Shell-model study of the lattice dynamics of hydroxyapatite -: art. no. 224304

A shell model has been developed and used in a study of the lattice dynamics of hydroxyapatite. The results give insight into the modes of vibration of the lattice, but in addition, the dynamics has been used to obtain quantities involved in x-ray and neutron diffraction patterns and in infrared spectra to help in the interpretation of experimerimental data. Phonons throughout the Brillouin zone were obtained and used to calculate atomic thermal factors entering the x-ray and neutron scattering intensity. The calculated values were in very good agreement with experiment. The phonon modes were also obtained for the Gamma-point taking into account the long range Coulomb correction to the dynamical matrix. They were used to calculate the infrared reflectivity for single crystals of hydroxyapatite through the dielectric function and using the dipole approximation, and the powder spectrum was also obtained using the dipole method. Although the positions of peaks in the measured intensities were in good agreement with the frequencies of features in the calculated phonon density of states, the calculated intensities were in poorer agreement with experiment.