Ferroelectric and ferromagnetic phase field modeling

Abstract

This chapter provides an introduction to phase field modeling. It is directed at the level of a graduate student with some background in mechanics. It begins with a review of the electro-statics, magneto-statics, and mechano-statics that are needed when setting up phase field models. These yield the various conservation laws that are used. After this review, thermodynamics of materials is discussed. The first law of thermodynamics is used to equate work done on a material plus heat added to the material to the increase of internal energy. This is used with the second law, a statement that irreversible processes generate entropy. This leads to fundamental relations that must be followed in postulating forms for the internal energy. The ways that internal energy is stored in a material are determined through observation. Once the mechanisms have been identified, work conjugate internal variables are introduced to enable writing a specific form for the internal energy and its derivatives. Observations are invoked once again regarding material symmetry to reduce the number of constants that must be determined when modeling a specific material.