Crystals Miller Indices

Single crystal. Miller indices of face exposed. 

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). 

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... 

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 ... 

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). 

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. 

In many cases ordering is no longer observable in the presence of steps. Ordered carbonaceous layers form on the Ir(l 11) crystal face, for example, while ordering is absent on the stepped iridium surface. Ordering is absent on stepped Pt surfaces for most molecules that would order on the low Miller-Index (111) or (100) surfaces. 

Table 3.1. Wood and matrix notation for a variety of superlattices on low Miller index crystal surfaces...

Low Miller index surfaces of metallic single crystals are the most commonly used substrates in LEED investigations. The reasons for their widespread use are that they have the lowest surface free energy and therefore are the most stable, have the highest rotational symmetry and are the most densely packed. Also, in the case of transition metals and semiconductors they are chemically less reactive than the higher Miller index crystal faces. 

The metal substrates used in the LEED experiments have either face centered cubic (fee), body centered cubic (bcc) or hexagonal closed packed (hep) crystal structures. For the cubic metals the (111), (100) and (110) planes are the low Miller index surfaces and they have threefold, fourfold and twofold rotational symmetry, respectively. 

In the last few years LEED studies of high Miller index or stepped surfaces have become more frequent. Almost all of these studies have been on fee metals, where the atomic structure of these surfaces consists of periodic arrays of terraces and steps. A nomenclature which is more descriptive of the actual surface configuration has been developed for these surfaces, as described in Section III. In Table 5.5 the stepped surface nomenclature for several high Miller index surfaces of fee crystals has been tabulated. In Fig. 5.1 the location of these high Miller index surfaces are shown on the... 

By the use of mainly LEED and lately ion scattering techniques the location of many atomic adsorbates, their bond distances and bond angles from their nearest neighbor atoms have been determined. The substrates utilized in these investigations were low Miller Index surfaces of fee, hep and bcc metals in most cases, and low Miller Index surfaces of semiconductors that crystallize in the diamond, zincblende and wurtzite structures in some cases that could be cleaned and ordered with good reproducibility. 

The slice through a bulk crystal can differ from both the 111 plane and the 100 plane by small angles. This produces a kink in the face of the step. By an extension of the analysis that leads to step characterization, these kinks can also be characterized. For example, a plane with Miller indices 10,8,7 has 111 terraces seven atoms wide, 110 steps one atom high, and kinks of 100 orientation every two atoms. Because of the greater thermodynamic stability of the planes of low Miller index, these surfaces of ordered roughness are stable and can be prepared and studied. Since it is sensitive to periodicity over a domain about 20 nm in diameter, LEED sees the pattern associated with terraces of various widths and may be used to characterize these surfaces. Satisfactory LEED patterns do not require absolute uniformity of terrace width but may be obtained with experimental surfaces that display a distribution of widths. 

II. The Atomic Structure of Surfaces. Structures of Low and High Miller Index Crystal Surfaces. 5... 

Structures of Low and High Miller Index Crystal Surfaces... 

Platinum crystal surfaces that were prepared in the zones indicated by the arrows at the sides of the triangle are thermally unstable. These surfaces, on heating, will rearrange to yield the two surfaces that appear at the end of the arrows. There is reason to believe that the thermal stability exhibited by various low and high Miller index platinum surfaces is the same for other fee metals. There are, of course, differences expected for surfaces of bcc solids or for surfaces of solids with other crystal structures. 

Fig. 6. A stereographic triangle of a platinum crystal depicting the various high Miller index surfaces of platinum that were studied.

One of the most exciting observations of LEED studies of adsorbed monolayers on low Miller index crystal surfaces is the predominance of ordering within these layers (18). These studies have detected a large number of surface structures formed upon adsorption of different atoms and molecules on a variety of solid surfaces. Conditions range from low temperature, inert gas physisorption to the chemisorption of reactive diatomic gas molecules and hydrocarbons at room temperature and above. A listing of over 200 adsorbed surface structures, mostly of small molecules, adsorbed on low Miller index surfaces can be found in a recent review (/). 

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. 

The chemisorption of over 25 hydrocarbons has been studied by LEED on four different stepped-crystal faces of platinum (5), the Pt(S)-[9(l 11) x (100)], Pt(S)-[6(l 11) x (100)], Pt(S)-[7(lll) x (310)], and Pt(S)-[4(l 11 x (100)] structures. These surface structures are shown in Fig. 7. The chemisorption of hydrocarbons produces carbonaceous deposits with characteristics that depend on the substrate structure, the type of hydrocarbon chemisorbed, the rate of adsorption, and the surface temperature. Thus, in contrast with the chemisorption behavior on low Miller index surfaces, breaking of C-H and C-C bonds can readily take place at stepped surfaces of platinum even at 300 K and at low adsorbate pressures (10 9-10-6 Torr). Hydrocarbons on the [9(100) x (100)] and [6(111) x (100)] crystal faces form mostly ordered, partially dehydrogenated carbonaceous deposits, while disordered carbonaceous layers are formed on the [7(111) x (310)] surface, which has a high concentration of kinks in the steps. The distinctly different chemisorption characteristics of these stepped-platinum surfaces can be explained by... 

The chemisorption of acetylene, ethylene, benzene, and cyclohexane were also studied on the Ir(lll) and stepped Ir[6(111) x (100)] crystal surfaces (30). Chemisorption characteristics of the Ir(lll) and Pt(lll) surface are markedly different. Also, the chemisorption characteristics of the low Miller index Ir(l 11) surface and the stepped Ir[6(l 11) x (100)] surface are markedly different for each of the molecules studied. The hydrocarbon molecules form only poorly ordered surface structures on either the Ir(l 11) or stepped iridium surfaces. Acetylene and ethylene (C2H2 and C2H4) form surface structures that are somewhat better ordered on the stepped iridium than on the low Miller index Ir(l 11) metal surface. The lack of ordering on iridium surfaces as compared to the excellent ordering characteristics of these molecules on... 

These studies are beginning to produce important kinetic information only in recent years. We shall summarize the experimental information available from studies of these reactions on the stepped [6(111) x (100)] and low Miller index (111) crystal surfaces and compare the low- and high-pressure rates when these data are available. 

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