Perovskite Research Paper

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A perovskite is a material that has the same crystal structures as the mineral cal- cium titanium oxide is knows as perovskite. The ABO 3 type perovskite crystals have been broadely studied because of their technical importance and the funda- mental interest in the physics of their phase transition. Perovskite family contains a large number of compounds ranges from insulators to superconductors.The min- eral Perovskite was discovered and named by Gustav Rose in 1839 from samples found in the Ural Mountains, named after a Russian mineralogist, Count Lev Alek- sevich Von Perovski [1]. The original compound found was calcium titanium oxide
(CaTiO 3 ). The name later was used to describe a general group of oxides possessing similar structures with
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The ions occupying the A and B lattice sites are detailed in Fig. (1.1).
Figure 1.1: Schematic of compositions ABO 3 [1].
The perovskite structure is versatile and robust. It can be cubic, tetrahedral, or orthorhombic at standard temperature and pressure (STP). The perovskite BaHfO 3 is A 3+ B 3+ O 3 type in which the B cations are located in the corners of the cube and the A cation occupies the centre of the cube. The anions are located at the cube edges, between two B cations. Each B cation is surrounded by six anions and forms the centre of the BO 6 octahedra [3]. The BO 6 octahedras extend infinitely in three dimensions. The structure of cubic perovskite is shown in Fig. (1.2).
Figure 1.2: The ideal ABO 3 perovskite structure space group position (No 221).
La 2 CuO 4 and YBa 2 Cu 3 O 7−δ (where δ is 0-0.5) are the most prominent examples where electron correlation are too strong to be properly treated in high temperature
2superconductor [4]. Electronic properties of YBa 2 Cu 3 O 7−δ is difficult to understand because of its complex structure. To understand this type of complex system, we
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The first-principles approaches mainly based on the Hartree-Fock approach, the DFT approach etc. The Hartree-Fock self consistent method is one-electron approximation in which the motion of each electron in the effective field of the other electrons is governed by a one electron
Schrdinger equation [9]. In the Hartree-Fock approximation, the antisymmetric product of one-electron wave functions is used i.e it takes into account of the corre- lation arising due to electrons of same spin, however, the motion of the opposite spin remains uncorrelated [10, 11, 12]. In density funtional theory (DFT), the exchange- correlation is expressed as a functional of the electron density and the electronic states are solved for self-consistency as in the Hartree-Fock approximation. The exchange-correlation potential includes the exchange interaction arising from the antisymmetry of the wave functions and the dynamic correlation effect arising due
3to the Coulomb repulsion between the electrons. In principle, DFT theory is ex- act but it also treat the exchange and dynamic correlation effects approximately
[13, 14, 15,

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