Interlayer Relaxations Research Articles

Structure of the hydrogen-stabilizedMgO(111)−(1×1)polar surface: Integrated experimental and theoretical studies

The surface structure of $\mathrm{MgO}(111)\text{\ensuremath{-}}(1\ifmmode\times\else\texttimes\fi{}1)$ bulk and thinned single crystals have been investigated by transmission and reflection high-energy electron diffraction, low-energy electron diffraction (LEED), and x-ray photoelectron and Auger electron diffraction. The $(1\ifmmode\times\else\texttimes\fi{}1)$ polar surface periodicity is observed both after 800 \ifmmode^\circ\else\textdegree\fi{}C annealing in air and also after oxygen plasma cleaning and annealing in ultrahigh vacuum. The x-ray photoelectron spectroscopy and diffraction results were analyzed by simulations based on path-reversed LEED theory and by first-principles calculations to help distinguish between different mechanisms for the stabilization of this extremely polar oxide surface: (1) stabilization by adsorption of a hydrogen monolayer; maintaining the insulating nature of the surface and (2) stabilization of the clean O or Mg terminated $1\ifmmode\times\else\texttimes\fi{}1$ surface by interlayer relaxations and two-dimensional surface metallization. The analysis favors stabilization by a single OH layer, where hydrogen sits on top of the O ions with O-H bond distance of 0.98\AA{}. The in-plane O and Mg positions fit regular rocksalt sites, the distance between the topmost O and Mg plane is 1.04 \AA{}, contracted by $\ensuremath{\sim}14%$ with respect to bulk MgO distance of 1.21 \AA{}, while the interlayer separation of the deeper layers is close to that of bulk, contracted by less than 1%. The presence of a monolayer of H associated with the terminal layer of oxygen reduces significantly the surface dipole and stabilizes the surface.

First-principles study of low-index surfaces of lead

We report a density-functional theory study for $\mathrm{Pb}(111)$, $\mathrm{Pb}(100)$, and $\mathrm{Pb}(110)$ surfaces using ab initio pseudopotentials and a plane-wave basis set. Creating the pseudopotential with the $6s$, $6p$, and $6d$ states in the valence shell is found to yield good results for the bulk lattice constant, bulk modulus, and cohesive energy. Convergence of the surface energies with plane-wave cutoff, $\mathbf{k}$-mesh, vacuum and slab thickness was carefully checked, as was the effect of the nonlinearity of the core-valence exchange-correlation interaction. Employing the local-density approximation of the exchange-correlation functional we obtain excellent agreement of the calculated surface energies and surface-energy anisotropies with recent experimental results. However, with the generalized gradient approximation the calculated surface energies are about 30% too low. For all three studied surfaces, the calculations give interlayer relaxations that are in reasonable agreement with low-energy electron diffraction analysis. The relaxations exhibit a damped oscillatory behavior away from the surface, which is typical for a metal surface.

First-principles investigation of the multilayer relaxation of stepped Cu surfaces

We performed density-functional theory calculations, employing the all-electron full-potential linearized augmented plane-wave (FLAPW) method, for the multilayer relaxations of the vicinal, high-Miller-index Cu(210), Cu(211), and Cu(331) surfaces, as well as for the flat, low-Miller-index Cu(100), Cu(110), and Cu(111) surfaces. Generally, it is expected that the interlayer relaxation-sequence at stepped metal surfaces with $n$ surface atom rows in the terraces exposed to the vacuum show $n\ensuremath{-}1$ contractions (indicated by $\ensuremath{-}$) followed by one expansion (indicated by $+$). However, recent studies based on low-energy electron diffraction (LEED) intensity analysis and all-electron FLAPW calculations suggested that the multilayer relaxation-sequence of the stepped Cu(331) surface, for which $n=3$, behaves anomalously, i.e., $\ensuremath{-}++\ensuremath{\cdots}$, instead of the expected $\ensuremath{-}\ensuremath{-}+\ensuremath{\cdots}$. From the results presented in this work, we did not find any indication of such anomalous behavior for Cu(331) or for any of the investigated stepped Cu surfaces. For the flat surfaces we obtained the expected contraction of the topmost interlayer distance. In the particular case of the Cu(110) surface, a pronounced alternating oscillatory behavior extending over six interlayer distances was found, i.e., $\ensuremath{-}+\ensuremath{-}+\ensuremath{-}+$. For all studied Cu surfaces in the present work, we found a good quantitative agreement between our interlayer relaxations and those obtained by LEED intensity analysis.

Structural relaxations of Cu vicinals

We have studied multilayer and atomic relaxations of vicinal (regularly stepped or high Miller index) surfaces of Cu with loosely and tightly packed step-edges, using many-body and semi-empirical interaction potential obtained from the embedded atom method. For all investigated surfaces, except for Cu(3 1 1), the calculated multilayer relaxations reveal non-uniform damping magnitudes in interlayer relaxations. Furthermore, we find that the vicinals with wider terrace width display quite different characteristics in the multilayer relaxations compared to the vicinals with narrower terrace width. We also investigate the local atomic relaxations around step and trace the atomic shifts to the changes in the associated local force fields, compared to those in the bulk.

Structure of Ag(410) and Cu(320)

We present results of calculations of atomic relaxations on two stepped surfaces Ag(410) and Cu(320) using interatomic potentials from the embedded atom method. Relaxations are found to extend several layers into the bulk, the most striking feature of which is the nonuniform character in damping magnitudes of interlayer relaxations away from the surface into the bulk. The calculated contractions (with respect to the bulk) of 11.6, 5.3, and 9.9 % for the top three interlayer separations of Ag(410) are followed by expansion of 2.1 and 6.7% for the subsequent two interlayer spacings. For Cu(320) contractions of 13.6 and 9.2% of the first two interplaner distances are followed by expansion of 2.9%, contraction of 8.8%, and expansion of 10.7% for the next three. These results are compared with the recent low energy electron diffraction data. Moreover, characteristics in the atomic relaxations around the steps are traced to the changes, relative to the bulk, in the local force fields in these vicinities.

Structural aspects of the fivefold quasicrystalline Al–Cu–Fe surface from STM and dynamical LEED studies

We investigate the atomic structure of the fivefold surface of an icosahedral Al–Cu–Fe alloy, using scanning tunneling microscopy (STM) imaging and a special dynamical low energy-electron diffraction (LEED) method. STM indicates that the step heights adopt (primarily) two values in the ratio of τ, but the spatial distribution of these two values does not follow a Fibonacci sequence, thus breaking the ideal bulk-like quasicrystalline layer stacking order perpendicular to the surface. The appearance of screw dislocations in the STM images is another indication of imperfect quasicrystallinity. On the other hand, the LEED analysis, which was successfully applied to Al–Pd–Mn in a previous study, is equally successful for Al–Cu–Fe. Similar structural features are found for both materials, in particular for interlayer relaxations and surface terminations. Although there is no structural periodicity, there are clear atomic planes in the bulk of the quasicrystal, some of which can be grouped in recurring patterns. The surface tends to form between these grouped layers in both alloys. For Al–Cu–Fe, the step heights measured by STM are consistent with the thicknesses of the grouped layers favored in LEED. These results suggest that the fivefold Al–Cu–Fe surface exhibits a quasicrystalline layering structure, but with stacking defects.

Adsorbate-induced demagnetization and restructuring of ultrathin magnetic films: CO chemisorbed onγ-Fe/Cu(100)

First-principles local-spin-density (LSD) investigations of the structural, magnetic, and electronic properties of clean and CO-adsorbed ultrathin $\ensuremath{\gamma}$-iron films epitaxially grown on Cu(100) surfaces demonstrate that both the geometrical and the magnetic structures of the films are profoundly modified by the adsorption of CO. The enhanced magnetic moments of the top-layer atoms are strongly quenched by the presence of the adsorbate. Due to the pronounced magnetovolume effect, this leads also to a correlated change in the interlayer relaxations. Strikingly, the adsorbate-induced demagnetization is primarily limited to those surface atoms directly bonded to the adsorbate. This leads to the formation of an in-plane magnetic pattern in a partially adsorbate-covered film. The comparison of the calculated vibrational eigenfrequencies of the CO adsorbate with experiment confirms the picture based on the LSD calculations.

First-principles investigation of the stability of 3d monolayer/Fe(001) against bilayer formation

Based on the full-potential linearized augmented plane-wave method combined with the generalized gradient approximation, we determine the ground-state spin configurations and the total energies of 3d transition- metal monolayer and bilayer films on Fe(001) within the c(2×2) unit cell. We find by energy analysis that V, Cr, and Mn layers prefer the layered antiferromagnetic coupling, and Fe, Co, and Ni layers favor the ferromagnetic coupling to Fe(001). One exception is the Mn monolayer, which favors the c(2×2) ferrimagnetic superstructure. We discuss the stability of the 3d transition-metal monolayer films on Fe(001) against the bilayer formation and find that, with the exception of Cr, all 3d monolayers on Fe(001) are stable against bilayer formation. We have confirmed that the interlayer relaxations do not change the overall features of the present results.

Surface structure of MBE-grown Fe 3O 4(001) by X-ray photoelectron diffraction and scanning tunneling microscopy

We have investigated the surface termination and interlayer relaxations of ( 2 × 2 )R45°-Fe 3O 4(001) as grown on MgO(001) by oxygen-plasma-assisted molecular beam epitaxy. Despite the fact that autocompensated surfaces can be constructed in principle by terminating with either a half layer of tetrahedral Fe, or a modified layer of octahedral Fe plus tetrahedral O, the combination of photoelectron diffraction and scanning tunneling microscopy suggests the former. The first four interlayer spacings are relaxed by −14, −57, −19, and +29% of the respective bulk value.

Classical Interatomic Potential for Nb-Alumina Interfaces

AbstractA modified-embedded-atom-method (MEAM) potential is derived for the ternary system Al-O-Nb in order to simulate the model oxide-metal interface sapphire-niobium. In the present work, MEAM parameters for Al and O given by Baskes were adopted, and the parameters for Nb are adjusted to match experimental data for pure Nb and calculated properties for Nb oxides and aluminides. The properties for niobium oxides and aluminides were obtained from local- density-functional-theory (LDFT) calculations. The resultant potential was tested in simulations for the Nb(111)/α -alumina(0001) interface. MEAM predictions of the work of separation and the interlayer relaxations for two interface terminations are in excellent agreement with LDFT calculations. The MEAM potential therefore appears suitable for large-scale computer simulation of oxide-metal interface properties.

Deep layer oscillatory segregation and relaxation of substitutionally disordered MoxRe1−x(100) surfaces

The surface structure and stoichiometry of the substitutionally disordered alloy MoxRe1−x(100) were determined by quantitative LEED I(E) analyses for bulk concentrations of x=0.75, 0.85 and 0.95. Diffraction intensities were measured and analysed for electron energies up to 600 eV in order to also access values of the physical parameters of deeper layers. An excellent theory-experiment agreement, together with a large data base for each bulk stoichiometry, allow the accurate detection of rather strong oscillatory interlayer relaxations. They extend unusually deep into the bulk, i.e. down to the sixth layer. Additionally, a “sandwich segregation” with Mo termination of the surface and Re enrichment in the second layer is found, which is held responsible for the deeper interlayer relaxations.

Strong relaxations at the Cr 2O 3(0001) surface as determined via low-energy electron diffraction and molecular dynamics simulations

The surface structure of Cr 2O 3(0001) was investigated by quantitative low-energy electron diffraction and molecular dynamic simulations. In qualitative agreement with each other, both methods indicate strong vertical relaxations at and near the surface. These relaxations are concomitant with a charge reduction and depolarization, which stabilize the surface, yielding energies close to those found for non-polar oxide surfaces with non-divergent surface potentials. The lateral arrangement of oxygen atoms is identical to that in the bulk, i.e. there are no lateral distortions to accomodate the strong interlayer relaxations. The latter extend extend deep into the surface, with the experimentally determined changes of the first four interlayer distances being −38%, −21%, −25% and +11% with respect to the unrelaxed bulk values.

Hydrogen-adsorption-induced phase transitions on Pt(100)-hex and the surface structure of Pt(100)-(1 x 1)H.

While adsorption of 100 L (1 L = 10(-6) Torr s) H-2 molecules at room temperature does not cause any phase transitions from a clean reconstructed Pt(100)-hex surface, a 10-L dose of dissociated H-2 can induce a phase transition from the Pt(100)-hex to an atomic-hydrogen-stabilized Pt(100)-(1 X 1)structure as observed using low-energy electron diffraction (LEED), This Pt(100)-(1 X 1) surface was subsequently cooled down using liquid nitrogen to a temperature around 80 K and LEED I-V (intensity vs electron energy) curves were measured at normal incidence. Dynamical tenser LEED calculations were performed using different surface structure models including neglecting hydrogen, ordered (1 X 1) hydrogen at atop, bridge, and fourfold hollow sites. It has been found that within the converging range of atomic displacements, the minimum overall Pendry R factors (R(p)) for the above models are 0.28, 0.35, 0.31, and 0.28, respectively. For the first model, Pt(100) interlayer relaxations down to the fifth layer were calculated. The fourfold hollow site model which also gave an overall small R(p) showed scattered R(p) for different beams and it is likely that the surface contained disordered hydrogen.

The Rh(110)-p2mg(2 × 1)-2O surface structure determined by automated tensor LEED: structure changes with oxygen coverage

Oxygen is dissociatively chemisorbed on Rh(110) and forms an ordered (2 × 1) surface structure at one monolayer coverage. The automated tensor LEED approach has been applied to the determination of atomic positions in the Rh(110)-p2mg(2 × 1)-2O structure. The oxygen atoms are confirmed to be in a zig-zag fashion in the (110) troughs to produce the glide plane symmetry observed in the LEED pattern. The clean surface interlayer relaxations are reduced and the oxygen atoms are bound asymmetrically in the three-fold fcc hollow-sites to the (111) facets of the steps. Two RhO bonds are formed to Rh atoms in the top metal layer with bond lengths of 1.86 ± 0.11 A ̊ and a third RhO bond of 2.07 ± 0.16 A ̊ is formed to a Rh atom in the second metal layer. A novel finding is that the second metal layer Rh atoms are shifted towards the oxygen positions, introducing a zig-zag lateral displacement of the atoms in the row by 0.10 ± 0.07 A ̊ .

Surface structure of Si(100)-(1 x 1)-2H determined by tensor LEED: Substrate interlayer relaxations.

Hydrogen molecules were dissociated into atoms and dosed on a clean reconstructed Si(100)-(2\ifmmode\times\else\texttimes\fi{}1) surface cooled down to 100-K temperature. A 2-ML coverage of hydrogen gives a dihydride Si(100)-(1\ifmmode\times\else\texttimes\fi{}1) LEED (low-energy electron-diffraction) pattern and I-V curves were measured at 100-K temperature. Dynamical tensor LEED calculations were carried out to determine the surface structure and interlayer relaxations. It has been found that the substrate of the Si(100)-(1\ifmmode\times\else\texttimes\fi{}1)-2H phase basically takes the form of the ideal bulk but there is a spacing change of 13% between the first and second Si layer. Interlayer relaxations down to the fifth layer were calculated.

Modelling of surfaces. 2. Metallic alloy surfaces using the BFS method

Using the semiempirical method for alloys developed by Bozzolo, Ferrante and Smith (BFS) [Bozzolo, G. et al., Phys. Rev., B45 (1992) 493] we study the surface structure of fcc-ordered binary alloys. We concentrate on the calculation of surface energies and surface relaxations for the L10- and L12 ordered structures. Different terminations of the low-index faces are studied. Also, we present results for the interlayer relaxations for planes close to the surface, revealing different relaxations for atoms of different species producing a rippled surface layer.

Multilayer relaxation and surface structure of ordered alloys

Using BFS, a new semiempirical method for alloys, we study the surface structure of fcc ordered binary alloys in the L1 2 structure (Ni 3Al and Cu 3Au). We show that the surface energy is lowest for the mixed-composition truncation of the low-index faces of such systems. Also, we present results for the interlayer relaxations for planes close to the surface, revealing different relaxations for atoms of different species producing a rippled surface layer.

Confirmation of an exception to the ‘‘general rule’’ of surface relaxations

Low-energy electron diffraction (LEED) I–V spectra for Al(111) have been remeasured and analyzed to resolve a conflict concerning interlayer relaxations that are induced by the creation of the surface. Previous measurements of the Al(111) surface relaxations generally report a small expansion of the first interplanar spacing with respect to the bulk spacing. Several recent theories not only predict a contraction, but also that an expansion is not even possible with the formalism used. A large database of I–V measurements at room temperature and at 160 K has been compared to a very extensive set of calculated spectra. It was determined that the surface was expanded, Δd12=+1.7±0.3%, Δd23=+0.5±0.7%. Importantly, the analysis has also identified surface-enhanced thermal motions and no temperature dependence for the static interplanar relaxation within an accuracy of 0.007 Å.

Interference of surface relaxations in unsupported thin films.

We present embedded-atom simulations of interlayer relaxations in very thin slabs of Al and NiAl with (110) and (210) surfaces. The interlayer spacing at a given depth from the surface depends strongly on the slab thickness. For example, the value of the first-layer contraction exhibits a decaying oscillation about that for a semi-infinite solid as the slab thickness is increased. These effects can be understood as an interference of the relaxations from each of the two free surfaces of the slab. This interference model provides quantitative predictions of the slab interlayer spacings.