Phase field model of interfaces in single-component systems derived from classical density functional theory

Details Phase field model of interfaces in single-component systems derived from classical density functional theory Phase field model of interfaces in single-component systems derived from classical density functional theory

2007-08-21

arxiv.org/abs/0708.2882v1

Physics

Condensed Matter

Materials Science

RevTeX, 14 pages, 1 figure

Scientific paper

10.1103/PhysRevB.77.054101

Phase field models have been applied in recent years to grain boundaries in single-component systems. The models are based on the minimization of a free energy functional, which is constructed phenomenologically rather than being derived from first principles. In single-component systems the free energy is a functional of a ``phase field'', which is an order parameter often referred to as the crystallinity in the context of grain boundaries, but with no precise definition as to what that term means physically. We present a derivation of the phase field model by Allen and Cahn from classical density functional theory first for crystal-liquid interfaces and then for grain boundaries. The derivation provides a clear physical interpretation of the phase field, and it sheds light on the parameters and the underlying approximations and limitations of the theory. We suggest how phase field models may be improved.

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