| The phenomenon of interaction between electrical and mechanical fields was discovered by Pierre and Jacque Curie in 1880 and is called piezoelectric effect. It has broad practical applications in modern electronics. In the classical theory, electric polarization depends on deformation as a linear function of the strain tensor. On the other hand, non-uniform deformation can also lead to appearance of electric polarization in solids. Using Taylor series approximation, polarization can be expressed as a linear function of the gradient of the strain tensor.; Based on this idea, we have constructed a mathematical model that can be used to describe some important phenomena of solid bodies on the atomic scale such as phenomenon of multilayer relaxation near surfaces of crystals. In addition to this, we obtained the displacement field of a point defect. We used a dilatation center model for a point defect and we showed that the displacement field has a dampening oscillatory behavior in directions away from the defect.; New expression for a free energy functional is proposed. Using Hamilton's Variational Principle, we derive the governing equations for the model. Solutions of these equations near surface boundaries exhibit dampening oscillatory behavior. For the case of a point defect, we used Fourier transform and Green function technique to obtain the displacement field of a dilatation center. Comparison is made with the classical theory of elasticity.; The proposed model of a solid body allows us to study and explain multilayer relaxation and other effects that occur near surfaces, spatial inhomogeneities, and other defects in solids. These effects are important in the development of modern microelectronics devices where the sizes of elements approach nanometers. The model can be further used to analyse dislocations, area of contacts between two materials, surface waves, etc. Inclusion of interaction between electrical polarization and nonuniform deformation may lead to possibly new effects or explain existing phenomena caused by defects and other spatial nonuniformities. |
