  Phase field crystal (PFC) models constitute a field theoretical approach to
solidification, melting and related phenomena at atomic length and diffusive
time scales. One of the advantages of these models is that they naturally
contain elastic excitations associated with strain in crystalline bodies.
However, instabilities that are diffusively driven towards equilibrium are
often orders of magnitude slower than the dynamics of the elastic excitations,
and are thus not included in the standard PFC model dynamics. We derive a
method to isolate the time evolution of the elastic excitations from the
diffusive dynamics in the PFC approach and set up a two-stage process, in which
elastic excitations are equilibrated separately. This ensures mechanical
equilibrium at all times. We show concrete examples demonstrating the necessity
of the separation of the elastic and diffusive time scales. In the small
deformation limit this approach is shown to agree with the theory of linear
elasticity.
