Numerically stable solution of coupled channel equations: The wave function

In two earlier papers a numerically stable solution of the stationary Schrödinger equation for coupled channels was presented. The Schrödinger function and its first derivative were expressed in terms of two matrices: A so-calledlocal reflection matrix (LORE) and aninverse local transmission matrix (INTRA). These matrices obey very simple boundary conditions: They approach asymptotically zero (one) on one side of the reaction path and the reflection (transmission) matrix on the other side. Hence by propagating both matrices along the reaction path one can determine directly the observable scattering matrix elements without ever having to calculate wave functions. On the other hand it is often useful to know the wave functions, for instance in order to interpret scattering data in terms of flow patterns etc. Although the relation between theINTRA-LORE and the wave function is simple, a straight forward calculation is not possible. It would involve an inversion of theINTRA which is numerically ill behaved. In this paper we describe a numerically stable method of computing the wave function and illustrate by two examples of surface reactions.Dedicated to Herbert Wagner on the occasion of his 60th birthday. One of the authors (W.B.) also recalls with great pleasure the stimulating discussions he had with his first graduate student     

Detailed balance and phonon assisted sticking in adsorption and desorption of H2/Si

Recent experimental results on the desorption of D₂ from Si show practically no translational heating indicating a low barrier for adsorption. This seems to be at variance with the extremely low sticking coefficient found in adsorption experiments indicating a very high barrier. In order to understand this apparent discrepancy we consider a simple model of local lattice relaxation allowing for different barriers in adsorption and desorption processes. After taking the dynamics of this relaxation into account it turns out that detailed balance in principle is valid. In practice, however, it can not be applied for very large energy releases from lattice distortions. Our model predicts very strong phonon assisted sticking.     

The dynamics of desorption induced by atomic hydrogen: HD/Cu(111)

Recent observations of a direct reaction between adsorbates and hydrogen atoms incident from the gas phase are interpreted in terms of an Eley-Rideal reaction. A detailed comparison of the experimental data for the HD/Cu(111) system with quantum mechanical model calculations corroborates such an interpretation. The peculiar isotope effect observed can be understood from the different dynamical implications of appropriately rescaled potential energy surfaces. The width of the measured time-of-flight spectrum is explained from the overlapping contributions of the populated vibrational levels. The angular distributions are rationalized by contributions both from ‘indirect’ events, where the incident atoms make several bounces in the surface well prior to reaction, and ‘direct’ reactive events.     

Phonons on surfaces: The importance of structure and adsorbates

Recent progress in detecting thermal energy vibrations at solid surfaces will be reviewed. Phonons on clean, well-ordered metals will be discussed as well as vibrations within ordered and disordered adlayers of adsorbed atoms and molecules. Simple lattice dynamical models will be used to demonstrate the interconnection between vibrations, structure, and force fields at a surface.     

Reversible Vertical Manipulations of Single Pt Adatom on Pt（111） Surface with a Triple-Apex Tip

With a triple-apex tip, we investigate theoretically the vertical manipulation of single Pt adatom on the Pt（111） surface. The adatom adsorbed on the f cc site of the flat Pt（111） surface can be transferred vertically to the tip by adjusting the tip height properly. Moreover, based on the strong vertical trapping ability and the relatively weak lateral trapping ability of the tip, we propose a simple method to realize a reversible vertical manipulation of the Pt adatom from the highly coordinated sites, the kink and the step sites, of the stepped Pt（111） surface. All the vertical manipulations are completed using only the atomic force between the tip and the adatom, without the electric field.     

Reliable Lateral Manipulation of Single Adatom on Metal fcc（lll） Surfaces with a Single-Atom Tip

Using molecular statistics simulations based on the embedded atom method potential, we investigate the reliability of the lateral manipulation of single Pt adatom on Pt（111） surface with a single-atom tip for different tip heights （tip-surface distance） and tip orientations. In the higher tip-height range, tip orientation has little influence on the reliability of the manipulation, and there is an optimal manipulation reliability in this range. In the lower tip- height range the reliability is sensitive to the tip orientation, suggesting that we can obtain a better manipulation reliability with a proper tip orientation. These results can also be extended to the lateral manipulation of Pd adatom on P d （111） surface.     

Elastic Analysis of Physisorption-Induced Substrate Deformation

Physisorption may cause a dimple on a deformable solid surface due to adsorbat-substrate interaction. The interactive force between the adsorbate and the crystal atoms depends on their distances, which may change with substrate deformation. This feature of displacement-dependence indicates that the equilibrium problem is a force-deformation coupled nonlinear procedure. In the present study, a continuum mechanics model, in which the force is considered as a function of the displacement field of the medium, is presented to calculate the physisorption-induced deformation in a semi-infinite elastic medium. It is found that the nonlinear effect due to force-deformation coupling should be taken in consideration in the adsorbate-substrate interaction analysis.     

Analysis of semiconductor surface phonons by Raman spectroscopy

Only recently Raman spectroscopy (RS) has advanced into the study of surface phonons from clean and adsorbate-covered semiconductor surfaces. RS allows the determination of eigenfrequencies as well as symmetry selection rules of surface phonons, by k-conservation limited to the Brillouin zone-center, and offers a significantly higher spectral resolution than standard surface science techniques such as high-resolution electron energy loss spectroscopy. Moreover, surface electronic states become accessible via electron–phonon coupling. In this article the fundamentals of Raman scattering from surface phonons are discussed and its potential illustrated by considering two examples, namely Sb-monolayer-terminated and clean InP(110) surfaces. Both are very well understood with respect to their atomic and electronic structure and thus may be regarded as model systems for heteroterminated and clean semiconductor surfaces. In both cases, localized surface phonons as well as surface resonances are detected by Raman spectroscopy. The experimental results are compared with surface modes predicted by theoretical calculations. On InP(110), due to the high spectral resolution of Raman spectroscopy, several surface modes predicted by theory can be experimentally verified. Surface electronic transitions are detected by changing the energy of the exciting laser light indicating resonances in the RS cross section. Received: 7 April 1999 / Accepted: 25 June 1999 / Published online: 16 September 1999     

Dissociative adsorption of H2: Time-dependent quantum studies

In this short review we consider some selected results for the dissociation of hydrogen on metal surfaces. In particular we focus our attention on the effects that surface corrugation have on the dissociation and also how rotations and vibrations couple in the interaction region. Results from time dependent quantum wavepacket calculations have been particularly helpful in forming our ideas of how diatomics dissociate. We describe this method along with two examples of propagation schemes. The power of limited dimensional models to rationalize experimental observations is clearly demonstrated.     

The structure and dynamics of crystal surfaces at high temperatures

After a brief review of the historical evolution of the understanding of crystal surfaces at high temperatures in general the subject is narrowed down to fcc metal surfaces, in particular to (110) surfaces. The recent work on these surfaces is reviewed, with emphasis on Pb, and the interpretation of the results in terms of various kinds of disordering such as surface melting, surface roughening, anharmonic vibrations and other processes is critically examined. While some of the results are now well established, others are contradictory, so that no unambiguous picture of metal surfaces at high temperatures can be given at present.     

Nonlinear optical investigations of the dynamics of hydrogen interaction with silicon surfaces

Optical second-harmonic generation (SHG) from silicon surfaces may be resonantly enhanced by dangling-bond-derived surface states. The resulting high sensitivity to hydrogen adsorption combined with unique features of SHG as an optical probe has been exploited to study various kinetical and dynamical aspects of the adsorption system H₂/Si. Studies of surface diffusion of H/Si(111)7×7 and recombinative desorption of hydrogen from Si(111)7 × 7 and Si(100)2 × 1 revealed that the covalent nature of hydrogen bonding on silicon surfaces leads to high diffusion barriers and to desorption kinetics that strongly depend on the surface structure. Recently, dissociative adsorption of molecular hydrogen on Si(100)2×1 and Si(111)7×7 could be observed for the first time by heating the surfaces to temperatures between 550 K and 1050 K and monitoring the SH response during exposure to a high flux of H₂ or D₂. The measured initial sticking coefficients for a gas temperature of 300K range from 10^–9 to 10^–5 and strongly increase as a function of surface temperature. These results demonstrate that the lattice degrees of freedom may play a decisive role in the reaction dynamics on semiconductor surfaces.     

Multi-Slit Diffraction of Evanescent Electromagnetic Waves

The well-known Fraunhofer multi-slit diffraction is described as the multi-slit interference modulated by the singleslit diffraction, namely the multiplication between the single-slit diffraction factor and the multi-slit interference factor. By considering the simplified argument we show that the multi-slit diffraction of evanescent waves which are in the near-field region also has the interference and diffraction effects, and that this two-fold effect can be expressed as the convolution of the diffraction factor and the interference factor. Our conclusion could be helpful to understand the contribution of evanescent waves to the optical responses of sub-wavelength structures such as slits and grooves.     

Permanent narrow-band reflection holograms for infrared light recorded in LiNbO3:Ti:Cu channel waveguides

Permanent refractive-index gratings are generated by thermal fixing of holograms in photorefractive lithium niobate channel waveguides. The guides are fabricated by successive indiffusion of titanium stripes and thin layers of copper. After high-temperature recording with green light, refractive-index modulations exceeding Δn=8×10^-5 for light of the telecommunication wavelength 1550 nm appear without the need of any development process of the written holograms. The gratings are stable in the dark and no compensation mechanism via dark conductivity is observed. Thus this method may be well suited for long-time applications in holography and integrated optics. Received: 2 October 2000 / Revised version: 25 January 2001 / Published online: 22 March 2001     

The kinetic energy dependent effective Debye temperature for CoS2 (100)

The effective Debye temperatures of the highly spin-polarized material CoS₂ were measured using temperature dependent low energy electron diffraction and shown to be dependent upon electron kinetic energy. The normal dynamic motion of the (100) surface results in the effective surface Debye temperature of compared to a bulk Debye temperature of . Similar values for the bulk Debye temperature have been obtained through LEED I(V) analysis and core level photoemission with a lower value for the bulk Debye temperature found from heat capacity measurements.     

Influence of steps and defects on the dissociative adsorption of molecular hydrogen on silicon surfaces

-4 . Neither the absolute values nor the temperature dependence of adsorption on the terraces are affected by the misorientation. Received: 3 November 1998     

Anharmonic effects on B2-FeAl(1 1 0) surface: A molecular dynamics study

Using molecular dynamics simulations and the analytic embedded-atom method (AEAM), the surface anharmonicity of B2-FeAl(1 1 0) has been studied in the temperature range from 0 K to 1400 K. The temperature dependence of the interlayer spacing, mean square vibrational amplitudes, surface phonon frequencies and line-widths, and layer structure factor have been calculated. The obtained results indicate that the anharmonic effects are small in the temperature range from 0 K to 900 K. The temperature dependences of the interlayer spacing indicates that the rippling effect of the B2-FeAl(1 1 0) surface is exhibited by the contraction of Fe surface atoms and the expansion of Al atoms, which persists at high temperatures. The temperature dependence of the layer structure factors shows that the B2-FeAl(1 1 0) surface does not disorder until the temperature of 1300 K.     

Ammonia adsorption and decomposition on silica supported Rh nanoparticles observed by in situ attenuated total reflection infrared spectroscopy

Attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR) is applied to study NH₃, adsorbed from the gas phase, and its decomposition products, i.e. NH_x species, on Rh nanoparticles, produced by spincoating from a RhCl₃ solution in water followed by reduction. A silicon ATR crystal with a hydroxilated SiO₂ layer acts as the support for the nanoparticles. Upon exposure to NH₃ in the vacuum chamber, NH₃ adsorbed to both silica and Rh is detected (sensitivity ∼5 × 10⁻⁵ absorbance units). Interaction of the NH₃ with the silica OH groups is observed around ∼2840 cm⁻¹ in combination with peaks showing the disappearance of unperturbed OH vibrations between 3500 and 3700 cm⁻¹. In addition, NH bend vibrations at 1634 cm⁻¹ and NH stretch vibrations at 3065 and 3197 cm⁻¹ are observed for substrate temperatures between 20 and 100 °C. The latter two correspond to NH on Rh, as verified with a sample without Rh, and probably correspond to undecomposed NH₃. Moreover, they remain after evacuation, suggesting strongly bound species. For a substrate temperature of 75 and 100 °C, additional NH stretch peaks at 3354 and 3283 cm⁻¹ are observed, possibly due to NH₂ intermediates, indicating NH₃ decomposition. It is shown that ATR-FTIR can contribute to the sensitive detection of adsorption and decomposition of gaseous species on realistic planar model catalysts.     

Quantum reflection of bright matter-wave solitons

We propose the use of bright matter-wave solitons formed from Bose-Einstein condensates with attractive interactions to probe and study quantum reflection from a solid surface at normal incidence. We demonstrate that the presence of attractive interatomic interactions leads to a number of advantages for the study of quantum reflection. The absence of dispersion as the soliton propagates allows precise control of the velocity normal to the surface and for much lower velocities to be achieved. Numerical modelling shows that the robust, self-trapped nature of bright solitons leads to a clean reflection from the surface, limiting the disruption of the density profile and permitting accurate measurements of the reflection probability.     

Formation of amorphous layers by solid-state reaction. from thin Ir films on Si(100)

Received: 18 November 1997 / Accepted: 16 October 1998 / Published online: 24 February 1999