Phase field modeling of ferroelectrics with point defects

• Main Author: Zuo, Yinan
• Format: Others
• Language: en
• Published: 2016
• Online Access: https://tuprints.ulb.tu-darmstadt.de/5825/2/Dissertation_Yinan_Zuo.pdf; Zuo, Yinan <http://tuprints.ulb.tu-darmstadt.de/view/person/Zuo=3AYinan=3A=3A.html> (2016): Phase field modeling of ferroelectrics with point defects.Darmstadt, Technische Universität Darmstadt, [Ph.D. Thesis]

The ferroelectrics which possess switchable polarization below the Curie temperature can be applied as actuators and memory storage devices. Oxygen vacancies are commonly present in perovskite ferroelectrics. Besides that, in order to enhance certain properties, perovskite ferroelectrics are doped with foreign atoms (e.g. iron, copper, manganese, etc) which again results in the appearance of certain kinds of point defects. In this thesis, the model has been set up to investigate those two effects: a model that incorporates the ferroelectric and semiconducting feature of ferroelectric perovskites at the same time and a model taking the internal bias field due to the defect dipole into account. The phase field model is derived in a thermodynamically consistent way. The phase field modeling was numerically realized by finite element method using FEAP. Since the domain structure evolution is certain change in the reference configuration, one is interested in the driving force or tendency of such change by making use of the concept configurational force from Eshelby. The semiconducting feature of ferroelectrics with point defects was studied. The role of donors and electronic charge carriers in the domain structure stabilization was studied in a quantitative way. By accounting for semiconducting properties of barium titanate, the appearance of depletion layers near the electrodes was predicted. The stabilization of the head-to-head and tail-to-tail domain structures through the space charge was also demonstrated. As an indication of the stability, the driving force on the domain wall in the ead-to-head domain structure was quantitatively investigated. The effects of an applied electric field and space charge compensation on the driving force and the driving moment were discussed, as well as the influence of the domain wall orientation. The study of the domain wall conductivity has shown that in both the simplified and the realistic defect systems in barium titanate, different domain configurations may be stabilized by the space charge which screens the bound charge. The phase field modeling of ferroelectrics with static defect dipole is developed and computation is conducted in order to study the dipole effect of oxygen vacancies on the different domain structures. The numerical simulations demonstrate that the internal bias electric field caused by the oxygen vacancies does play a notable role in modifying the overall domain switching behavior of ferroelectric single crystals. The domain memory effect, in which the zero overall polarization and the initial domain patterns are recovered after electric unloading and thus the double hysteresis loops take place, are well reproduced in the modeling. A kinetic model is derived that enables investigation of the time evolution of defect dipoles in the presence of electric fields in PZT. The simulation shows that after each switching of spontaneous polarization, the migration of oxygen vacancies also change their migration direction due to the change of energy landscape. For a initially aged material in which the defect dipoles formed by Cu-substitutes and oxygen vacancies are coaligned with the spontaneous polarization, the simulations show that, after sufficient loading cycles, the sample can be deaged in the sense of defect dipole reorientation. Studying this problem will give a good perspective and understanding of the evolution of fatigue and aging in ferroelectrics.