Miller indices, crystallography

Miller indices (crystallography) The nomenclature defining crystallographic planes in a crystal. Example (111) plane in a cubic crystal. 

The adsorption and ordering characteristics of the various hydrocarbon molecules on the low Miller index platinum surfaces are discussed in great detail elsewhere. These two surfaces appear to be excellent substrates for ordered chemisorption of hydrocarbons, which permit one to study the surface crystallography of these important organic molecules. The conspicuous absence of C-H and C-C bond breaking during the chemisorption of hydrocarbons below 500 K and at low adsorbate pressures (10 9-10-6 Torr) clearly indicates that these crystal faces are poor catalysts and lack the active sites that can break the important C-C and C-H chemical bonds with near zero activation energy. 

Surface Crystallography and Composition. Platinum (11) and nickel (8,9,12) have been the metal surfaces examined in our surface science studies to date. The surface coordination chemistry has been examined as a function of surface crystallography and surface composition. Surfaces specifically chosen for an assay of metal coordination number and of geometric effects were the three low Miller index planes (111), (110) and (100) as well as the stepped 9(lll)x(lll) and stepped-kinked 7(lll)x(310) surfaces (both platinum and nickel are face centered cubic). 

Let us first concentrate on the surfaces of flat, low-Miller-index planes. Figure 8 shows the (100) crystal face of platinum. When clean, this surface is reconstructed and its diffraction pattern indicates the presence of a 5 x20 surface structure. When the surface is impure or has a fraction of a monolayer of adsorbates, the square unit cell shown in figure 8 is obtained, which is what one would expect from projection of the bulk unit cell up to the surface. While this 5 x20 surface structure was first detected in our laboratory in 1965 [9], it was actually solved by surface crystallography in 1981 [10]. 

The theory of diffraction can be found in any crystallography book. The so-called structure factor F(h,k,l), where h, k, and / are the Miller indexes for the diffraction spots, is the Fourier transformation of the electron densities inside... 

---