Homogenized energy (HE) models were developed in a series of publications by Smith et al.. [318–322] Initially proposed for 180° polarization reversal [318; 320] they were extended to account for 90° polarization reversal later on [321; 322]. In the framework of these models, constitutive relations are constructed on the unit cell level. While these can be directly
applied to describe the polarization reversal in homogeneous single crystalline materials, in polycrystalline materials properties such as the coercive field, the critical driving forces, and the interaction fields are assumed to be homogeneously distributed. An example is outlined in Fig. 2.19h. Here, it is displayed that nonuniformities in the lattice, as expressed by different lattice constants, a1>a2, produce a variation in the Gibbs free energy profiles,∆G1<∆G2, resulting in a variation
3 Objective of the work
The possibility to switch the polarization vector is the main property distinguishing ferroelectrics from other polar materials. The understanding of this process represents a challenging scientific problem and is crucial for technical applications. Despite this, some fundamental questions have not yet been answered sufficiently:
1. What is the sequence of 180° and non-180° switching events in polycrystalline ferroelectric materials?
2. How does the microstructure of a polycrystalline material influence the activation barrier for switching and the distribution of switching times?
3. What is the correlation between mechanical stresses, domain structure or other microstructural parameters, and the macroscopically observable dynamic switching response?
Although different experimental techniques shed light on various aspects of the switching process and a broad range of models were provided, the first question was not sufficiently answered. Even more, different experiments report contradicting results. Some researchers claim that polarization reversal happens by two successive non-180° switching events [120; 124], others predominantly observe 180° processes [125; 126], while again others propose only a single 180° event [127]. A similar discrepancy is found when comparing the theoretical switching models. The state of the art statistical models assume only one single 180° event [290], while non-180° events were already included in other models more than a decade ago [17; 321].
The first aim of this work is to develop a combined approach to tackle the first question. A device was constructed which allows to apply sharp HV pulses to the material and measure its dynamic response over several decades, ranging from 1 µs to several s. A detailed description of the construction of this device will be given in Sec. 4.2.1. Thereby, the macroscopic polarization and strain response are measured simultaneously. This allows to separate between purely ferroelectric, and ferroelectric/ferroelastic domain contributions. Both contribute to polarization, while only the latter contributes to the strain response of the sample. Combining the setup with high-energy synchrotron diffraction allows to simultaneously track the structural changes of the material, giving additional information about ferroelastic domain switching and internal mechanical stresses. The latter can be incorporated into a Landau energy landscape and the influence of combined electric and mechanical loads on the stable states of a domain can be revealed. The obtained results will be presented in detail in Sec. 5.1.
Figure 3.1.: Schematic representation of the different parameters to be investigated in this work. a) Crystallographic structure, b) grain size, and c) crystallographic texture. The blue solid lines in b) and c) represent grain boundaries.
The literature related to the second and third question was reviewed in Sec. 2.4. While easier and faster switching has been observed for polycrystalline BT samples with larger grain sizes [214], or a higher degree of crystallographic texture [224], little is known about the influence of microstructural parameters on the dynamics of the polarization reversal process. In particular, the origin of the broad distribution of switching times in polycrystalline ceramics remains unclear. The specific objective of the second part of this study is to investigate the effect of the different microstructural boundary conditions and degree of disorder on the polarization reversal process. In this context, a set of three series of parameters, as summarized in Fig. 3.1, is investigated.
The influence of the crystal structure was studied on a PZT series with different Zr/Ti ratios and thus different crystallographic structures, including pure tetragonal, morphotropic phase boundary, and rhombohedral compositions. The influence of the grain size was studied for rhombohedral PZT materials with a grain size ranging from 4.1 to 11.3 µm. The influence of the degree of crystallographic texture was studied for polycrystalline materials on Ba0.85Ca0.15TiO3samples
with microstructures ranging from a random orientation to a high degree of crystallographic texture. The synthesis procedures for the different series of samples will be summarized in Sec. 4.1, while the obtained experimental results will be presented in Sec. 5.2. Thereby, the distribution of switching times is discussed with respect to internal stresses, mechanical boundary conditions, the domain configuration, and the inhomogeneous field distribution. State of the art statistical models claim that the broad distribution of the switching times is solely a result of the inhomogeneous distribution of the applied electric field [290], while the chemistry and the microstructure of the material are completely neglected. Therefore, the systematic correlation between the microstructure and the switching dynamics of polycrystalline materials, presented in this work, represents the basis for future improvement of theoretical models.
4 Materials and methods
4.1 Materials
Different ferroelectric ceramics were investigated as model materials. The mechanism of polarization reversal was investigated on a commercial PZT material, while the influence of crystal structure was revealed on PZT materials with different Zr/Ti ratios. Various grain sizes were realized by changing the sintering conditions for a PZT materials with a rhombohedral composition. Materials on the basis of BT were used as model materials to investigate the influence of the degree of crystallographic texturing.