Showing papers in "Acta Crystallographica in 1979"

Independent Fourth Order Elastic Coefficients for all Crystal Classes

Abstract: Numerical methods can be used to obtain the dependence relations between components of an nth-rank tensor for the particular symmetries of each crystal class. The program has been used successfully to calculate the fourth-order elastic coefficients, corresponding to a tensor of eighth rank for all crystal classes and the isotropic case.

The use of electric field gradient calculations in charge density refinements. II. Charge density refinement of the low-quartz structure of aluminium phosphate

Abstract: The experimental determination of the electron distribution in quartz (SiO2) is problematic since the structure is pronouncedly non-centrosymmetric. The structure of AlPO4 is derived from the quartz structure by replacing half the Si atoms by Al and the other half by P. The physical properties of the two substances are similar. The electric field gradient tensor ∇E at the site of Al (site symmetry 2) has already been measured. This electrostatic information, which is not available for quartz itself, is used in the determination of the charge density. Deformation parameters describing multipolar deformation functions are refined by least-squares methods with respect to X-ray data and the elements of the field gradient tensor simultaneously. A κ refinement yielded the atomic charges + 1.4 for Al, + 1.0 for P and -0.6 for O. The electron distribution obtained with a standard charge density refinement does not reproduce the correct ∇E. Inclusion of ∇E in the refinement leads to a different least-squares minimum. The minimum is ill-defined by the X-ray data alone, whereas ∇E stabilizes the phases of the superstructure reflections (l odd). ∇E is extremely sensitive to the deformation density distribution. The resulting deformation maps show the maxima and minima always in the same places but the inclusion of ∇E changes the heights drastically and indicates the P-O bond to be more covalent than the Al-O bond. The trigonal arrangement of the lone-pair and bonding densities around the O atoms indicates sp2 hybridization. This leads to bent covalent bonds, the angle Al-O-P being 142.3° Double bonding appears to extend over nearly planar structural fragments defined by five atoms; metal-oxygen--metal-oxygen-metal.