Configurational force distribution during perovskite phase growth in a ferroelectric film

The propagation of the interphase boundary during the growth of the perovskite phase in a pyrochlore matrix in thin ferroelectric lead zirconate titanate films on a silicon substrate is studied using the methods of configurational force mechanics. A numerical solution of the boundary value problem of the growth of a perovskite inclusion in an initially pyrochlore film is obtained in axisymmetric and three-dimensional formulations. The growth of cylindrical, conical, and spherical inclusions is considered. The growth of single and multiple regularly and irregularly located inclusions were studied. A comparison of the solutions to the problem in linear-elastic and elastoplastic formulations was made. The dependence of the configurational force on the inclusion size and on the distance from the substrate is obtained. In the modeling, the interphase boundary rate was determined by a power-law dependence on the configurational force. Based on the results of finite-element computations of the spatial and temporal distribution of the configurational force and the evolution equation for the growth rate of the interphase boundary, the gradient of the growth axis angle deviation was determined, correlating with the experimental data obtained from X-ray diffraction analysis and scanning electron microscopy.