Measurements of the normal-mode frequencies of magnesium

Abstract

The normal-mode frequencies of magnesium at 290 K have been determined by the inelastic scattering of slow neutrons. The frequencies of about 3500 phonons with wavevectors in the (0001) and (01T0) planes have been measured with a time-of-flight apparatus, and an interpolation technique has been used to deduce the dispersion curves along closely spaced lines in the two planes. Measurements with a triple-axis crystal spectrometer have been used to supplement the time-of-flight data along several symmetry directions. In order to generate the frequencies throughout the entire Brillouin zone a simple force-constant model extending to eight-nearest neighbours has been used. The values of the force constants were obtained from the phonons along five symmetry directions. Although the model has little physical significance, it gives frequencies in good agreement with the experimental values over the two planes for which measurements have been made. The model has been used to calculate the phonon density of states, and hence the Debye temperatures for the specific heat. The latter are in satisfactory agreement with the values deduced from calorimetric measurements.