A new method of calculating interatomic spacing: the equal-ratio method

Based on a simple principle of analytical geometry, a new equal-ratio method has been developed to calculate the interatomic spacing of crystal structures. If an atom (x 2, y 2, z 2) or its equi-position atom (e + x 2, f + y 2, g + z 2) (e, f and g are integers) is located at the 1/r ≤ 1 of one interatomic spacing period d′[uvw] on the [uvw] atomic row passing through the atom (x 1, y 1, z 1), the distance between the two atoms can be calculated by the formula d [uvw] (1/r) = d′[uvw]/r, where d′[uvw] = (u 2 a 2 + v 2 b 2 + w 2 c 2 + 2uvabcosγ + 2vwbccosα + 2uwaccosβ)1/2 is the interlattice point spacing of the corresponding primary lattice of the crystal structure, 1/r is the interatomic spacing coefficient, and r is equal to the reciprocal of the common factor of (x 2 − x 1), (y 2 − y 1) and (z 2 − z 1). The reliability and advantages (no auxiliary view is required, suitable for arbitrary directions and for all crystal structures) of the equal-ratio method have been examined by calculations for the β-cristobalite SiO2 structure and Cu3Au I superstructure as well as face-centred cubic, body-centred cubic and hexagonal close-packed structures.

Hartree–Fock calculation for the electronic structure of H+3 using numerically optimized orbitals

The Hartree–Fock wave functions for the ground state of the H2 molecule and the H+3 molecular ion are computed using radial orbitals that are numerically optimized. It is shown that these orbitals yield results comparable in accuracy to those obtained using much larger bases of Gaussian orbitals. As in previous calculations, the equilibrium geometry for H+3 is found to be that of an equilateral triangle, with an interatomic spacing of 1.64a0. PACS No.: 13.15+q

The Properties of Twinning Dislocations in Alpha-Titanium Simulated With A Many-Body Interatomic Potential

ABSTRACTComputer simulation of the atomic structure and movement of twinning dislocations in four twin boundaries in the h.c.p. metal α-Ti is described. These dislocations have the form of steps on the twin boundary, and whereas some have cores which are very widely spread over the interface, others are only an interatomic spacing or so across. These configurations are determined mainly by whether or not atomic shuffles are required to restore the h.c.p. crystal structure when the dislocation is introduced. The mobility of the dislocations is also controlled by the same effect, and is found to correlate well with experiment.