Showing papers in "Acta Crystallographica in 1987"

The Further Geometry of Grain Boundaries in Hexagonal Close-Packed Metals

Abstract: A technique is given for finding partial DSC vectors appropriate to crystals with more than one atom per lattice site. The DSC lattice is made up of vectors that represent displacements of one crystal with * Now at Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. respect to the other that leave the boundary structure shifted, but not complete. A new, rapid method for finding the step vectors associated with perfect DSC dislocations is described. Partial DSC vectors and step vectors for perfect DSC dislocations in hexagonal close-packed crystals are determined. The availability of reactions between lattice partial dislocations and grain boundaries in hexagonal closepacked crystals is also assessed. 0108-7681/87/050416-07501.50 (~ 1987 International Union of Crystallography FU-RONG CHEN AND A. H. KING 417

Rigid-Link Constraints and Rigid-Body Molecules

Abstract: The rigid-bond condition for harmonic thermal parameters states that the difference of the mean-square displacements of atoms A and B along the covalent bond A-B is negligible. In this paper, the corresponding condition for non-bonded intramolecular distances is called a rigid link. Rigid-body motion according to the TLS formalism requires all intramolecular links to be rigid. Conversely, a cornpiece set of rigid links is not necessarily equivalent to rigid-body motion. An algorithm is presented for the determination of the maximum number QN of independent rigid links of an N-atom molecule. In general for site symmetry 1, QN = N-1 for linear and 3N-6 for planar molecules. For three-dimensional molecules, QN = N(N - 1)/2, N ≤ 8 and 6N-20, N ≥ 8. For particular geometries, QN may be smaller. For many molecules, QN rigid links are equivalent to rigid-body motion. Notable exceptions are most linear and planar molecules, and all molecules with six or seven atoms. Higher site symmetries reduce and often eliminate these differences between rigid links and rigid-body motion. The use of rigid-link restraints in crystallographic least squares is recommended. They provide a computationally simple means of relaxing the constraints imposed on the displacement parameters by the TLS model for any molecular site symmetry.