The phonon drag force acting on a mobile crystal defect: full treatment of discreteness and non-linearity

Phonon scattering calculations predict the drag force acting on defects and dislocations rises linearly with temperature, in direct contradiction with molecular dynamics simulations that often finds the drag force to be independent of temperature. Using the Mori-Zwanzig projection technique, with no recourse to elasticity or scattering theories, we derive a general Langevin equation for a crystal defect, with full treatment of discreteness and non-linearity in the defect core. We obtain an analytical expression for the drag force that is evaluated in molecular statics and molecular dynamics, extracting the force on a defect directly from the inter-atomic forces. Our results show that a temperature independent drag force arises because vibrations in a discrete crystal are never independent of the defect motion, an implicit assumption in any phonon-based approach. This effect remains even when the Peierls barrier is effectively zero, invalidating qualitative explanations involving the radiation of phonons. We apply our methods to an interstitial defect in tungsten and solitons in the Frenkel-Kontorova model, finding very good agreement with trajectory-based estimations of the thermal drag force.Comment: 20 pages, 8 figure