Atomic beam diffraction

Fig. 4.12. Atomic-beam diffraction. A nearly monochromatic beam of helium, generated by a nozzle, falls on the solid surface with an angle of incidence. The diffracted beam is collected at an outgoing angle. The angular distribution of the diffracted helium beam contains the information about the topography and structure of the...

Diffraction, by X-rays or neutrons, has been the standard method for determining the structures of crystals. The mean free path of X-rays and neutrons is very long, and thus is not sensitive to surfaces. To probe the structures of surfaces, the probing particles must have a very short mean free path in solids. Two methods are extensively used for determining surface structures low-energy electron diffraction (LEED) and atomic-beam diffraction. A helium... 

Atomic-beam diffraction was first demonstrated in 1930, as a verification of the concept of the de Broglie wave (Estermann and Stem, 1930). In the 1970s, it was developed into an extremely informative method for determining topography and atomic structure of solid surfaces (Steele, 1974 Goodman and Wachman, 1976). 

Lapujoulade, J., Salanon, B., and Gorse, D. (1984). Surface structure analysis by atomic beam diffraction. In The Structure of Surfaces, edited by Van Hove, M. A., and Tong, S. Y., Springer-Verlag, Berlin. 

See Atomic metallic ion emission Anomalous corrugation theory 31, 142 breakdown 146 graphite, and 31, 144 Apparent barrier height 63,171 anomalously low 171 attractive force, and 49, 209 definition 7 image force, and 72 repulsive force, and 171, 198, 209 square-barrier problem, in 63 Apparent radius of an atomic state 153 Atom charge superposition I 11 analytic form 111 Au(lll), in 138 in atomic beam scattering 111 Atom-beam diffraction 107 apparatus 109... 

Atomic beams are suitable for diffraction experiments. The repulsive interaction with the surface is so strong that low-energy atoms are already reflected by the topmost atomic layer. Due to its pronounced sensitivity to the topmost surface layer, the method of atomic beam diffraction is especially useful for the study of adsorbates and superlattices. Typical energies of the incident atoms are under 0.1 eV. At such low energies no radiation damage occurs. In... 

A thermal energy atomic beam (20-200 meV) has a wavelength on the order of inter-atomic distances. The atomic beam diffracts from a contour of the surface potential corresponding to the beam energy. This contour is located 3-4 A above the ion cores in the outermost layer of the surface. Atomic beam diffraction patterns are normally interpreted using model surface scattering calculations, where the scattering is described as a Van der Waals interaction. 

Such waves can be used to probe the structure of crystal surfaces, through low-energy electron diffraction (LEED) or atomic beam diffraction. The latter is usually confined to He atoms, but even Ar atom diffraction can be discerned... 

Farias D, Rieder KH (1998) Atomic beam diffraction from solid surfaces. Rep Prog Phys 61 1575... 

RIE Rieder, K. H. Surface structural research with atom beam diffraction helium versus neon Surf. Rev. Lett. 1 (1994) 51. 

Engel T and Rieder K H 1982 Structural studies of surfaces with atomic and molecular beam diffraction Structural Studies of Surfaces With Atomic and Molecular Beam Scattering (Springer Tracts in Modern Physics vol 91) (Berlin Springer) pp 55-180... 

The underlying principle of X-ray diffraction is as follows. When a beam of X-rays passes through a crystalline solid it meet various sets of parallel planes of atoms. The diffracted beams cancel out unless they happen to be in phase, the condition for which is described in the Bragg relationship ... 

In crystallography, the difiiraction of the individual atoms within the crystal interacts with the diffracted waves from the crystal, or reciprocal lattice. This lattice represents all the points in the crystal (x,y,z) as points in the reciprocal lattice (h,k,l). The result is that a crystal gives a diffraction pattern only at the lattice points of the crystal (actually the reciprocal lattice points) (O Figure 22-2). The positions of the spots or reflections on the image are determined hy the dimensions of the crystal lattice. The intensity of each spot is determined hy the nature and arrangement of the atoms with the smallest unit, the unit cell. Every diffracted beam that results in a reflection is made up of beams diffracted from all the atoms within the unit cell, and the intensity of each spot can be calculated from the sum of all the waves diffracted from all the atoms. Therefore, the intensity of each reflection contains information about the entire atomic structure within the unit cell. 

The problems associated with quantitative studies of structure based upon this viewpoint of X ray absorption-edge spectra may be similar to those encountered using electron beams of comparable energy, 3 to 100 ev., to carry out electron diffraction studies of crystal structure. Qualitatively, this analogy can be carried further, as both the X ray spectra and the electron beam diffraction in this energy range are influenced by only the first few atom layers. 

The typical kinetic energy of a He beam generated by a nozzle is between 20 and 200 meV, corresponding to wavelength ranges between 0.1 and 1.0 A. By directing an atomic beam to a solid surface, diffraction occurs. 

The detailed data from He-scattering experiments provide information about the electron density distribution on crystalline solid surfaces. Especially, it provides direct information on the corrugation amplitude of the surface charge density at the classical turning point of the incident He atom, as shown in Fig. 4.13. As a classical particle, an incident He atom can reach a point at the solid surface where its vertical kinetic energy equals the repulsive energy at that point. The corrugation amplitude of the surface electron density on that plane determines the intensity of the diffracted atomic beam. 

The determination of the atomic structure of surfaces is the cornerstone of surface science. Before the invention of STM, various diffraction methods are applied, such as low-energy electron diffraction (LEED) and atom beam scattering see Chapter 4. However, those methods can only provide the Fourier-transformed information of the atomic structure averaged over a relatively large area. Often, after a surface structure is observed by diffraction methods, conflicting models were proposed by different authors. Sometimes, a consensus can be reached. In many cases, controversy remains. Besides, the diffraction method can only provide information about structures of relatively simple and perfectly periodic surfaces. Large and complex structures are out of the reach of diffraction methods. On real surfaces, aperiodic structures such as defects and local variations always exist. Before the invention of the STM, there was no way to determine those aperiodic structures. 

Hitherto only the positions of the X-ray beams diffracted by crystals have been considered unit cell dimensions are determined from the positions of diffracted beams without reference to their intensities. To discover the arrangement and positions of the atoms in the unit cell it is necessary to consider the intensities of the diffracted beams. 

The repetitions of the atoms or molecules in all directions in the crystal form many sets of parallel planes that act as diffraction gratings. When a beam of X rays impinges on a crystal that has a set of planes in a proper orientation with respect to the direction of the beam, diffraction will take place, i.e., some of the X rays will be bent away from the main beam, forming a new beam. The angle at which scattering takes place depends on... 

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