ELECTRON ENERGIES AND EFFECTIVE PAIRWISE INTERACTIONS IN A BINARY ALLOY OF SIMPLE METALS
HARVARD UNIV CAMBRIDGE MA DIV OF ENGINEERING AND APPLIED PHYSICS
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The pseudopotential formalism which has been developed to calculate the properties of periodic crystals is extended to treat the case of a binary alloy with an arbitrary degree of order. A self-consistent screening potential which includes the effect of the total conduction electron charge is derived to first order in a perturbation theory expansion in the pseudopotential. The conduction electron contribution to the total energy of the crystal is expressed to second order in the pseudopotential. The applicability of these perturbation theory expansions is discussed extensively. Expressions for the part of the conduction electron energy which contributes to the ordering energy and for the effective pairwise interactions between the ions in the alloy are derived from the expression for the total energy. If the conduction electron energy may be expressed accurately to second order in the pseudopotential, we demonstrate that this energy depends only upon correlations between pairs of ions. Otherwise, accurate individual electron energies near band gaps are shown to depend upon correlations between three or more ions for an alloy below its critical temperature. The procedure for selecting an optimal form for the pseudopotential is examined in detail. A Hermitian pseudopotential is chosen and its advantages are discussed. Our calculations on a 50-50 alloy of lithium and magnesium indicate that the selection of an appropriate pseudopotential is quite important.
- Solid State Physics