Introduction to Computational Materials Science Fundamentals to Applications

The phase-field method is a thermodynamics-based approach most often employed to model phase changes and evolving microstructures in materials. It is a mesoscopic method, in which the variables may be abstract non-conserved quantities measuring whether a system is in a given phase (e.g., solid, liquid, etc.) or a conserved quantity, such as a concentration. Interfaces are described by the smooth variation of those quantities from one phase to another and are diffuse, not sharp.

The phase-field method is increasingly being used in materials science and engineering because of its flexibility and utility. We discuss the basic method here, but researchers are continually creating new features and new approaches within the basic phase-field framework.

We first introduce the basic mathematical formalism, followed by some simple examples of the phase field in one and two dimensions. Implementation of the phase field requires some new computational methods, which will be discussed in the regular text and an appendix. Finally, we will discuss some applications of the phase-field method in materials research.

CONSERVED AND NON-CONSERVED ORDER PARAMETERS

In phase-field modeling, the state of a system is described by a function of position and time. This function could be a specific property of the system such as concentration or it could be a parameter that indicates what phase the system is in, e.g., solid or liquid. This function is generally referred to as an order parameter.