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.     

Molecular dynamics simulation of the (0 0 0 1) α-Al2O3 and α-Cr2O3 surfaces

A simple, rigid pair-potential model is applied to investigate the dynamics of the (0 0 0 1) α-Al₂O₃ and α-Cr₂O₃ surfaces using the molecular dynamics technique. The simulations employ a two-stage equilibration process: in the first stage the simulation-cell size is determined via the constant-stress ensemble, and in the second stage the equilibration of the size-corrected simulation cell is continued in the canonical ensemble. The thermal expansion coefficients of bulk alumina and chromia are evaluated as a function of temperature. Furthermore, the surface relaxation and mean-square displacement of the atoms versus depth into the slab are calculated, and their behaviour in the surface region analysed in detail. The calculations show that even moderate temperatures (∼400 °C) give rise to displacements of the atoms at the surface which are similar to the lattice mismatch between α-alumina and chromia. This will help in the initial nucleation stage during thin film growth, and thus facilitate the deposition of α-Al₂O₃ on (0 0 0 1) α-Cr₂O₃ templates.     

Atomic structure of Cu2O(1 1 1)

Low-energy electron diffraction and scanning tunneling microscopy have been used to probe the surface atomic structure of Cu₂O(1 1 1) after various sample preparations. Annealing in oxygen gives a stoichiometric (1 × 1) oxygen terminated surface and further annealing in ultra-high vacuum results in a clear reconstruction and surface faceting. Tunneling from filled states in the reconstructed surface reveals a hexagonal pattern of large protrusions, which show an internal structure. The reconstruction is believed to be due to one-third of a monolayer of ordered oxygen vacancies. At areas on the surface where the large features are missing, another smaller type of protrusions is visible, which is associated with the ideal (1 × 1) surface. The relative position of the two types of features gives two possible models of the (1 1 1) surface. In the first model, the (1 × 1) surface is the ideal bulk terminated surface and coordinatively unsaturated oxygen ions are missing in the reconstructed surface. The second model agrees with the first model with the exception that coordinatively unsaturated copper ions in the outmost copper layer are missing in both the (1 × 1) and the reconstructed surface. The latter model is supported by previous surface free energy calculations. Since the undercoordinated copper ions have been suggested to be the catalytic active sites of Cu₂O(1 1 1), the presence or absence of these cations could be of great importance for the fundamental understanding of the surface reactivity of Cu₂O and of copper-based catalysts.     

The kaolinite (0 0 1) polar basal plane

Kaolinite is thought to be an efficient ice nucleating agent because kaolinite crystals expose perfect unreconstructed (0 0 1) basal surfaces which provide a suitable template for ice growth. However, we show here with the aid of density functional theory calculations that the unreconstructed basal surface is polar. Various mechanisms to eliminate the macroscopic dipole and in so-doing stabilize the basal surface are considered. The most promising option identified so far involves the adsorption of foreign atoms (for example, Na and Cl atoms) on the perfect basal surface, since this yields a non-metallic surface with a cleavage energy lower than the unreconstructed polar basal surface. A quantitative experimental structure determination of the kaolinite basal surface is called for.     

Initial stages of H2O adsorption and hydroxylation of Fe-terminated α-Fe2O3(0 0 0 1) surface

The adsorption modes of H₂O on a Fe-terminated hematite(0 0 0 1) surface have been investigated by first principles Density Functional theory within a periodic slab model and the generalized gradient approximation. Molecular adsorption and dissociative adsorption in monolayer coverage, one H₂O per surface Fe, were both considered. Five plausible orientations were studied to determine the most favorable adsorption position. Molecular adsorption is shown to have a small effect on the underlying surface structure, while hydroxylation has a strong effect on the surface geometry. Electronic densities of state calculations reveal details of these different interactions. The heterolytic dissociation, which produces two types of surface hydroxyls, is the preferable adsorption mode, being slightly favored energetically over the molecular adsorption. Homolytic dissociative adsorption, forming a single hydroxyl on surface Fe, is energetically unfavored, even though strong binding interaction (∼3 eV) is found between the OH radical and surface. Dissociative adsorption on an oxidized ferryl site was also studied to investigate suggested local reactivity enhancement.     

Density functional theory investigation of the structure of SO2 and SO3 on Cu(1 1 1) and Ni(1 1 1)

Density functional theory (DFT) slab calculations, mainly using the generalised gradient approximation, have been used to investigate the minimum energy structures of molecular SO₂ and SO₃ on Cu(1 1 1) and Ni(1 1 1) surfaces. On Ni(1 1 1) the optimal local adsorption structures are in close agreement with experimental results for both molecular species obtained using the X-ray standing wavefield technique, although for adsorbed SO₂ the energetic difference between two alternative lateral positions of the lying-down molecule on the surface is marginally significant. On Cu(1 1 1) the results for adsorbed SO₂, in particular, were sensitive to the DFT functional used in the calculations, but in all cases failed to reproduce the experimentally-established preference for adsorption with the molecular plane perpendicular to the surface. This result is discussed in the context of previously published DFT results for these species adsorbed on Cu(1 0 0). The optimal geometry found for SO₃ on Cu(1 1 1) is similar to that on Ni(1 1 1), providing agreement with experiment regarding the molecular orientation but not the adsorption site.     

O2 dissociation on Pd(2 1 1) and Cu(2 1 1) surfaces

We have performed ab initio Density Functional Theory (DFT) based calculations to observe the reactivity of the Pd(2 1 1) and Cu(2 1 1) surfaces towards O₂. In order to properly address the adsorption dynamics, the static potential energy surface calculations have been complemented with first principles molecular dynamics calculations, which reveal interesting steering effects that complicate the dissociation dynamics. We have found that on both surfaces the step microfacets are very reactive and the dissociation of the O₂ molecule at room temperature occurs mostly on those sites.     

(6 × 2) Reconstruction of the Ag/Si(1 1 1) surface at 77 K

The ground state of the Ag/Si(1 1 1)-(3 × 1) has been investigated by low temperature scanning tunneling microscopy (STM) and density-functional theory. The Fourier transform of the STM image reveals a (6 × 2) reconstruction, which is theoretically found to yield a reconstruction with lower energy than the (3 × 1). The most stable (6 × 2) structural model leads to excellent correspondence between experimental and simulated STM images, and reveals a dimerization of the silver atoms in the channels formed by neighbouring honeycomb Si chains.     

The influence of thermal fluctuations on electronic and structural properties of Ge(0 0 1) surface

We present a theoretical study (within the density functional theory) of the influence of thermal fluctuations of the Ge(0 0 1) structure on its electronic properties, mainly in the context of possible metallization of this surface observed in experiment. Analysis is based on the results of three series of long-time molecular dynamics (MD) simulations performed for p(1 × 2), c(2 × 4) and p(2 × 4) surface unit cells. We have found that for the p(1 × 2) unit cell thermal fluctuations lead to the appearance of a sharp peak in the density-of-states distribution at the Fermi level, and consequently, to metallization of the germanium surface, while the energy structure of the c(2 × 4) reconstructed surface remains non-metallic even at high temperatures. This result is in an agreement with recently published scanning tunneling spectroscopy data. Our MD simulations show that, depending on the translational symmetry of the surface, thermal fluctuations may modify its electronic structure in quite a distinct way. The obtained results also indicate that the observed Ge(0 0 1) surface metallization is an averaged effect of the variations of the local density of states caused by thermal fluctuations.     

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.     

Theoretical and experimental studies of the structure and dynamics of the CaF2(1 1 1) surface

The structure and dynamics of the CaF₂(1 1 1) surface were investigated by means of low-energy electron diffraction (LEED) and molecular dynamics (MD) simulations at 300 K. LEED beam intensities were recorded as a function of electron energy and were analyzed with the tensor LEED approach. Positions as well as mean square amplitudes of the ions in the first layers were fitted to the experimental I(E) curves. According to both LEED and MD, the CaF₂(1 1 1) surface structure is similar to the bulk-terminated structure with only small relaxation of the outermost ions. Moreover, both methods show an enhancement of vibrational amplitudes in the outermost F-Ca-F triple layer.     

First principles study of Si(3 3 5)-Au surface

The structural and electronic properties of gold decorated Si(335) surface are studied by means of density-functional calculations. The resulting structural model indicates that the Au atoms substitute some of the Si atoms in the middle of the terrace in the surface layer. Calculated electronic band structure near the Fermi energy features two metallic bands, one coming from the step edge Si atoms and the other one having its origin in hybridization between the Au and neighboring Si atoms in the middle of the terrace. The obtained electronic bands remain in good agreement with photoemission data.     

First-principles study on field evaporation of surface atoms from W(0 1 1) and Mo(0 1 1) surfaces

The simulations of field-evaporation processes for surface atoms on W(0 1 1) and Mo(0 1 1) surfaces are implemented using first-principles calculations based on the real-space finite-difference method. The threshold values of the external electric field for evaporation of the surface atoms, which are ∼6 V/Å for tungsten and ∼5 V/Å for molybdenum, are in agreement with the experimental results. While the threshold value of the electric field and the local-field enhancement around the evaporating atoms agree with those expected from the conclusion of the previous study using structureless jellium, the induced charge around the surface atom has a significant difference from that obtained by the jellium model.     

First principles study of the electronic and geometric structure of Cu(5 3 2)

Using density functional theory with the generalized gradient approximation and ultra-soft pseudo-potentials, we have calculated structural relaxations of the Cu(5 3 2) surface which contains steps and kinks. We find the relaxation pattern to oscillate dramatically for atoms in the first 10 layers before decaying rapidly in the bulk. The most striking feature is an outward expansion of the relative interlayer separation d₁₂ of 25%. We also find serious discrepancies with relaxation pattern and relaxation amplitudes calculated using embedded atom method potentials that may reflect the limitation of these potentials to accurately describe systems with complex geometries. Full potential calculations reveal a dispersionless surface state along a high symmetry direction in the surface Brillouin zone. Valence charge density along several planes show excess of charge around kink atom and the nature of bonding with other (5 3 2) atoms.     

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.     

Adsorption dynamics of O2 on Cu(1 0 0)

We have studied the adsorption of O₂ on the Cu(1 0 0) surface using both static potential energy surface (PES) calculations and ab initio molecular dynamics. The dynamical calculations complement the PES results, revealing steering effects which could not be predicted based on the static calculations only. We study the effect of oxidation and Ag doping on O₂ adsorption dynamics. The results are discussed in the light of recent molecular beam experiments.     

Determining the GaSb/GaAs-(2 × 8) reconstruction

Highly strained thin layers of GaSb/GaAs possess a (2 × 4) reconstruction at low Sb overpressures, and a (2 × 8) reconstruction at high Sb overpressures. While the atomic details of the Sb/GaAs-(2 × 4) are well known, the details of the (2 × 8) are not understood. In this paper, we use density functional theory to analyze possible (2 × 8) structures. Comparing scanning tunneling microscope images from both simulation and experiment and examining the relative energies of possible (2 × 8) structures, we show the α(2 × 8) and β(2 × 8) are the thermodynamically stable surface reconstructions for high Sb content films strained to the GaAs lattice parameter. The α and β(2 × 8) reconstructions are related to the GaAs-α2(2 × 4) and GaAs-β2(2 × 4) through the addition of 2 cations and 8 anions into the trench between adjacent (2 × 4) unit cells.     

Electronic structure and surface reconstruction of adsorbed oxygen on copper(0 0 1)

The electronic structure of the c(2 × 2) and the missing row phases of chemisorbed O on Cu(0 0 1) at a coverage of 0.5 monolayers has been calculated using a full-potential semi-infinite embedding technique. Calculations are made over a range of Cu-O layer spacings, and from the change in the work function, the effective charge on O is obtained. The effective charge is the same for both phases of the O/Cu(0 0 1) surface with a value of −0.3|e| on O, and consequently too small to drive any surface instability. The angular momentum-resolved density of states and energy-resolved charge densities are used to describe the binding and the spatial electronic overlap at the surfaces. In the reconstructed phase the O and the surface Cu atoms undergo displacements, which optimises the bonding.     

Formation of oxygen vacancies on the TiO2(1 1 0) surfaces

Density functional theory was employed to investigate the formation and properties of the oxygen vacancies on the rutile TiO₂(1 1 0) surface. It is found that the formation of the positively charged bridging-oxygen vacancy (BOV⁺, 4.2 eV) is the most favored one, followed by the positively charged in-plane-oxygen vacancy (POV⁺, 4.5 eV). In contrast, the formation of the neutral bridging-oxygen and in-plane-oxygen vacancies (BOV and POV), and their dication oxygen vacancies (BOV²⁺ and POV²⁺) needs much higher energies (7.9 and 8.3 vs. 8.1 and 8.6 eV), respectively.     

Density functional theory calculations of surface properties and H2 adsorption on the Cu2O (1 1 1) surface

First-principles calculation on the basis of the density functional theory (DFT) and generalized gradient approximation have been applied to study the adsorption of H₂ on the stoichiometric O-terminated Cu₂O (1 1 1), Cu₂O (1 1 1)-Cu_CUS and Cu-terminated Cu₂O (1 1 1) surfaces. The optimal adsorption position and orientation of H₂ on the stoichiometric O-terminated Cu₂O (1 1 1) surface and Cu-terminated Cu₂O (1 1 1) surface were determined and electronic structural changes upon adsorption were investigated by calculating the Local Density of States (LDOS) of the Cu_CUS 3d and Cu_CUS 4s of stoichiometric O-terminated Cu₂O (1 1 1) surface. These results showed that H₂ molecule adsorption on Cu_CUS site parallel to stoichiometric O-terminated Cu₂O (1 1 1) surface and H₂ molecule adsorption on Cu₂ site parallel to Cu-terminated Cu₂O (1 1 1) surface were the most favored, respectively. The presence of surface copper vacancy has a little influence on the structures when H₂ molecule adsorbs on Cu_CSA, O_CUS and O_CSA atoms and the H₂ molecule is only very weakly bound to the Cu₂O (1 1 1)-Cu_CUS surface. From the analysis of stoichiometric O-terminated Cu₂O (1 1 1) Local Density of States, it is observed that Cu_CUS 3d orbital has moved to a lower energy and the sharp band of Cu_CUS 4s is delocalized when compared to that before H₂ molecule adsorption, and overlapped substantially with bands due to adsorbed H₂ molecule. The Mulliken charges of H₂ adsorption on Cu_CUS site showed that H₂ molecule obtained electron from Cu_CUS which was consistent with the calculated electronic structural changes upon H₂ adsorption.