Phonon-Radiation Force in Defect Crystal Lattices

Abstract

We derive expressions for the force exerted on any atom in a defect crystal lattice due to the scattering of phonons. This force is called the phonon-radiation force, and is essentially the microscopic counterpart of the radiation pressure in classical continuum mechanics; as such it finds its origins in lattice anharmonicity and is related to local thermal expansion. Although our analysis is entirely distinct from a pseudomomentum approach, we find that in the low-frequency limit the net phonon-radiation force on the entire crystal may be roughly approximated by associating with each phonon in mode $\overrightarrow{\mathrm{q}}$ a momentum equal to the pseudomomentum $\hslash \overrightarrow{\mathrm{q}}$. A calculation based on a one-dimensional chain reveals that the force field generally depends quite strongly on atomic position and is rather sensitive to the details of the scattering center. The phonon-radiation force does not appear to be important for vacancy migration, but should be important for other migration mechanisms.