Estimates for Diffusion Barriers and Atomic Potentials in MGO: CNDO/2 Calculations for the Study of Microwave Effects in
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ESTIMATES FOR DIFFUSION BARRIERS AND ATOMIC POTENTIALS IN MGO: CNDO/2 CALCULATIONS FOR THE STUDY OF MICROWAVE EFFECTS IN SINTERING L.
Skala,* V.M. Kenkre,* M.W. Weiser," and J.D. Katz*** *Center for Micro-Engineered Ceramics and Department of Physics and Astronomy, University of New Mexico, NM 87131 **Center for Micro-Engineered Ceramics and Mechanical Engineering Department, University of New Mexico, NM 87131 ***Los Alamos National Laboratories, Los Alamos, NM 87475
ABSTRACT As part of a program of investigation of microwave sintering, self-consistent CNDO/2 calculations are presented for diffusion barriers and potentials for the motion of interstitial atoms and vacancies in MgO. Clusters of 30 atoms are used in the calculations. Activation energies, diffusion barriers, shape of the potentials and electron densities are obtained. INTRODUCTION This paper is one of a series in which we address the microscopic theory of ionic diffusion. As a representative material of relevance to sintering, we investigate MgO . As a result of the fact that the character of bonding in MgO is primarily ionic, the most significant mechanism of diffusion is the motion of ions or vacancies. In this paper, we discuss such diffusion for magnesium and oxygen ions in the directions.
CLUSTER MODEL AND POTENTIAL FOR VACANCY MOTION Our approach to the microscopic calculation of the potential seen by the magnesium or oxygen ion during its motion from its original lattice site to a neighboring vacancy is one based on the solution of the stationary Schroedinger equation for a reasonably large cluster of ions isolated conceptually from the semi-infinite MgO crystal. The MgO crystal has the rock salt structure with a lattice constant of a - 0.421 run. In order to describe the vacancy motion, we investigated the clusters Mg2 00 10 (no vacancy), Mg1 90 10 (one magnesium vacancy), O20 Mg1 0 (no vacancy), and O15 Mg10 (one oxygen vacancy). Clusters consist of five layers of magnesium and oxygen ions. The central layer (denoted as x-0) of the Mg2 0 010 cluster shown in figure la is the magnesium (111) layer consisting of two overlapping magnesium hexagons. The two magnesium ions centered in these hexagons (denoted by I and 2) have the same nearest magnesium and oxygen neighbors as in the infinite crystal. These two sites are used to model the vacancy motion. The model for the magnesium vacancy motion is Mg1 9 0 10 cluster shown in figure lb. We take site 1 to be occupied by the magnesium ion and site 2 to be the vacancy site. The magnesium ion at site 1 can move from its original position to site 2. The corresponding coordinate determining the position of the magnesium ion during its motion is denoted as z. It changes in the interval z-(-R/2,R/2) where R is the nearest neighbor distance in the magnesium (111) plane: R-a/j2. The model for describing the oxygen vacancy motion is the same as for the magnesium vacancy except for an exchange in the roles played by magnesium and oxygen ions. To determine the potential V(z) seen by an ion during its motion f
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