Multilayer Relaxation Research Articles

LEED structure analysis of Pb(110)

The multilayer relaxation of Pb(110) was investigated by LEED. Data were taken at 130 and 300 K using a computer controlled video based technique. They were analyzed by full dynamical calculations. A quantitative comparison between experiment and theory via the Pendry R-factor confirms the strong contraction of the first layer spacing found in earlier work, as well as the oscillatory relaxation of deeper spacings. The results for the relaxations of the first three layer spacings are −17.1 ± 2.9%, + 3.4 ± 2.9%, −6.8 ± 4.6% for 130 K and −19.4 ± 2.9%, + 4.6 ± 4.6%, -6.8 ± 2.9% for 300 K. This means that within the limits of error there is no relaxational change between 130 and 300 K in agreement with earlier ion scattering results. The agreement between experimental and computed spectra is only mediocre though a number of attempts were made to improve the fit.

The termination and multilayer relaxation at the Co{10 [formula omitted]0} surface

Utilising a large normal-incidence data base the surface termination and multilayer relaxation parameters have been determined for a Co{10 1 0}-(1×1) surface utilising fully dynamic LEED calculations and a multi- R factor analysis. The surface is shown to be uniquely terminated by a short interlayer spacing (0.68 Å). An oscillatory relaxation occurs at the cobalt surface with a first layer contraction of −6.5±2% and a small second layer expansion of 1.0±2%, with subsequent layer spacings equal to the bulk values within the precision of the analysis. The high level of agreement of theory and experiment (Rp=0.26) indicates the absence of stacking faults in the selvedge region. A pair potential calculation demonstrates a significantly lower surface energy for the short outermost interlayer termination. In contrast to fcc {110} surface no surface reconstruction has been detected for this surface, either clean or in the presence of alkali metal.

Fe(111) surface relaxation analysis by in- and out-of-plane MEIS

Multilayer relaxation structure of clean single crystal Fe(111) surface has been studied as one of a series analysis of iron surfaces by using medium energy ion scattering with both in- and out-of-plane channeling and blocking geometries. One of the advantages of out-of-plane scattering is that it provides a greater range of choice of scattering geometries, which can be critical in high index surface analysis. When compared with a full crystal Monte Carlo simulation, the results indicate an oscillatory relaxation pattern of Fe(111) surface structure with a − 29% of first layer ( ΔD 12) contraction and a 7% of second layer ( ΔD 23) expansion.

Low-energy electron diffraction study of multilayer relaxation on a Pb{001} surface.

Multilayer relaxation on clean Pb{001} has been determined by analysis of low-energy electron diffraction (LEED) intensity data collected from a sample at -140 \ifmmode^\circ\else\textdegree\fi{}C. The first interlayer spacing is compressed from the bulk value by 8%, the second interlayer spacing is expanded by 3.1%, and the third interlayer spacing is compressed by 3.0%. These results confirm the remarkably large first-interlayer contraction that was first observed on Pb{110} both by ion scattering and by LEED. The modified point-ion model, which was rather successful in predicting the magnitude of multilayer relaxation on several surfaces of fcc and bcc metals, fails to explain the behavior of Pb surfaces.

Spin-polarized electron diffraction from Pb(110): Surface barrier and non-spherical potential effects

Intensity and polarization spectra of the specular beam in spin-polarized low-energy electron diffraction (SPLEED) from Pb(110) have been measured - using a polarized-electron gun - and calculated by means of a fully relativistic multiple scattering formalism. Comparison between experiment and theory supports multilayer relaxation. At very low energy, surface barrier resonances in the spin-asymmetry spectra were observed and theoretically reproduced. Non-spherical contributions to the crystal-atom potential are visible in the theoretical results but smaller than remaining discrepancies with the experimental data.

Multilayer relaxation and reconstruction in bcc and fcc transition and noble metals

Using a tight-binding scheme and a ‘quenched-molecular dynamics’ method, we calculate the multilayer relaxation of bcc transition metals for the (110), (100) and (111) faces (which present only perpendicular relaxations) and the (211), (310) and (210) faces (for which both parallel and perpendicular components are present). Moreover, we account for the multilayer reconstruction of W(100) and its non-occurrence for Ta(100). Then performing similar calculations in the case of all fcc transition and noble metals, we obtain the multilayer relaxation of the low index surfaces: (111), (100) and (110). Finally, we explain the material dependence of the (1 × 2) reconstruction of the (110) face, which is only observed for the 5d metals (Ir, Pt, Au). The model allows us to predict order-disorder surface phase transition for the (110) face of all these fcc metals.

Structure determination of the SrTiO 3(100) surface

The surface of SrTiO 3 (100) was analysed by low energy electron diffraction. Intensity spectra were taken using a tv camera whose signal is evaluated under computer control. Model intensities were calculated fully dynamically for energies above 200 eV where details of the scattering potential are of minor influence. The best theory-experiment fit (Pendry R-factor = 0.53) shows the surface to be terminated by both Sr-O and O-Ti-O layers. The top layers are buckled by oxygen ions displaced out of the surface by 0.08 and 0.16 A in the Ti and Sr terminated domains, respectively. The buckling, which creates a static dipole moment in the surface layer, is accompanied by a multilayer relaxation which for the first two layers is d 12 (Ti)/d 0 = +2%, d 23 (Ti)/d 0 = −2% for the Ti termination and d 12 (Sr)/d 0 = −10%, d 23 (Sr)/d 0 = +4% for the Sr terminated domains.

Reconstructive adsorption of H [sbnd]Rh(110)—a multiphase study

The adsorption of hydrogen on a clean rhodium(110) surface develops—with increasing coverage—a number of commensurate phases (1 × 3-H, 1 × 2-H, 1 × 3-2H, 1 × 2-3H, 1 × 1-2H). Low Energy Electron Diffraction (LEED) was used to investigate both the phase diagram and the position of adsorbate and substrate atoms. Hydrogen adsorption not only weakens the multilayer relaxation but also causes a slight reconstruction of the rhodium substrate which is reduced with increasing coverage. At low coverages hydrogen atoms occupy threefold co-ordinates sites with a Rh-H bond length of 1.84 A ± 0.1 A and a hydrogen radius of 0.54 A ± 0.1 A. At higher coverages repulsive interactions between adjacent hydrogen atoms make adatoms move up to allow for maximum horizontal distances. Coverage dependent transition temperatures and angular beam profile analyses allow the determination of the phase diagram. The critical temperatures for the primitive phases 1 × 3-H and 1 × 2-H are TC = 132 ± 5 K and TC = 150 ± 5 K, respectively. The 1 × 3-H phase transforms to lattice gas disorder through a continuous phase transition, whereas in the case of the 1 × 2-H phase, a reversible transition to an incommensurate phase is observed. For the non-primitive phases TC is near or above the desorption boundary and thermal desorption is a competing process to the order-disorder transition. Order-order transitions are of first order as observed for the transitions of the primitive phases 1 × 3-H to 1 × 2-H as well as for the non-primitive phases 1 × 3-2H to 1 × 2-3H.

Direct methods in surface crystallography

Inspired by the heavy atom technique used in X-ray diffraction, the inversion of the Tensor LEED method is used to obtain structure information directly from experimental IV spectra i.e. without the usual trial and error procedure. From a LEED calculation for a certain reference structure (‘heavy atom’), intensities for neighboured structures can be computed by first order perturbation theory. In this approximation the intensities depend in a simple way on the structural deviations from the reference structure, so that the true geometry can be retrieved directly from the deviations between experimental and reference structure intensities. However, as both experimental and calculated data are not without error an additional error minimization procedure is applied leading to a system of nonlinear equations for the atomic displacements which can be solved numerically. Instead of intensities Y-functions can also be used. The direct method is reported to apply successfully to the determination of multilayer relaxation of simple metal surfaces such as Rh(110) and W(100). Also, structures of adsorbates (even including induced reconstruction) can be solved. As demonstrated for the case Ni(100) c(2 × 2)-O adsorption height, substrate relaxation as well as buckling of the second substrate layer is reproduced qualitatively and quantitatively as compared to a conventional analysis.

Low-energy electron diffraction study of multilayer relaxation on a Pb{110} surface.

A low-energy electron diffraction (LEED) experiment was carried out on a Pb{110} surface at -140 \ifmmode^\circ\else\textdegree\fi{}C. Intensity data were collected for ten nondegenerate beams at normal incidence and 15 nondegenerate beams at \ensuremath{\theta}=15\ifmmode^\circ\else\textdegree\fi{}, \ensuremath{\varphi}=0\ifmmode^\circ\else\textdegree\fi{}. Quantitative intensity analyses of the two sets confirmed the substantial contraction of the first interlayer spacing that was found by other workers with room-temperature ion-shadowing and -blocking measurements. The results of the LEED analyses, averaged over the two experimental data sets, are the following: first-interlayer spacing compressed by 16.3%, second-interlayer spacing expanded by 3.4%, and third-interlayer spacing compressed by 4.0%. The modified point-ion model can be made to predict relaxation values in good agreement with experiment for the first and the third layer, but not for the second, if the restoring force to bulk positions that opposes surface relaxation is made much smaller than in other metals.

Quasidynamic computation of multilayer relaxations, repulsion between steps and kink formation energy on copper vicinal surfaces

Multilayer relaxations, the kink formation energy, the repulsion between steps and surface energies are computed for (11 n) and (331) vicinal surfaces of copper using a quasidynamic minimization algorithm. We used two different models for the interatomic forces, A and B, which correspond respectively to the empirical Morse potential and to a N-body, semi-empirical potential derived from a simple tight binding scheme. The ability of these models to reproduce the temperature dependence of dynamical properties of copper is tested by comparing the computed atomic mean square displacements with available experimental data. Only model B reproduces satisfactorily the dynamical behavior of bulk copper at T ≠ 0 K: experimental and computed atomic mean square displacements are in excellent agreement. Further comparison with the experiment shows that model A leads to wrong surface relaxations and overestimates surface and kink formation energies, whereas good agreement is obtained for model B. Both models fail, however, to predict the correct repulsion energy between steps.

Quasidynamic computation of multilayer relaxations, repulsion between steps and kink formation energy on copper vicinal surfaces

Quasidynamic computation of multilayer relaxations, repulsion between steps and kink formation energy on copper vicinal surfaces

A re-examination of multilayer relaxation of Ag(110) by LEED structural analysis

Although the existence of an oscillatory relaxation of the topmost two interlayer spacings of Ag(110) is well established by both low energy electron diffraction (LEED) and Rutherford backscattering spectroscopy (RBS) the magnitude of the first layer contraction and second layer expansion is still a matter of considerable dispute. In an attempt to clarify the situation we have performed an independent LEED study utilising a large normal incidence data set and 7 different reliability factors ( R-factors) to judge the level of theory-experiment agreement. The distance dz 12 between the first and second layers is smaller than the bulk interlayer distance by 7 ± 2% and the distance dz 23 between second and third layers is expanded by 1 ± 2%. Furthermore, a contraction of 2 ± 2% of the third interlayer spacing ( dz 34) has been extracted, with subsequent interlayer spacings equal to the bulk value within the precision of this analysis. These results are compared with theoretical embedded atom method and tight binding predictions of changes of up to the top four interlayer spacings. These results confirm and extend the surface geometry determined in an earlier LEED study of Davis and Noonan. Finally, the multilayer relaxations obtained by LEED are compared with recent RBS studies and possible reasons for discrepancies discussed.

A re-examination of multilayer relaxation of Ag(110) by LEED structural analysis

A re-examination of multilayer relaxation of Ag(110) by LEED structural analysis

A re-examination of multilayer relaxation of Ag(110) by leed structural analysis

A re-examination of multilayer relaxation of Ag(110) by leed structural analysis

Reconstructive adsorption structure of 1 × 3-H/Rh(110)

Adsorption of hydrogen on Rh(110) leads to a 1×3 superstructure at coverage 13. A computer controlled video method was used to measure the LEED intensities of this phase at a temperature of 90 K. The weak superstructure spots were safely detected by an amplifier TV camera. The intensity spectra of four substrate spots and five superstructure spots were analysed by full dynamical calculations. Comparison between theory and experiment was realized using R-factors and the ratio between average intensities of superstructure and substrate spots. The best fit develops for a slight reconstruction of the substrate induced by adsorption whereby the multilayer relaxation found for the clean surface is only slightly changed towards bulk layer distances. Every third [110] rhodium row is lifted by 0.03±0.02 Å and is shifted laterally by 0.04±0.03 Å towards the adjacent row of hydrogen atoms. Reconstruction is necessary to bring superstructure spot intensities to the experimentally observed level. Hydrogen adsorbs in nearly ideally threefold coordinated sites with a Rh-H bond length of 1.86±0.1 Å from which a hydrogen atomic radius of 0.52±0.1 Å is deduced. The model favours the picture of a locally induced substrate reconstruction. Calculated and experimental intensity spectra are in fair agreement mirrored by a Pendry .R-factor of R = 0.25.

Application of out-of-plane MEIS to surface structure analysis

Multilayer relaxation of clean Ni(110) surface has been measured by using medium energy ion scattering (52 keV H +) utilizing channeling and blocking techniques with a compact medium energy electrostatic analyzer. These measurements include the first reported use of an out-of-plane scattering geometry to test consistency with the normal in-plane methods. An added advantage of out-of-plane scattering geometry is the ability to tailor the analysis to a particular surface layer relaxation structure without sacrificing good double alignment conditions. When compared with a full crystal Monte Carlo simulation, the results indicate a first layer contraction of (8.0 ± 1.5)% and a second layer expansion of (4.0 ± 2.0)% of the Ni(110) surface which are in excellent agreement with the recent MEIS and LEED measurements.

Corrected effective-medium method. IV. Bulk cohesive and surface energies of second- and third-row metals and multilayer relaxation of Al, Fe, and Ni.

We provide a detailed analysis and discussion of the recently developed corrected effective-medium method (CEM) as applied to calculations of the bulk cohesive energies of the second- and third-row metals. The results demonstrate that a quantitatively accurate description of these quantities requires a new ``covalent'' embedding function instead of the self-consistent-field local-density ``ionic'' embedding function of Puska and co-workers. Construction of these covalent embedding functions from diatomic and bulk electron-density binding potentials is detailed. We present the formalism within the CEM method for the calculation of the surface energy of infinitely periodic two-dimensional solid surfaces. Calculations of the surface energies for the perfectly terminated low-Miller-index faces of Na, Mg, Al, K, Ca, Fe, Ni, and Cu are carried out. These results are compared to experimental measurements and very good agreement is found for almost all of these metals. More demanding multilayer surface-relaxation calculations are performed for Al(111), (110), and (100), Ni(110) and (100), and Fe(100). Very good agreement with experimental observations is obtained for these systems with the exception of Al(111) and (100). Detailed analysis of these calculations leads to an explanation of the relaxation process and its driving components.

On the possibility of measuring the tensor of surface stress in thin crystalline plates

We have emphasized that in a free crystalline plate the surface stress causes the lattice strain ( both perpendicular to the plate plane and tangent-plane ), which is inversely proportional to the plate thickness. The similar dependence of lattice strain on the interface surface stress ought to be in two-component multilayer crystalline films ( bilayer superlattices ). The surface-induced lattice strain makes it possible to determine the value of the tensor of surface stress by measuring the thickness dependence of the relative change of lattice parameters in extended thin crystalline plates. We also derive a simple relation between the surface stress tensor and the integral characteristic of multilayer surface relaxation in a crystal with a plane boundary and relatively small near-surface disturbances of the bulk elastic moduli.

Surface relaxation in alpha-iron

A new formalism for calculating multilayer relaxation is presented. The method is suitable for short-range potentials. The best results for α-iron have been achieved with an empirical model consisting of an effective pair potential with non-central corrections and a linear volume dependent term. The model reproduces the elastic constants and predicts well the damped oscillatory character of surface relaxation in α-iron. In addition, it can ensure equilibrium in the bulk crystal and at the surface, simultaneously.