Phase field method

In an ideal scenario, a phase field model is able to compute quantitative aspects of the evolution of microstructure without explicit intervention. The method is particularly appealing because it provides a visual impression of the development of structure, one which often matches observations. The essence of the technique is that phases and the interfaces between the phases are all incorporated into a grand functional for the free energy of a heterogeneous system, using an order parameter which can be translated into what is perceived as a phase or an interface in ordinary jargon. There are, however, assumptions which are inconsistent with practical experience and it is important to realise the limitations of the method. The purpose of this review is to introduce the essence of the method, and to describe, in the context of materials science, the advantages and pitfalls associated with the technique.