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Rapid calculation of individual ion Madelung constants and their convergence to bulk values
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Image of Fig. 1.
Fig. 1.

Seed structure used for zincblende expanding polyhedra. The zinc and sulfide ions are shaded differently.

Image of Fig. 2.
Fig. 2.

The two smallest neutral expanded polyhedra of zincblende based on the seed structure shown in Fig. 1. The clusters contain 136 and 1472 ions, respectively.


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Table I.

Madelung constants for a 64-ion cubic NaCl nanoparticle. The origin is arbitrarily set at a corner ion. In all cases the cation-anion near neighbor distance is set to unity.

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Table II.

Madelung constants for the inner eight ions and the eight corner ions in NaCl rocksalt structures with even numbers of ions on each edge. The values have been truncated to five decimal places from the 12 decimal place output of the computer program.

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Table III.

Calculated central-ion Madelung constants as a function of polyhedron size. All polyhedra are uncharged cubes and rhombohedra for NaCl and CsCl, respectively. The Madelung constants for CsCl are the averages of the two Madelung constant values obtained for the central ions in different environments in the rhombohedral seed. Our results using clusters (both cubic and rhombohedral) with an even number of ions are compared to recent work on odd clusters. The number of ions for the odd cubes studied in Refs. 3 and 4 was evaluated from the cubic side lengths, , (where is the side length, is the interionic distance, and is an integer) given in Table I in Ref. 3.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Rapid calculation of individual ion Madelung constants and their convergence to bulk values