Nanostructured materials are of widespread interest in science, engineering, and technology. For the purpose of thermodynamics, it is useful to define nanomaterials as materials with structural features of approximately 10 nm or smaller, i.e., tens of atoms across. Important physical properties of nanomaterials originate from one or two basic features:

1. • Nanomaterials have a high surface-to-volume ratio, and a large fraction of atoms located at, or near, surfaces.

2. • Nanomaterials confine electrons, phonons, or polarons to relatively small volumes, altering their energies. The confinement of structural defects such as dislocations or internal interfaces alters their energies and interactions, too.

A practical question is whether nanostructures are adequately stable at modest temperatures. A more basic question is how the thermodynamics of nanostructured materials differs from conventional bulk materials. In short, their internal energy is raised by the surfaces, interfaces, or composition gradients in nanostructures. Chapter 16 discusses the thermodynamics of interfaces, but Sections 6.6 and 11.2 covered important aspects of surface energy, including surface relaxation and reconstruction processes that are driven by chemical energy. Some basic issues for the confinement of electrons in nanostructures are presented here.

The free energy of nanostructured materials is altered by the entropy from the configurations of nanostructural degrees of freedom and their excitations. These entropy contributions tend to stabilize a nanomaterial at finite temperatures.