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We have simulated the diffraction patterns of both periodic and quasiperiodic monatomic chains using the code Laue (written by Silsbee and Drager) and investigated the effects of the shape of the atomic potential. Three fundamental differences between the diffraction patterns of periodic and quasiperiodic monatomic chain were observed. The width and modulated shape of the diffraction pattern formed by the quasiperiodic chain was found to depend on the shape of the atomic potential. For guassian and exponential atomic shapes, the width decreases as the lattice constant is increased. It also decreases as the size of the atom is increased. For a pseudoatomic shape, the width varies with lattice constant and size of atom in an un-orderly manner.

One of the most crucial aspect in any band structure calculation in solids is the construction of the one-electron potential. In this work, we studied the local potential due to the WignerÈSeitz cell in the crystals of the diamondstructure semiconductors, namely carbon, silicon, germanium, and a-tin. The only inputs in our calculations are the atomic number and the lattice parameter. The various potentials are calculated using these inputs, and employing the normalized Slater radial orbital factors and the real solid harmonics. The major areas studied include the potential of some speciÐc electrons, the radial variation of the potential, and the convergence of v ce with respect to the summation over L . The results are presented and discussed.

Solving the Poisson equation for the electrostatic potential in a solid is an integral part of a modern electronic structure calculation. In this work, the Poisson equation for the diamond-structure semiconductors is solved using the Green Function Cellular Method. The charge density was obtained from a ¢rst principle consideration of the atomic wave functions for the electrons. The real solid harmonics J L , and H L are used in expanding the Poisson equation Green function, therefore, most of the calculations were done in the spherical coordinates system. The maximum value of the index L considered is six. The Poisson equation is solved only for the state k 0 in this work. The results show that the total electron-electron Coulomb potential, V CE r n is given mainly by the central cell contribution and thus varies in a similar fashion. From a certain value at the origin, the total potential initially increases with the distance up to a certain point and then decreases as the distance is further advanced. The peak potential is roughly at about 0.05d in carbon, 0.03d in silicon and germanium, and 0.02d in gray tin. The rate of convergence of the external cells potential contribution over the l summation is faster than the central cell contribution, while the total potential rate is the slowest. In general the rate of convergence at a given point depends on the distance and direction of the point. The mathematical formulation and the results of the calculations are presented and discussed. Physica Scripta 64# Physica Scripta 2001