Fermi Surface of Aluminum from Kohn Anomalies

Abstract

A careful and detailed neutron inelastic scattering measurement of the phonon-dispersion function of Al has been made along all symmetry branches and a portion of [211] $L$ (longitudinal). The measurements were made on a three-axis spectrometer that has a double-crystal monochromator. Particular emphasis was placed on small-$q$ increments, high relative precision in the determination of phonon frequencies, and on uniformity of conditions within runs in order to extract significant Kohn-anomaly data. Theoretical predictions on positions and relative sizes of anomalies have been compared with the observed slope curves, $\frac{\ensuremath{\Delta}\ensuremath{\omega}}{\ensuremath{\Delta}q}$ versus $q$, to yield 11 fairly certain Kohn anomalies and 8 more possible or questionable ones. Of these, 15 give Fermi-surface diameters with uncertainties of 0.5 to 1%, which are compared with the calculations of Ashcroft and of Faulkner. At least two clearly observed anomalies could not be assigned by any simple argument.