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В. Л. Карбівський, А. П. Сорока, В. Х. Касіяненко
«Структура фононних спектрів апатитів кальцію і кадмію, розрахована з перших принципів»
523–533 (2011)

PACS numbers: 63.20.D-, 63.20.dk, 71.15.Ap, 71.15.Dx, 71.15.Mb, 77.84.Bw, 82.75.Fq

Phonon densities of states, dispersion laws for particular phonon curves and interatomic-force tensor for the Me10(РO4)6Х2 apatites, where Me???Са or Сd, and Х???F, OH, Cl or Br, are calcu-lated, basing on the state-of-the-art density functional per-turbation theory and using the pseudopotential approach with plane waves set as a basis. Changes of interatomic force con-stants for Ca10(РO4)6F2 are analysed, when Ca is substituted for Cd and F is replaced for OH, Cl or Br. Phonon densities of states for all investigated apatites, except for cadmium bro-mapatite, are revealed to have the band character with differ-ent subbands widths. The first band involves most of the vibra-tional modes and is located within the range from 0 to 370 cm?1 and from 0 to 330 cm?1 for calcium and cadmium apatites, respec-tively. The second band ranges from 380 cm?1 to 470 cm?1. The third and fourth bands range from 500 cm?1 to 600 cm?1 and from 800 cm?1 to 1150 cm?1, respectively.