The understanding of many non-equilibrium processes has been enhanced by the use of phase-field
modeling methods. The basic idea behind this method is to propose a free energy that is a functional of a
continuum or phase-field that distinguishes between liquid and solid phases and then assumes that the
dynamics of the field are driven by energy minimization. This formulation has proven very successful in
modeling many aspects of solidification phenomena and is now incorporated in commercially available
software packages. More recently the PI and collaborators have introduced a second generation of
phase field models that describe phenomena on atomic length and diffusive time scales. This phase
field crystal (PFC) method naturally incorporates elasticity, plasticity, anisotropy and multiple crystal
orientations in addition to all the physics of traditional models of solidification and phase segregation.
While the PFC models developed for monatomic and binary alloys can describe many physical phenomena
(such as grain growth, epitaxial growth, eutectic solidification, the yield strength of polycrystalline
materials, climb and glide, grain boundary melting, etc.), there are many important phenomena
that are beyond description by the current models. For example, the binary model cannot describe
sublattice ordering in multi-component alloys. This is a key issue since sublattice ordering is extremely
common and influences structural properties. Another limitation of current PFC models is that they
describe spherically symmetric particles and thus cannot describe the physics associated with extra degrees
of freedom (such as rotation). A technologically important example which exploits these freedoms
are elastomers, in which the rotation of elongated cross-linked polymers allows shear strains at almost
zero energy cost. The goal of the proposed work is to greatly extend the applicability PFC modeling to
incorporate sublattice ordering and anisotropic particles. Preliminary calculations have been conducted
to develop models of B2, B3 and DO3 sublattices and two dimensional liquid crystal elastomers.
The PI also plans to extend the amplitude expansion of the monatomic PFC developed by Goldenfeld
et al. to binary systems. The amplitude approach incorporates much of the essential elastic and
plastic behavior and is more amenable to analytic and numerical calculations. While there are some
disadvantages to this method (e.g., no Peierls barrier) it is clear that this is a very promising approach.
The resulting model will be used to examine the influence of the discrete nature of the crystalline lattice
and compositional inhomogeneities on morphological instabilities in strained epitaxial films.