Subsurface Relaxation Research Articles

Accounting for relaxation during pulse effects for long pulses and fast relaxation times in surface nuclear magnetic resonance

Surface nuclear magnetic resonance (NMR) is a geophysical technique providing noninvasive insight into aquifer properties. To ensure that reliable water content estimates are produced, accurate modeling of the excitation process is necessary. This requires that relaxation during pulse (RDP) effects be accounted for because they may lead to biased water content estimates if neglected. In surface NMR, RDP is not directly included into the excitation modeling, rather it is accounted for by adjusting the time at which the initial amplitude of the signal is calculated. Previous work has demonstrated that estimating the initial amplitude of the signal as the value obtained by extrapolating the observed signal to the middle of the pulse can greatly improve performance for the on-resonance pulse. To better understand the reliability of these types of approaches (which do not directly include RDP in the modeling), the performance of these approaches is tested using numerical simulations for a broad range of conditions, including for multiple excitation pulse types. Hardware advances that now allow the routine measurement of much faster relaxation times (where these types of approaches may lead to poor water content estimates) and a recent desire to use alternative transmit schemes demand a flexible protocol to account for RDP effects in the presence of fast relaxation times for arbitrary excitation pulses. To facilitate such a protocol, an approach involving direct modeling of RDP effects using estimates of the subsurface relaxation times is presented to provide more robust and accurate water content estimates under conditions representative of surface NMR.

Surface stress changes in the Ir(001)/H system: Density functional theory study

Density functional theory calculations of the surface energy and surface stress changes associated with the formation of the Ir(001)(5 \ifmmode\times\else\texttimes\fi{} 1)-hex clean-surface reconstruction and its transformation to a (5 \ifmmode\times\else\texttimes\fi{} 1)-added row (AR) structure in the presence of adsorbed atomic hydrogen have been performed and compared with experimental results. The calculations clearly show that the clean-surface (1 \ifmmode\times\else\texttimes\fi{} 1)-to-(5 \ifmmode\times\else\texttimes\fi{} 1)-hex reconstruction is not driven by a reduction in tensile surface stress. While the surface energy is reduced by this transformation, the surface stress increases; proper convergence of the calculated surface stress requires the use of slabs containing at least nine atomic layers, due to the substantial subsurface relaxations associated with the (5 \ifmmode\times\else\texttimes\fi{} 1)-hex phase. By contrast, the H-induced reconstruction leads to a calculated reduction in the tensile surface stress in the range 1.76--2.06 Nm${}^{\ensuremath{-}1}$ for an H coverage range of 0.6--0.8 ML, in excellent agreement with the experimentally determined value of 1.7 Nm${}^{\ensuremath{-}1}$.

Relaxations in the 1 × 5 reconstruction of Pt(1 1 0)

Pt(1 1 0) is one of the most closely investigated metal surface structures because it displays a variety of “missing-row” reconstructions, which are only marginally stable. The ground state is usually found to have 1 × 2 translational symmetry, but a 1 × 3 form has also been seen. Between 1 × 2 and 1 × 3, a series of disordered structures has been recorded, which shows a slight preference for 1 × 5 periodicity. Under the preparation conditions used in this study, a stable 1 × 5 structure was found for Pt(1 1 0). Investigation by surface X-ray diffraction has led to a complete three-dimensional structure, which closely resembles an alternation of 1 × 2 and 1 × 3 unit cells. Pt(1 1 0) shows an interesting example of two “homometric” structures that are indistinguishable by diffraction, but are distinguishable by virtue of their subsurface relaxation pattern.

Multilayer structural determination of theGaAs(1¯1¯1¯)2×2reconstruction by automated tensor LEED

The multilayer atomic coordinates for the $\mathrm{GaAs}(1\ifmmode\bar\else\textasciimacron\fi{}1\ifmmode\bar\else\textasciimacron\fi{}1\ifmmode\bar\else\textasciimacron\fi{})(2\ifmmode\times\else\texttimes\fi{}2)$ surface have been determined using automated tensor low-energy electron diffraction. The results confirm the As adatom trimer model found by total-energy calculations and scanning tunneling microscopy studies although details of the displacements are different. The low-energy electron diffraction analysis, being sensitive to multilayer spacings in the surface region, shows that substantial subsurface relaxations are present.

Formation of well-ordered surface compounds by coadsorption of thallium and bromide on the Au(111) electrode surface

The structures of the adlayers formed on Au(111) in acid solution containing thallium and bromide have been investigated by using in situ surface X-ray diffraction. At the most positive potentials, where Br forms close-packed rotated-hexagonal monolayers, the surface is free of Tl. The Br adlayer disorders at the potential where thallium starts to coadsorb. With further decreasing potential, two well-ordered commensurate and one weakly-ordered incommensurate phases appear over a 0.7 V potential region prior to the formation of the close-packed rotated-hexagonal Tl monolayer. The structure factor analysis for the commensurate phases shows the formation of TlBr 2 and TlBr surface compounds in the 3-( 13 × 13 ) and 2-(3× 3 ) phases, respectively. In addition, an adlayer-induced subsurface relaxation has been observed. Under the 2TlBr-(3× 3 ) adlayer, where bromide ions are at the bridge sites and thallium ions are situated near the hollow sites, the top layer of Au atoms displaces laterally along the 3 direction. This results in more uniform spacings between Tl and the three neighboring gold atoms, as well as an increase of the Br–Au separation.

Is it Really that Easy to Solve Surface Structures Using Direct Methods?

A basic problem in surface science is that, unlike bulk materials, very few of the atomic scale structures are known despite many years of effort. Even the advent of STM has not helped that much since it is difficult to impossible to interpret images without a-priori information. Transmission electron diffraction (or x-ray diffraction) data from surfaces represent a unique opportunity for the application of Direct Methods to solve surface structures, opening up new avenues for science. Diffraction from a surface when the bulk is only weakly dynamical is at least 90% kinematical, but it may be the case that strong (surface) scattering is buried under bulk reflections including the lxl or “surface forbidden bulk-allowed” reflections. In addition, further out in the diffraction pattern subsurface relaxation effects become very important, and these cannot be considered using conventional Direct Methods; instead of sharp atomic-features the true exit wave will have small positive/negative dipoles.

Measuring the structure of etched silicon surfaces with Raman spectroscopy

We have measured the unenhanced, nonresonant surface Raman spectra of one monolayer of hydrogen bound to flat and stepped Si(111) surfaces prepared using a novel, aqueous fluorine etch. The orientation and normal mode composition of adsorbate vibrations are obtained from polarized, angle-resolved Raman spectra using a 3-layer dielectric model. This approach requires the experimental determination of both the anisotropy in the dynamic polarizability of the adsorbate bond and the effective dielectric constant in the vicinity of the adsorbate. The measured Si–H bond anisotropy is 0.263±0.028 in good agreement with gas phase measurements. The adsorbate dielectric constant is measured to be 3.78±0.20; this response is clearly nonlocal and predominantly due to polarization of the underlying silicon lattice. Using this technique, we find that the step dihydride on a Si[6(111)-(1̄1̄2)] surface is rotated 37°±4° from the surface normal in good agreement with the 31° predicted by ab initio cluster techniques, but significantly larger than the 12.5° predicted by pseudopotential slab calculations. In contrast to both theoretical predictions, the normal modes of this step dihydride display little concerted motion indicating that subsurface relaxation near the step edge reduces steric interactions much further than predicted. The observed anisotropic etch rates, evidenced by the production of atomically straight steps, are explained in terms of the measured distortion at the step edge.

Structure of Si(100)-(2 x 1) surface using UHV transmission electron diffraction.

Details of the atomic structure for the Si(100)-(2\ifmmode\times\else\texttimes\fi{}1) surface using UHV transmission electron diffraction are described. Reliability factor minimizations of the dynamical diffraction intensities establish conclusively the asymmetry in the structure. Fits performed using multilayer subsurface relaxations to match analytical strain solutions demonstrate the existence of long range subsurface strain fields extending up to six layers into the bulk.

X-ray diffraction investigation of the sulphur induced 4 × 1 reconstruction of Ni(110)

The atomic structure of the Ni(110)4 × 1-S reconstruction has been determined on the basis of surface X-ray diffraction measurements. An analysis of the in-plane diffraction data shows that the model consists of Ni rows along the [001] direction, two for every 4 × 1 unit cell, corresponding to 0.5 ML Ni coverage. The S is chemisorbed in pseudo two-fold hollow sites both on the Ni rows and in the troughs between the rows with a S coverage of 0.75 ML. Furthermore, rod-scans along fractional-order reflections reveal sub-surface relaxations. The results are in good agreement with recent STM and previous AES and radioactive tracer studies.

UHV transmission electron microscopy of Ir(001): II. Atomic positions of the (5 × 1) reconstructed surface from HREM and R-factor refinements

A partial solution of the atomic scale structure of the Ir(001)−(5 × 1) reconstructed surface is reported combining direct high resolution electron microscopy and R-factor analyses of transmission electron diffraction data. From the high resolution imaging, the structure can be uniquely identified as a hexagonal monolayer on the surface with at most small distortions. R-factor minimization of the near surface structure based upon 8-bit digitization of the diffraction data shows systematic differences for models using single and multiple layers, demonstrating the existence of sub-surface strain fields. Unfortunately, the intrinsic error of 8-bit digital data is too large for a full multilayer minimization. Fitting was also performed using sub-surface relaxations constrained to match analytical strain solutions. These models indicate a two-fold bridge registry of the surface hexagonal layer with a three-fold hollow registry of the sub-surface atoms with respect to the surface layer and small sub-surface relaxations. The data reduction is quantitative with a 20–30% coverage, in agreement with experimental imaging data, and the accuracy of the atomic positions is about ±0.005 nm.

Multiple-scattering evaluation of RHEED intensities from the GaAs(001)2 x 4 surface: Evidence for subsurface relaxation.

Experimental reflection high-energy electron-diffraction (RHEED) rocking curves in the [1\ifmmode\bar\else\textasciimacron\fi{}10] azimuth from the molecular-beam-epitaxy (MBE) grown As-rich GaAs(001)2\ifmmode\times\else\texttimes\fi{}4 surface have been analyzed by fitting rocking curves computed using elastic multiple-scattering (dynamical) theory. The surface is assumed to be composed of unit cells having the ``missing row'' structure in which the 2\ifmmode\times\else\texttimes\fi{} periodicity arises from symmetrically dimerized As atoms and the 4\ifmmode\times\else\texttimes\fi{} periodicity from a regular array of missing dimers, such that the As surface coverage is three-quarters of a monolayer. The surface model permits relaxation in both the surface layer (As) and the second layer (Ga). The best fit to the experimental data occurs for a surface unit-cell structure in which the triplets of surface As dimers are ``rumpled'' and the second layer (Ga) atoms relax in both the in-plane and perpendicular directions. The effect upon the fit of tilts and twists of the As dimers has been studied by imposing small displacements on the dimerized surface As atoms away from the best-fit configuration. We find evidence to suggest that the As dimers are symmetrical to within possible tilt angles of \ensuremath{\sim}1\ifmmode^\circ\else\textdegree\fi{} and/or twist angles of \ensuremath{\sim}1\ifmmode^\circ\else\textdegree\fi{}.

The Ge(001) (2 × 1) reconstruction: asymmetric dimers and multilayer relaxation observed by grazing incidence X-ray diffraction

Grazing incidence X-ray diffraction has been used to analyze in detail the atomic structure of the (2 × 1) reconstruction of the Ge(001) surface involving far reaching subsurface relaxations. Two kinds of disorder models, a statistical and a dynamical were taken into account for the data analysis, both indicating substantial disorder along the surface normal. This can only be correlated to asymmetric dimers. Considering a statistical disorder model assuming randomly oriented dimers the analysis of 13 symmetrically independent in-plane fractional order reflections and of four fractional order reciprocal lattice rods up to the maximum attainable momentum transfer q z = 3c ∗ ( c ∗ = 1.77 × 10 −1 A ̊ −1 ) indicates the formation of asymmetric dimers characterized by R> D = 2.46(5) A ̊ as compared to the bulk bonding length of R = 2.45 A ̊ . The dimer height of Δ z = 0.74(15) A ̊ corresponds to a dimer buckling angle of 17(4)°. The data refinement using anisotropic thermal parameters leads to a bonding length of R D = 2.44(4) A ̊ and to a large anisotropy of the root mean-square vibration amplitudes of the dimer atoms ( 〈u 11 2〉) 1 2 = 0.25 A ̊ , ( 〈u 22 2〉) 1 2 = 0.14 A ̊ , ( 〈u 33 2〉) 1 2 = 0.50 A ̊ ). We have evidence for lateral and vertical disp tenth layer below the surface.

Structure and energetics of Ge(111) c(2 × 8) reconstruction

We present self-consistent MNDO calculations of atomic clusters modelling the structure of adatom generated 2 × 2, √3 × √3 and 2 × 8 reconstructions of the Ge(111) surface. Comparisons are made of the T4 and H3 adsorption sites and of closed shell singlet and open shell (spin triplet) RHF wavefunctions. We find that √3 × √3 prefers the T4 site energetically, but 2 × 2 prefers H3. Subsurface relaxation up to three layers deep plays a crucial role in the energetics and we also find significant charge transfers between rest atoms and adatoms as well as between layers. A consistent interpretation can be given of the similarities and differences between the configurations in terms of bond rehybridization and polarization effects as well as the different surface topologies.

Surface structure and long-range order of the Ge(111)-c(2 x 8) reconstruction.

We have performed an x-ray diffraction study of the Ge(111)-c(2\ifmmode\times\else\texttimes\fi{}8) surface. From the analysis of 43 in-plane, symmetry-inequivalent structure factors, a simple adatom model with subsurface relaxation is deduced. The relaxations around the adatoms are similar to those observed in the adatom complexes on Si(111)-(7\ifmmode\times\else\texttimes\fi{}7) and Sn/Ge(111)-(\ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 ), -(5\ifmmode\times\else\texttimes\fi{}5), and -(7\ifmmode\times\else\texttimes\fi{}7), suggesting that the adatoms are located in threefold sites above the second-layer atoms (${T}_{4}$ sites). Significant distortions around the rest atoms are seen due to rehybridization of the dangling bonds. The diffraction peaks from the eighth-order reflections are displaced away from their nominal positions. This is explained by a model where the long-range order of the c(2\ifmmode\times\else\texttimes\fi{}8) structure is disturbed by faults due to rows of 2\ifmmode\times\else\texttimes\fi{}2 unit cells.

Adsorbate registry and subsurface relaxation of the [formula omitted] reconstructions

We have performed a surface X-ray diffraction study of submonolayer √3 structures of Sn and Pb on Ge(111). The structure factor analysis of fractional-order Bragg reflections shows a significant relaxation in the Ge substrate induced by the Sn/Pb adatoms. The registry of the adatoms is determined from the analysis of the integer-order intensities. The adatoms are situated on top of the second layer of Ge atoms. The intensity profile normal to the surface of a subset of the fractional-order Bragg rods were measured. They display a pronounced intensity variation for both Sn and Pb, which can be explained only by a subsurface relaxation extending at least four atomic layers into the bulk.

Adsorbate registry and subsurface relaxation of the α-Ge(111)√3×√3-Sn/Pb reconstructions

Adsorbate registry and subsurface relaxation of the α-Ge(111)√3×√3-Sn/Pb reconstructions

A model potential study of the Si(001) 2 × 1 surface

The Stillinger-Weber model potential is applied to study the Si(001) 2 × 1 surface. Molecular dynamics computer simulation has used a cluster of 1280 atoms with periodic boundary conditions in two dimensions, the surface-vacuum interface being modelled by a slab configuration containing twenty atomic planes. It is shown that the model potential readily leads to a dimer model with substantial sub-surface relaxations. The model is free of any y-twist (direction normal to the dimerization direction) which was invoked by a LEED investigation. The electronic total energy calculations for the present model give significantly lower energy than a simple dimer model without sub-surface relaxations but not lower than the asymmetric buckled dimer model. The calculation also suggests that molecular dynamics with a model silicon potential may provide a useful starting point for a complex reconstruction which can be further imporved by other first principles methods.

A model potential study of the Si(001) 2×1 surface

The Stillinger-Weber model potential is applied to study the Si(001) 2×1 surface. Molecular dynamics computer simulation has used a cluster of 1280 atoms with periodic boundary conditions in two dimensions, the surface-vacuum interface being modelled by a slab configuration containing twenty atomic planes. It is shown that the model potential readily leads to a dimer model with substantial sub-surface relaxations. The model is free of any y-twist (direction normal to the dimerization direction) which was invoked by a LEED investigation. The electronic total energy calculations for the present model give significantly lower energy than a simple dimer model without sub-surface relaxations but not lower than the asymmetric buckled dimer model. The calculation also suggests that molecular dynamics with a model silicon potential may provide a useful starting point for a complex reconstruction which can be further improved by other first principles methods.

Subsurface relaxations in Si(111)-(7 × 7) structure models

Virtually all structure models proposed for the Si(111)-(7 × 7) surface have such drastic changes in the surface topology that substrate relaxations are an important part of the structure. The extent of such relaxations has been studied with Keating-type calculations. The importance of these relaxations in the interpretation of experimental results (Medium Energy Ion Channeling and Blocking and Transmission Electron Diffraction) has been investigated. Quantitative comparisons between experiments and models can only be made if substrate relaxations are taken into account.

Subsurface relaxations in Si(111)-(7 × 7) structure models

Abstract Virtually all structure models proposed for the Si(111)-(7 × 7) surface have such drastic changes in the surface topology that substrate relaxations are an important part of the structure. The extent of such relaxations has been studied with Keating-type calculations. The importance of these relaxations in the interpretation of experimental results (Medium Energy Ion Channeling and Blocking and Transmission Electron Diffraction) has been investigated. Quantitative comparisons between experiments and models can only be made if substrate relaxations are taken into account.