell for the defect structure. Note that the new defect structure is periodic with the periodicity of the chosen supercell, and thus the number, n , of original unit cells making up the supercell must be chosen large enough not only to sample diffraction space sufficiently finely, but also to keep the images of adjacent defects from interfering. Such interferences can arise if electrons scattered from non-perfect regions near to the defect in one supercell contribute to the image of the defect in an adjacent supercell. In addition, if a smooth “periodic continuation” of the structure at the supercell boundary is not possible, the area immediately surrounding the defect of interest must be far enough away from the unsmooth boundary to avoid interferences between the image of the defect and that of the (probably nonphysical) boundary.