Normal Modes of Germanium by Neutron Spectrometry

The frequency wave-number relations of the lattice vibrations in germanium which propagate in the symmetric 100 and 111 directions (and some results in other directions) have been obtained by studying energy distributions of neutrons scattered by a germanium single crystal. The characters of the phonons were ascertained from the intensities and positions of the neutron groups in the reciprocal lattice. The methods are discussed. The results cannot be fitted by simple models using the Born-von K\'arm\'an theory, but explain satisfactorily the specific heat. The far-infrared spectrum of germanium can be interpreted as combination bands in terms of our results.