Five-layer Slab Research Articles

Mechanism of the Hydrogen/Platinum(111) Fuel Cell

We discuss our recently proposed mechanism for the electro-oxidation/reduction on Pt(111) surfaces (J. Electroanal. Chem. 2002, 537, 7) in the presence of sulfuric acid. The bisulfate ion has a large dipole moment and is strongly adsorbed on the positive electrode. Due to the large field gradients, the oxygen atoms of the adsorbed water molecules (and the dipoles) point down and bind to the on-top positions of the platinum substrate. As the electrode becomes more negative, the field gradient changes direction, and the water dipoles gradually reverse their orientation. At a certain critical value of the orientational parameter (which depends also on the bisulfate surface concentration), a two-dimensional honeycomb array of hydrogen bonded water molecules is formed. This is a new form of solid water, a true two-dimensional “ice”. For these negative potentials, the stable structure has one of the hydrogen atoms of the water pointing down, and this means that it is adsorbed by the hollow site of the Pt lattice. To satisfy the stoichiometry of the hydrogen bonds, we need to adsorb one-third of the surface sites of H+ ions. The following reversible reaction occurs: (H5 )3 + 6e- ⇌ 6H + (H3 )3. For the (111) surface of platinum and because of the geometrical matchup (the Pt−Pt distance is 2.77 Å, and the water diameter is 2.76 Å) this reaction occurs as a first-order transition, visible in the voltammogram as a sharp peak. From the [H+] concentration dependence of this sharp spike, we get an effective charge of 1.02 ± 0.02 for the adsorbed moiety. High-accuracy quantum calculations on a five-layer platinum metal slab show that this compound is stable in the absence of bisulfate ions. The quantum calculations show also that the hydrogen atoms in the hollow positions are neutralized. Since there are two-thirds of the Pt sites in the hollow positions, our model gives a natural explanation to the well-known fact that the hydrogen yield is 2/3 on this surface. We have revised our theory to shift the turning point of the water molecules to the transition potential where the HER honeycomb phase is formed. The turning point is in general agreement with the recent laserinduced measurements of the potential of zero charge.

An Approximate Technique for Solving the Time-Domain Inverse Scattering Problem of a Stratified Medium.

This paper deals with the inverse problem of estimating the refractive-index profile of a lossless stratified medium by using back-scattering responses of pulsed waves.In the reconstruction procedure, the stratified medium is approximated by a multilayered model, and back-scattering responses from the estimated profile is obtained in a sense of geometrical optics.Introducing a cost functional concerning the responses from the estimated profile and the responses from the true profile, we can derive a simultaneous equation to update iteratively the refractive index of each layer of the model.Two-layered slabs and a five-layered slab located in free space are reconstructed, and the validity of the presented technique is numerically investigated.

Formation of an ordered Si dimer structure onHfB2(0001)

An ordered surface structure formed after exposure of the ${\mathrm{HfB}}_{2}(0001)$ surface at $800\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ to ${\mathrm{SiH}}_{4}(g)$ followed by annealing at $900\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ has been characterized experimentally with low-energy electron diffraction, scanning tunneling microscopy, and x-ray photoelectron spectroscopy (XPS). The structure is described by a $(\sqrt{7}\ifmmode\times\else\texttimes\fi{}\sqrt{3})$ lattice with a bonded pair of Si atoms in each overlayer unit cell. An absolute Si coverage estimate of 0.48 monolayer based on XPS also supports this structure. Calculations using psuedopotentials within the framework of density functional theory and a five-layer slab model of the substrate show that the threefold hollow site is energetically favored for isolated Si atoms and that Si atoms at next-nearest-neighbor three fold hollow sites will form dimers with a Si-Si distance of $\ensuremath{\approx}2.4\mathrm{\AA{}}.$

Effect of the cluster size in modeling the H2 desorption and dissociative adsorption on Si(001)

Three different clusters, Si9H12, Si15H16, and Si21H20, are used in density-functional theory calculations in conjunction with ab initio pseudopotentials to study how the energetics of H2 dissociative adsorption on and associative desorption from Si(001) depends on the cluster size. The results are compared to five-layer slab calculations using the same pseudopotentials and high quality plane-wave basis set. Several exchange-correlation functionals are employed. Our analysis suggests that the smaller clusters generally overestimate the activation barriers and reaction energy. The Si21H20 cluster, however, is found to predict reaction energetics, with Eades=56±3kcal/mol (2.4±0.1eV), reasonably close (though still different) to that obtained from the slab calculations. Differences in the calculated activation energies are discussed in relation to the efficiency of clusters to describe the properties of the clean Si(001)-2×1 surface.

Formation and dynamics of hot-precursor hydrogen atoms on metal surfaces: Trajectory simulations and stochastic models

The results of a theoretical study of H atoms colliding with a Cu(111) surface are presented. The metal is treated as a five-layer slab of 150 atoms, and all dynamics are classical. The formation of trapped “hot-precursor” atoms on the surface is examined, as well as the nature of their motion on the surface and their energy and momentum dissipation. Connections are made with recent Eley–Rideal experiments, for which hot-atom precursors may play an important role. To facilitate future simulations of Eley–Rideal and hot-atom reactions on metals, simple stochastic models are developed to describe hot-atom energy dissipation. A Fokker–Planck equation is used to model the hot-atom energy distribution. Quasi-Langevin terms, which simulate fluctuation and dissipation consistent with this Fokker–Planck description, are developed for the hot-atom equations of motion. These quasi-Langevin terms are different from the hydrodynamic forms used for Brownian-type motion.

Abrupt transition coupling between two five-layered symmetric slab waveguides

The abrupt transition coupling between two five-layered symmetric slab waveguides is analyzed by means of an integral equation appropriate for the boundary-value problem. A complete set of modes is employed to describe the fields inside both waveguides, and the integral equation is solved by a Neumann-series iterative procedure giving highly accurate results, especially in the case of small difference (∼1%) between the refractive indices of the core and cladding regions. The reflection and coupling coefficients of the guided waves as well as the total power of the radiation modes are computed. Numerical results are presented for several coupling geometries, and misalignment losses are also calculated. Finally, a comparison with relevant previously published papers is made.

Radiation properties of an abruptly terminated five-layer symmetric slab waveguide

The radiation characteristics of an abruptly terminated five-layer symmetric monomode slab waveguide are treated analytically by means of an integral equation, which has been appropriately chosen for the corresponding boundary-value problem of the even TE modes. To obtain the solutions of this equation, representing the electric-field distribution on the terminal plane, a Neumann-series iterative procedure is applied. Then the reflection coefficient of the surface wave, the power of the reflected radiation modes, and the far-field radiation pattern are computed. Numerical results are presented for several cases of abruptly terminated waveguides.

A comparison of calculated and measured absorbed doses of electron beams

A semiempirical code to compute the absorbed dose in a single- to five-layer slab absorbers irradiated by electron beams has been developed. The doses estimated by the code have been compared with the experimental results obtained with a pyrolitic-graphite calorimeter for the electron beams of 1.5- and 1.75-MeV energy, and these have shown agreement within about 3%.

Radiation modes of a five-layer symmetric slab waveguide

The radiation modes of a five-layered symmetric slab waveguide are treated in detail. Since the slab is assumed to be infinitely extended in the yz plane, all field quantities are considered to be independent of y. The analysis is based on modal expansion formulation and the modes can be classified as TE and TM as well as even and odd ones. Applying the boundary conditions at interfaces, the expansion coefficients of the field components are easily calculated. In addition, the normalization factors and the orthogonality properties are determined by deriving appropriate integrals over the cross section of the waveguide. Finally, the validity of the orthogonality relations between the radiation modes and the guided ones, which propagate in such a waveguide, is proved explicitly.

Radiation loss of Y-junctions in rib waveguide

In this paper we analyze the effects of radiation in Y-junctions in rib waveguide by combining the effective dielectric constant method and the concept of local modes of a five-layer slab guide. The evaluation of the fields of the junction is performed together with the analysis of the radiation effects at the end of the transition; various kinds of junctions are examined and discussed, in both LSE and LSM polarizations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Silicon phthalocyanine/methyl methacrylate copolymer slab directional couplers for all‐optical switching

AbstractSlab waveguide directional couplers were fabricated from the third‐order nonlinear optical polymer silicon phthalocyanine/methyl methacrylate 2/98 copolymer as the active material and poly(methyl methacrylate) as the cladding layer. The monomethacrylate copolymer was synthesized, device fabrication conditions determined, and five‐layer slab directional couplers fabricated. Completed couplers demonstrated waveguide loss on the order of 5 dB/cm and coupling lengths of 0.5 mm at 1.29 μm. These vertically coupled devices may be useful for all‐optical switching. © 1994 John Wiley &amp; Sons, Inc.

Hyperfine interactions in bcc (110) iron coated with ruthenium

Using FLAPW method we have calculated the electronic structure of the Ru/Fesystem simulating it by a three- layer slab of an ideally constructed bcc Fe(110) film covered on each side with Ru(110) monolayer. For comparison, results for five layer iron slab as well as the Ag 3Fe Ag slab in the same geometry are presented. I have calculated hyperfine magnetic field and electric field gradient (EFG). Valence charge distribution and moments are also calculated. The major feature is the strong change in the valence electrons contribution to hyperfine field in the outermost Fe layers in both Ag/3Fe/Ag and Ru/3Fe/Ru systems, as compared to five-layer Fe slab. The influence of Ag and Ru does not differ much if moments and valence charged in muffin-tin spheres of Fe are concerned. Electric field gradients change for different coating which is the evidenceof strong modifications in distribution of the local electron densities.

Computation of coupling coefficient contours for a five-layer trapezoidal grating structure

The coupling coefficient contour map of a five-layer slab waveguide structure having a general trapezoidal grating has been computed. Calculations have been carried out for both the first and the second-order Bragg diffraction gratings.

Embedding effects on core level shifts of surface cluster models

Core eigenvalue spectra of naked and embedded cluster models of the Li (100) surface are compared to each other and to the core level energies of a five-layer 2D-periodic slab model. The electronic structure calculations have been carried out in the frame work of density functional theory, cluster embedding was performed by means of the moderately large embedded cluster scheme. The results for naked clusters reflect the inhomogeneous environment of the atoms due to artificial model boundaries. On the other hand, embedding yields discrete spectra that exhibit a close similarity to the energetic distribution of the slab core energies.

Surface electronic structure of gamma -uranium.

It is interesting to study the surface electronic structure of uranium in the context of f-electron localization as the 5f shell is filled. Accordingly, we have used the film-linearized-muffin-tin-orbital method to calculate the surface electronic structure of \ensuremath{\gamma}-uranium with body-centered-cubic structure. This all-electron self-consistent fully relativistic calculation has been done for a five-layer slab with (100) surface using two lattice constants (differing by about 1%) corresponding to different experimental information. Our calculated work functions of 3.60 and 3.82 eV for the two lattice constants both provide excellent agreement with the experimental results, which range from 3.63 to 3.90 eV. The calculated density of states and the charge distribution show stronger hybridization of 5f with 6d electrons than that of \ensuremath{\delta}-plutonium. Our calculations indicate that the surface enhancement of 5f localization (i.e., relative to the bulk behavior) is much stronger for uranium than for plutonium. This increase of localization at the surface may have important consequences for surface reconstruction, chemisorption, and other surface behavior.

Possibility of a delta -like surface for alpha -Pu: Theory.

The electronic structure of a Pu square-mesh monolayer, a five-layer Pu (100)-orientation slab cut from a fcc lattice, and bulk fcc Pu have been calculated. For the monolayer calculation we allowed for spin and orbital polarization; and at all densities, from below the \ensuremath{\delta} to above the \ensuremath{\alpha} density, we found large spin and orbital moments. The equilibrium lattice constant for the monolayer was found to be expanded by about \ensuremath{\sim}7%, compared to our bulk result (which is contracted \ensuremath{\sim}7% from experiment). At both the theoretical and experimental \ensuremath{\alpha} densities we found the five-layer slab to spin polarize, with spin moments close to that of the monolayer. Together with the experimental grazing-incidence photoemission, our results provide support for the existence of a small-moment \ensuremath{\delta}-like surface state for the surface behavior of \ensuremath{\alpha} plutonium.

Electronic structure of the (111) and (100) surfaces of delta -Pu.

An all-electron self-consistent surface-electronic-structure calculation of an actinide system has been performed using the film-linearized muffin-tin-orbital method. The calculations have been performed using both (100)- and (111)-oriented five-layer plutonium slab geometries. Our calculated work functions for the system are 3.68 and 4.14 eV for the (100) and (111) surfaces, respectively, with the 6{ital p} electrons treated as core states. The calculations include the spin-orbit coupling, and the calculated work functions are in good agreement with experimental values of 3.4--3.9 eV for uranium. The narrow bandwidth of the 5{ital f} electrons and the position relative to the {ital s} and {ital d} bands relate to the intermediate delocalization of the 5{ital f} electrons and the existence of hybridization with the {ital s} and {ital d} electrons.

Electronic properties of stoichiometric Ba and O overlayers adsorbed on W(001).

In order to understand better the mechanisms responsible for the lowering of the work function that is observed when surface layers containing barium and oxygen are adsorbed on refractory metals such as tungsten, we have initiated a series of full-potential linearized augmented-plane-wave (FLAPW) electronic-structure calculations on well-defined model systems representing the Ba/O/W interface. We report here our initial results for models in which c(2\ifmmode\times\else\texttimes\fi{}2) monolayers of barium and oxygen have been positioned on both sides of a five-layer W(001) film, with the adsorbate atoms being placed above the fourfold-hollow sites of the tungsten surface. Two different adsorbate configurations have been investigated: ``tilted,'' where the adsorbed monolayers have been arranged so that the barium and oxygen atoms each cover a different fourfold-hollow site in the c(2\ifmmode\times\else\texttimes\fi{}2) unit cell, and ``upright,'' where the overlayers are aligned vertically so that both adsorbates lie above the same site. We have minimized the total energy of the system to determine the optimal adsorbate positions within this set of configurations. We find that the calculated work function of the clean five-layer tungsten slab (4.65 eV) is lowered by approximately 2 eV by the adsorption of the barium and oxygen surface layers in either configuration, but the tilted structure has a significantly lower energy than does the upright. In addition, the position of the oxygen 2s state, which is very sensitive to the adsorbate geometry, strongly favors the tilted model. In both cases we find evidence of significant bonding between the d-like surface states of the tungsten substrate and both the Ba d and the oxygen 2p adsorbate levels. As a result, multiple dipoles are formed at the interface, and the competition between these polarized charge distributions leads to a net lowering of the work function.

Surface electronic behavior of actinide metals

The self-consistent film linearized muffin-tin orbital method has been used to calculate the surface electronic structure of plutonium. This has been done using a (111)-oriented five-layer slab geometry. We believe this is the first self-consistent all-electron surface electronic structure calculation for an actinide system. We use the full potential in the interstitial and vacuum, while the non-muffin-tin (NMT) potential in the spheres is approximated by the extended interstitial NMT potential. The interest and difficulty of dealing with actinide electronic structure is associated with the large number of electrons in the atom, the importance of relativistic effects, and especially the behavior of the 5f electrons which typically are intermediate between itinerant and localized. The calculated work function of plutonium is strongly affected by the treatment of the 6p electrons, and with spin–orbit coupling effects included is 4.3 eV with 6p electrons treated as core, in good agreement with experimental values of 3.4 to 4.3 eV for uranium. A much higher calculated value of 8.4 eV, if the 6p electrons are treated as valence electrons, shows that the 6p electrons are largely localized. The narrow bandwidth of the 5f electrons and the position relative to s and d bands relate to the intermediate delocalization of the 5f electrons and the existence of hybridization with the s and d electrons.

Electronic properties of BaO on W(001)

In order to better understand the mechanisms responsible for the lowering of the work function that is observed when surface layers containing barium and oxygen are adsorbed on refractory metals such as tungsten, we have initiated a series of full-potential linearized augmented plane wave electronic structure calculations on well-defined model systems representing the Ba–O/W interface. We report here our initial results for a model in which c(2×2) overlayers of upright BaO molecules have been positioned on both sides of a five-layer W(001) film. Three independent self-consistent calculations were performed involving two different Ba–O separations and two different distances between planes of Ba and surface W atoms. We find that the work function of the clean five-layer tungsten slab (4.65 eV) is lowered by ∼1.8–2 eV by the adsorption of the Ba–O surface layer in this geometry, and that this result is relatively insensitive to the Ba–O separation in the overlayer. The most important factor determining the value of the work function seems to be the position of the barium plane above the W substrate. We find evidence of significant bonding between the d-like surface states of the tungsten substrate and both the Ba d and the oxygen 2p adsorbate levels. As a result, multiple dipoles are formed at the interface and the competition between these polarized charge distributions leads to a net lowering of the work function.