Determination of Madelung constants for infinite and semi-infinite lattices by direct summation

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Publication Type Journal Article
School or College College of Mines & Earth Sciences
Department Metallurgical Engineering
Creator Miller, Jan D.
Other Author Calara, J.V.
Title Determination of Madelung constants for infinite and semi-infinite lattices by direct summation
Date 1976
Description Lattice sums for the electrostatic interactions in ionic crystals, first evaluated by Madelung, are now known to high degrees of accuracy. The problem of conditional convergence has been solved either by manipulations of a mathematical model of the lattice, or by directly summing over neutral groups of the lattice as was done by Evjen and Frank. Although the first method has been modified and extended to encompass semi-infinite lattices, there are no corresponding works on direct summation techniques. Dahl has corrected the Evjen method to expand its range to more complex crystals but did not indicate its applicability to bounded lattices. This communication describes a novel direct summation approach broad enough to handle any infinite or semi-infinite lattice that can be decomposed into finite, neutral, linear charge arrays. The technique is unique in that it is the only direct summation method demonstrated capable of calculating surface Madelung constants.
Type Text
Publisher American Institute of Physics (AIP)
Volume 65
Issue 2
Subject Lattices; Madelung constants
Subject LCSH Lattice theory; Crystallography
Language eng
Bibliographic Citation Calara, J.V. and Miller, J.D. (1976). Determination of madelung constants for infinite and semi-infinite lattices by direct summation. Journal of Chemical Physics, 65 (2), 843.
Rights Management (c)American Institute of Physics. The following article appeared in J. Chem. Phys. 65, 843 (1976) and may be found at http://link.aip.org/link/?JCPSA6/65/843/1
Format Medium application/pdf
Format Extent 167,784 Bytes
Identifier ir-main,4276
ARK ark:/87278/s6p565wf
Setname ir_uspace
Date Created 2012-06-13
Date Modified 2021-05-06
ID 705209
Reference URL https://collections.lib.utah.edu/ark:/87278/s6p565wf
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