钙钛矿型PbZrO_3电子能带结构的第一性原理研究

First-principle study of the electronic band structure of lead zirconate

采用第一性原理局域密度近似下的投影缀加平面波方法精确计算并比较了钙钛矿材料PbZrO3低温正交相(反铁电相)、高温立方相(顺电相)的电子能带结构.PbZrO3作为一种重要的反铁电材料,在高密度储能电容器,换能器和可控开关电容等领域具有重要的应用前景,同时关于其反铁电来源和电场驱动下的反铁电相变的理论研究具有重要意义.第一性原理方法可以从微观上揭示结构与性能之间的内在联系,有助于理解一些性质产生的根源.PbZrO3晶体从立方相到正交相的结构相变源于氧八面体ZrO6的扭曲畸变和阳离子Pb2+相对于阴离子O2-的移动.第一性原理计算结果显示:PbZrO3正交相及立方相的能带均为直接带隙绝缘体,带隙大小分别约为2.61eV、2.35eV,两相价带和导带主要是O的2p态及Zr的4d态、Pb的6p态组成;相对于立方相,PbZrO3正交相大约在-5eV附近,Pb的6p态、Zr的4d态及O的2p态有一个强峰,表明O、Zr与Pb的杂化效应比顺电相的增强,这是PbZrO3与BaTiO3同为钙钛矿结构但有不同的铁电行为的原因;由顺电相到反铁电相时,局域的Pb 6s态向低能移动,且O 2p也向低能移动并伴随着能带展开,这与Pb-O之间形成的杂化效应增强有关,它们的杂化起着降低原子间的短程排斥力的作用,有利于反铁电畸变的形成.能量计算结果也表明,反铁电相能量比顺电相的低0.44eV,进一步证实了PbZrO3基态为反铁电相.

The structural and electronic properties of low-temperature orthorhombic PbZrO3(antiferroelectric phase) and high-temperature cubic phase(paraelectric)are calculated using the first-principle methods,which are performed within the density functional theory using the projector augmented wave implemented in the Vienna ab initio Simulation Package,and the exchange-correlation potential is treated in the local density approximation using the Ceperly-Alder scheme.The first-principles methods have been a powerful tool for obtaining accurate ground state and indicating the relevance between the microscopic structure and the properties,such as the ferroelectric phase transition of BaTiO3,PbTiO3.The ground state of PbZrO3 has been known to be antiferroelectric and the space groups of antiferroelectric and cubic phaseare Pbam and Pm3m respectively.The initial structural parameters are adopted within previous studies.The structural relationship between cubic paraelectric and orthorhombic antiferroelectric phase can be understood with two distortions from the cubic geometry: one is the cooperative distortion of the adjacent oxygen octahedra and the other is the opposite displacement of Pb ions between the adjacent unit cells,which dominates the antiferroelectric origin of the orthorhombic phase.This low-temperature structure is characterized by antiparallel displacement of Pb atoms in the ab plane with subsequent rotation of ZrO6 octahedra,meanwhile,the positions of Zr atoms mainly remain unchanged.The lattice parameters and atomic positions are relaxed until the total energy changed by less than 10-5 eV per conventional cell and residual force is smaller than 0.01 eV/.All the calculations reach good convergence.The calculated results show that the cubic and orthorhombic phase are both direct gap insulators,and the band gaps correspond to the values about 2.61 and 2.35 eV,respectively.In both cubic and orthorhombic PbZrO3,the valence band and the conduction band are mainly composed of O 2p,Zr 4d and Pb 6p states.Compared to the cubic phase,the main difference for the orthorhombic PbZrO3 is the enhanced peak around-5 eV,which consists mainly of O 2p and Pb 6s and 6p orbits.This behavior reflects the increase of Pb-O bond hybridization,indicating the different ferroelectric behavior from structurally similar perovskites BaTiO3.Meanwhile,the results of the DOS show that the local Pb 6s states and O 2p states of the orthorhombic phase shift to the lower energy,which reduce the total energy of the system,in favor of stabilizing the orthorhombic ground state of PbZrO3.Actually,our results of calculations indicate the energy of antiferroelectric phase PbZrO3 is lower than that of cubic phase about 0.44 eV.In summary,the conclusion is that the additional hybridization of O 2p and Pb 6s and 6p orbits in orthorhombic PbZrO3 could provide a deeper insight for understanding the antiferroelectric properties,as compared with the cubic phase.