Electric field gradients and charge density in corundum, α-Al₂O₃

Abstract

733potential, 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. AbstractThe 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-fieldgradient tensors at both atomic sites, using Hirshfeldtype 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.

Towards extinction-free experimental diffraction data on Al2O3

“…1. This map compares well the experimental Ag Kc~ maps of Lewis et al (1982) and the theoretical results obtained by Blaha & Schwarz (1996) with the Wien95 DFT program, and by Rerat and coworkers (Rerat & Lichanot, 1996) reflections only. The multipole analysis is also possibly not the best model to recover all the valence density, but, as the quality of this high-energy data set from AI203 is excellent, we now have the opportunity to test more appropriate electron density models for simple systems.…”

Residual Stress Measurements of Alumina-Zirconia Ceramics by Time-of-Flight Neutron Diffraction

“…Consequently, all the studied A/Y-TZP composites were analyzed by using a two-phase model consisting of the hexagonal α-Al 2 O 3 phase and tetragonal Y-TZP phase. The space groups and initial atomic structure information used in refinements are taken from [15] [16].…”

Some diffractometer test crystals: a summary

“…14-801. (s) Webster (1995b), (t) Webster (1992) Gabe (1981), (ac) Dam et al (1983), (ad) Wang et al (1985), ( Stadnicka et al (1992), (aj) Deshpande & Khan (1963), (ak) Webster (1995a), (al) Webster (1991b), (am) Lewis et al (1982), (an) Webster (1994), (ao) Barrett & Wallace (1954), (ap) Short & Roy (1963), (aq) Batchelder & Simmons (1964), (ar) Maslen et al (1993), ( …”