Phase diagram of the fcc(1 1 0) surfaces with adsorbate-induced missing-row reconstructions

The phase diagram of the fcc(1 1 0) surfaces with missing-row reconstructions induced by adatoms, is calculated by use of the Blume–Emmery–Griffiths model. In the model, we introduce adatom–adatom interactions to determine surface structures and dipole–dipole interactions to describe the effect of zigzag adsorption. The interactions between nearest-neighbor (NN) and next-nearest-neighbor (NNN) rows are considered. The calculation of the temperature versus adatom chemical potential phase diagram is performed using mean-field approximation. It is indicated that if NN and NNN interactions are competitive, there appear either dipole or coverage modulated (incommensurate) phases at high temperatures for a wide range of the interactions.     

Structure and electronic properties calculation of ultrathin α-Al2O3 films on (0 0 0 1) α-Cr2O3 templates

Ab initio total energy Hartree-Fock calculations of ultrathin films of α-Al₂O₃ on (0 0 0 1) α-Cr₂O₃ templates are presented. The surface relaxation, the in-plane reconstruction and the surface and strain energies of the slabs are studied as a function of alumina film thickness. The surface Al layer is found to relax inwards considerably, with the magnitude of the inwards relaxation depending on the thickness of the ultrathin alumina film in a non-linear manner. The calculations also reveal that ultrathin films of alumina lower the surface energy of (0 0 0 1) α-chromia substrates. This indicates that the (0 0 0 1) α-chromia surface provides favourable conditions for the templated growth of α-alumina. However, increasing the alumina film thickness is found to give rise to a significant increase in strain energy. Finally, the electronic properties at the surface of the (0 0 0 1) α-Al₂O₃/α-Cr₂O₃ slabs are investigated. Here it is found that the alumina coating gives rise to an increase in the covalency of the bonds at the surface of the slabs. In contrast, the influence of an alumina layer on the electrostatic potential at the surface of the chromia slab is relatively minor, which should also be beneficial for the templated growth of α-alumina on (0 0 0 1) α-chromia substrates.     

First-principles studies of the oxygen adsorption on unreconstructed and reconstructed Ni(1 1 0) surfaces

First-principles calculations have been performed to investigate the adsorption of oxygen on unreconstructed and reconstructed Ni(1 1 0) surfaces. The energetics, structural, electronic and magnetic properties are given in detail. For oxygen adsorption on unreconstructed surface, (n×1)(n=2,3) substrate with oxygen atom on short-bridge site is found to be the most stable adsorption configuration. Whereas energetically most favorable adsorption phase of reconstructed surface is p(n×1) substrate with oxygen atom located at long-bridge site. Our calculations suggest that the surface reconstruction is induced by the oxygen adsorption. We also find there are redistributions of electronic structure and electron transfer from the substrate to adsorbate. Our calculations also indicate surface magnetic moment is enhanced on clean surfaces and oxygen atoms are magnetized weakly after oxygen adsorption. Interestingly, adsorption on unreconstructed surface does not change surface magnetic moment. However, adsorbate leads to reduction of surface magnetic moment in reconstructed system remarkably.     

Step patterns on vicinal reconstructed surfaces

Step patterns on vicinal (2 × 1) reconstructed surfaces of noble metals Au(110) and Pt(110), miscut towards the (100) orientation, are investigated. The free energy of the reconstructed surface with a network of crossing opposite steps is calculated in the strong chirality regime when the steps cannot make overhangs. It is explained why the steps are not perpendicular to the direction of the miscut but form in equilibrium a network of crossing steps which make the surface to look like a fish skin. The network formation is the consequence of competition between the — predominantly elastic — energy loss and entropy gain. It is in agreement with recent scanning tunnelling microscopy observations on vicinal Au(110) and Pt(110) surfaces.     

Reconstruction on Au(0 0 1) vicinal surfaces in UHV and in sulfuric acid solution

Using scanning tunneling microscopy we have studied the reconstruction on Au(1 1 n) surfaces in ultra-high vacuum and in electrolyte. Similar to the well-known (5 × 20) quasi-“hex” reconstruction on Au(0 0 1), the reconstruction consists of parallel reconstruction lines along the steps indicative of a higher atom density in the first Au layer. In contrast to nominally flat Au(0 0 1) where the reconstruction period is 1.44 nm, we find considerably larger reconstruction periods (1.8−1.96 nm) on incidentally flatter regions of nominal Au(1 1 9), Au(1 1 11), and Au(1 1 17) surfaces. The enlarged reconstruction period is attributed to the stress field on stepped surfaces. In agreement with previous studies we find a reconstruction free zone at the step edges.     

Shell model calculations of the adsorption and diffusion of K, Cl, and KCl on KCl(0 0 1)

Equilibrium adsorption positions and diffusion pathways of the ions K⁺ and Cl⁻ as well as of the molecule KCl on the terrace of the (0 0 1) surface of KCl were determined by shell model calculations allowing relaxations of the crystal lattice in the vicinity of the adsorbed species. For the ions each one adsorption position was found, in which the ions are located above the hollow site at the center of a slightly distorted square formed by two cations and two anions of the uppermost surface layer of the KCl crystal. Adsorption energies of −1.52 eV for K⁺ and −1.61 eV for Cl⁻ were calculated. Jumps of the ions occur from these positions to adjacent hollow positions in the ±[1 0 0] and ±[0 1 0] directions with a jump distance of a₀/2. The activation energies for the jumps result as 0.142 for K⁺ and 0.152 eV for Cl⁻ and the mean diffusion lengths as and . For the KCl molecule four distinct adsorption minima with energies between −0.932 and −0.825 eV were found. Because of the smaller lattice relaxation caused by the molecule the adsorption energies are considerably lower than for the single ions. In the position with the largest adsorption energy the ions of the admolecule are again placed above adjacent hollow sites. In two more adsorption positions only one ion is at the hollow site and the other one in a top position above an oppositely charged ion of the surface. In the fourth position with the smallest adsorption energy both ions are in top positions. Jumps between the different adsorption positions proceed by rotations of the molecule, in which one of its ions remains essentially attached to a local minimum position. The diffusion and desorption of a KCl molecule was studied by a Monte Carlo method, resulting in a mean diffusion length x_s (nm) = 0.39 exp[0.84 (eV)/2kT], which agrees rather well with an experimental value of . Values for the mean stay time as well as for the surface diffusion coefficient are derived.     

The stability of fcc (1 1 1) metal surfaces

The results of a theoretical study on the stability of fcc (1 1 1) metal surfaces to certain commensurate-incommensurate reconstructive phase transformations is presented. Specifically, we have performed computer simulation studies of the 22×√3 surface reconstruction of Au(1 1 1). This reconstruction involves a uniaxial contraction of the top monolayer corresponding to a surface strain of about 4.3% and has been observed to be the stable structure for the clean surface at low temperatures. The driving force for the reconstruction has been associated with the quantity (f−γ), where f is the surface stress and γ is the surface free energy, while the opposing force is due to the disregistry with the underlying lattice. A continuum model yields a stability criterion that depends on the knowledge of a small number of physical quantities: f, γ, the equilibrium nearest-neighbor spacing r₁ and the shear modulus G. We have performed molecular dynamics simulations as a general stability analysis of these types of reconstructions. The results are in excellent agreement with the continuum model. The simulations using embedded-atom method potentials also accurately reproduce many observed features of the reconstruction on Au(1 1 1).     

Surface properties of rutile TiO2(1 1 0) from molecular dynamics and lattice dynamics at 300 K: Variable-charge model results

Geometric structure, atomic vibrations and atomic charges and their thermally induced fluctuations have been calculated as a function of depth in, and thickness of, rutile TiO₂(1 1 0) slabs, within the framework of the variable-charge potential of Swamy and Gale [V. Swamy, J.D. Gale, Phys. Rev. B 62 (2000) 5406] at 300 K. Molecular dynamics simulations and lattice dynamics calculations were performed with a 2D periodic slab model for slab thicknesses between 3 and 11 triple layers (approximately 9-35 Å). Odd-even oscillations with respect to the number of slab layers are found for the surface relaxation for very thin slabs, and for the (slowly converging) rumpling in the middle of the slab. The Ti and O atomic charges in the outermost three atomic layers differ from the rest of the slab (they are less ionic); the thermal vibrations do not alter this picture. The atomic mean-square amplitudes are some 50% larger (more for O, less for Ti) at the surface than in the middle of the slab and decay rather slowly to the bulk values. Comparisons with the results of a rigid-ion potential for titania [M. Matsui, M. Akaogi, Mol. Simul. 6 (1991) 238] are presented for non-electronic properties.     

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.     

The Na-adsorbed Ge(0 0 1) surface: Structure and STM image simulations

Sodium adsorbed on the Ge(0 0 1) surface causes reconstruction of the surface with the type of reconstruction depending on the amount of the adsorbate. We present theoretical investigations of the structure and electronic properties of Na-adsorbed Ge(0 0 1) for the coverage of 0.5 monolayer using the combination of two methods: a plane-wave basis method and a local-orbital minimal-basis method. Two possible minimum-total-energy atomic configurations have been found, namely, the Na/Ge(0 0 1)-p(2 ×1) and Na/Ge(0 0 1)-p(4 × 1) reconstructions. The surface electronic structure for all calculated configurations occurs to be metallic. Our investigations are completed by a simulation of STM images for the obtained atomic structures.     

Decay of multilayer holes on SrTiO3(0 0 1)

We have studied the decay kinetics of nanoscale multilayer holes on SrTiO₃(0 0 1) surfaces, using variable temperature scanning tunneling microscopy. We have performed real time observation of the decay of multilayer holes with diameters of 10 nm order at 750 °C. We have found that the hole decays, filling layer by layer from the bottom while expanding the periphery of the hole. We have performed numerical simulations of hole decay based on a step flow model. The observed decay kinetics is found to be diffusion limited with local mass conservation.     

A multi-scale Monte Carlo study of oxide structures on the Cu(1 0 0) surface

We present a multi-scale Monte Carlo study of the oxidation of the Cu(1 0 0) surface based on the Bortz-Kalos-Lebowitz model with the equilibrium energetics obtained from ab initio calculations. The radial and island size distribution functions are examined and Cu-O structures are analyzed at different temperatures and coverages. We concentrate on the coverages of 0.3 monolayer O or less, with variable sub-monolayer coverages of Cu. The results show that even though the ab initio calculations yield a higher barrier for O than for Cu adatom diffusion on Cu(1 0 0), the stability of Cu structures causes the O adatoms to be more mobile on the Cu(1 0 0) surface than the Cu adatoms. We are able to reproduce the c(2 × 2)-O domains seen in the experiments. However, we give an alternative explanation based on the repulsive interactions of O that, on one hand, cause the local ordering and, on the other hand, prohibits large well-ordered domains. We also give interpretation on the formation of the R45°-O reconstruction of Cu(1 0 0) above the O coverages of 0.3 monolayer based on the ab initio energetics.     

Simulations of iodine adsorbed Ge(0 0 1) surface and its STM images

A layer of iodine at Ge(0 0 1) surface develops an ordered structure of iodine atoms bound to Ge dimers. Here are discussed atomic structures of Ge(0 0 1) surface covered by 0.25 monolayer of iodine. The p(2×4), p(2×2), c(2×4) and p(1×4) surface structures are found in calculations. The structure with two iodine atoms of the dissociated I₂ molecule adsorbed at both ends of the same germanium dimer is found to be energetically favourable over iodine adsorption at neighbouring dimers. Simulated STM images of the obtained surface structures are presented and compared with experimental data.     

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.     

A dynamical mean field theory for the study of surface diffusion constants

We present a combined analytical and numerical approach based on the Mori projection operator formalism and Monte Carlo simulations to study surface diffusion within the lattice-gas model. In the present theory, the average jump rate and the susceptibility factor appearing are evaluated through Monte Carlo simulations, while the memory functions are approximated by the known results for a Langmuir gas model. This leads to a dynamical mean field theory (DMF) for collective diffusion, while approximate correlation effects beyond DMF are included for tracer diffusion. We apply our formalism to three very different strongly interacting systems and compare the results of the new approach with those of usual Monte Carlo simulations. We find that the combined approach works very well for collective diffusion, whereas for tracer diffusion the influence of interactions on the memory effects is more prominent.     

Influence of surface stress in the missing row reconstruction of fcc transition metals

Surface stress relief is often invoked as the driving force for surface reconstruction. The present ab initio total energy calculations show that it is not the case, at least for the missing row reconstruction undergone by the (1 1 0) surface of the face centered cubic transition metals. Instead, they show that the tendency to reconstruct or not is closely related to the sign and magnitude of the strain derivative of surface energy. Finally, they unambiguously confirm that relativistic effects are at the origin of this reconstruction.     

High resolution images of Mo2C(0001)- structure by scanning tunneling microscopy

A C-terminated structure on Mo₂C(0001) was observed by scanning tunneling microscopy. The structure was observed as a honeycomb structure with dark depressions corresponding to C atoms which make up the lattice. High resolution imaging was possible at low tunneling resistance less than 1 MΩ. Each C atom appears as a shallow sombrero protrusion predicted by theoretical calculations of C atoms on a metal substrates. It is concluded that the C atoms occupied threefold hollow sites of the (1×1) Mo layer of the substrate and a model for the structure is proposed.     

CF interaction with Si(1 0 0)-(2 × 1): Molecular dynamics simulation

In this study, the interaction of CF with the clean Si(1 0 0)-(2 × 1) surface at normal incidence and room temperature was investigated using molecular dynamics simulation. Incident energies of 2, 12 and 50 eV were simulated. C atoms, arising from dissociation, preferentially react with Si to form Si-C bonds. A Si_xC_yF_z interfacial layer is formed, but no etching is observed. The interfacial layer thickness increases with increasing incident energy, mainly through enhanced penetration of the silicon lattice. Silicon carbide and fluorosilyl species are formed at 50 eV, which is in good agreement with available experimental data. The level of agreement between the simulated and experimental results is discussed.