G. Armand

Diffraction of helium from Cu(110), (113), (115) and (117); Interaction potential and surface crystallography

We present data obtained by helium scattering on different faces of copper: (110), (113), (115) and (117). It is shown that they are well fitted by model potentials, a corrugated Morse (CMP) for all faces and a modified form (MCMP) for the low corrugated (110) and (113) faces. Then, the isopotentials ZE(R), representing the effective corrugation for an incident helium atom of energy E are compared to those resulting from a method of superposition of atomic densities calculated in two different ways. So, starting from the tables of atomic wave functions given by Clementi and Roetti, a good agreement is obtained with experiment, provided that the proportionality constant between the potential and the electronic density is taken to be α = 600 eV03.

Elastic and inelastic scattering of neutral atoms by a corrugated hard wall

Abstract A general treatment of the elastic and inelastic scattering of neutral atoms by a corrugated hard wall potential is presented. The influence of the atomic thermal motion is divided into two parts, one corresponding to a translation of the whole profile and due to long wavelength phonons, and the other inducing a deformation of the potential shape corresponding predominately to short wavelength phonons. The Debye-Waller factor (for both the elastic and inelastic contributions) has the expected form and contains terms which correspond to a translation of the profile. However a correction term is introduced by the profile deformation. The one phonon exchange can occur with all the crystal phonons but it appears more important with those of long wavelength. The inelastic cross section is expected to be larger in the vicinity of diffracted peaks of large intensity. The only approximation is made in the determination of the source function where one supposes that a limited and small amount of energy is exchanged between the particle and the crystal.

Diffraction of He from Cu(110) in the 20–240 meV range; comparison with a realistic model potential

Abstract The results of the diffraction of helium from Cu(110) are presented in the 21–240 meV energy range. The corrugated Morse potential gives a good fit but its corrugation amplitude increases with incident energy. A new form of potential, the Modified Corrugated Morse Potential, is presented and its main properties are examined. With this potential, a good fit of the experimenal results for various incidence angles is obtained; no change of the parameters is necessary in the whole range of incident energies. So one gets a realistic picture of the He/Cu(110) interaction.

The Dynamics of Cu(100) Surface Atoms at High Temperature

We present a comparison between theoretical calculation and experimental data for the thermal attenuation of helium diffraction peaks for a beam scattered from Cu(100). The calculations take into account 2-phonon exchange exactly and multiphonon exchange with a good approximation up to the highest temperatures. It is shown that there is good agreement up to T = 450 K with the model of crystal surface atom thermal displacements developed by Jayanthi et al. Above, there is a significant enhancement of these displacements which indicates either an enhancement of anharmonicity in the surface or the onset of a thermal structural roughening.

Threshold resonances in the diffraction of atoms and molecules by surfaces

Abstract We examine the problem of threshold resonances in the diffraction of atomic and molecular beams by solid surfaces. We show that the divergence in the slope of the intensity as a function of incident polar angle appears generally in all diffraction peaks. However, for interactions with realistically soft repulsive parts we find that the resonances are weakened to the point where they will be difficult to observe experimentally.

Thermal attenuation in resonant atom-surface scattering

Abstract A method is presented to account for thermal effects in soft potential atom-surface scattering by taking the thermal average of decoupled t-matrix elements. This approach is applied under conditions of resonance. Comparison is made between the calculated and experimental resonance line shapes for 21 meV He atoms incident upon the Cu(113) surface. The calculations show that the specular intensity under resonance conditions has a temperature dependent structure which is different from that away from a resonance. This presently unobserved behavior is discussed.

Band structure of an atom adsorbed on a surface; application to the He/Cu (113) system

Abstract We present a method of exactly calculating the band energies of an atom adsorbed on a surface based on Neumann iteration of the projected transition matrix equations. The band structure calculated for a model of He on a Cu(113) surface shows large shifts and band gaps and differs substantially from the nearly free particle model. Comparison with an approximate calculation shows that the contributions to the energy shifts due to continuum state transitions are nearly negligible except for the higher band levels.

Transition matrix methods in atom-surface scattering theory

Abstract A review of transition matrix methods as applied to the theory of atom-surface scattering at thermal energies is presented. The theory is applied to examples of elastic scattering, inelastic scattering, and scattering from defects and disorder on the surface.

An Exact Theory of Inelastic Atom Surface Scattering the “Debye-Waller” Factor

The particle surface interaction is decomposed into two parts. The first one is the static periodic potential and yields the elastic diffraction pattern. The second contains the phonon operators and is responsible for the inelastic effects. In the T matrix equation the elastic potential is projected out. The total T matrix element is then given by its elastic component to which is added an expansion containing the phonon operatorsand the coupling between elastic and inelastic channels. A new but simple procedure is presented which allows one to perform the thermal average to all orders in perturbation. Limiting ourselves to the calculation of the thermal attenuation of the diffracted beams the thermal average of T matrix element, which gives directly the diffracted intensity, is written down explicitely. This general and exact procedure is applied to the scattering of a particle by a flat surface. With the simple potential model used the influence of the relation between the reflection coefficient and crystal temperature is not a pure exponential function. This fact is confirmed by careful examination of the experimental data.

Simple approximation to thermal attenuation in low‐energy atom–surface scattering

We present a set of simple approximations for models of the thermal attenuation of elastic intensities as a function of surface temperature. The results illustrate the complexity of the strongly interacting atom–surface system, yet provide simple closed‐form expressions which are no more difficult to apply than a standard Debye–Waller factor. Very good agreement is obtained with existing experimental data. The importance of the various types of multiphonon contributions is assessed and the resummation of bubble diagrams is demonstrated.