Lattice dynamics of nickel

The normal modes of vibration of nuclei in nickel at room temperature have been investigated by means of one-phonon coherent scattering of neutrons. The incident monochromatic cold neutron beam was obtained by Bragg reflection from a Pb single crystal of a Be-filtered reactor beam, and the energy analysis of the scattered neutrons was performed by the time-of-flight technique. The experimental data were treated to give the scattering curves, in the (011) plane of Ni, corresponding to scattering angles of 70°, 90° and 100°, and to an incident neutron wavelength of 4.094 Å. From these scattering curves, points of the phonon dispersion curves ν(q) in the symmetry directions [100], [110] and [111] were deduced. A least squares analysis of the Fourier expansion of ν² for the various branches of the dispersion curves shows that the forces extend up to at least third neighbours, but that nearest neighbour interactions dominate. The results have been compared with calculations based on a model proposed by Krebs for face-centered and body-centered cubic metals. The values of the three most sensitive parameters in the theory were obtained by fitting to measured elastic constants and an appropriate value for the effective density of free electrons was chosen. The calculated dispersion curves and scattering curves show very good agreement with the experimental results.