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First principle calculations of phonon spectrum in nitride niobium by framework density functional theory
are considered. The approach is based on calculation in the first order on displacement of potential and
charge density with use of linear response theory and linear MT (muffin-tin) orbitals method. In view of
directed to each other fluctuations of atoms essentially deform electronic density in interstitial to an unit cell,
at calculation of total energy of a crystal as functions of displacement of nucleuses, in this set we allowed of
effects of nonspherical distribution of electronic density and potential. Moreover for finding of distribution
of electronic density were used a representation of spherical harmonics both in MT-spheres’ region, and in
interstitial. Crystal space was partitioned on polyhedral Wigner-Zeits primitive unit cell, and MT-orbitals
are represented as one-centred expansions on spherical harmonics inside the spheres which are encircling
the polyhedra. Thus, the calculation problem of potential’s matrix elements from boundary region between
spheres is reduced to a finding of an effective method of integration of functions on region between sphere
and boundary of polyhedra. And for realization last procedure, expansion technique on spherical harmonic of
µ-function is applied. Dispersion curves have been calculated along directions Γ-H, Γ-P and P-H of Brillouin
zone, that responds directions (00x) and (xxx) in inverse space. Lattice constant was chosen equal 4,16 at.un.,
as is theoretically predicted by calculation on total energy method (experimental lattice constant is equal 4,39
at.un.). Radius of MT-sphere was fixed equal 2,55 at.un. |