So far, Part III has described melting, precipitation, and unmixing phase transformations. For alloys, these all require the diffusion of atoms over moderate distances, for which continuum diffusion equations provide much of the essential behavior. Ordering transformations also require the movements of individual atoms, but during ordering the atom movements are over such short distances that a diffusion equation is not appropriate. Nevertheless, the atoms move independently (often by a vacancy mechanism), and the configurational entropy can undergo large changes with only a few jumps per atom.

This chapter describes diffusionless transformations, in which the atoms in a crystal move cooperatively, and the crystal is distorted into a new shape. The atoms may not move at exactly the same time, but the transformation is very fast, and does not require a vacancy mechanism for the motions of individual atoms. Diffusionless transformations include “twinning,” in which a crystal transforms into a different variant of the same type of crystal. Martensitic transformations are changes in crystal structure that occur by shears and dilatations, but again without long-range diffusion. Vacancy migration is not important for either twinning or martensitic transformations. Because the atoms do not move with individual independence, the change in configurational entropy is small. The entropy of martensitic transitions is primarily vibrational, sometimes with magnetic entropy as in the case of iron.