Inelastic Scattering of Slow Neutrons by Lattice Vibrations in Aluminum

The lattice vibrations of aluminum have been studied by means of the inelastic scattering of "cold" neutrons, in which the neutron absorbs a phonon whose energy is typically much larger than the incident neutron energy. Neutrons with a wavelength about 5 A were obtained by filtering a beam of thermal neutrons through eight inches of beryllium. After scattering in an aluminum single crystal, the neutron energy distribution was determined by time of flight, using a mechanical chopper. The peaks observed in the energy distribution of the scattered neutrons for various crystal orientations were used to determine the "scattering surface" in a plane parallel to one face of the cubic lattice. The scattering surface gives the dispersion law for the crystal, that is, the frequency, $\omega$, of the lattice vibration phonons as a function of the wave vector, q. Dispersion curves, obtained for three different directions in the crystal, agree well with x-ray results and with theoretical calculations of the dispersion based on the assumption of harmonic forces.