Mathematical modeling of the metrical parameters of hexagonal close-packed metalls

Abstract

The electronic, magnetic, mechanical and other properties of crystalline substances are due to the feature of their structure — the periodicity and symmetry of the lattice, therefore, the determination of the metrical parameters is an important stage in the study of the characteristics of such materials. The paper considers a number of metals having a crystal lattice of the hcp structural type (hexagonal close packing) – beryllium, cerium, cobalt, dysprosium, erbium, gadolinium, hafnium, holmium, lanthanum, lutetium, magnesium, neodymium, osmium, praseodymium, rhenium, ruthenium, scandium, terbium, titanium, thallium, thulium, yttrium, zirconium. The paper shows the application of the annealing simulation algorithm to find the metric parameters of the materials under consideration using the dense packing model, which is widely used in crystallographic calculations. The own software implementation of the annealing simulation algorithm presented in the paper makes it possible to determine the coordinates of the atoms included in the unit cell of the crystal lattice, to calculate the lattice constants and the packing density of atoms in the cell of the crystal of the hcp structural type, using the given chemical formula and space symmetry group. These structural characteristics can be used as input parameters in modeling the electronic, magnetic, and other properties of the considered materials. The paper compares the values of the crystal lattice constants obtained as a result of numerical simulation with published data.