Mesoscale constitutive behavior of ferroelectrics
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The main goal of this study is the in-situ investigation of the ferroelectric domain structure inside polycrystalline BaTiO3 under thermo-electro-mechanical loading conditions. The outcome is two-fold: (i) the characterization techniques were improved to study the polycrystalline ferroelectrics in the mesoscale; and (ii) the texture, lattice strain and volume fraction of domains were tracked under applied electric field and mechanical stress.
Two novel synchrotron-based characterization techniques, three-dimensional X-ray diffraction (3-D XRD) and Scanning X-ray Microdiffraction (ySXRD) were used in this study. The methodology and standards in both techniques differ from each other and the present study provides a framework to bridge these techniques. Although these methods have been developed earlier, their application and adaptation to ferroelectrics required some care. For instance, diffraction spots often overlapped and made it difficult to identify individual domains and/or grains. In order to eliminate the spot overlap, the polycrystalline BaTiO3 sample was heated above the Curie temperature where the (tetragonal) domains disappear and attain the orientation of the grain. Next, the sample was cooled slowly to the room temperature and the evolution of the ferroelectric domains was studied at temperature and under electric field. The orientation relationships, volume fractions and lattice strain evolution of 8 domain systems were studied.
Whereas the orientation of the domains remained unchanged under electric field, the fraction of the energetically favorable domain variants increased. Due to local constraints, complete switching from one domain variant to another was not observed. The misorientation angles between domain variants slightly deviated from the theoretical value (=89.4y) by 0.2-0.3y. The deviation angle can be explained with the phase-matching angle developed during the cubic-tetragonal phase transformation to maintain strain compatibility of neighboring domains. The multiscale strain evolution of ferroelectric domains in a polycrystal was investigated quantitatively for the first time. Under electric field, lattice strains of up to 0.1% were measured along the applied field direction.
The present study offers a framework to characterize the polycrystalline materials with complex twin structures. By using the methodology described in this study, 3D-XRD and ySXRD techniques can be employed to study texture and lattice strain evolution in polycrystalline materials in the mesoscale.