Lattice registry

Incoherent Clusters. As described in Section B.l, for incoherent interfaces all of the lattice registry characteristic of the reference structure (usually taken as the crystal structure of the matrix in the case of phase transformations) is absent and the interface s core structure consists of all bad material. It is generally assumed that any shear stresses applied across such an interface can then be quickly relaxed by interface sliding (see Section 16.2) and that such an interface can therefore sustain only normal stresses. Material inside an enclosed, truly incoherent inclusion therefore behaves like a fluid under hydrostatic pressure. Nabarro used isotropic elasticity to find the elastic strain energy of an incoherent inclusion as a function of its shape [8]. The transformation strain was taken to be purely, dilational, the particle was assumed incompressible, and the shape was generalized to that of an... 

It is noted in Sections XVII-10 and 11 that phase transformations may occur, especially in the case of simple gases on uniform surfaces. Such transformations show up in q plots, as illustrated in Fig. XVU-22 for Kr adsorbed on a graphitized carbon black. The two plots are obtained from data just below and just above the limit of stability of a solid phase that is in registry with the graphite lattice [131]. 

To obtain a reliable value of from the isotherm it is necessary that the monolayer shall be virtually complete before the build-up of higher layers commences this requirement is met if the BET parameter c is not too low, and will be reflected in a sharp knee of the isotherm and a well defined Point B. For conversion of into A, the ideal adsorptive would be one which is composed of spherically symmetrical molecules and always forms a non-localized film, and therefore gives the same value of on all adsorbents. Non-localization demands a low value of c as c increases the adsorbate molecules move more and more closely into registry with the lattice of the adsorbent, so that becomes increasingly dependent on the lattice dimensions of the adsorbent, and decreasingly dependent on the molecular size of the adsorbate. 

CAS Registry Number mol wt crystal system space group lattice constants, nm... 

In the conesponding model of an interface, when tire lattice parameters of the two phases in contact are different, there will be a dis-registry at the interface defined by... 

Figure 7 Projections of atoms from the bottom (solid circles) and top (open circles) surfaces into the plane of the walls. (A through C) The two walls have the same structure and lattice constant, but the top wall has been rotated by 0°, 11.6°, and 90°, respectively. (D) The walls are aligned, but the lattice constant of the top wall has been reduced by 12/13. The atoms can only achieve perfect registry in the commensurate case (A). Reprinted with permission from Ref. 14.

Figure 4.10. Schematic representation of the possible modes of registry. Overlayer and substrate lattice points are depicted as dark grey and light grey balls, respectively, and the primitive cell vectors s, and o, are also indicated. Ag(llO) has been selected as substrate (Fm3m, a = 0.409 nm). Examples of (a) commensurate registry, (b) coincidence-IA registry, (c) coincidence-IB registry, (d) coincidence-II registry and (e) incommensurate registry.

Multilayers of Cd on Ti(0001) have been studied as well, indicating a Cd crystal growth according to the sequence. . acacABAB... the Cd film has the expected hep structure known for the bulk material. In this case the Ti and Cd lattice constants are sufficiently close to allow growth of the film in registry with the substrate mesh. 

Fig. 14. A grid superimposed on the basal plane of a triangular single-layer M0S2 nanocluster. The intersections of the white lines indicate the sulfur atomic positions on the basal plane. At the edges, the protrusions are observed to be shifted out of registry with the basal plane lattice. An STM line scan across the bright brim of the single-layer M0S2 nanocluster is illustrated on the right. The arrow indicates the direction and position of the scan in the image.

Phase CAS registry no. Crystal system Lattice constants, nm a b c Density, g/cm3... 

In some cases of localised adsorption the adsorbate is ordered into a two-dimensional lattice or net in a particular range of surface coverage and temperature. If the net of the ordered adsorbed phase is in registry with the lattice of the adsorbent the structure is called coherent, if not it is called incoherent (see also 1.2.4). 

Cases of chemisorption are known in which at high coverages the net (two-dimensional lattice) of the adsorbate is not in registry with the lattice of the adsorbent. In such situations, the concept of sites of precise location and fixed number may not be applicable. Similar difficulties about the definition of sites will occur if surface reconstruction takes place upon interaction of adsorbate and adsorbent. 

If a rotation operation must be included in order to bring two domains on a surface to coincide, we speak of rotational domains . If, by no means, a regular adlattice can be brought into a periodic relation with the underlying substrate lattice, the superstructure is incommensurate. In this case, the lateral interactions are so strong that the substrate registry cannot govern the lateral order. 

Noble-gas adsorption is often assumed to be the least complicated form of physisorption. However, on clean solid surfaces the molecular area may depend on the formation of ordered structures of the adsorbate in registry with the adsorbent lattice. 

Figure 9. Some of the more symmetrical registries of the benzene molecule with respect to the Ni(100) lattice plane. Although none of these registries can have as close a 1 1 correspondence of H—Ni atom positions as on the (111) surface (Figure 8), benzene appears to be more strongly bound (9) on this surface than on the (111)...

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