Microscopic origin of lattice contraction and expansion in undoped rutile TiO<sub>2</sub>nanostructures

Santara, Batakrushna; Giri, P. K.; Imakita, Kenji; Fujii, Minoru

doi:10.1088/0022-3727/47/21/215302

Cited by 124 publications

(67 citation statements)

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“…Before this DFT work, TiO 2 was reported to be a direct gap semiconductor. This prediction that TiO 2 is an indirect gap material was confirmed 16 in 2014. Bagayoko and Franklin 17 were the first to settle definitively (with ab-initio computational results) the discrepancy between measured band gaps of 2 eV, mostly before the year 2000, and of less than 1 eV, mostly after 2000, for wurtzite InN.…”

Section: Some Failures Of Dft Calculations Ascribed To Dft: "Thementioning

confidence: 66%

Understanding density functional theory (DFT) and completing it in practice

2014

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We review some salient points in the derivation of density functional theory (DFT) and of the local density approximation (LDA) of it. We then articulate an understanding of DFT and LDA that seems to be ignored in the literature. We note the well-established failures of many DFT and LDA calculations to reproduce the measured energy gaps of finite systems and band gaps of semiconductors and insulators. We then illustrate significant differences between the results from self consistent calculations using single trial basis sets and those from computations following the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF). Unlike the former, the latter calculations verifiably attain the absolute minima of the occupied energies, as required by DFT. These minima are one of the reasons for the agreement between their results and corresponding, experimental ones for the band gap and a host of other properties. Further, we note predictions of DFT BZW-EF calculations that have been confirmed by experiment. Our subsequent description of the BZW-EF method ends with the application of the Rayleigh theorem in the selection, among the several calculations the method requires, of the one whose results have a full, physics content ascribed to DFT. This application of the Rayleigh theorem adds to or completes DFT, in practice, to preserve the physical content of unoccupied, low energy levels. Discussions, including implications of the method, and a short conclusion follow the description of the method. The successive augmentation of the basis set in the BZW-EF method, needed for the application of the Rayleigh theorem, is also necessary in the search for the absolute minima of the occupied energies, in practice. C

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Section: Some Failures Of Dft Calculations Ascribed To Dft: "Thementioning

confidence: 66%

Understanding density functional theory (DFT) and completing it in practice

2014

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“…Strain caused by the large density of oxygen defects creates a lattice expansion and therefore, nanocrystallites preferentially grow in the direction of (311) planes ,. D‐spacings calculated using Bragg's law indicate the variation of inter‐planar distances upon Mo incorporation (Figure ).…”

Section: Discussionmentioning

confidence: 99%

Enhanced Catalytic Properties of Molybdenum Promoted Mesoporous Cobalt Oxide: Structure‐Surface‐Dependent Activity for Selective Synthesis of 2‐Substituted Benzimidazoles

Weerakkody

Rathnayake

et al. 2018

ChemCatChem

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High‐valent molybdenum ions were substituted into the cobalt oxide lattice through a one step, sol‐gel method and investigated for selective synthesis of 2‐substituted benzimidazoles. Catalyst synthesis involves surfactant assisted soft templating inverse micelle method, which forms mesopores by interconnected intraparticle voids. Substitutional doping of Mo6+ resulted in materials with modified structural, morphological, surface, and redox properties. The catalytic activity increased with Mo concentration until an optimum amount (3 % Mo incorporation). Modified material shows lattice expansion, increased surface oxygen vacancies, and high surface area, which are responsible for the higher catalytic activity in selective benzimidazole synthesis reaction. A strong correlation between surface properties of the catalyst and the product selectivity was observed and plausible mechanistic and kinetic data are proposed and collected, respectively.

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“…The results are summarized in Table 2, where it was found using both methods that a higher t a resulted in increasing crystallite size. It was found also that the lattice parameters have a small expansion with higher t a , particularly in the c -direction (Figure S1b, Supporting Information File 1) [49]. Finally, a unit cell was built with the aid of the software TOPAS depicting the growth orientation with an expanded representation of 3 × 3 × 4 cells as shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

Impact of the anodization time on the photocatalytic activity of TiO₂ nanotubes

Díaz-Real¹,

Bandomo²,

Galindo‐de‐la‐Rosa³

et al. 2018

Beilstein J. Nanotechnol.

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Titanium oxide nanotubes (TNTs) were anodically grown in ethylene glycol electrolyte. The influence of the anodization time on their physicochemical and photoelectrochemical properties was evaluated. Concomitant with the anodization time, the NT length, fluorine content, and capacitance of the space charge region increased, affecting the opto-electronic properties (bandgap, bathochromic shift, band-edge position) and surface hydrophilicity of TiO2 NTs. These properties are at the origin of the photocatalytic activity (PCA), as proved with the photooxidation of methylene blue.

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Microscopic origin of lattice contraction and expansion in undoped rutile TiO₂nanostructures

Cited by 124 publications

References 50 publications

Understanding density functional theory (DFT) and completing it in practice

Understanding density functional theory (DFT) and completing it in practice

Enhanced Catalytic Properties of Molybdenum Promoted Mesoporous Cobalt Oxide: Structure‐Surface‐Dependent Activity for Selective Synthesis of 2‐Substituted Benzimidazoles

Impact of the anodization time on the photocatalytic activity of TiO₂ nanotubes

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Microscopic origin of lattice contraction and expansion in undoped rutile TiO2nanostructures

Cited by 124 publications

References 50 publications

Understanding density functional theory (DFT) and completing it in practice

Understanding density functional theory (DFT) and completing it in practice

Enhanced Catalytic Properties of Molybdenum Promoted Mesoporous Cobalt Oxide: Structure‐Surface‐Dependent Activity for Selective Synthesis of 2‐Substituted Benzimidazoles

Impact of the anodization time on the photocatalytic activity of TiO2 nanotubes

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Microscopic origin of lattice contraction and expansion in undoped rutile TiO₂nanostructures

Impact of the anodization time on the photocatalytic activity of TiO₂ nanotubes