Finding equilibrium lattice parameters of different HCP-monocrystals with use of mie interatomic potential

The approach to developing numerical identification of two dimensionless parameters (exponents of powers) of interatomic Mie potential for monocrystalline HCP-metals was validated. Two equilibrium lattice parameters exist for such materials. One of them is the distance between atom layers with the same distribution of the atoms. The other one is the interatomic spacing at the layer. Equality of the ratio between two lattice parameters known from experiments with the ratio obtained from simulation was taken as a criterion for choosing potential Mie exponents. Any pair of Mie potential indexes of power was shown to be corresponded to the definite value of HCP-lattice parameters ratio. The power exponents of Mie potential for some HCP-metals were obtained, e.g. for titan, magnesium, cobalt, zirconium, beryllium and others. An estimation of elastic properties of different HCP-metals would be given further using the found Mie exponents. Comparison of two approaches to find equilibrium interatomic distances was made. The first approach is based on the interatomic forces consideration. From numerical point of view it gives a simpler way to calculate lattice parameters. The second approach is based on the specimen potential energy minimization. It was shown that the deference between equilibrium interatomic distances in HCP-lattice obtained with the use of both mentioned approaches is lower than 1%. The dependence of mechanical properties on the specimen size was also found.