The impact of interfaces on variety of materials properties scales with the density of interfaces within a material. This statement holds true independent of the specific interfacial mechanism, as long as the density of interfaces is rather low. If the spacing between interfaces is being further reduced, interesting non-trivial effects are expected and have also been observed. In this paper, the ionic conductivity in ionic conductors and the storage capacity (non-stoichiometry) of mixed conductors as a function of size are considered. The discussion is based on the core-space charge model in which we assume that only the core of an interface exhibits its own defect energetics, while the energetics of the space charge layers remain unaltered (compared to the bulk). It is shown that in the case of Schottky profiles anomalous conductivity effects are predicted. As regards the non-stoichiometry effects, it is demonstrated that at sizes small compared to the Debye length the difference between a composite consisting of an ionic and an electronic conductor and a "true" mixed conductor becomes blurred. The latter effect has recently been detected in the field of Li-batteries and is here commented on. (c) 2005 Elsevier B.V. All rights reserved.