Single Crystal Elastic Constants and Calculated Aggregate Properties. A Handbook

Abstract

733 potential, steep towards the Pb 2+ ions, flat towards the unoccupied center of the elementary cell. Our investigations do not show a difference in the potentials towards the nearest F-neighbours ((110) and (100) directions), but these potentials are clearly steeper than in the (l 1 l) directions towards the center of the elementary cell. Our investigations demonstrate that elastic X-ray diffraction data allow refinements of anharmonic temperature factors up to sixth order for the Pb 2+ ions. These temperature factors and the corresponding p.d.f. maps allow the determination of one-particle potentials, which can be used to study the thermal vibrations of the Pb 2+ ions in arbitrary directions. We are very indebted to Dr J. Schoonman for supplying us with crystals and to Mr B. Mfihlmann for technical assistance. Abstract The charge density in ~-A1203 has been refined with respect to X-ray structure factors [complete spheres for both Mo Ka and Ag Kt~ radiations with (sin 0/2)m,x = 1.19 and 1.495,/k-~ respectively] and electric-field-gradient tensors at both atomic sites, using Hirshfeld-type deformation functions. Atomic charges from a x refinement are + 1.32 (5) for AI and-0.88 (8) e for O. The charge distribution of O is polarized towards the four A1 neighbours, and metal-metal bonds are clearly absent. Quadrupole coupling constants and asymmetry parameters of the field-gradient tensors cannot be determined from the structure factors. They define the quadrupolar deformations near the atomic centers, and the X-ray data define the charge density between the atoms. The orientational parameters of the tensors and the signs of their largest eigenvalues can be qualitatively retrieved from the X-ray data. The 0567-7394/82/050733-07501.00 refinement of anisotropic secondary-extinction parameters may, however, destroy this information. Refinement with respect to the field gradients affects mainly the quadrupolar deformation terms, and has little influence on the X-ray scale factor (i.e. monopolar terms) and computed electrostatic fields (i.e. dipolar terms). Properties of the charge density with different angular symmetries are thus only weakly correlated.