Point-defect thermodynamics and size effects

The introductory part reviews some basic aspects of bulk point-defect thermodynamics. It makes use of the fact that for the purposes under consideration, the real structure can be decomposed in a perfect ground structure and a superimposed defect structure. Then modifications of the point-defect concentration and distribution are considered occurring if interfaces are approached. A simple treatment is possible for the abrupt core-space charge situation in which the standard chemical potentials are assumed to change in a step-like way. Evidence is given that in very many cases this is a reasonable model. There, the adjustment at interfaces occurs solely via space charge regions. ‘Trivial’ size effects are brought about by the changed surface (i.e. core plus space charge layer) to volume ratio. A mesoscale size effect is expected if the width of the space charge layers is no longer small compared with the distance of neighbouring interfaces (Debye-length λ as scaling parameter). In some situations, e.g. if extremely small clusters are treated, distinct deviations in the ground structure also occur, affecting energetic and entropic standard terms. Since such modifications usually decay steeply with increasing interfacial distance (L), another scaling parameter (ℓ) defines a further mesoscopic regime. As examples, micro- and nano-sized particles, films, polycrystals and composites are discussed.