Известия Томского политехнического университета: Инжиниринг георесурсов (Jun 2009)
Energy method to calculate elastic modules of finite size samples with HCP-lattice
Abstract
The elastic modules of the finite size samples with hexagonal close-packed lattice have been calculated on the basis of theoretical research algorithm for elastic properties of metal micro- and nanomonocrystals with cubic lattice developed before [1, 2]. The sample form is matched with the lattice symmetry [3]. The power potential Mie is selected as a potential. The approach of atomic statics is used to research the elastic properties. The type of deformation gradient is prescribed and crystal current configuration is determined. To calculate the elastic modules in crystal current configuration the total potential energy of the sample taken relative to its volume is determined. The elastic modules of the sample are determined equating the square terms in its power series expansion by deformation parameters to elastic potential. It was shown that hexagonal close-packed lattice consisting of two simple sublattices cannot be deformed uniformly at preset affine kinematics. Relative shift of sublattices depending on deformation parameters should be predetermined to support the minimum of potential energy of hexagonal close-packed crystal in current configuration. It was ascertained that the elastic modules of hexagonal close-packed crystal depend on the sample size. This dependence has horizontal asymptote conforming to macroscopic monocrystal body with known elastic properties; it allows identifying the parameters of atom interaction potential. All the computations have been carried out in symbolic form in Wolfram Research "Mathematica".
