  A new 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 the model governing equations. The equations obtained
describe dislocation motion in an elastically stressed solid, and serve as an
extension of the equations of plasticity to the Phase Field Crystal setting.
Both finite and small deformation theories are considered, and the
corresponding kinetic equations for the fields derived.
