LEED, definition

LEED, definition, 12-1 to 4 Legendre polynomials, A-83 to 85 Legendre s equation, A-46 to 56 Leptons, summary of properties, 11-1 to 55 Lifetime... 

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. 

Because of the inverse relationship between interatomic distances and the directions in which constructive interference between the scattered electrons occurs, the separation between LEED spots is large when interatomic distances are small and vice versa the LEED pattern has the same form as the so-called reciprocal lattice. This concept plays an important role in the interpretation of diffraction experiments as well as in understanding the electronic or vibrational band structure of solids. In two dimensions the construction of the reciprocal lattice is simple. If a surface lattice is characterized by two base vectors a and a2, the reciprocal lattice follows from the definition of the reciprocal lattice vectors a and a2 ... 

Figure 6.8 Definition and properties of the two-dimensional reciprocal lattice a, and a2 are base vectors of the surface lattice, and a and a2 are the base vectors of the reciprocal lattice. The latter is equivalent to the LEED pattern.

As an example of the analysis of the ordering of an overlayer of adsorbates, we may take the question of detecting island formation. LEED provides a means for identifying when island formation takes place " although it does not always give a definitive answer. To monitor island formation the presence of adsorbate-induced extra spots in the diffraction is necessary. Thus the adsorbate must produce a superlattice and we assume this case in the following discussion. 

We call this Pt(100) surface reconstructed. Surface reconstruction is defined as the state of the clean surface when its LEED pattern indicates the presence of a surface unit mesh different from the bulklike (1 x 1) unit mesh that is expected from the projection of the bulk X-ray unit cell. Conversely, an unreconstructed surface has a surface structure and a so-called (1 x 1) diffraction pattern that is expected from the projection of the X-ray unit cell for that particular surface. Such a definition of surface reconstruction does not tell us anything about possible changes in the interlayer distances between the first and the second layers of atoms at the surface. Contraction or expansion in the direction perpendicular to the surface can take place without changing the (1 x 1) two-dimensional surface unit cell size or orientation. Indeed, several low Miller index surfaces of clean monatomic and diatomic solids exhibit unreconstructed surfaces, but the surface structure also exhibits contraction or expansion perpendicular to the surface plane in the first layer of atoms (9b). 

In this case the oscillations are definitely not linked to a periodic hex 1 x I structural transformation of the surface. The coverages are always high enough to keep the surface in the nonreconstructed state. As becomes evident from Fig. 38, the LEED pattern did not exhibit any evidence for the intermediate appearance of the hex phase during the oscillations. The reaction proceeds through the following steps ... 

A variety of model catalysts have been employed we start with the simplest. Single-crystal surfaces of noble metals (platinum, rhodium, palladium, etc.) or oxides are structurally the best defined and the most homogeneous substrates, and the structural definition is beneficial both to experimentalists and theorists. Low-energy electron diffraction (LEED) facilitated the discovery of the relaxation and reconstruction of clean surfaces and the formation of ordered overlayers of adsorbed molecules (3,28-32). The combined application of LEED, Auger electron spectroscopy (AES), temperature-programmed desorption (TPD), field emission microscopy (FEM), X-ray and UV-photoelectron spectroscopy (XPS, UPS), IR reflection... 

LEED-IV derived coordinates of oxygen atoms in water molecules (Mj) for MgO( 100)3x2-H2O. The error bars are estimated to be 0.15 A for the in-plane x,y distances (see Fig. 2 for definition of x and y axes) and 0.05 A for the surface-atom distances z. The positions obtained from semi-empirical calculations are in parentheses (from Ref 9). 

Coordinates of the centres of mass and orientations of the two acetylene molecules (1 and 2) in the (2x2) unit cell on MgO(lOO). The values obtained from LEED-IV data [24], neutron diffraction (ND) [26], and semi-empirical potential calculations [24,25] are tabulated. The definitions of x, y, and O are given in Fig. 4. 9 is the polar tilt of the molecule away from the surface plane, and z is with respect to the surface MgO layer. The two calculated z values are for effective charges of 1.2 and 2, respectively. 

The Leeds Northrup Co. has developed a two-couple continuous curve recorder for automatically heating furnaces to definite temperatures. As applied in carburizing and tempering of steel one thermocouple is placed in the furnace chamber and the other in contact with the steel piece. The controller automatically maintains the furnace for instance at 1,000°C. until the steel has reached 900°C. and then it drops the furnace to 900 C. Such an arrangement for control can be applied to a great many processes. 

Confusion can arise if the Park-Madden symbol is made to refer to an ad-layer mesh alone, rather than to the proper combined mesh of the surface structure which by definition inclvdes the substrate mesh (Section IIA). The temptation to describe just the adlayer structure arises because the symmetry of the combination mesh is commonly lower, and the combination mesh can be awkwardly large. In such a situation LEED patterns can be very complicated even though structure is basically simple. Suitable conventional notation to handle this has not been formulated, and in such cases it is appropriate and desirable to describe the overlayer mesh separately, in addition to describing the combination mesh. This is particularly useful for coincidence lattices (Section IVE). 

The definition of the powder surfaces tends to be in terms of the process for making it (23). This limits interpretation of their properties and also limits generalization of properties to surfaces which have been generated by atmospheric corrosion. Conversely, the LEED, Auger electron spectroscopy, photo emission properties, etc, are measured on fresh surfaces in UHV, because interpretation is difficult for more complex configurations and because experience has shown that these properties are profoundly modified and confused by exposure to real atmospheres. 

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