I am going through research papers in phase-field modeling and every paper has different free energy functional equation. Where those equation come from? How to decide which equation is appropriate for your situation? Is there any book you should follow?
Dear Vishesh Dharaiya,
Your choice of the energy density functional essentially depends on the problem you are dealing with. For a homogenous system, we are often interested in having an expression that provides an energy minimum within the phases and a maximum at the interface, for such case a simple double well potential function has been classically used. Other functions can do exactly the same job but can be of preference in some cases for numerical considerations such as the double opstacle potential.
Since you have asked about a book, I highly recommend the book: Phase field methods in materials science and engineering by Nikolas Provatas and Ken Elder.
Best of luck.
For the free energy density functional, its highly dependent on the physics of your problem. There are several established free energy functionals based on various physical problems like crack propagation, dendrite growth, phase-change (solid to liquid), etc. You can go through the details to get an idea. Generally a double well potential is preferred by many authors. However, phase-field methods are relatively complicated to understand and if other techniques are available to you, like direct mathematical modeling, its better to implement it using those techniques.
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