Overlayer unit mesh

The simplest diffraction measurement is the determination of the surface or overlayer unit mesh size and shape. This can be performed by inspection of the diffraction pattern at any energy of the incident beam (see Figure 4). The determination is simplest if the electron beam is incident normal to the surface, because the symmetry of the pattern is then preserved. The diffraction pattern determines only the size and shape of the unit mesh. The positions of atoms in the surface cannot be determined from visual inspection of the diffraction pattern, but must be obtained from an analysis of the intensities of the diffracted beams. Generally, the intensity in a diffracted beam is measured as a fimction of the incident-beam energy at several diffraction geometries. These intensity-versus-energy curves are then compared to model calculations. ... 

The four common types of unit mesh are hexagonal, square, rectangular, and oblique. Figure 4 illustrates the manner in which typical overlayer unit meshes up to (6 x 6) originate on an hexagonal substrate mesh. 

Figure 2 Examples of overlayer structures with appropriate notation, (a) fee (100) p(2X2) (b) fee (100) c(2X2) (c) fee (111) p(73 X 73>R30< (d) bee (110 ) p(2 X 1) and bee (110) p(1 X 2). The two orientations for the unit mesh in (d) are both possible because of the symmetry of the substrate they have the same free energy and are called degenerate.

Any periodicity in the surfiice or overlayer different from that of the clean unreconstructed surface produces addidonal diffracted beams. A unit mesh latter than... 

Subsequently, Mitchell s group in Vancouver, by means of a tensor-LEED study17 of the Cu (110)-(2 x 3)N surface structure, supported a reconstruction model in which the topmost layer is described as a pseudo-(100)-c(2 x 2)N overlayer with metal corrugation of about 0.52 A in the reconstructed layer. Each nitrogen adatom is almost coplanar with the local plane formed by the four neighbouring copper atoms. Of the four N atoms present in the unit mesh, three are also bonded to Cu atoms in the layer below and therefore are five coordinate. 

Fig. 3. Relationship between unit cell (mesh) vectors of a LEED pattern and unit mesh vectors of the corresponding surface structure, x = Integral-index LEED spots (due to substrate) x = fractional-index LEED spots (due to overlap) O = (2v/3 x 2N/3)R30° overlayer lattice (mesh) Grid = substrate mesh A, B = unit cell (mesh vectors of LEED pattern a, b = unit mesh vectors of overlayer structure I = unit mesh vectors of substrate LEED pattern and i = unit mesh vectors of substrate surface.

In a first approximation, the overlayer lattice is taken to be perfectly plane and regular. Its own unit mesh vectors can lie either parallel with those of the substrate or can be rotated. The overall periodicity of the combined meshes, that is the periodicity of the coincidence of the lattices, is then the periodicity of the resulting surface structure as defined in Section IIB. With this concept one sees how LEED patterns having fractional order beams corresponding to very large repeat distances are... 

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... 

Fig. 25. Structure factor integrated over 2.3% of the surface Brillouin zone (radius of 5 mesh lengths in Fig. 24) vs. TtoclesL plotted with the rescaled energy (crosses) for the J i x overlayer on the triangular lattice. Rescaling involves multiphc-ation by a negative number and shifting by a constant. Temperature is measured in units of

Long-range periodicity of surface nets is readily obtained from LEED patterns, and unit repeating meshes having dimensions over one hundred angstroms on a side are sometimes measured. This is impossible with field ionization microscopy. Only in rare cases has a periodic overlayer ever been observed by FIM on an individual plane, and structures with repeat distances larger than a few atomic diameters can never be recognized. 

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