Investigations On The Structural Phase Transition And Surface Stabilities Of A²⁺B⁴⁺O₃ Perovskite Crystals

The lattice dynamics, band structures, and atomic potential energy surfaces of six typical ABO3 perovskites were systematically investigated by using density functional theory plane-wave pseudopotential technique. The computation results indicated that the phase transition behavior of ABO3 perovskties is closely related to the interaction of A-O ionic pair and interaction of B-O ionic pair. The long-range interactions of A-O pairs are responsible for the R25 antiferrodistortive soft mode while the Coulomb interactions of B-O pairs for theΓ15 ferroelectric soft mode. The Coulomb interaction of Sr-O pair in SrTiO3 results in an antiferrodistortive transition, and the repulsive interaction of Ti-O pairs lead to the absence of ferroelectric soft mode. In BaTiO3 exactly opposite to SrTiO3, the interaction of Ba-O ionic pair and interaction of Ti-O ionic pair in BaTiO3 lead to the existence of ferroelectric instability and the lack of antiferrodistortive instability in BaTiO3. In PbTiO3, the covalency of Pb-O pair suppresses the contribution of Ti displacement to the soft mode and enhances the ferroelectric instability in PbTiO3.The interaction of B-O ionic pair become repulsive as B site is occupied by Zirconium instead of Titanium. Zr ion not only significantly increases lattice volume but also suppresses the contributions of Zr displacements to the unstable phonons. The interaction of Ba-O ionic pair and interaction of Zr-O ionic pair are both repulsive and cubic BaZrO3 becomes the stable ground-state phase. In comparison with SrTiO3, stronger Coulomb force of Sr-O pair enhances the instability of R25 mode. The long-range interaction of Pb-O pair in PbZrO3 is strongest. Therefore, antifferrodistortive and ferroelectric instabilities coexist in PbZrO3. Analysis of band structures and atomic potential energy surfaces further confirm the aforementioned conclusions.As the lattice volume decreases, theΓ15 phonons of cubic SrTiO3 and BaTiO3 shows a similar trend and the Ti-O repulsions get stronger, and ferroelectric instability disappears. Analysis of the real-space interatomic force constants confirms that the ionic radius of Sr and Ba are crucial for different A-O interactions. Furthermore, because ionic radius of Sr is smaller than that of Ba, the lattice constant of SrTiO3 is much smaller than BaTiO3. SrTiO3 does not show ferroelectric instability. The substitution and different lattice volumes make the phase transitions of SrTiO3 and BaTiO3 entirely different.Calculations of the vibrational modes in different crystalline phases indicated that low-temperature phase transition does not exist for PbTiO3; whereas the tetragonal-orthogonal and orthogonal-rhombohedral phase transitions exist for BaTiO3. We found that the soft mode frequency increases with larger tetragonal strain, and the unstable soft mode turns into stable vibration mode at a critical tertragonal strain. The tetragonal phase of PbTiO3 is very stable thanks to its large tetragonal strain (~6%). Smaller tetragonal stain of BaTiO3 (~1%) is important for its low-temperature phase transition. The results from band structure analysis and atomic potential energy surface analysis confirms that the covalency of the Pb-O pair is responsible for the large tetragonal strain of PbTiO3.On BaTiO3 (110) surfaces, significant atomic relaxations and charge redistributions occurs. Analysis of charge redistribution shows that the polarity compensation can be achieved for both stoichiometric and non-stoichiometric terminations; however their compensation mechanisms are quite different. For the BaTiO-(110) termination, however, the Fermi level located at the bottom of the conduction bands, which leads to a considerable filling of surface states. In the O2-(110) termination, the surface peroxo group render the surface insulating. The intensive electronic structure changes of the stoichiometric surface with respect to bulk crystal cause larger relaxations and higher cleavage energy than the non-stoichiometric surface. For the TiO, Ba, and O non-stoichiometric terminations, their electronic structures are similar to that of the bulk crystal; thus their insulating characteristics are retained because surface states were empty. Furthermore, the study of the surface grand potentials (SGPs) shows that four stable (110) terminations coexist. The BaTiO stoichiometric termination can only exist in a narrow region in the phase diagram with oxygen deficient condition.Comparing the SGPs of various oriented surfaces confirms that TiO- and Ba-(110) non-stoichiometric surfaces can coexist with the stable (100) surfaces. BaO2- and O-(111) non-stoichiometric surfaces competite with stable (100) surface. The surface relaxation, surface electric structure, bonding nature and surface stability areas of SrTiO3 and BaTiO3 are similar because of similar valence configuration of Sr with respect to Ba. The covelency of Pb-O pair in PbTiO3 causes significant different surface relaxation and electronic structure of its (110) surface with respect to SrTiO3 and BaTiO3. PbTiO-(110) surface does not exist stably.