The influence of soft vibrational modes on our understanding of oxide surface structure

Abstract

We examine the reasons for the poor quantitative agreement between the structures predicted from the minimum energy configuration of first principles calculations and those deduced from surface xray diffraction experiments for the structure properties of the TiO 2 (110) surface. In order to confine all numerical approximations very large scale all-electron first principles calculations are used. We find a very soft, anisotropic and anharmonic surface rigid-unit vibrational mode which involves displacements of the surface ions of approximately 0.15Å for thermal vibrations corresponding to room temperature. It is concluded that in order to perform an accurate comparison between theory and experiment for this and perhaps other oxide surfaces it will be necessary to take account of such anisotropic vibrations in models used to interpret experimental data. In addition the contribution of the vibrational entropy to the surface free energy is likely to be significant and must be taken into account when computing surface energies and structures.

Adsorption of acetic and trifluoroacetic acid on the TiO2(110) surface

“…Initial calculations for the surface itself 14 were performed on a 36-atom cell ͓͑1ϫ1ϫ3͒ in terms of the sixatom surface unit cell͔ using 12 k-points ͑4ϫ4ϫ1 k-point mesh͒, a mesh cutoff of 126 Ry, and an energy shift of 15 meV. We found that this gives surface relaxations in reasonable agreement with the previous ab initio calculations 11 and experiments. 6 To check the dependence of our results on the slab thickness, we also calculated the ͑1ϫ1ϫ6͒ and ͑1 ϫ1ϫ7͒ slabs, and found that the surface relaxations have converged to less than 0.01 nm ͑and much better than this in most cases͒.…”

“…The basic physical and electronic structure of the most stable ͑110͒ surface has been well studied both experimentally 5,6 and theoretically, [7][8][9][10][11] and now, many investigations focus on defected surfaces, especially oxygen vacancies, [12][13][14] adsorption, 10,[15][16][17] or even adsorption onto defected surfaces. 18 -20 Due to their particular relevance to catalysis, many studies have also investigated the properties of adsorbed carboxylic ͑RCOOH͒ acids on the TiO 2 (110) surface.…”

First-principles thermodynamic modeling of atomic ordering in yttria-stabilized zirconia

“…19 The electronic free-energy contributions can be similarly added to the cluster expansion and would likely be significant in soft phonon or surface systems. 20 In most crystalline systems at normal working temperatures, the structural and vibrational free energies dominate over the electronic free-energy contributions. Interspecies forces, obtained from first-principles calculations on local perturbations of several of the training structures' equilibrium atomic positions at varied cell volumes, are used to obtain interspecies stiffness vs length force equations applicable across concentration space.…”

Revisiting the Surface Structure ofTiO2(110): A Quantitative low-Energy Electron Diffraction Study

“…1 for a schematic of the bulk-terminated structure), a prototypical metal oxide surface, whose precise surface structure remains a topic of some debate [2 -4], is determined with the well-established technique of quantitative lowenergy electron diffraction (LEED-IV) [5]. Importantly, we examine the impact on the structure determination of both charge transfer in the calculation of scattering phase shifts [5], and of soft surface vibrational modes [6].…”