Study of Constitutive Behavior of Ferroelectrics via Self-Consistent Modeling and Neutron Diffraction

The central goal of this study is to develop a reliable self-consistent model to describe the constitutive behavior of polycrystalline ferroelectrics and to predict their lattice strain and texture evolution. Starting with the model developed by Huber et al. formulations and refinements were added to increase both the functionality and the accuracy of the model’s results. These refinements include methods for calculating lattice strain, tracking the number of domains contributing to diffraction patterns, locking the domain switching at a specified level, inputting initial grain orientation distribution, and a correction for a major flaw in the previous model: the phenomenon of reverse domain switching.;To validate the model’s predictions, in-situ neutron diffraction experiments were conducted on polycrystalline BaTiO3 under uniaxial compression. It was found that the data analysis required a close inspection due to lattice strain anisotropy and leading to a systematic study of different analysis methods: the single peak method, the regular whole-pattern Rietveld method (with no strain anisotropy), and the improved Rietveld method which offers limited strain anisotropy analysis. The latter was judged to be the most appropriate for ferroelectrics and it was further improved by new formulations to permit lattice strain anisotropy analysis for tetragonal and hexagonal crystal structures.;The comparison of model predictions and diffraction data from BaTiO 3 yielded the following observations: (i) domain switching starts at very low stresses (< 10 MPa) and proceeds gradually; (ii) domains with c-axes closer to the loading axis start switching earlier and experience more switching; (iii) lattice-plane-specific (hkl) strains, with the exception of (111), exhibit apparent hardening after switching starts. The level of agreement between the model and the experimental data was satisfactory, particularly considering the relative simplicity of the model. Keeping in mind the basic assumptions present in the model, it can be a useful analytical tool in the study of ferroelectric constitutive behavior when combined with diffraction experiments.