The calculation of the power and the elastic constants of metals with a hexagonal close-packed structure

In the De Laon model the expressions for the elements of the dynamic matrix of hexagonal close-packed structures are presented, of which formulas for the calculation of elastic constants C11, C12, C13, C33, C44 are derived in the long-wave approximation. The formulas were used for the calculations of the elastic constants Mg, Ti, Zr, Hf, Co, Ru and Os through the radial and tangential force constant of the interatomic interaction, the values of which were calculated by the method of pseudopotential for the first eight coordinative areas. The results of the calculations were compared with the corresponding experimental data of elastic constants. Also, using the obtained expressions from the experimental values of the elastic constants of the metals under consideration, the force constants for the first three coordinative spheres were calculated, which were compared with the results of calculations by the pseudopotential method.