Expressions for Elements of Dynamical Matrix for HCP Crystals

Within the conceptual framework of the De Launay model, this study delineates the formulations for elements constituting the dynamical matrix of hexagonal close-packed (HCP) crystals, incorporating the effect of interatomic forces exerted by the first eight nearest neighboring atoms. To validate these derived formulations, the phonon dispersion of magnesium was computed and juxtaposed against the empirical phonon dispersion results reported by other researchers. Subsequently, leveraging the fit of experimental phonon dispersion data of yttrium, as reported by secondary sources, this research delineates the radial and tangential force constants pertaining to the first three neighboring atoms. These constants were then employed to approximate the elastic constants of yttrium. The calculated phonon dispersion branches along the Γ-M and Γ-A directions, as well as the derived values of yttrium's elastic constants, exhibit congruence with the corresponding empirical observations reported in literature.