Electron Microscopic Investigations And First-principles Calculations Of Typical Barium-based Ferroelectrics And Relaxor Ferroelectrics

The microstructure of typical ferroelectric BaTiO₃and relaxor ferroelectricBa(Ti_1-xSn_x)O₃were investigated to understand their ferroelectric and dielectric proper-ties using electron microscopy and first-principles calculations.The dynamic structure, the eigenfrequency of ferroelectric soft mode as a functionof temperature and dielectric divergence in the paraelectric-ferroelectric phase transitionof BaTiO₃were studied by effective Hamiltonian molecular dynamics and Girshberg-Yacoby model. The calculation results showed that the phase transition of BaTiO₃is oforder-disorder type and the eigenfrequency of soft mode as a function of temperatureobeys the Cochran linear law. Using the Girshberg-Yacoby model, it was revealed thatthe physical mechanism of dielectric divergence in the phase transition originates fromthe coupling between soft mode and the order-disorder Ti ions. As a result, the dielec-tric function is strongly dependent upon temperature and characterized by a divergentbehavior.The microstructure of Ba(Ti_1-xSn_x)O₃（x=16%,20%and25%） was studied usingdark-field imaging and aberration-corrected high-resolution transmission electron mi-croscopy. The characterized structural diffuse scatterings along {100} were used fordark-field imaging and we found that there are characterized by bright static spot struc-tures in the relaxor BTSn （x=20%and25%）, while they were not observed in the ferro-electric BTSn （x=16%）. The atomic-resolution structures of BTSn were further inves-tigated and quantitative analysis of the HRTEM images showed that there exist staticpolar nanoregions in relaxor BTSn（x=20%and25%） with size of2nm. In ferroelec-tric BTSn（x=16%）, only structures with small displacements were found. The resultsindicated that the static polar nanoregions may be a key factor of the materials’ relaxorproperties.The energy-loss fucntions （ELF） of BTSn were studied by combining electronenergy-loss spectroscopy and first-principle calculations. The theoretically predictedELFs are qualitatively in agreement with the experimental results. All the peaks in thedielectric functions and ELFs are explained based on the calculated electronic structuresbelow the Fermi surface. It is found that the Ti-O bond is strongly hybridized, whichhelps to stabilize the ferroelectric distortions. As a comparison, the ferroelectric instable Sn-O is suppressed due to the weak hybridization of Sn-O bond.The valence electronic structures, Born effective charges （BEC） as well as inter-atomic force constants （IFC） of BaMO3（M=Ti,Zr,Hf and Sn） were systematically stud-ied by first-principles calculation. The spatial distribution of O2p valence electrons ofthesecompoundsare obtainedintheframeworkof Wannierfunctions. Wefoundthatthed orbitals of the transition metals Ti, Zr and Hf are all hybridized with O2p orbitals andthe3d orbitals of titanium are the most delocalized, while those of Zr and Hf are morelocalized. There are no evident hybridizations between tin and O2p orbitals. Furtheranalysis of the BECs revealed that the BECs are intimately associated with orbital hy-bridizations. Analysis of the IFCs indicate that the BECs and long-range dipole-dipoleinteractions between atoms play important roles in the promotion of ferroelectric insta-bilities.