Miller indexing

Empirically, however, the results are reasonably accurate, and the approach is a very useful one. An application of it to various Miller index planes is given by... 

In describing a particular surface, the first important parameter is the Miller index that corresponds to the orientation of the sample. Miller indices are used to describe directions with respect to the tluee-dimensional bulk unit cell [2]. The Miller index indicating a particular surface orientation is the one that points m the direction of the surface nonual. For example, a Ni crystal cut perpendicular to the [100] direction would be labelled Ni(lOO). 

Figure Bl.21.1. Atomic hard-ball models of low-Miller-index bulk-temiinated surfaces of simple metals with face-centred close-packed (fee), hexagonal close-packed (licp) and body-centred cubic (bcc) lattices (a) fee (lll)-(l X 1) (b)fcc(lO -(l X l) (c)fcc(110)-(l X 1) (d)hcp(0001)-(l x 1) (e) hcp(l0-10)-(l X 1), usually written as hcp(l010)-(l x 1) (f) bcc(l 10)-(1 x ]) (g) bcc(100)-(l x 1) and (li) bcc(l 11)-(1 x 1). The atomic spheres are drawn with radii that are smaller than touching-sphere radii, in order to give better depth views. The arrows are unit cell vectors. These figures were produced by the software program BALSAC [35]-...

Figure Bl.21.1 shows a number of other clean umeconstnicted low-Miller-index surfaces. Most surfaces studied in surface science have low Miller indices, like (111), (110) and (100). These planes correspond to relatively close-packed surfaces that are atomically rather smooth. With fee materials, the (111) surface is the densest and smoothest, followed by the (100) surface the (110) surface is somewhat more open , in the sense that an additional atom with the same or smaller diameter can bond directly to an atom in the second substrate layer. For the hexagonal close-packed (licp) materials, the (0001) surface is very similar to the fee (111) surface the difference only occurs deeper into the surface, namely in the fashion of stacking of the hexagonal close-packed monolayers onto each other (ABABAB.. . versus ABCABC.. ., in the convenient layerstacking notation). The hep (1010) surface resembles the fee (110) surface to some extent, in that it also...

Figure Bl.21.2. Atomic hard-ball models of stepped and kinked high-Miller-index bulk-temiinated surfaces of simple metals with fee lattices, compared with anfcc(l 11) surface fcc(755) is stepped, while fee...

A superlattice can be caused by adsorbates adopting a different periodicity than the substrate surface, or also by a reconstmction of the clean surface. In figure B 1.21.3 several superlattices that are conmionly detected on low-Miller-index surfaces are shown with their Wood notation. 

The temperature behavior of low446,491,503 558 as well as high Miller index crystal faces of Au447,448 has been examined in 0.01 M perchloric acid solutions. For all gold surfaces studied, C, was found to decrease and Ea=Q moved to less negative values with increasing t 446-448 491503-558... 

Miller index of the face Lang notation r.o 0.01/Vv8. SHE dEa dTfmV K-1... 

The electrochemically induced creation of the Pt(lll)-(12xl2)-Na adlayer, manifest by STM at low Na coverages, is strongly corroborated by the corresponding catalyst potential Uwr and work function O response to galvanostatic transients in electrochemical promotion experiments utilizing polycrystalline Pt films exposed to air and deposited on (T -AbCb. 3637 Early exploratory STM studies had shown that the surface of these films is largely composed of low Miller index Pt(lll) planes.5... 

Structure Sensitivity over Pe. Table II presents the rates of ammonia synthesis over each of the low Miller index planes of Pe. 

Figure 1,2 Atomic arrangement on various clean metal surfaces. In each of the sketches (a) to (h) the upper and lower diagrams represent top and side views, respectively. Atoms drawn with dashed lines lie behind the plane of those drawn with thick lines, Atoms in unrelaxed positions (i.e. in the positions they occupy in the bulk) are shown as dotted lines. From G.A. Somorjai, Chemistry in Two Dimensions, Cornell University Press, London, 1981, p. 133, For the Miller index convention in hexagonal close-packed structures, see also G.A. Somorjai loc. cit, Used by permission of Cornell University Press,...

A.R. Siedle, 3M Central Research Laboratory If one of the extended structures described by Professor McCarley were truncated through a low Miller index plane, can one, following the appproach of Solomon, predict what metal orbitals would protrude from the surface so generated Have ultraviolet photoelectron spectra been obtained on single crystals of any of these materials ... 

For an fee lattice a particularly simple surface structure is obtained by cutting the lattice parallel to the sides of a cube that forms a unit cell (see Fig. 4.6a). The resulting surface plane is perpendicular to the vector (1,0,0) so this is called a (100) surface, and one speaks of Ag(100), Au(100), etc., surfaces, and (100) is called the Miller index. Obviously, (100), (010), (001) surfaces have the same structure, a simple square lattice (see Fig. 4.7a), whose lattice constant is a/ /2. Adsorption of particles often takes place at particular surface sites, and some of them are indicated in the figure The position on top of a lattice site is the atop position, fourfold hollow sites are in the center between the surface atoms, and bridge sites (or twofold hollow sites) are in the center of a line joining two neighboring surface atoms. 

Unlike the case of diffraction of light by a ruled grating, the diffraction of x-rays by a crystalline solid leads to the observation that constructive interference (i.e., reflection) occurs only at the critical Bragg angles. When reflection does occur, it is stated that the plane in question is reflecting in the nth order, or that one observes nth order diffraction for that particular crystal plane. Therefore, one will observe an x-ray scattering response for every plane defined by a unique Miller index of (h k l). 

Copper high Miller index, 26 12 Copper oxide, 27 184-187, 199 as adsorbent, 21 44 on alumina, 27 80-85 -manganese oxide, 27 91, 92 oxidation of CO over, 24 86 -platinum catalyst, 27 86-88 propylene oxidation, 30 141 Coprecipitation, perovskite preparation, 36 247-250... 

Gadolinia, conversion rates, 27 35 Gallium arsenide, high Miller index, 26 12 Gallosilicate zeolite, Si MAS NMR studies of, 33 233-236... 

More recently, the question of thermal roughening has also been addressed in the study of metal surfaces. Detailed He difiraction studies from the high Miller index (113) surface of Cu and Ni proved the existence of a roughening transition on these surface. These studies were performed by means of He scattering. Let us make first two short comments. 

The first term a i. h is the Miller index component h, which is an integer. Thus in the interference fimction it becomes unity since exp(2 ni)=l. This corresponds to strong Bragg diffraction when q=0. The second term when put in the interference fimction becomes... 

To decide which of these many vectors to use, it is usual to specify the points at which the plane intersects the three axes of the material s primitive cell or the conventional cell (either may be used). The reciprocals of these intercepts are then multiplied by a scaling factor that makes each reciprocal an integer and also makes each integer as small as possible. The resulting set of numbers is called the Miller index of the surface. For the example in Fig. 4.4, the plane intersects the z axis of the conventional cell at 1 (in units of the lattice constant) and does not intersect the x and y axes at all. The reciprocals of these intercepts are(l/oo,l/oo,l/l), and thus the surface is denoted (001). No scaling is needed for this set of indices, so the surface shown in the figure is called the (001) surface. 

If the vector defining the surface normal requires a negative sign, that component of the Miller index is denoted with an overbar. Using this notation, the surface defined by looking up at the bottom face of the cube in Fig. 4.4 is the (001) surface. You should confirm that the other four faces of the cube in Fig. 4.4 are the (100), (010), (100), and (010) surfaces. For many simple materials it is not necessary to distinguish between these six surfaces, which all have the same structure because of symmetry of the bulk crystal. ... 

This surface is therefore the (111) surface. This surface is an important one because it has the highest possible density of atoms in the surface layer of any possible Miller index surface of an fee material. Surfaces with the highest surface atom densities for a particular crystal structure are typically the most stable, and thus they play an important role in real crystals at equilibrium. This qualitative argument indicates that on a real polycrystal of Cu, the Cu(l 11) surface should represent a significant fraction of the crystal s surface total area. 

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