Dispersion Relations for Phonons in Aluminum at 80 and 300°K

Abstract

The dispersion relations for aluminum have been determined at 80 and 300\ifmmode^\circ\else\textdegree\fi{}K by neutron spectrometry, using a three-axis crystal spectrometer. Particular attention was paid to precision, in order to investigate small effects---e.g., Kohn anomalies, phonon frequency widths, frequency shifts with temperature---and to establish an accurate experimental routine. A focusing method used throughout to optimize resolution is described, as well as a method for calculating energy resolution and extracting phonon widths from observed one-phonon resonances. Results are presented as dispersion curves for phonons in the three principal directions, accompanied by phonon widths, and as contour maps of phonon frequency on the surface of an elemental tetrahedron in q space. Measurements at points off the principal directions are utilized in the latter maps. Kohn anomalies have been observed, but are reported elsewhere. Phonon widths at 80\ifmmode^\circ\else\textdegree\fi{}K are interpreted semiquantitatively in terms of the interaction between phonons and conduction electrons. Exceptionally large phonon widths in two regions may be due to singularities in the phonon-phonon interaction: the conservation rules for decay of a phonon into two phonons suggest a source for such singularities, but the suggestion has not been confirmed by computation.