Relaxation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>TiO</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mo>(</mml:mo><mml:mn>110</mml:mn><mml:mo>)</mml:mo></mml:math>-(<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mo>×</mml:mo><mml:mn>1</mml:mn></mml:math>) Using Surface X-Ray Diffraction

Charlton, G.; Howes, P.B.; Nicklin, Chris; Steadman, P.; Taylor, J.S.G.; Muryn, Christopher A.; Harte, S.P.; Mercer, John R.; McGrath, R.; Norman, D.; Turner, Tracy; Thornton, G.

doi:10.1103/physrevlett.78.495

Cited by 306 publications

(160 citation statements)

References 17 publications

Supporting

Mentioning

135

Contrasting

Order By: Relevance

“…͑a͒ Stoichiometric surface, ͑b͒ reduced surface without spin-polarization, ͑c͒ reduced spin-polarized surface. 29 Very recent surface x-ray-diffraction measurements 30 show that the structure proposed by Ramamoorthy et al is in good agreement with experiment. Since we find essentially the same structure, these conclusions may be extended to our results.…”

Section: A the Stoichiometric Surfacesupporting

confidence: 67%

First-principles spin-polarized calculations on the reduced and reconstructedTiO2(110) surface

et al. 1997

View full text Add to dashboard Cite

We have performed plane-wave pseudopotential density-functional theory calculations on the stoichiometric and reduced TiO 2 ͑110͒ surface, the 2ϫ1 and 1ϫ2 reconstructions of the surface formed by the removal of bridging-oxygen atoms, and on the oxygen vacancy in the bulk. The effect of including spin polarization is investigated, and it is found to give a qualitatively different electronic structure compared with a spin-paired description. In the spin-polarized solutions, the excess electrons generated by oxygen reduction occupy localized band-gap states formed from Ti (3d) orbitals, in agreement with experimental findings. In addition, the inclusion of spin polarization substantially lowers the energy of all the systems studied, when compared with spin-paired solutions. However, spin-polarization does not change the relative stability of the two reconstructions, which remain energetically equivalent. ͓S0163-1829͑97͒02724-0͔

show abstract

Section: A the Stoichiometric Surfacesupporting

confidence: 67%

First-principles spin-polarized calculations on the reduced and reconstructedTiO2(110) surface

et al. 1997

View full text Add to dashboard Cite

show abstract

“…1,9 We find that atomic relaxations are converged to within 0.01 Å only for slabs containing 9 or more trilayers. Thinner slabs give significantly poorer convergence.…”

mentioning

confidence: 96%

“…An earlier surface x-ray diffraction study 9 had reported a significant inward relaxation for the bridging oxygen. Thus, the relaxed structure of the surface oxygen atoms has been a source of confusion both experimentally and theoretically.…”

mentioning

confidence: 99%

Revisiting the (110) surface structure ofTiO2: A theoretical analysis

Thompson

Lewis

2006

Phys. Rev. B

View full text Add to dashboard Cite

A detailed reexamination of the (110) surface structure of rutile TiO 2 has been carried out using first-principles total-energy methods. This investigation is in response to a recent high-precision LEED-IV measurement revealing certain significant quantitative discrepancies between experiment and previous theoretical calculations. We have been able to resolve these discrepancies and achieve excellent quantitative agreement with experiment by judicious attention to reducing computational approximation errors. Our analysis also reveals that bond lengths converge much faster with slab thickness than do relaxed absolute atomic positions, which are the structural parameters typically reported in the literature for this and related systems. The effect this observation has on both the choice of slab models and the way in which surfaces structures should be reported for covalently bonded solids is discussed. Finally, the efficacy of freezing the lowest several atomic layers of TiO 2 slab models in their bulk-like positions is examined. A recent LEED-IV experiment1 has produced what is arguably the highest precision measurement to date of the structure of the (110) surface of rutile TiO 2 .Comparison of these data to various published firstprinciples theoretical investigations of this system [2][3][4][5][6][7][8] reveals that, while some predicted atomic positions are in good agreement with the new experiment, othersmost noticeably those of the surface oxygen atomsare not. Indeed, the vertical relaxation of the bridging oxygen atoms was consistently predicted to be negative (i.e., inward relaxation relative to bulk termination), but was measured to be positive in Ref.[1]. An earlier surface x-ray diffraction study 9 had reported a significant inward relaxation for the bridging oxygen. Thus, the relaxed structure of the surface oxygen atoms has been a source of confusion both experimentally and theoretically.Given the prominence of TiO 2 (110) in applications and basic research, 10 as well as the extensive number of first-principles investigations on systems that build on TiO 2 (110) as a starting point, we felt this confusion was significant and merited further inquiry. As a result, we have undertaken an extensive first-principles analysis of the structure of TiO 2 (110), focusing on convergence and characterization issues. Our calculations resolve the discrepancy between theory and experiment on the relaxations of the surface oxygen atoms, while maintaining agreement in the other atomic relaxations. Furthermore, we find that much thicker slabs than have been typically used are necessary to achieve convergence not only in surface energy, as found previously, 11 but also in absolute atomic positions. However, if bond lengths are chosen as the "figures of merit" for assessing convergence, then our results show that the thinner slabs used to date in theoretical studies of this system are acceptable. We argue below in favor of switching to reporting bond lengths (and perhaps bond angles) as a more physically relevant descri...

show abstract

“…[16][17][18] The development of surface x-ray diffraction as a noninvasive probe of oxide surface structures has provided a new test for ab initio theories of these systems as reliable and accurate structural data for the surface region is obtained. 9,19 The ab initio theories applied to these systems differ in their treatment of electron exchange and correlation effects as well as in the numerical approximations made. Most are based on either Hartree-Fock ͑HF͒ theory, in which exchange is treated exactly and correlation effects neglected, or density-functional theory ͑DFT͒, in which both exchange and correlation are approximated.…”

Section: Introductionmentioning

confidence: 99%

Effects of exchange, correlation, and numerical approximations on the computed properties of the rutileTiO2(100) surface

1999

Self Cite

View full text Add to dashboard Cite

We present fully converged, all-electron, ab initio calculations of the structural relaxation at the TiO 2 (100)-(1ϫ1) surface. The effects of electron exchange, correlation, and various numerical approximations are isolated and quantified. We find that the predicted relaxations are insensitive to the treatment of exchange and correlation, but do depend on numerical approximations. The results of previous ab initio calculations are discussed in the light of these findings. ͓S0163-1829͑99͒05003-1͔

show abstract

Relaxation ofTiO2(110)-(1×1) Using Surface X-Ray Diffraction

Cited by 306 publications

References 17 publications

First-principles spin-polarized calculations on the reduced and reconstructedTiO2(110) surface

First-principles spin-polarized calculations on the reduced and reconstructedTiO2(110) surface

Revisiting the (110) surface structure ofTiO2: A theoretical analysis

Effects of exchange, correlation, and numerical approximations on the computed properties of the rutileTiO2(100) surface

Contact Info

Product

Resources

About