Normal and “Anomalous” isotope shifts of phonon frequencies in mono- and polyisotopic germanium crystals

The shifts of the phonon frequencies in ⁷⁰Ge and ⁷⁴Ge monoisotopic crystals have been studied using inelastic neutron scattering. It has been shown that the frequency shifts for all of the branches are normal, i.e., inversely proportional to √M. At the same time, the gap between acoustic and optical frequencies in monoisotopic crystals appears to be much wider (by about 2 meV in the [111] direction) than that in natural polyisotopic crystals containing “isotopic defects.” In this case, the phonon frequencies undergo “anomalous” shifts; i.e., the oscillation frequency of the heavier isotope is higher than that for the lighter isotope. The effect is in qualitative agreement with old theoretical calculations of the effect of mass defects on the phonon spectra of diatomic lattices.