Modelling needle domains with dislocations: A dislocation pile-up model and comparison with synchrotron experiment

Abstract

The shape and strain field of a needle domain in a barium titanate single crystal are modelled using a distribution of dislocations and line charges. The arrangement of these dislocations and charges is a result of the balance of modified Peach–Koehler forces acting among the dislocations and a lattice friction assumed to act at each dislocation site. Based on measurements of needle shape by synchrotron X-ray diffraction, dislocation pile-up theory is used to compute the distribution of discrete dislocations along the needle and hence estimate the lattice friction. It is found that the lattice friction in this model is proportional to the opening angle of a wedge-shape needle domain and consistent with the observed magnitude of stress required to mobilize needle domains. The microstrain distribution around an a-a needle domain tip, obtained from X-ray diffraction measurement, is further used to test the dislocation model, with a similar pattern and magnitude of strains identified in the model and the experiment.