Effect of Defects on Lattice Vibrations: Interaction of Defects and an Analogy with Meson Pair Theory

Publisher Website
Google Scholar
Abstract
An analysis is given of the determination of additive functions of the frequencies of the normal mode vibrations of a lattice. The method is applied to the problem of calculating the self-energies and interaction energies of defects in lattices of any dimension. In particular results are derived for the self-energies and interaction energies of isotopes, holes, and "source" defects in simple cubic monatomic and diatomic lattices. For example it is shown that two holes in a simple cubic lattice attract each other, the energy of interaction being inversely proportional to the cube of the distance of separation. The general method is also applied to the problem of the interaction of lattice defects with the boundaries of the lattice. Finally, if the lattice approaches the limit of a continuum, it is shown that the energy of interaction between two holes is just that obtained by Wentzel for the interaction between two fixed nucleons according to the scalar meson pair theory.