LEED Pattern

Because the electrons do not penetrate into the crystal bulk far enough to experience its three-dimensional periodicity, the diffraction pattern is determined by the two-dimensional surface periodicity described by the lattice vectors ai and ai, which are parallel to the surface plane. A general lattice point within the surface is an integer multiple of these lattice vectors  

The two-dimensional Bragg condition leads to the definition of reciprocal lattice vectors at and aj which fulfil the set of equations  

These reciprocal lattice vectors, which have units of and are also parallel to the surface, define the LEED pattern in k-space. Each diffraction spot corresponds to the sum of integer multiples of at and at- 

The integer numbers (ni,K2) are used as indices to label the spot. The parallel component of the corresponding wave vector is  

This equation also limits the set of observable LEED spots by the condition that the expression inside the brackets must be greater than zero. With increasing electron energy the number of LEED spots increases while the polar emission angle relative to the surface normal, 6 = arctan(k /kz), decreases for each spot except for the specular spot (0,0) which does not change. Eig. 2.47 shows examples of common surface unit cells and the corresponding LEED patterns. 

---

Dynamic models for ionic lattices recognize explicitly the force constants between ions and their polarization. In shell models, the ions are represented as a shell and a core, coupled by a spring (see Refs. 57-59), and parameters are evaluated by matching bulk elastic and dielectric properties. Application of these models to the surface region has allowed calculation of surface vibrational modes [60] and LEED patterns [61-63] (see Section VIII-2). 

Finally, it has been possible to obtain LEED patterns from films of molecular solids deposited on a metal-backing. Examples include ice and naphthalene [80] and various phthalocyanines [81]. (The metal backing helps to prevent surface charging.)... 

Fig. VIII-10. (a) Intensity versus energy of scattered electron (inset shows LEED pattern) for a Rh(lll) surface covered with a monolayer of ethylidyne (CCH3), the structure of chemisorbed ethylene, (b) Auger electron spectrum, (c) High-resolution electron energy loss spectrum. [Reprinted with permission from G. A. Somoijai and B. E. Bent, Prog. Colloid Polym. ScL, 70, 38 (1985) (Ref. 6). Copyright 1985, Pergamon Press.]...

A LEED pattern is obtained for the (111) surface of an element that crystallizes in the face-centered close-packed system. Show what the pattern should look like in symmetry appearance. Consider only first-order nearest-neighbor diffractions. 

Some general points are the following. One precondition for a vertical step in an isotherm is presumably that the surface be sufficiently uniform that the transition does not occur at different pressures on different portions, with a resulting smearing out of the step feature. It is partly on this basis that graphitized carbon, BN, MgO, and certain other adsorbents have been considered to have rather uniform surfaces. Sharp LEED patterns are another indication. 

The surface unit cell of a reconstructed surface is usually, but not necessarily, larger than the corresponding bulk-tenuiuated two-dimensional unit cell would be. The LEED pattern is therefore usually the first indication that a recoustnictiou exists. However, certain surfaces, such as GaAs(l 10), have a recoustnictiou with a surface unit cell that is still (1 x i). At the GaAs(l 10) surface, Ga atoms are moved inward perpendicular to the surface, while As atoms are moved outward. 

So it is essential to relate the LEED pattern to the surface structure itself As mentioned earlier, the diffraction pattern does not indicate relative atomic positions within the structural unit cell, but only the size and shape of that unit cell. However, since experiments are mostly perfonned on surfaces of materials with a known crystallographic bulk structure, it is often a good starting point to assume an ideally tenuinated bulk lattice the actual surface structure will often be related to that ideal structure in a simple maimer, e.g. tluough the creation of a superlattice that is directly related to the bulk lattice. 

Many fonns of disorder in a surface structure can be recognized in the LEED pattern. The main manifestations of disorder are broadening and streaking of diffraction spots and diffuse intensity between spots [1]. 

To date, the usual way of recording the LEED pattern is a light-sensitive video camera with a suitable image-processing system. In older systems movable Earaday cups (EC) were used which detected the electron current directly. Because of long data acquisition times and the problems of transferring motion into UHV, these systems are mostly out of use nowadays. 

Often (adsorption, reconstruction) the periodicity at the surface is larger than expected for a bulk-truncated surface of the given crystal this leads to additional (superstructure) spots in the LEED pattern for which fractional indices are used. The lattice vectors bi and b2 of such superstructures can be expressed as multiples of the (1 X 1) lattice vectors ai and Zx. ... 

Analysis of the LEED pattern or of spot profiles does not give any quantitative information about the position of the atoms within the surface unit cell. This type of information is hidden in the energy-dependence of the spot intensities, the so-called LEED 7-Vcurves. 

Figure 4.25 shows an example LEED pattern that was obtained after exposing a dean single crystal of Fe(lll) to nitrogen under conditions where N2 dissociates and the surface becomes saturated with N atoms. The surface is believed to reconstruct significantly to accommodate these high coverages. 

Figure4.25. LEED pattern obtained from N atoms on Fe(l 11) at Ep = 42 eV. The surface is estimated to have a coverage of 0.96 Ml nitrogen and is reconstructed into a 5x5 overlayer structure. The dark shadow in the...

Figure 4.26. Schematic drawing of the LEED experiment on a single costal with a unit cell given by vectors a-i and O2. The LEED pattern corresponds to the reciprocal lattice described by vectors and 02. ...

The methods for depositing chlorine adatoms on the (110) surface have been described previously (26), and resulted in surface structures and LEED patterns identical to those achieved by dissociative CI2 adsorption. A c(4x2)-Cl pattern at 6 , = 0.75 (26) was used to calibrate chlorine coverages, which were taken proportional to the ratio of Cl Ag AES intensities (26). 

The growth direction of MgCl2 is independent of the substrate symmetry [93]. Growth on a cubic crystal, namely Pd(lOO), leads to hexagonal LEED pattern. However, the structure of the films is much more complex due to the... 

Fig. 8 LEED pattern as observed during preparation of a MgCL-film. a Pd(lll), b 1 ML MgCl2(001)/Pd(lll), c multilayer MgCl2(001)/Pd(lll). d Schematic real space representation of b the mesh represents the Cl lattice and spots the underlying Pd lattice...

As an example. Fig. 8.1 shows a result from Bardi and co-workers obtained on a bimetallic AusPdClOO) single-crystal alloy [Kuntze et al., 1999]. The LEED pattern indicates a sharp (1 x 1) unit cell that corresponds to the bulk-tmncated stmcture of the substitutionaUy disordered Au3Pd alloy. Additionally, the authors determined the composition of the first outermost layer to be pure Au. These findings revealed that the (100) oriented surface of Au over AusPd alloy is not reconstmcted, which is unique, since pure Au, Pt, and Ir (100) crystals are all known to be reconstmcted in similar ways [Van Hove et al., 1981 Ritz et al., 1997]. In this case, the presence... 

Figure 8.1 LEED pattern of Au3Pd(100), showing a sharp (1 x 1) unit cell. (Reprinted with permission from Kuntze et al. [1999]. Copyright 1999. The American Physical Society.)...

Figure 8.8 Series of iniiared spectra during (a) CO2 production and (b) progressive oxidation of COaj[ on Pt3Sn(l 11) in 0.5 M H2SO4 saturated with CO each spectrum was accumulated ftom 50 interferometers at the potential indicated, (c, d) LEED pattern and schematic representation of the p(4 X 4) structure observed on PtsSnflll) after exposing the surface to O2 and electrolyte. The gray dicles are Pt surface atoms, the black circles are Sn atoms covered with OH, and the dotted circles are Sn atoms that are chemically different from Sn atoms modified with OH. (Reprinted with permission from Stamenkovic et al. [2003]. Copyright 1999. The American Chemical Society.)...

Figure 14.2 Cyclic base voltainmograms of Ru(OOOl) in 0.1 M HCIO4, 50mVs scan range 0.1-1.05 V (solid line) and —0.12 —1.05 V (dotted Une). Also indicated are LEED patterns reported in [Zei and Ertl, 2000] after emersion at 0.35, 0.75, and 1.2 V and anodic charges per surface atom transferred at different potentials according to El-Aziz and Kibler [2002].

Figure 10.3 Adsorbed sulfur structures on Cu(100). (a, b) LEED patterns from the p(2 x 2) and ( 17 x 1) R14° structures, respectively, (c) STM image (9.3 x 9.3 nm) of the (y 17 x f17) R14° structure formed after annealing the sulfur adlayer to 1173 K. (d) High-resolution STM image (2.9x2.9nm) of (c). (e) Proposed model of the ( 17x 17) R14° structure black circles are sulfur adatoms in four-fold sites in the top layer shaded circles are sulfur adatoms which have replaced a terrace copper atom dashed circles indicate a copper atom which may be missing. (Adapted from Ref. 12).

Perdereau and Oudar s early paper20 reported LEED patterns and surface concentration data for the (111), (100) and (110) surface planes. For Ni(lll) a sequence of structures was observed starting with p(2 x 2), changing to ( /3 x v/3) 30° with increasing sulfur concentration and finally to a structure labelled SBAII , which Edmonds et al,21 identify as a (5 /3 x 2) structure. The low-concentration structures agree well with a model involving sulfur... 

---