  The velocity of dislocations is derived analytically to incorporate and
predict the intriguing effects induced by the preferential solute segregation
and Cottrell atmospheres in both two-dimensional and three-dimensional binary
systems of various crystalline symmetries. The corresponding mesoscopic
description of defect dynamics is constructed through the amplitude formulation
of the phase-field crystal model which has been shown to accurately capture
elasticity and plasticity in a wide variety of systems. Modifications of the
Peach-Koehler force as a result of solute concentration variations and
compositional stresses are presented, leading to interesting new predictions of
defect motion due to effects of Cottrell atmospheres. These include the
deflection of dislocation glide paths, the variation of climb speed and
direction, and the change or prevention of defect annihilation, all of which
play an important role in determining the fundamental behaviors of complex
defect network and dynamics. The analytic results are verified by numerical
simulations.
