Lakhasly

Perovskite compounds have a distinct crystalline structure and therefore have unique physical properties.Since lead is a toxic element, the most suitable compounds to replace CsPbI3 compound and have the same electronic properties are: CsCaI3 and KGeI3 for halides.It gives the detail of the crystalline accommodation law which states that; V_F/V_B =n VEC/2 where VF is the volume of Fermi sphere, VB is the volume of Brillouin zone, n is the number of atoms per lattice point and VEC is the number of valence electrons per the number of atoms.In addition, we found that the compounds suitable for applications in optoelectronics and solar cells have the lowest Fermi energy, the lowest quantum state volume, and the largest number of Brillouin zones in the valence band as for the compound CsPbI3, which is used in these applications.In results, it is found that the crystalline accommodation law achieved a great success in classifying halides and perovskite oxides according to the ratio of shared valence electrons in bonds to the number of atoms (VEC).Perovskite oxides also have various physical properties, such as: ferromagnetism, antiferromagnetism, ferroelectricity, antiferroelectricity, piezoelectricity, peroelectricity, and superconductivity.In view of the great success achieved by the law of crystal accommodation to explain the crystal structure of materials, the aim of the present work was to use the law of crystal accommodation to explain the crystal structure of perovskite compounds, halides and oxides, and to study their electronic structure and electrical properties based on this model.The classification was as follows: Perovskite halides and oxides molecules are bonded by a ratio of 4.8 of the valence electrons to the number of atoms.Accordingly, the cubic system is formed, whether in oxides or halides, when VF/VB equals 12.For cubic perovskite oxides and halides the valence band consists of 12 Brillouin zones.The hexagonal oxides and halides perovskites are formed when VF/VB equals 24.The orthorhombic oxides and halides perovskites are formed when, when VF/VB equals 48.In the hexagonal pervoskites, the valence band contains 48 electrons.

Perovskite compounds have a distinct crystalline structure and therefore have unique physical properties. For example, perovskite halides are used in solar cells and optoelectronic devices. Perovskite oxides also have various physical properties, such as: ferromagnetism, antiferromagnetism, ferroelectricity, antiferroelectricity, piezoelectricity, peroelectricity, and superconductivity. Therefore, studying its crystal structure is very important to understand these various unique properties. In this thesis, we reviewed the different models that attempted to explain the crystalline structure of these compounds. Then we used the crystalline accommodation model, which succeeded in explaining the crystalline structure of various elements and compounds.
The thesis consisted of three chapters, the first chapter is the introduction and aim of the work, the second chapter is the computational methodology, the third is the results and discussion, and finally the conclusion. In the introduction, we reviewed all the models that attempted to explain the crystalline structure of perovskite halides and oxides. It gives the detail of the crystalline accommodation law which states that;
V_F/V_B =n VEC/2
where VF is the volume of Fermi sphere, VB is the volume of Brillouin zone, n is the number of atoms per lattice point and VEC is the number of valence electrons per the number of atoms.
In view of the great success achieved by the law of crystal accommodation to explain the crystal structure of materials, the aim of the present work was to use the law of crystal accommodation to explain the crystal structure of perovskite compounds, halides and oxides, and to study their electronic structure and electrical properties based on this model.
The second chapter, entitled Computational Methodology, dealt with the scientific basis of the crystal accommodation law and its application to halides and perovskite oxides. Code for the calculations was created using the Fortran-90 language. We also used the International Center for Diffraction Data (ICDD) cards in the calculations.
In results, it is found that the crystalline accommodation law achieved a great success in classifying halides and perovskite oxides according to the ratio of shared valence electrons in bonds to the number of atoms (VEC). The classification was as follows: Perovskite halides and oxides molecules are bonded by a ratio of 4.8 of the valence electrons to the number of atoms. Accordingly, the cubic system is formed, whether in oxides or halides, when VF/VB equals 12. This number is the number of filled Brillouin zones in the valence band. For cubic perovskite oxides and halides the valence band consists of 12 Brillouin zones. The hexagonal oxides and halides perovskites are formed when VF/VB equals 24. The orthorhombic oxides and halides perovskites are formed when, when VF/VB equals 48.
In this model, the Brillouin zone contains one quantum state that has two energy levels for the two electrons. The first level is for electron which has spin-down and the second level for the electron, which has spin-up. On this basis, the valence band of the cubic system is filled with 24 electrons, 12 electrons with spin-up and 12 electrons with spin-down. In the hexagonal pervoskites, the valence band contains 48 electrons. 24 electrons have spin-up and 24 electrons have spin-down. The valence band of the orthorhombic perovskite is filled with 96 electrons, 48 electrons with spin-up and 48 electrons with spin-down.
We also found that the Fermi energy for perovskite halides ranges from 8.17 to 20.12 eV, while its value for perovskite oxides ranges from 15.57 to 27.88 eV. We note that the average Fermi energy for oxides is greater than that for halides. We also found that the quantum state volume for halides ranges from 0.27 to 3.91, while it ranges from 0.93 to 4.7 Å-3 for oxides. In addition, we found that the compounds suitable for applications in optoelectronics and solar cells have the lowest Fermi energy, the lowest quantum state volume, and the largest number of Brillouin zones in the valence band as for the compound CsPbI3, which is used in these applications. Since lead is a toxic element, the most suitable compounds to replace CsPbI3 compound and have the same electronic properties are: CsCaI3 and KGeI3 for halides. For perovskite oxides we found that the low-temperature superconducting compound SrTiO3 has a large quantum state volume of 4.19 Å-3.