Energy of Step Defects on the TiO₂ Rutile (110) Surface: An ab initio DFT Methodology

Abstract

We present a novel methodology for dealing with quantum size effects (QSE) when calculating the energy per unit length and step-step interaction energy of atomic step defects on crystalline solid surfaces using atomistic slab models. We apply it to the TiO 2 rutile (110) surface using density functional theory (DFT) for which it is well known that surface energies converge in a slow and oscillatory manner with increasing slab size. This makes it difficult to reliably calculate step energies because they are very sensitive to supercell surface energies, and yet the surface energies depend sensitively on the choice of slab chemical formula due to the dominance of QSE at computationally practical slab sizes. The commonly used method of calculating surface energies by taking the intercept of a best fit line of total supercell energies against slab size breaks down and becomes highly unreliable for such systems. Our systematic approach, which can be applied to any crystalline surface, bypasses such statistical estimation techniques and cross-checks and makes robust what is otherwise a very unreliable 2 process of extracting the energies of steps. We use the calculated step energies to predict island shapes on rutile (110) which compare favourably with published scanning tunneling microscopy (STM) images.

Interplay between Steps and Oxygen Vacancies on Curved TiO2(110)

“…1 (b). In such a z-scan the sample is displaced vertically (z-scale in Fig have been reported to migrate from terraces to steps, leading to O br vac´s-depleted terrace fringes in the proximity of [1][2][3][4][5][6][7][8][9][10][11]-oriented steps 13 . Such O br vac´s migration effect supports our results displayed in Fig.…”

“…Only a few studies [11][12][13][14][15] on vicinal rutile planes exist, but they reveal the potential of stepped surfaces to further tailor the physical and chemical properties of r-TiO 2 . Martinez et al 13 have reported the existence of oxygen vacancies at [1][2][3][4][5][6][7][8][9][10][11] step edges (O s vac´s), as these are easier to form than O br vac´s at terraces.…”

“…Only a few studies [11][12][13][14][15] on vicinal rutile planes exist, but they reveal the potential of stepped surfaces to further tailor the physical and chemical properties of r-TiO 2 . Martinez et al 13 have reported the existence of oxygen vacancies at [1][2][3][4][5][6][7][8][9][10][11] step edges (O s vac´s), as these are easier to form than O br vac´s at terraces. For [1][2][3][4][5][6][7][8][9][10] steps Lutrell et al 12 have proposed an atomic model without missing oxygen atoms (i.e., no O s vac´s) that still explains the bright features they observe by Scanning Tunneling Microscopy (STM).…”

“…All STM images presented here are high-pass filtered, which enhances the contrast at the terraces. [1][2][3][4][5][6][7][8][9][10][11] segments, abundant at position e, and straight [1][2][3][4][5][6][7][8][9][10] [1][2][3][4][5][6][7][8][9][10] step, from Ref. 12 , with two-fold coordinated O s atoms highlighted in blue.…”

Energetics of Rutile TiO2 Vicinal Surfaces with ⟨001⟩ Steps from the Energy Density Method

“…6,7,19 The ⟨110⟩ step has the highest step energy even after it reconstructs, 7 and the ⟨001⟩ step has only two stable structures that are ⟨001⟩ O and ⟨001⟩ Ti steps. 19 Recently, Hardcastle et al 6 and Stausholm-Møller et al 7 computed the isolated step energies and the step−step interactions of the ⟨001⟩ step, and they showed that the ⟨001⟩ O and ⟨001⟩ Ti steps have similar step energies, and the step−step interactions for both steps are negligible. Complicating all of these step energy calculations is "odd−even" oscillations in the TiO 2 (110) surface energy with the number of layers, 23 which must be addressed carefully.…”