Band 207, Heft 2

Single-crystal structure determinations of wolframite-type structures were performed using a diamond anvil cell with beryllium gaskets. Unit cell parameters of MgWO 4 , MnWO 4 and CdWO 4 were determined at several pressures up to 8.0 GPa and structure refinements were performed up to 6.0 GPa. The high pressure behaviour is compared with the behaviour of the related scheelite-type structure. All investigated compounds compress anisotropically with the b -axis 1.5 to 2.5 times more compressible than the c -axis and 1.2 to 2.1 times more compressible than the a -axis. In all compounds, the WO 6 polyhedra are significantly less compressible than the AO 6 octahedra; the compressions of the latter are comparable with the bulk compressions of the compounds. Anisotropies in the pressure response of the AO 6 and WO 6 polyhedra result in the anisotropic unit-cell compression. With increasing pressure the oxygen atomic positions remain constant within one standard deviation, while the heavy atoms positions show a different pressure dependence: a shift of y (Mg) to smaller values and of y (Cd) to higher values, while y (Mn) undergoes little if any change. With increasing pressure the A and W cations approach each other, indicating a tendency of a transition from the wolframite structure to the scheelite structure, where the A and W cations lie in the same plane.

An extension of Buerger's concept of complementary point sets has been used to determine homometric pairs of point sets of the plane groups. A procedure is outlined to derive tautoeikonic pairs (these include congruent, enantiomorphic and homometric pairs) of point sets by means of point configuration splitting.

The crystal structures of two hydrothermally synthesized AgCu-arsenates were determined by single crystal X-ray work: Ag 5 Cu(AsO 4 )(As 2 O 7 ) [ a = 5.859(1), b = 9.019(2), c = 10.384(2) Å, α = 97.18(2), β = 90.98(2), γ = 92.11(2)°, space group P [unk], Z = 2, R w = 0.034 for 5827 observed data and 185 variable parameters] and Ag 7 Cu(As 2 O 7 ) 2 Cl [ a = 10.335(2), b = 8.992(2), c = 16.546(3) Å, β = 95.21(2)°, space group C c, Z = 4, R w = 0.035 for 3202 observed reflections and 243 variable parameters]. The environment of the Cu atom in Ag 7 Cu(As 2 O 7 ) 2 Cl is peculiar: the Cu–O bond lengths of 1.914(7), 1.945(6), 2.136(8), 2.147(7), 2.250(8), and 2.344(7) Å show an uncommon [2+2+2] coordination (distorted octahedron). The two Cu atoms in Ag 5 Cu(AsO 4 )(As 2 O 7 ) are [4] and [4+2] coordinated, all the Ag atoms are irregularly [5], [6], and [7] coordinated to O (and Cl) atoms. The geometry of the pyroarsenate groups are compared to data from literature.

In the general case of a Karle-Hauptman matrix containing no symmetry equivalent reflections, maximizing the determinant as a function of the phases does not necessarily lead to an unambiguous solution of the phase problem. Individual phases may be shifted from their correct values in a seemingly completely arbitrary way. This problem is discussed in simple mathematical terms and a method is proposed allowing the identification of those elements in a Karle-Hauptman matrix possibly suffering from the effects discussed, given the space-group symmetry and the composition of the matrix. The conclusion reached in this paper is that only the presence of a sufficiently large number of symmetry equivalent reflections and/or Friedel opposites in a Karle-Hauptman matrix causes the Generalized Maximum Determinant Rule to be an effective tool in ab initio phase determination.