Theory of chemisorption

The electronic structure of a semiinfinite crystal with a partial coverage by adatoms is studied within the tight-binding formalism. The effect of the surface is described via the surface Green function method, and the effect of disorder is treated within the coherent potential approximation. The local state densities at/near the surface and the interaction energy of adatoms are calculated as functions of the coverage. The examples representing the case of a gas adsorption on the transition metal surfaces, as well as the adsorption of the transition metal atoms on the transition metal surfaces are investigated numerically.     

Surface atom displacement processes

Progress in field ion microscope studies of adatom displacements on metal surfaces is reviewed. It is concluded that of the displacement processes that contribute to surface diffusion only displacements between low-coordination (terrace) sites are well characterised. Procedures and preliminary results of FIM studies of adatom displacement over steps are described. Activation energies measured for passage of Ta, W, Re, Ir and Pt adatoms across (110) W steps are found to equal activation energies for diffusion over (110) W, despite the highly reflecting character of the step for all the adsorbates except Pt. Displacements of adatoms interacting with other adatoms are discussed. Results presented show that interaction of transition metal adatoms forming close-packed dimers on (110) W is rather weak, with a minimum interaction energy [?U(r) < 4kJ/mol] for Re₂ corresponding to a very weak attraction for Re adatoms 0.27 nm apart.     

Site-blocking effects of preadsorbed H on Pt(1 1 1) probed by 1,3-butadiene adsorption and reaction

The influence of hydrogen coadsorption on hydrocarbon chemistry on transition metal surfaces is a key aspect to an improved understanding of catalytic selective hydrogenation. We have investigated the effects of H preadsorption on adsorption and reaction of 1,3-butadiene (H₂CCHCHCH₂, C₄H₆) on Pt(1 1 1) surfaces by using temperature-programmed desorption (TPD) and Auger electron spectroscopy (AES). Preadsorbed hydrogen adatoms decrease the amount of 1,3-butadiene chemisorbed on the surface and chemisorption is completely blocked by the hydrogen monolayer (saturation) coverage (θ_H = 0.92 ML). No hydrogenation products of reactions between coadsorbed H adatoms and 1,3-butadiene were observed to desorb in TPD experiments over the range of θ_H investigated (θ_H = 0.6-0.9 ML). This is in strong contrast to the copious evolution of ethane (CH₃CH₃, C₂H₆) from coadsorbed hydrogen and ethylene (CH₂CH₂, C₂H₄) on Pt(1 1 1). Hydrogen adatoms effectively (in a 1:1 stoichiometry) remove sites from interaction with chemisorbed 1,3-butadiene, but do not affect adjacent sites. The adsorption energy of coadsorbed 1,3-butadiene is not affected by the presence of hydrogen on Pt(1 1 1). The chemisorbed 1,3-butadiene on hydrogen preadsorbed Pt(1 1 1) completely dehydrogenates to H₂ and surface carbon upon heating without any molecular desorption detected, which is identical to that observed on clean Pt(1 1 1). In addition to revealing aspects of site blocking that should have broad implications for hydrogen coadsorption with hydrocarbon molecules on transition metal surfaces in general, these results also provide additional basic information on the surface science of selective catalytic hydrogenation of butadiene in butadiene-butene mixtures.     

Angle and speed distributions of hydrogen desorbing thermally from metal surfaces

A quantum theoretical treatment of the angle and speed distributions of recombinatively desorbing hydrogen from metal surfaces is proposed. The desorption rate is discussed in the framework of the transition state theory. The recombinative reaction process of hydrogen due to thermal activation leads to the formation of an activated complex in the transition state. In the vicinity of a saddle point on a three-dimensional potential energy surface, the translational motion of the activated complex in the direction perpendicular to the metal surface is accompanied by its center-of-mass vibrational motion parallel to the metal surface. In order to carry out the quantum mechanical calculation, the potential surface is replaced by a simplified model potential, which provides a square potential barrier along the surface normal. It is shown that, on leaving the potential barrier, the activated complex is reflected by the boundary of the potential barrier with a certain probability and, at the same time, the center-of-mass modes of vibration with frequencies v ₁ and v ₂ are coupled with the translational motion along the surface normal. Vibrational wave functions in the momentum representation are used to calculate the transmission coefficient, which is incorporated into the conventional rate formula. The angle-dependent speed distributions of desorbing molecules are derived from the rate formula.     

Electronic structure and magnetism of surfaces,interfaces and modulated structures (superlattices)

Recent developments in the study of surfaces and interfaces of metals and of artificial materials such as bimetallic sandwiches and modulated structures are described. Key questions include the effects on magnetism of reduced dimensionality and the possibility of magnetically dead layers. These developments have stimulated an intensified theoretical effort to investigate and describe the electronic and magnetic structure of surfaces and interfaces. One notable success has been the development of a highly accurate full-potential all-electron method (the FLAPW method) for solving the local spin density equations self-consistently for a single slab geometry. We describe here this advanced state of ab initio calculations in determining the magnetic properties of transition metal surfaces such as those of the ferromagnetic metals Ni(001) and Fe(001) and the Ni/Cu(001) interface. For both clean Fe and Ni(001) we find an enhancement of the magnetic moments in the surface layer. The magnetism of surface and interface Ni layers on Cu(001) (no dead layers are found) is described and compared to the clean Ni(001) results. Finally, the role ofSR experiments in answering some of the questions raised in these studies will be discussed.     

Explicit inertial range renormalization theory in a model for turbulent diffusion

The inertial range for a statistical turbulent velocity field consists of those scales that are larger than the dissipation scale but smaller than the integral scale. Here the complete scale-invariant explicit inertial range renormalization theory for all the higher-order statistics of a diffusing passive scalar is developed in a model which, despite its simplicity, involves turbulent diffusion by statistical velocity fields with arbitrarily many scales, infrared divergence, long-range spatial correlations, and rapid fluctuations in time-such velocity fields retain several characteristic features of those in fully developed turbulence. The main tool in the development of this explicit renormalization theory for the model is an exact quantum mechanical analogy which relates higher-order statistics of the diffusing scalar to the properties of solutions of a family ofN- body parabolic quantum problems. The canonical inertial range renormalized statistical fixed point is developed explicitly here as a function of the velocity spectral parameter, which measures the strength of the infrared divergence: for<2, mean-field behavior in the inertial range occurs with Gaussian statistical behavior for the scalar and standard diffusive scaling laws; for>2 a phase transition occurs to a fixed point with anomalous inertial range scaling laws and a non-Gaussian renormalized statistical fixed point. Several explicit connections between the renormalization theory in the model and intermediate asymptotics are developed explicitly as well as links between anomalous turbulent decay and explicit spectral properties of Schrödinger operators. The differences between this inertial range renormalization theory and the earlier theories for large-scale eddy diffusivity developed by Avellaneda and the author in such models are also discussed here.     

Determinants of Laplacians on surfaces of finite volume

Determinants of the Laplace and other elliptic operators on compact manifolds have been an object of study for many years (see [MP, RS, Vor]). Up until now, however, the theory of determinants has not been extended to non-compact situations, since these typically involve a mixture of discrete and continuous spectra. Recent advances in this theory, which are partially motivated by developments in mathematical physics, have led to a connection, in the compact Riemann surface case, between determinants of Laplacians on spinors and the Selberg zeta function of the underlying surface (see [DP, Kie, Sar, Vor]).Our purpose in this paper is to introduce a notion of determinants on non-compact (finite volume) Riemann surfaces. These will be associated to the Laplacian shifted by a parameters(1–s), and will be defined in terms of a Dirichlet series (w, s) which is a sum that represents the discrete as well as the continuous spectrum. It will be seen to be regular atw=0, and our main theorem (see Sect. 1) will express exp as the Selberg zeta function of the surface times the appropriate -factor.A Sloan Fellow and partially supported by NSF grant DMS-8701865     

Nuclear structure effect in internal conversion of the 166 kev hinderedM1 transition in139La

The internal conversion coefficients were calculated for the 165.853 keV 5/2⁺7/2⁺ hindered transition in ₅₇ ¹³⁹ La using the new computer program NICC for conversion coefficients of all atomic shells. The algorithm employed in this code is described. The analysis of precise experimental data yielded the nuclear penetration parameter=4.2±0.8. This value was found to be in accord with theoretical estimates and to correspond to the Nilsson deformation parameter=–0.056±0004 of the¹³⁹La nucleus. Using the Nilsson wave functions for above the mixing ratio ² = N(E2)/N(M1) was determined to be less than 8.10^–5, which supports the assumption of a pureM1 multipolarity of this transition.Presented at the 26th All-Union Conference on Nuclear Spectroscopy and Nuclear Structure (February 1976, Baku, USSR).We are obliged to Dr. B. N.Subba Rao for the communication of his value for the investigated transition.     

Phase transitions in the Ising model with transverse field

We show the existence of a phase transition in the Ising model with transverse field for dimensionsv 2 provided the transverse term is sufficiently small. This is done by proving long-range order occurs using the reflection positivity of the Hamiltonian and localization of eigenvectors.     

A diffusion model of metal surface modification during plasma nitriding

A diffusion model of metal surface modification by plasma nitriding has been developed. This model takes into account the erosion effects at the plasma/solid interface occurring due to the ion bombardment of the surface. For constant sputtering rate, which is the usual situation during plasma nitriding, the growth of the sub-layers is well described by the analytical expressiong(t) =g ₀,f ^–1 (t/t ₀), whereg(t) is the sub-layer thickness at timet,g ₀ andt ₀ are parameters which depend on the treated material and plasma characteristics,f ^–1 is the inverse of the function — In(1 - x) + x), 0 x 1. Under negligible erosion effects, the expression forg(t) reduces to the parabolic law. The diffusion zone (substratum) growth does not follow the parabolic law as well. However, the deviation occurs after long plasma nitriding time. The model can be used for experimentally determining the effective diffusion coefficients and the erosion rate during plasma nitriding of metal surfaces.     

Scaling behavior of surface irregularity in the molecular domain: From adsorption studies to fractal catalysts

For an unexpected variety of solids, the surface topography from a few up to as many as a thousand angstroms is very well described by fractal dimension,D. This follows from measurements of the number of molecules in surface monolayers, as function of adsorbate or adsorbent particle size. As an illustration, we present a first case, amorphous silica gel, whereD has been measured independently by each of the two methods. (The agreement, 3.02±0.06 and 3.04±0.05, is excellent, and the result is modeled by a heavy generalized Menger sponge.) The examples as a whole divide into amorphous and crystalline materials, but presumably all of them are to be modeled as random fractal surfaces. The observedD values exhaust the whole range between 2 and 3, suggesting that there are a number of different mechanisms by which such statistically self-similar surfaces form. We show that fractal surface dimension entails interfacial power laws much beyond what is the source of theseD values. Examples are reactive scattering events when neutrons of variable flux pass the surface (this is of interest for locating fractal substrates that may support adlayer phase transitions); the rate of diffusion-controlled chemical reactions at fractal surfaces; and the fractal implementation of the traditional idea that the active sites of a catalyst are edge and apex sites on the surface.     

Cross-Over Between First-Order and Critical Wetting at the Liquid-Vapour Interface of n-Alkane/Methanol Mixtures: Tricritical Wetting and Critical Prewetting

A simple mean-field theory is presented which describes the basic observations of recent experiments revealing rich wetting behaviour of n-alkane/methanol mixtures at the liquid-vapour interface. The theory, qualitative and in part heuristic, is based on a microscopic lattice-gas model from which a Cahn–Landau approach is distilled. Besides the physics associated with the short-range components of the intermolecular interactions, effects of the long-range tails of the net van der Waals forces between interfaces are also taken into account. Further, gravitational thinning of the wetting phase is incorporated. The calculation of the spreading coefficient S is extended to the experimentally relevant situation in which the bulk adsorbate is slightly away from two-phase coexistence due to gravity. Analysis of this novel approximation to S for systems with short-range forces leads to the conclusion that the surface specific heat exponents _s =1,1/2, and 0, for first-order wetting, tricritical wetting and critical wetting, respectively, are robust with respect to (weak) gravitational thinning, consistently with experiment. For three different systems the adsorption is calculated as a function of temperature and compared with the experimentally measured ellipticity. Including weak long-range forces which favour wetting in the theory does not visibly alter the critical wetting transition for the nonane/methanol mixture, in contrast with the generic expectation of first-order wetting for such systems, but in good agreement with experiment. For decane/methanol weak long-range forces bring the transition very close to the prewetting critical point, leading to an adsorption behaviour closely reminiscent of short-range tricritical wetting, observed experimentally for alkane chain length between 9.6 and 10. Finally, for undecane/methanol the transition is clearly of first order. First-order wetting is also seen in the experiment.     

A scanning tunneling microscopy study of PH3 adsorption on Si(1 1 1)-7 × 7 surfaces, P-segregation and thermal desorption

PH₃ adsorption on Si(1 1 1)-7 × 7 was studied after various exposures between 0.3 and 60 L at room temperature by means of scanning tunneling microscopy (STM). PH₃-, PH₂-, H-reacted, and unreacted adatoms can be identified by analyzing empty-state STM images at different sample biases. PH_x-reacted rest-atoms can be observed in empty-state STM images if neighboring adatoms are hydrogen terminated. Most of the PH₃ adsorbs dissociatively on the surface, generating H- and PH₂-adsorbed rest-atom and adatom sites. Dangling-bonds at rest-atom sites are more reactive than adatom sites and the faulted half of the 7 × 7 unit cell is more reactive than the unfaulted half. Center adatoms are overwhelmingly preferred over corner adatoms for PH₂ adsorption. The saturation P coverage is ∼0.18 ML. Annealing of PH₃-reacted 7 × 7 surfaces at 900 K generates disordered, partially P-covered surfaces, but dosing PH₃ at 900 K forms P/Si(1 1 1)- surfaces. Si deposition at 510 K leaves disordered clusters on the surface, which cannot be reordered by annealing up to 800 K. However, annealing above 900 K recreates P/Si(1 1 1)- surfaces. Surface morphologies formed by sequential rapid thermal annealing are also presented.     

The Ising square lattice in aL×M geometry: A model for the effect of surface steps on phase transitions in adsorbed monolayers

Critical phenomena in adsorbed monolayers on surfaces are influenced by limited substrate homogeneity, such as surface steps. We consider the resulting finite-size and boundary effects in the framework of a lattice gas system with nearest neighbor attraction in aL×M geometry, with two free boundaries of lengthML, and periodic boundary conditions in the other direction (along the direction of the steps). This geometry thus models a terrace of the stepped surface, and adatoms adsorbed on neighboring terraces are assumed to be non-interacting. Also the effect of boundary fields is considered (describing the effects of missing neighbors and changed binding energy to the substrate near the boundary). Extensive Monte Carlo calculations on this model performed on a multi-transputer system are presented and analyzed in terms of phenomenological finite size scaling concepts. The fact that two scaling variables occur (/L,L/M, with being the correlation length in the bulk) is demonstrated explicitly. In the absence of boundary fields, the system forML orders nearT _c in a domain state, with domain walls running across the terrace, while at some temperature belowT _c a transition to a monodomain state occurs. This domain state slightly belowT _c is suppressed, however, by rather weak boundary fields. These results are interpreted in terms of exact theoretical predictions.     

Adatom-adatom interaction mediated by an underlying surface phase transition

Low temperature scanning tunneling microscopy measurements on the adsorption of single Pb adatoms on Si(111)-(square root 3 x square root 3)-Pb surfaces reveal the vertical displacement patterns induced on the substrate by these Pb adatoms as well as a novel adatom-adatom interaction. The origin of both can be traced back to the (square root 3 x square root 3)<-->(3 x 3) phase transition taking place at lower temperatures. A Landau-like approach explains the displacement patterns as due to the corresponding order parameter and shows that the vicinity of a surface phase transition gives rise to a nonmonotonic adatom-adatom interaction.     

The spherical-model limit in a random field

The spherical-model limitn of then-vector model in a random field, with either a statistically independent distribution or with long-range correlated random fields, is studied to demonstrate the correctness of the replica method in which then and replica limits limits are interchanged, provided the replica and thermodynamic limits are taken in the right order, in the case of long-range correlated random fields. A scaling form for the two-point correlation function relevant to the first-order phase transition below the lower critical dimensionality of the random system is also obtained.     

Spherical models with a Gates-Penrose-type phase transition

Gates and Penrose have given criteria under which classical gases with weak long-range interactions fail to be described by the van der Waals equation with Maxwell's rule. Unfortunately, examples of equations of state for such systems have not yet been produced. This paper examines the Gates-Penrose class of interactions-i.e.,U (r)=q(r)+(r), in the limit0, where the Fourier transform (p) has a minimum at a nonzero value ofp-for the spherical model on a one-dimensional lattice. Free energy and magnetization isotherms are computed; it is seen that there is a phase transition, but that the zero-field spontaneous magnetization is always zero (a parahelicoidal phase). However, the pair-correlation function may exhibit either long-range order or the appearance of oscillation.     

Anomalous internal conversion ofE1 transitions in outer atomic shells

The experimentalN andO shell conversion coefficients of highly hinderedE1 transitions were found to be anomalous. The discrepancies as well as those for theL andM shells were removed by using the following values of the nuclear current parameter: 9·2±0·1 for the 6·21 keV transition in¹⁸¹Ta, 8·5±0·5 or –7·5±0·5 for the 84·20 keV transition in²³¹Pa and 1·9±0·2 for the 26·38 keV one in²³⁷Np.     

The wetting transition in a random surface model

We continue our analysis of the phase diagram of a discrete random surface, with no downward fingers, lying above a flat two-dimensional substrate. The surface is closely related to the 2D Ising model and its free energy is exactly solvable in much (but not all) of the phase diagram. There is a transition at temperatureT _w from a high-T infinite height or wet phase to a low-T finite height or partially wet phase. Previously it was shown that when a parameterb, related to the contact interaction, is positive,T _w is independent ofb and there is a logarithmic specific heat divergence asT _w is approached fromeither side. Here we show that forb<0,T _w does depend onb and there isno thermodynamic singularity from the wet phase. The partially wet phases forb0 andb>0 differ in the absence or presence of a monolayer covering the entire substrate; this results in a first-order transition across the lineb=0,T<T _w.This paper is dedicated to Jerry Percus.     

Improved SPR technique for determination of the thickness and optical constants of thin metal films

A novel method with single-wavelength light is developed to determine the optical constants and the thickness of a thin metal film. It bases on a new geometry that consists of a coupling prism, a transparent coating layer directly deposited onto the prism base, a thin metal film to be detected, and the air. The attenuated total reflection technique is employed in our configuration to excite two different kinds of surface plasmon waves simultaneously. As a result, the reflection curve shows two obvious surface plasmon resonant dips. Using the Chen's et al. (Opt. Soc. Am. 71 189, 1981) method, we can obtain two sets of () and thickness of the thin metal film through one resonant dip (surface plasmon), then the real value can be determined through the other resonant dip (modified long-range surface plasmon). Compared to conventional double wavelength method and the double-medium technique (Yang et al. Appl. Opt. 27 11, 1988), the present single-scan method avoids both the ambiguity of different conditions caused by two-scan technique, and the dispersion problem with different light wavelength.