# Computational experiment for identifying of cubic period of hexagonal diamond

### Abstract

The coefficient of compactness and the Madelung constant are key parameters in researches of substances in condensed state. The method of compact matrix description of crystal lattice makes calculation of these parameters faster and simpler. However, since this method is based on cubic symmetry of the crystal structure, it cannot be applied to substances of noncubic syngony. In this paper, we study the crystal lattice of a hexagonal diamond to determine existence of the cubic period and cube-generator. The goals of our study are the following: 1) to determine the presence or absence of the cubic period and cube-generator of the crystal lattice; 2) to determine the space orientation of the cube-generator; 3) to determine the value of the cubic period; 4) to verify preservation of the discovered periodicity for an extensive crystal fragment. The results of the computational experiment prove the existence of the cubic period and cube-generator. The value of the cubic period is obtained (36 notational units, ∼ 2, 14 nm). Its preservation for an extensive crystal fragment is shown. It is shown that the space orientation of the cube-generator and basic elements of a two-component cubic model of the crystal lattice of the hexagonal diamond is the same. The obtained results lead to applicability of the method of compact matrix description to the crystal lattice of the hexagonal diamond, thus optimizing the calculation of the compactness coefficient and the Madelung constant for this substance.

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*Mathematical notes of NEFU*, 26(2), pp. 80-93. doi: https://doi.org/10.25587/SVFU.2019.102.31513.

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