Strontium titanate is seeing increasing interest in fields ranging from thin-film growth to water-splitting catalysis and electronic devices. Although the surface structure and chemistry are of vital importance to many of these applications, theories about the driving forces vary widely 1,2 . We report here a solution to the 3 × 1 SrTiO 3 (110) surface structure obtained through transmission electron diffraction and direct methods, and confirmed through density functional theory calculations and scanning tunnelling microscopy images and simulations, consisting of rings of six or eight cornersharing TiO 4 tetrahedra. Further, by changing the number of tetrahedra per ring, a homologous series of n × 1 (n ≥ 2) surface reconstructions is formed. Calculations show that the lower members of the series (n ≤ 6) are thermodynamically stable and the structures agree with scanning tunnelling microscopy images. Although the surface energy of a crystal is usually thought to determine the structure and stoichiometry, we demonstrate that the opposite can occur. The n × 1 reconstructions are sufficiently close in energy for the stoichiometry in the near-surface region to determine which reconstruction is formed. Our results indicate that the rules of inorganic coordination chemistry apply to oxide surfaces, with concepts such as homologous series and intergrowths as valid at the surface as they are in the bulk.The structure of SrTiO 3 is a cubic close-packed lattice of strontium and oxygen with strontium at the corners and oxygen at the face centres, and titanium at the body centres occupying those octahedral holes that are surrounded only by oxygen. Along the (110) direction SrTiO 3 is polar, composed of alternating layers of SrTiO 4+ and O 2 4− , that is, alternating layers with uncompensated nominal valence charges of 4+/4−. In a fully ionic model, this leads to an unbalanced macroscopic dipole and infinite surface energy. Therefore, we expect a (110) surface to have a nominal excess surface valence of either 2+ or 2− per surface unit cell, as otherwise energetically unfavourable holes in the valence band or electrons in the conduction band would be formed. There has been extensive discussion of the mechanisms of this 'charge compensation' for polar oxide surfaces in the literature (see for instance refs 3-5 and references therein). Various theories, such as a reduction of Coulomb forces 2 or a minimization of 'dangling bonds' 1 , have been described as the driving force behind surface structure formation. An alternative model for oxide surfaces, first proposed for the SrTiO 3 (001) 2 × 1 surface 6 , is that the rules of inorganic coordination chemistry dominate, although, as the (001) surface is not polar, we might question the generality of this model.

SrTiO 3 (111) samples, doped with Nb, are Ar + ion sputtered and annealed in ultrahigh vacuum (UHV) and in varying pressures of oxygen and investigated using scanning tunneling microscopy (STM) and Auger electron spectroscopy (AES). STM images show that a number of reconstructions constituting a family of (n × n) surfaces are able to form on the surface by varying the sputtering conditions and O 2 annealing pressures. The family of (n × n) reconstructions is due to variations in the oxygen stoichiometry, with (3 × 3) the most oxygen-rich, followed by (4 × 4), (6 × 6), and finally (5 × 5). Annealing in atmospheric pressure of air causes a (9/5 × 9/5) reconstruction to form. Highly reducing the surface, through extended UHV annealing, produces a TiO (111)-(2 × 2) nanophase.Step heights are always found to be equivalent to integer multiples of the distance between two similar (111) planes (the d 111 lattice parameter). AES analysis indicates no detectable impurities and shows all the surfaces to be Ti-enriched and either stoichiometric or deficient with respect to Sr. The concentration of Ti at the surface increases as the surface becomes more reduced.

Scanning tunneling microscopy, Auger electron spectroscopy ͑AES͒, and low energy electron diffraction are used to investigate 0.5 wt % Nb doped SrTiO 3 ͑110͒ samples, which are annealed in ultrahigh vacuum. An ͑n ϫ 1͒ family of reconstructions constituting ͑3 ϫ 1͒, ͑4 ϫ 1͒, and ͑6 ϫ 1͒ periodicities form on the surface at varying annealing temperatures. Wood's notation of the reconstructions is defined such that the first integer represents the multiple of the bulk terminated periodicity in the ͓001͔ direction and the second digit shows the multiple of the periodicity in the ͓110͔ direction. AES reveals that all the reconstructions are O deficient, but the ͑4 ϫ 1͒ is also Ti enriched and the ͑6 ϫ 1͒ is Sr enriched with respect to stoichiometry. The ͑3 ϫ 1͒ surface possesses step edges which are decorated with a ͑1 ϫ 4͒ reconstruction on the upper terrace. Similarly, step edges on the ͑6 ϫ 1͒ surface often possess small regions of ͑1 ϫ 2͒ reconstruction on the lower terrace. Step heights are always found to be equivalent to integer multiples of the distance between two similar ͕110͖ planes ͑the d 110 lattice parameter, 0.28 nm͒.

The surfaces of metal oxides often are reconstructed with a geometry and composition that is considerably different from a simple termination of the bulk. Such structures can also be viewed as ultrathin films, epitaxed on a substrate. Here, the reconstructions of the SrTiO3 (110) surface are studied combining scanning tunneling microscopy (STM), transmission electron diffraction, and X-ray absorption spectroscopy (XAS), and analyzed with density functional theory calculations. Whereas SrTiO3 (110) invariably terminates with an overlayer of titania, with increasing density its structure switches from n × 1 to 2 × n. At the same time the coordination of the Ti atoms changes from a network of corner-sharing tetrahedra to a double layer of edge-shared octahedra with bridging units of octahedrally coordinated strontium. This transition from the n × 1 to 2 × n reconstructions is a transition from a pseudomorphically stabilized tetrahedral network toward an octahedral titania thin film with stress-relief from octahedral strontia units at the surface.

Nb-doped SrTiO 3 ͑111͒ samples are annealed in UHV at 850°C for 30 min and investigated using scanning tunneling microscopy ͑STM͒, low-energy electron diffraction ͑LEED͒, and Auger electron spectroscopy ͑AES͒. STM images show that both ͑ ͱ 7 ϫ ͱ 7͒R19.1°and ͑ ͱ 13ϫ ͱ 13͒R13.9°reconstructions coexist on the surface.Step heights of 0.21± 0.02 nm on the surface are equivalent to the d 111 lattice parameter, which is the distance between two adjacent, similar ͑111͒ planes in the bulk crystal. The calculated LEED pattern for this co-reconstruction corresponds to the observed LEED pattern, which resembles a six-petal flower. AES analysis indicates no detectable impurities, and shows the surface to be Ti and Sr enriched and O deficient compared to the bulk stoichiometry. This change in surface composition is proposed to provide the stability for the polar surface.