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Calculation of coulomb crystal potentials

Authors
Journal
Journal of Physics and Chemistry of Solids
0022-3697
Publisher
Elsevier
Publication Date
Volume
6
Issue
1
Identifiers
DOI: 10.1016/0022-3697(58)90219-1

Abstract

Abstract The calculation of the lattice sums of coulomb crystal potential is discussed. It is assumed that the electron density is spherically symmetric about each site and given in analytic form. It is shown that the total charge density at each site must be split into two parts in order to make the calculation. One part gives rise to an infinite average value of crystal potential and must be compensated. The other gives rise to a finite average potential and may (Ewald convention) or may not (Frenkel-Bethe convention) be compensated; a choice cannot at present be made between the two alternatives. It is shown that an identity exists which relates the lattice sums of potential for general densities to the Ewald sums, and hence permits simplification of the numerical calculations. The generalization to more complex densities is indicated.

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