Supercell Model of V-Doped TiO2: Unrestricted Hartree-Fock Calculations

Abstract

The host crystal space group and the point defect site symmetry group being given the procedure of generation of the imperfect space group in the supercell or periodic defect model is considered. The approach developed is applied to the symmetry analysis of the possible space groups of metal‐doped rutile and anatase structures in the supercell model. The results of unrestricted Hartree‐Fock calculations of the V‐doped rutile electronic structure (an impurity atom charge, valence states, an impurity level position in the energy gap) are given. Supercells of 36, 60, 84 atoms chosen on the base of the symmetry analysis are calculated. The convergence of the results with the supercell increasing is demonstrated.

Investigating the Impact of Ag Nanoparticles on N and S Co‐Doped TiO2 for Battery‐Type Supercapacitor Application

“…[18] TiO 2 has three polymorphic crystalline forms, namely rutile, anatase, and brookite, each exhibiting unique lattice structures. [19][20] In accordance with literature, the anatase phase of TiO 2 has considered to be more stable when its crystallite size is reduced to the nanoscale. [21] Additionally, the band gap of TiO 2 dependent on the size of the crystallite and can range from 3.0 eV to 3.3 eV.…”

“…Recently, there has been significant research focused on utilizing TiO 2 as an electrode material in supercapacitors because of non‐toxicity, high stability, higher electrical conductivity (∼10 −5 –10 −2 S cm −1 ), [8,17] high charge density, and cost‐effectiveness [18] . TiO 2 has three polymorphic crystalline forms, namely rutile, anatase, and brookite, each exhibiting unique lattice structures [19–20] …”

Spectroscopy Study on the Location and Distribution of Eu3+ Ions in TiO2 Nanoparticles

“…37) When the Eu 3þ ion has no inversion symmetry, the emission lines related to the 7 F 2 state are much stronger than those related to the 7 F 1 state. 32,38) Two intense emission lines related to the 7 F 2 state are observed at 617.2 and 624.8 nm in Eu500 and Eu900 [ Fig.…”

“…Sharp Eu 3þ emission lines have certainly been observed in various single crystals when Eu 3þ ions are substituted for heavy metal ions and all the Eu 3þ ions have the same site symmetry, e.g., in NaGdO 2 , 31,32) YVO 4 , 33) The site symmetry of Ti 4þ is D 2d (with the absence of an inversion center) in the anatase phase of TiO 2 and D 2h in the rutile phase. 37) When the Eu 3þ ion has no inversion symmetry, the emission lines related to the 7 F 2 state are much stronger than those related to the 7 F 1 state. 32,38) Two intense emission lines related to the 7 F 2 state are observed at 617.2 and 624.8 nm in Eu500 and Eu900 [Fig.…”

Design of porous Ni and rare earth metal (Ce, Ho, and Eu) Co-doped TiO2nanoarchitectures for energy conversion and storage applications

“…Nanocrystalline TiO 2 exists in different polymorphic crystalline forms: rutile, anatase, and brookite, which have different lattice structures. 18,19 The most thermodynamically stable form among these is the rutile phase. However, the other two forms are also converted into the rutile phase via heating at 400 °C to 1200 °C.…”