Nanomaterial clusters as macroscopically small size-effects bodies. Part I

Abstract

One of unusual features of macroscopically small three-dimensional nanocrystalline clusters is the dependence of their properties on the grain size as well as on the cluster size. Consequently, such clusters are ensembles of atoms or particles where the size effect becomes apparent. A phenomenological model of the description of thermomechanical properties of macroscopically small nanomaterial clusters is proposed. The model is based on the concept of size-effect bodies, the thermomechanical properties, dynamics and thermodynamics of which are referred to one whole body, not an infinite system of subbodies. It is pointed out that the proposed model of the size effect leads to an analogy with the theory of capillarity. A class of size-effect bodies generalizing this analogy is introduced and discussed. Particularly, it is stated that the heat capacity reveals not only the size effect but, contrary to the elastic properties, should depend also on the topological invariant of the compact and connected cluster.