The discovery of the nature of giant electrostriction and strong electromechanical coupling in relaxor ferroelectrics, as well as the management of these properties, play a fundamental role in the development of new generations of various devices including supercapacitors, electrochemical converters, piezoactuators, etc. The fundamental physical nature of these phenomena is still not clear and is explained by the emergence of polar nanodomains due to structural disorder and random electric fields that disrupt the phase transition to the polar state. The project is aimed at studying the nature of the relaxor state and nanodomain states in the model systems of the relaxers SrxBa1-xNb2O6 (SBN) and Pb (1-X) Lax (Zr0.65Ti0.35) (1-X / 4) O3 (PLZT) using the latest methods , based on scanning probe microscopy (SPM) and surface analysis. To achieve this, the techniques of power microscopy of piezoelectric response (SMPO), Kelvin probe microscopy, X-ray photoelectron spectroscopy (XPS) for the analysis of surface states, statistical analysis of three-dimensional domain structures, simulation of the interaction between the SPM probe and the surface of the relaxor and detailed investigation of the local piezo response , including the distance from the surface. A technique will be developed for layer-by-layer etching of the surface of relaxors to visualize domains in order to study their three-dimensional topology. The microscopic mechanism of the formation of the phase of the phase in the relaxors and its relation to macroscopic parameters, such as dielectric constant and the coefficient of electrostriction, will be elucidated. At the final stage of the project, physical phenomena arising under the action of a strong electric field applied by the SPM probe to the surface of the relaxor will be studied, including a local transition from the relaxor phase to the ferroelectric phase, interaction with defects and the creation of specified domain configurations. The acquired knowledge of the behavior of the materials under study at the nanoscale will make it possible to understand the mechanism of formation of polar nanodomains on the surface and to formulate physical bases for the development of relaxor materials and instruments.