LEED Low-Energy Electron Diffraction

LEED is the surface analogue of X-ray diffraction. As the name indicates, the major difference is that one uses electrons instead of X-rays. As electrons of low kinetic energy (40-200 eV) do not penetrate very far into the material without losing energy, the elastically reflected electrons carry only information on the outermost layers of the surface (see Eig. 4.7). 

The LEED experiment relies on the duality of electrons, which have both particle and wave character. Electrons of primary energy, p, somewhere in the minimum of the mean-free path curve (Eig. 4.7) possess a wavelength, 1, that is comparable with the distance between atoms in a lattice  

Since the wavelength is of the order of lattice distances, electrons that are scattered elastically undergo constructive and destructive interference (as with X-rays in XRD). The back-scattered electrons form a pattern of spots on a fluorescent screen from which the symmetry and structure of the surface may be deduced. 

The prindple of a LEED experiment is shown schematically in Fig. 4.26. The primary electron beam impinges on a crystal with a unit cell described by vectors ai and Uj. The (00) beam is reflected direcdy back into the electron gun and can not be observed unless the crystal is tilted. The LEED image is congruent with the reciprocal lattice described by two vectors, and 02 . The kinematic theory of scattering relates the redprocal lattice vectors to the real-space lattice through the following relations 

Two sets of notation are commonly used to describe overlayer structures observed in diffraction experiments, the Wood notation [92] and a matrix notation. Although the latter is more flexible, the former is more widely used and we shall restrict ourselves to it in this review. The nomenclature is based on a comparison between the unit mesh of the topmost layer, the overlayer, and that of the second, unreconstructed, substrate layer. If a and b are the unit mesh vectors of the substrate layer and a, and bg the unit mesh vectors of the overlayer, then Wood s notation for an overlayer of adsorbed species A on the hkl plane of a crystal M is 

Adsorbate structures on a b.c.c. l00 surface which would produce a c(2 x 2) pattern in LEED. 

All three structures in Fig. 4 produce the same LEED pattern. This is more explicilty shown in Fig. 5 all these structures are equivalent in LEED display. Note, however, that they would all produce different 

Edited by H. Bubert and H. Jenett Copyright 2002 Wiley-VCH Verlag GmbH ISBNs 3-527-30458-4 (Hardback) 3-527-60016-7 (Electronic) 2.4 Low-energy Electron Diffraction (LEED) 

When Davisson and Germer reported in 1927 that the elastic scattering of low-energy electrons from well ordered surfaces leads to diffraction spots similar to those observed in X-ray diffraction [2.238-2.240], this was the first experimental proof of the wave nature of electrons. A few years before, in 1923, De Broglie had postulated that electrons have a wavelength, given in A, of  

2e = h/m v = (150/Eidn) and a corresponding wave vector of length k = 2nlX  

Eor further details of the history, experimental set-up, and theoretical approaches of LEED please refer to books by Pendry [2.241], van Hove and Tong [2.242], van Hove, Weinberg, and Chan [2.243], and Clarke [2.244]. This article relies extensively on these works. 

Surface and Interface Science Concepts and Methods, First Edition. Edited by Klaus Wandelt. 

With the mentioned availability of commercial equipment in the 1960s, there was, of course, an increased demand for a correct LEED theory triggering, new efforts in the field. A number of theoreticians, for example, Beeby, Duke, Heine, Holland, Jepsen, Kambe, McRae, Marcus, Moli re, Tong, and Webb worked to overcome the difficulties imposed by multiple scattering. A kind of breakthrough was made in 1971 by Pendry who included the strong atomic scattering [15] and 

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The technique of low-energy electron diffraction, LEED (Section VIII-2D), has provided a considerable amount of information about the manner in which a chemisorbed layer rearranges itself. Somotjai [13] has summarized LEED results for a number of systems. Some examples are collected in Fig. XVlII-1. Figure XVIII-la shows how N atoms are arranged on a Fe(KX)) surface [14] (relevant to ammonia synthesis) even H atoms may be located, as in Fig. XVIII-Ih [15]. Figure XVIII-Ic illustrates how the structure of the adsorbed layer, or adlayer, can vary wiA exposure [16].f There may be a series of structures, as with NO on Ru(lOTO) [17] and HCl on Cu(llO) [18]. Surface structures of... 

Low-Energy Electron Diffraction, LEED 252 Reflection High-Energy Electron Diffraction, RHEED 264... 

This chapter contains articles on six techniques that provide structural information on surfaces, interfeces, and thin films. They use X rays (X-ray diffraction, XRD, and Extended X-ray Absorption Fine-Structure, EXAFS), electrons (Low-Energy Electron Diffraction, LEED, and Reflection High-Energy Electron Diffraction, RHEED), or X rays in and electrons out (Surfece Extended X-ray Absorption Fine Structure, SEXAFS, and X-ray Photoelectron Diffraction, XPD). In their usual form, XRD and EXAFS are bulk methods, since X rays probe many microns deep, whereas the other techniques are surfece sensitive. There are, however, ways to make XRD and EXAFS much more surfece sensitive. For EXAFS this converts the technique into SEXAFS, which can have submonolayer sensitivity. 

To measure the goodness of fit, and to quantify the structural determination, a reliability (i -factor) comparison is used. In comparing the data and simulation of the experiment for many trial structures, a minimum R factor can be found corresponding to the optimal structure. In this way atomic positions can be determined in favorable cases to within a few hundredths of an A, comparable to the accuracy achieved in Low-Energy Electron Diffraction (LEED). 

Low-energy Electron Diffraction (LEED) 73 crystal lens... 

The most appropriate experimental procedure is to treat the metal in UHV, controlling the state of the surface with spectroscopic techniques (low-energy electron diffraction, LEED atomic emission spectroscopy, AES), followed by rapid and protected transfer into the electrochemical cell. This assemblage is definitely appropriate for comparing UHV and electrochemical experiments. However, the effect of the contact with the solution must always be checked, possibly with a backward transfer. These aspects are discussed in further detail for specific metals later on. 

The methods of X-ray diffraction usually were used to determine the orientation of crystal faces. Low-energy electron diffraction (LEED) gives more accurate results. However, such measurements provide an exact characterization only of the initial surface state of the electrodes. It is more difficult to determine the surface state after the electrochemical studies, and even more so during these studies. 

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