A DFT + U description of oxygen vacancies at the TiO2 rutile (1 1 0) surface

Experimental observations indicate that removing bridging oxygen atoms from the TiO₂ rutile (1 1 0) surface produces a localised state approximately 0.7 eV below the conduction band. The corresponding excess electron density is thought to localise on the pair of Ti atoms neighbouring the vacancy; formally giving two Ti³⁺ sites. We consider the electronic structure and geometry of the oxygen deficient TiO₂ rutile (1 1 0) surface using both gradient-corrected density functional theory (GGA DFT) and DFT corrected for on-site Coulomb interactions (GGA + U) to allow a direct comparison of the two methods. We show that GGA fails to predict the experimentally observed electronic structure, in agreement with previous uncorrected DFT calculations on this system. Introducing the +U term encourages localisation of the excess electronic charge, with the qualitative distribution depending on the value of U. For low values of U (?4.0 eV) the charge localises in the sub-surface layers occupied in the GGA solution at arbitrary Ti sites, whereas higher values of U (?4.2 eV) predict strong localisation with the excess electronic charge mainly on the two Ti atoms neighbouring the vacancy. The precise charge distribution for these larger U values is found to differ from that predicted by previous hybrid-DFT calculations.     

A surface X-ray diffraction study of TiO2(1 1 0)(3 × 1)-S

Surface X-ray diffraction has been used to investigate the structure of TiO₂(1 1 0)(3 × 1)-S. In concert with existing STM and photoemission data it is shown that on formation of a (3 × 1)-S overlayer, sulphur adsorbs in a position bridging 6-fold titanium atoms, and all bridging oxygens are lost. Sulphur adsorption gives rise to significant restructuring of the substrate, detected as deep as the fourth layer of the selvedge. The replacement of a bridging oxygen atom with sulphur gives rise to a significant motion of 6-fold co-ordinated titanium atoms away from the adsorbate, along with a concomitant rumpling of the second substrate layer.     

SrTiO3(0 0 1) reconstructions: the (2 × 2) to c(4 × 4) transition

Scanning tunneling microscopy (STM) is used to investigate the (0 0 1) surface structure of Nb doped SrTiO₃ single crystals annealed in ultra high vacuum (UHV). Atomically resolved images of the (2 × 2) reconstructed surface are obtained after annealing a chemically etched sample. With further annealing dotted row domains appear, which coexist with the (2 × 2) reconstruction. The expansion of these domains with further annealing gives rise to the formation of a TiO₂ enriched c(4 × 4) reconstruction.     

Facetting and (n × 1) reconstructions of SrTiO3(1 1 0) surfaces

(n × 1) reconstructions and facetting of the (1 1 0) polar surface of SrTiO₃ are studied by means of a combination of shell model and density functional calculations. The polarity compensation can be achieved through the formation of {1 0 0} nano-facets, which play a crucial role in the reconstruction process. The behaviors of various possible terminations (Sr, Ti, and O) are analyzed, as well as their atomic structure and energetics. Their stability in different chemical environments is discussed, with respect to previous formulations and experimental results. The Sr-terminated surface tends to expose large facets, while the TiO and O terminations are marginally stabilized or even destabilized by (n × 1) reconstructions, respectively. Trend to facetting results from a subtle competition between the thermodynamic stability of the ideal non stoichiometric (n × 1) surfaces, and huge atomic relaxations that contribute to the lowering of the surface energy differently for each termination.     

Assignment of surface IR absorption spectra observed in the oxidation reactions: 2H + H2O/Si(1 0 0) and H2O + H/Si(1 0 0)

Infrared reflection absorption spectroscopy that used buried metal layer substrates (BML-IRRAS) and density functional cluster calculations were employed to investigate the water related oxidation reactions of 2H + H₂O/Si(1 0 0)-(2 × 1), 2D + H₂O/Si(1 0 0)-(2 × 1), and H₂O + H/Si(1 0 0)-(2 × 1). In addition to the oxygen inserted coupled monohydrides, which were previously reported in the former reaction system, we report several other oxidized Si hydride species in our BML-IRRAS experiments. Three new pairs of vibrational bands are identified between 900 and 1000 cm⁻¹. These vibrational frequencies were calculated using Si9 and Si10 cluster models that included all possible structures from zero to five oxygen insertions into the top layer silicon atoms using a B3LYP gradient corrected density functional method with a polarized 6-31G** basis set for all atoms. The three pairs of vibrational modes are assigned to the scissoring modes of adjacent and isolated SiH₂ with zero, one, and two oxygen atoms inserted into the Si back bonds. All the other newly observed vibrational peaks related to Si oxidation are also assigned in this study. The Si-O stretching bands observed in the reaction 2D + H₂O/Si(1 0 0)-(2 × 1) show an isotope effect, which suggests that in the system 2H + H₂O/Si(1 0 0)-(2 × 1) also, hydrogen atom tunneling plays an important role for the insertion of oxygen atoms into Si back bonds that form oxidized adjacent dihydrides.     

Surface evolution of rutile TiO2 (1 0 0) in an oxidizing environment

Transmission electron microscopy (TEM) has been used to study the rutile TiO₂ (1 0 0) surface in an oxidizing environment. By changing annealing conditions, TiO₂ surfaces with different morphologies are obtained. We report a new centered (2 × 2) surface reconstruction on this surface. Our experimental data indicates that this is a meta-stable, oxygen deficient structure formed as the disordered surface regains its stoichiometry in an oxidizing annealing environment.     

The small unit cell reconstructions of SrTiO3(1 1 1)

We analyze the basic structural units of simple reconstructions of the (1 1 1) surface of SrTiO₃ using density functional calculations. The prime focus is to answer three questions: what is the most appropriate functional to use; how accurate are the energies; what are the dominant low-energy structures and where do they lie on the surface phase diagram. Using test calculations of representative small molecules we compare conventional PBE-GGA with higher-order methods such as the TPSS meta-GGA and on-site hybrid methods PBE0 and TPSSh, the later being the most accurate. There are large effects due to reduction of the metal d oxygen sp hybridization when using the hybrid methods which are equivalent to a dynamical GGA + U, which leads to rather substantial improvements in the atomization energies of simple calibration molecules, even though the d-electron density for titanium compounds is rather small. By comparing the errors of the different methods we are able to generate an estimate of the theoretical error, which is about 0.25 eV per 1 × 1 unit cell, with changes of 0.5-1.0 eV per 1 × 1 cell with the more accurate method relative to conventional GGA. An analysis of the plausible structures reveals a new low-energy TiO₂-rich configuration with octahedral co-ordination. This structure can act as a template for layers of either TiO or Ti₂O₃, consistent with experimental results. The results also suggest that both the fracture surface and the stoichiometric SrTiO₃(1 1 1) surface should spontaneously disproportionate into SrO and TiO₂ rich domains.     

First-principles study of CaTiO3 oxygen-vacancies (0 0 1) surface

The structural and electronic properties of fully relaxed CaTiO₃ oxygen-vacancies (0 0 1) surface with CaO and TiO₂ terminations are investigated by first-principles plane waves ultrasoft pseudopotential method based on local density approximation. The present results show that the direction and the magnitudes of the atomic relaxations for oxygen-vacancies surface are different from that of the perfect surface. Compared with the TiO₂-terminated oxygen-vacancy surface, the CaO-terminated oxygen-vacancy surface are likely to be observed in oxygen environment conditions. Much different from the perfect surface, the oxygen-vacancy surface becomes metallic caused by some states in the conduction band are lowered and pulled down in the band-gap region.     

Combined STM, LEED and DFT study of Ag(1 0 0) exposed to oxygen near atmospheric pressures

We have investigated the interaction of molecular oxygen with the Ag(1 0 0) surface in a temperature range from 130 K to 470 K and an oxygen partial pressure ranging up to 10 mbar by scanning tunneling microscopy, low electron energy diffraction, Auger electron spectroscopy and ab initio density functional calculations. We find that at 130 K, following oxygen exposures of 6000 Langmuirs O₂, the individual oxygen atoms are randomly distributed on the surface. When the sample is exposed to 10 mbar O₂ at room temperature, small, p(2 × 2) reconstructed patches are formed on the surface. After oxidation at ≈470 K and 10 mbar O₂ pressure the surface undergoes a c(4 × 6) reconstruction coexisting with a (6 × 6) superstructure. By ab initio thermodynamic calculations it is shown that the c(4 × 6) reconstruction is an oxygen adsorption induced superstructure which is thermodynamically stable for an intermediate range of oxygen chemical potential.     

The adsorption of and reaction of NO2 on Ag(1 1 1)-p(4 × 4)-O and formation of surface nitrate

The adsorption and reaction of nitrogen dioxide on the Ag(1 1 1)-p(4 × 4)-O surface has been investigated with RAIRS, TPRS and STM. At 300 K NO₂ initially reacts with the oxygen overlayer to form nitrate in p(3 × 3) and p(4 × 4) structures, which convert to a new p(3 × 3) at saturation coverage. Surface pitting during nitrate adsorption is suggestive of the incorporation of silver atoms into the NO₃ structure. With heating NO₃ decomposes into NO₂ and O at 396 K and 497 K, and oxygen desorbs at 578 K.     

The 2 × 1 reconstruction of the rutile TiO2(0 1 1) surface: A combined density functional theory, X-ray diffraction, and scanning tunneling microscopy study

An extensive search for possible structural models of the (2 × 1)-reconstructed rutile TiO₂(0 1 1) surface was carried out by means of density functional theory (DFT) calculations. A number of models were identified that have much lower surface energies than the previously-proposed ‘titanyl’ and ‘microfaceting’ models. These new structures were tested with surface X-ray diffraction (SXRD) and voltage-dependent STM measurements. The model that is (by far) energetically most stable shows also the best agreement with SXRD data. Calculated STM images agree with the experimental ones for appropriate tunneling conditions. In contrast to previously-proposed models, this structure is not of missing-row type; because of its similarity to the fully optimized brookite TiO₂(0 0 1) surface, we call it the ‘brookite (0 0 1)-like’ model. The new surface structure exhibits two different types of undercoordinated oxygen and titanium atoms, and is, in its stoichiometric form, predicted to be rather inert towards the adsorption of probe molecules.     

Scanning tunnelling microscopy and spectroscopy of the reduced TiO2(1 0 0) surface

Scanning tunnelling microscopy and current imaging tunnelling spectroscopy were used to study the topographic and electronic structure of a reduced TiO₂(1 0 0) surface. The STM results showed that the TiO₂(1 0 0) surface is capable to form (1 × 7) reconstruction which can transform to (1 × 3) reconstruction due to reoxidation of the surface. The CITS results showed that the (1 × 7) reconstruction is much more metallic in compared to the (1 × 3) reconstruction showing pronounced surface states at energy 1.3 eV and 0.8 eV below the Fermi level and at energy 1.0-1.2 eV above the Fermi level.     

Anomalous hybridization in the In-rich InAs(0 0 1) reconstruction

The surface bonding arrangement in nearly all the confirmed reconstructions of InAs(0 0 1) and GaAs(0 0 1) have only two types of hybridization present. Either the bonds are similar to those in the bulk and the surface atoms are sp³ hybridized or the surface atoms are in a tricoordinated bonding arrangement and are sp² hybridized. However, dicoordinated In atoms with sp hybridization are observed on the InAs(0 0 1), In-rich, room temperature and low temperature surfaces. Scanning tunneling microscopy (STM) images of the room temperature (300 K) InAs(0 0 1) surface reveal that the In-rich surface reconstruction consists of single-atom rows with areas of high electron density that are separated by ∼4.3 Å. The separation in electron density is consistent with rows of undimerized, sp hybridized, In atoms, denoted as the β3′(4 × 2) reconstruction. As the sample is cooled to 77 K, the reconstruction spontaneously changes. STM images of the low temperature surface reveal that the areas of high electron density are no longer separated by ∼4.3 Å but instead by ∼17 Å. In addition, the LEED pattern changes from a (4 × 2) pattern to a (4 × 4) pattern at 77 K. The 77 K reconstruction is consistent with two (4 × 2) subunit cells; one that contains In dimers on the row and another subunit cell that contains undimerized, sp hybridized, In atoms on the row. This combination of dimerized and undimerized subunit cells results in a new unit cell with (4 × 4) periodicity, denoted as the β3(4 × 4) reconstruction. Density functional theory (DFT) and STM simulations were used to confirm the experimental findings.     

First-principles study for the atomic structures and electronic properties of PbTiO3 oxygen-vacancies (0 0 1) surface

The structural and electronic properties of fully-relaxed PbTiO₃ (0 0 1) oxygen-vacancy surface with PbO and TiO₂ terminations are investigated by first-principles calculations. In contrast to the perfect surface, the smaller surface rumples and interlayer distances have been found. The largest relaxation occurs on the second layer atoms not on the surface layer ones, and some in-gap Ti 3d states at about −1.1 eV below the Fermi-level are observed in the TiO₂-terminated surface caused by oxygen-vacancies. For the PbO-terminated surface, some in-gap Ti 3d states and Pb 6p states also move into the bulk midgap region to become partially occupied, and two different chemical states of the Pb 6s states were found. One is attributed to the bulk perovskite Pb atoms and another one is caused by the relaxation of surface Pb atoms. These theoretical results would give a good reference for the future experimental studies.     

The surface stress of the (1 1 0) and (1 0 0) surfaces of rutile and the effect of water adsorbents

The surface stress on clean TiO₂ (1 1 0) and (1 0 0) surfaces, and those with four types of adsorbent - (i) molecularly adsorbed water, (ii) dissociatively adsorbed water, (iii) dissociatively adsorbed water at an oxygen vacancy, and (iv) adsorbed hydrogen - was investigated in the framework of density functional theory using a slab model. The calculations were intended to rationalize the effect of the artificially introduced stress that occurs in experimentally photoinduced hydrophilicity. Tensile stress was observed for a clean (1 1 0) surface, and a mixture of tensile and compressive stress for a clean (1 0 0) surface. The adsorbate-induced surface stresses were analyzed in terms of the sixfold coordinated character of the surface titanium atoms, hydrogen bonds between the adsorbents and the bridging oxygen atoms, and the change in electron density in the vicinity of the surface.     

Geometric and electronic structure of positively and negatively poled LiNbO3 (0 0 0 1) surfaces

The effect of ferroelectric poling direction on the structure and electronic properties of the LiNbO₃ (0 0 0 1) surface was characterized. Low energy and reflection high energy electron diffraction indicated that both the positively and negatively poled surfaces were (1 × 1) with no evidence of longer range periodic reconstructions. Low energy ion scattering spectra from both surfaces were dominated by scattering from oxygen atoms. X-ray and ultraviolet photoelectron spectra also showed little difference between the positively and negatively poled surfaces, with the exception of a high binding energy shoulder on the O 1s core level of the negative surface. Exposure of the surfaces to atomic hydrogen caused reduction of the surface Nb rather than an increase in intensity on the high binding energy side of the O 1s peak, indicating that the shoulder on the O 1s peak on the negative surface was not due to surface hydroxyl groups. Temperature programmed desorption measurements indicated that the nearly stoichiometric LiNbO₃ samples were susceptible to loss of Li₂O starting at temperatures as low as 500 K, independent of the poling direction. An adatom/vacancy model is proposed in which oxygen ad-anions accumulate on one side of the crystal while oxygen anion vacancies are created on the opposite surface. This model can explain the apparent oxygen termination of both surfaces and the observed (1 × 1) periodicity of the surfaces, and also effectively screens the thickness dependent electric field associated with the polar orientation of the crystal.     

Structural investigation of the c(√2 × 5√2)R45° surface alloy formed by Ti deposition on Cu(0 0 1)

The alloying process of Ti deposited on Cu(0 0 1) was studied by means of XPS, LEIS, XPD and LEED intensity analysis. With the sample held at 570 K, a linear decrease of the Cu LEIS signal as a function of the amount of Ti deposited is observed in the early stages of deposition until a constant value is reached. At the onset of the plateau a c(√2 × 5√2)R45° LEED pattern starts to be visible. XPD and LEED intensity measurements were performed for the c(√2 × 5√2)R45° phase prepared depositing ca. 1.5 monolayer of Ti. The angle-scanned XPD curves measured for the phase c(√2 × 5√2)R45° reveal that Ti atoms substitute Cu atoms in the fcc lattice of the substrate. The polar XPD curves show that at least the first four layers of the substrate are involved in the alloying process. We found that the (3 1 0) plane of the Cu₄Ti alloy (D1_a type-structure) fits, without significant contraction or expansion of the lattice parameters, the c(√2 × 5√2)R45° structure. The intensity versus energy curves of the diffracted beams were calculated on the basis of this structural model using the tensor LEED method. The results of the LEED intensity analysis provide a further evidence of the formation of a slab of Cu₄Ti(3 1 0) layers.     

Driving force for the WO3(0 0 1) surface relaxation

The optimized structure of the WO₃(0 0 1) surface with various types of termination ((1 × 1)O, (1 × 1)WO₂, and c(2 × 2)O) has been simulated using density functional theory with the Perdew-Wang 91 gradient corrected exchange-correlation functional. While the energy of bulk WO₃ depends weakly on the distortions and tilting of the WO₆ octahedra, relaxation of the (0 0 1) surface results in a significant decrease of surface energy (from 10.2 × 10⁻² eV/Ų for the cubic ReO₃-like, c(2 × 2)O-terminated surface to 2.2 × 10⁻² eV/Ų for the relaxed surface). This feature illustrates a potential role of surface relaxation in formation of crystalline nano-size clusters of WO₃. The surface relaxation is accompanied by a dramatic redistribution of the density of states near the Fermi level, in particular a transformation of surface electronic states. This redistribution is responsible for the decrease of electronic energy and therefore is suggested to be the driving force for surface relaxation of the WO₃(0 0 1) surface and, presumably, similar surfaces of other transition metal oxides.     

Reconstruction and de-reconstruction of the Ir(1 0 0) surface and ultrathin Fe/Ir(1 0 0) films

The structure, energetics and magnetic properties of the quasihexagonal reconstruction of the Ir(1 0 0) surface and nanostructures formed by Fe atoms on this surface have been investigated using first-principles density functional theory with generalized gradient corrections. We find the reconstructed (1 × 5) surface to be 0.10 eV/(1 × 1) area lower in energy than the unreconstructed surface and we demonstrate that first-principles calculations can achieve quantitative agreement with experiment even for such long-period and deep-going reconstructions. For Fe coverage of 0.4 monolayers (ML) we have studied the stripe-like structure with biatomic Fe rows placed in the troughs of the (1 × 5)-reconstructed surface. Results of nonmagnetic calculations agree well with the structure inferred from STM data. Higher Fe coverages lead to a de-reconstruction of the Ir substrate. At 0.8 ML coverage a surface compound with composition Fe₄Ir is formed, which shows an appreciable buckling. In this case, a ferromagnetic calculation leads to good agreement with the low-temperature LEED data. We predict that the (1 × 5) periodicity of the mixed interface layer will persist also in thicker films with a pure Fe surface. Films with 1-4 ML Fe are predicted to be tetragonally distorted and ferromagnetic, with an axial ratio corresponding well to an elastic distortion of the Fe lattice.