Field dislocation mechanics and phase field crystal models

A formulation of the phase field crystal model is presented that is consistent with the necessary microscopic independence between the phase field, reflecting the broken symmetry of the phase, and both mass density and elastic distortion. Although these quantities are related in equilibrium through a macroscopic equation of state, they are independent variables in the free energy and can be independently varied in evaluating the dissipation functional that leads to some of the model governing equations. The equations obtained describe dislocation motion in an elastically stressed solid and serve as an extension of the equations of dislocation mechanics to the phase field crystal setting. Both finite and small deformation theories are considered, and the corresponding kinetic equations for the fields are derived.