Crystal lattice identification on the basis of assessing unit cell parameters

The paper is devoted to the problem of crystal lattice identification in three- dimensional space. Two identification methods based on assessing the parameters of unit cells have been developed to solve this problem. The first method is based on the calculation and comparison of the six basic cell parameters: the three lengths of the cell sides and the three magnitudes of angles between the sides. The second method is based on the calculation and comparison of Wigner-Seitz cell volumes using the Monte-Carlo method. Both methods include normalized similarity measures for the parameters calculated: the edge similarity and the angle similarity measure for Bravais unit cells and the volume similarity measure for Wigner-Seitz cells. A number of computational experiments for crystal lattice identification were carried out using these methods. In the course of the experiments, first, the dependence of the accuracy of defining the volume of a Wigner-Seitz cell on the number of the points included and, second, the probability of accurate Bravais lattice identification when comparing different sets of the parameters assessed have been specified. As a result of the experiments carried out, the accuracy of identification for four systems of Bravais lattices exceeded 95 per cent.