Journal Article10.1088/0022-3719/7/21/007
Electrostatic potential in hexagonal ionic crystals
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TL;DR: In this paper, a simple method of direct summation is applied to hexagonal lattices, and Hund's identity (1935) is found to apply in this oblique system.
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Abstract: A simple method of direct summation is applied to hexagonal lattices. An oblique coordinate system is used to represent the hexagonal lattice, and Hund's identity (1935) is found to apply in this oblique system. However, the hexagonal lattice can be represented by two different oblique systems resulting in two unit cells. Both auxiliary structures defined have surface charges or electric moments, and the object is to calculate the potential of a structure which does not have these. A very short computer program is presented. The potential is computed at a few points inside a simple hexagonal lattice neutralized by a uniform charge. The results agree with the results of Hund. The self potential is computed as a function of lattice spacing and is found to be a potential well. Moreover, this method is extended to cover all oblique structures.
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Citations
A simple method for the potential in ionic crystals
TL;DR: In this paper, a basis theory is found which explains the failures, the successes, and the strange procedures of these methods, and a satisfactory definition is found based on this theory, which is based on the fact that the finite block which represents the "infinite" crystal and which is used for computing the potential must be free from electric moments, the most important of which are the dipole, quadrupole, and octapole moments.
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References
Cohesion of Ionic Solids in the Born Model
TL;DR: The Born model was originally proposed for the purpose of evaluating the lattice energy of crystals, which approach this idealized picture, and because of its success and simplicity it has subsequently been applied to the description of a variety of physical properties of ionic crystals, with varying degrees of success.
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Vergleich der elektrostatischen Energien einiger Ionengitter
TL;DR: In this article, die elektrostatischen Energien von Ionengittern vom Typus des Rotnickelkieses, des Cuprits, β-Cristobalits and β-Tridymits, sowie einiger nicht in der Natur gefundener Typen werden berechnet die Regel, das die Energie auser durch Anzahl und Ladung der Ionen im wesentlichen durch die Koordinationszahlen bestimmt ist,
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Coulomb Potential in Ionic Crystals by Direct Summation
TL;DR: In this paper, the shape and size of the finite crystal piece to be used in the calculations of the Coulomb potential at points in the unit cell of ionic crystals is determined.
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