Section 6.5 gave an introduction to the elastic energy that is generated in a solid material when an internal region transforms into a new phase of different size or shape. Both the new particle and the surrounding matrix are distorted, and the positive elastic energy tends to suppress the phase change. Elastic energy can be large, and usually influences the thermodynamics, nucleation, growth, and morphology of solid–solid phase transformations, especially at low temperatures. Section 15.4 explained how the selection of a habit plane for a martensite plate is so dominated by the elastic energy that the problem is reduced to a set of geometrical conditions based on the transformation strain. Detailed calculations of the elastic energy are difficult, however, and analytical results are not practical in most cases when the elastic constants of the new precipitate differ from those of the matrix. Even with the assumption that the elastic constants are equal for both phases, the solid mechanics of optimizing the shape of the precipitate for minimum elastic energy is an advanced topic. Crystallographic anisotropy is essential for understanding the orientation relationship between precipitate and matrix, and proper tensorial analysis is required for calculating the elastic energy.

Chapter 21 describes some of the methods for calculating the elastic energy of solid–solid phase transformations. A first approach finds a condition on the elastic field in real space that can guide the search for the minimum elastic energy.