Dimensional effects and surface energy of ferroelectric crystals

Abstract

To describe the surface tension, a model of the surface layer of atomically smooth ferroelectrics was considered, neglecting the surface roughness. It is believed that a necessary condition for the manifestation of nanostructured properties of a condensed medium is the size dependence of its properties. The surface layer of an atomically smooth crystal consists of two layers, d(I) and d(II). The layer with thickness h = d is called layer (I), and the layer at h≈10d is called layer (II) of an atomically smooth crystal. At h≈10d, the size dependence of the physical properties of the material begins to appear. When h = d, a phase transition occurs in the surface layer. It is accompanied by abrupt changes in physical properties, for example, the direct Hall-Petch effect is reversed. It can be concluded that both previous and current results of studies of the surface of condensed media (metals, dielectrics, ferroelectrics, etc.) are due to size effects and the final structures of their existence.