Unravelling the atomic structure of cross-linked (1 × 2) TiO2(110).

The cross-linked (1 × 2) reconstruction of TiO(2)(110) is a frequently observed phase reflecting the surface structure of titania in a significantly reduced state. Here we resolve the atomic scale structure of the cross-linked (1 × 2) phase with dynamic scanning force microscopy operated in the non-contact mode (NC-AFM). From an analysis of the atomic-scale contrast patterns of the titanium and oxygen sub-structures obtained by imaging the surface with AFM tips having different tip apex termination, we infer the hitherto most accurate model of the atomic structure of the cross-linked (1 × 2) phase. Our findings suggest that the reconstruction is based on added rows in [001] direction built up of Ti(3)O(6) units with an uninterrupted central string of oxygen atoms accompanied by a regular sequence of cross-links consisting of linear triples of additional oxygen atoms in between the rows. The new insight obtained from NC-AFM solves previous controversy about the cross-linked TiO(2)(110) surface structure, since previously proposed models based on cross-links with a lower O content do not appear to be consistent with the atom-resolved data presented here. Instead, our measurements strongly support the Ti(3)O(6) motif to be the structural base of the cross-linked (1 × 2) reconstruction of TiO(2)(110).

Evidence of subsurface oxygen vacancy ordering on reduced CeO2(111).

Surface and subsurface oxygen vacancies on the slightly reduced CeO(2)(111) surface have been studied by atomic resolution dynamic force microscopy at 80 K. Both types of defect are clearly identified by the comparison of the observed topographic features with the corresponding structures predicted from recent first-principles calculations. By combining two simultaneously acquired signals (the topography and the energy dissipated from the cantilever oscillation), we are able to unambiguously locate subsurface oxygen vacancies buried at the third surface atomic layer. We report evidence of local ordering of these subsurface defects that suggests the existence of a delicate balance between subtle interactions among adjacent subsurface oxygen vacancy structures.

Wang-Landau algorithm for continuous models and joint density of states.

We present a modified Wang-Landau algorithm for models with continuous degrees of freedom. We demonstrate this algorithm with the calculation of the joint density of states of ferromagnet Heisenberg models and a model polymer chain. The joint density of states contains more information than the density of states of a single variable-energy, but is also much more time consuming to calculate. We present strategies to significantly speed up this calculation for large systems over a large range of energy and order parameter.