Close-packing, atoms

Second, as their size increases, these adislands can be limited by two kinds of close-packed atomic rows corresponding to two different types of microfacets (001) for type A and (HI) for type B. In the above mentioned experiments, Wang and Ehrlich have shown that triangular Ir trimers with type B borders are energetically favoured. 

Many metals have close-packed structures, with the atoms stacked in either a hexagonal or a cubic arrangement close-packed atoms have a coordination number of 12. Close-packed structures have one octahedral and tivo tetrahedral holes per atom. 

Crystal approximants. Several crystalline phases contain more or less closely packed atomic assemblies (polyhedra, clusters) which have been considered fundamental constituents of several quasicrystals, metal glasses and liquids. Such crystalline phases (crystal approximants), as reported in the previous paragraph, are often observed in the same (or similar) systems, as those corresponding to the formation of quasicrystals and under similar preparation conditions. Crystalline phases closely related to the quasicrystals (containing similar building blocks) have generally complex structures as approximants to the ico-quasicrystals we may, for instance, mention the Frank-Kasper phases (previously described in 3.9.3.1). 

Adatom diffusion, at least under the low temperature of field ion microscope measurements, almost always follows the direction of the surface channels. Thus adatoms on the W (112) and Rh (110) surfaces diffuse in one direction along the closely packed atomic rows of the surface channels. Such one-dimensional surface channel structures and random walks can be directly seen in the field ion images, and thus the diffusion anisotropy is observed directly through FIM images. Unfortunately, for smoother surfaces such as the W (110) and the fee (111), no atomic or surface channel structures can be seen in field ion images. But even in such cases, diffusion anisotropy can be established through a measurement of the two-dimensional displacement distributions, as discussed in the last section. Because of the anisotropy of a surface channel structure, the mean square displacements along any two directions will be different. In fact this is how diffusion anisotropy on the W (110) surface was initially found in an FIM observation.120... 

The concept of additivity is unsatisfactory when applied to closely packed atoms in a condensed body. In this case, a new approach to the energy of interaction needs to be developed or a modification of Hamaker s constant is desirable. 

The (110) surfaces of Au [24], Pt [25] and Ir [26] display (2 x 1) LEED patterns, which are described by missing row reconstructions, in which every other closed-packed atomic row along [110] is missing. The driving force in this case seems to be the formation of (111) microfacets with their lower surface energy [22]. The resulting ID channels have been used as a template for assembling molecular wires , e.g. of the amino acid cysteine [27]. 

Dipole-dipole interactions have been used to assess the conformational populations of 2-haloketones (Eliel et al., 1965). With respect to SS, however, there are few applications in which these and related effects are considered. It is interesting that dipole induction and London dispersion effects were used some thirty years ago to account for the high endo over exo preference in the Diels-Alder reaction (Wassermann, 1965). Although effects are small for any pair of atoms, there are many closely packed atoms in a Diels-Alder transition state. At a carbon-carbon distance of 2-0 a between the atoms to be bonded, the energy favoring endo addition is 2-7 for dipole induction and 3-4 kcal/mole for dispersion in the reaction of cyclopentadiene with p-benzoquinone (Wassermann, 1965). These nonbonding attractive energies cooperate with the secondary HMO effects discussed earlier to lead to an endo product. 

The 17 rare-earth metals are known to adopt five crystalline forms. At room temperature, nine exist in the hexagonal closest packed structure, four in the double c-axis hep (dhep) structure, two in the cubic closest packed structure and one in each of the body-centered cubic packed and rhombic (Sm-type) structures, as listed in Table 18.1.1. This distribution changes with temperature and pressure as many of the elements go through a number of structural phase transitions. All of the crystal structures, with the exception of bep, are closest packed, which can be defined by the stacking sequence of the layers of close-packed atoms, and are labeled in Fig. 18.1.1. 

The gliding motion of closed-packed atomic planes. 

Clusters of the semiconductor elements Si and Ge are much more dense than carbon clusters, but they are not spherical, either, as expected for closed packed atomic spheres. Si+ and Ge+ clusters are prolate with geometries based on stacked tricapped trigonal prisms [127-131]. At a certain cluster size (n 25 for SiJ) a structural transition occurs from prolate (n<25) to near spherical (n>25). Interestingly, clusters of tin, which is a metal at room temperature, exhibit very similar structures as Si and Ge, indicating that they are semiconductors as well [131,132]. Bulk Sn does have a semiconductor form (a-tin), that has the same diamond lattice as Si and Ge. Typical metal clusters appear to pack as tightly as possible and exhibit near spherical shapes as observed for the lead [131,133],indium [134],andgold [135] clusters. However, the smaller gold clusters AuJ (n<7) are completely planar [135]. 

Much effort has gone into developing theoretical expressions for A, which must reflect the temperature independence. The origin of this behavior can be seen by referring back to Figure 6.5. An appreciable local distortion of the lattice must take place, for example, before an interstitial jump can occur. Energy must be supplied to the lattice to cause closed-packed atoms to move apart and let the interstitial through. The difficulty with which this is accomplished constitutes the activation barrier to interstitial diffusion and it can be used to estimate A in Eq. 6.36. Thus, E in Eq. 6.35 has been described by ... 

Finally, the structural modifications of elemental boron exhibit complex extended lattices of cages in the solid state, whereas those of metals possess much simpler close-packed atomic lattices. These differences are a direct reflection of atomic properties and result in the respective nonmetallic and metallic behavior. However, boron combines with most other elements including metals. There are a wide range of metal borides known with stoichiometric as well as nonstoi-chiometric atomic ratios. The amazingly varied interpenetration of the two characteristic structural motifs and the subtly balanced competition between the two modes of solid state bonding found in the metal borides constitutes further justification of our theme. This is discussed in some detail in Section II,C. 

Fig. 4.12 (a) Sites created by layer I and available to accept atoms in layer 2. (b) Covering all sites by atoms in the second layer, making the t sites (relabeled o) unavailable for occupancy by close-packed atoms. 

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