Stacking of 111 planes

Figure 9.8 Stacking of 111 planes in spinel viewed along (211). AqBoCq refers to oxygen stacking, ABC to Al stacking in the Kagome layers, abc to Al stacking in the mixed cation...

As depicted in Fig. 2.7(a), when the structure of a fully oxidized CcgZrsOg pyrochlore is projected along any direction perpendicular to the <111> direction, the distribution of the cation sublattice can be easily described in terms of a stacking of 111 planes. Two variants of these 111 planes are present a Zr-rich one and a Ce-rich... 

This is achieved by coupling the system to a suitably defined order parameter that is sensitive to the crystal order (the stacking sequence of 111 planes in this case), and doing umbrella sampling with this quantity. The result of the simulation is the free energy difference between both candidate structures—and the winner is fed... 

Dislocation movement in copper is described by a slip plane 111 and a slip direction, the direction of dislocation movement, [110]. Each 111 plane can be depicted as a hexagonal array of copper atoms (Fig. 3.11a). The stacking of these planes is represented by the sequence. .. ABC. .. where the first layer is labeled A, the second layer, which fits into the dimples in layer A is labeled B... 

Diamond has two basic crystal stmctures, one with a cubic symmetry (more common and stable) and the other with a hexagonal symmetry (rare but well established, found in nature as the mineral lonsdaleite). The close-packed layers, 111 for cubic and 100 for hexagonal, are identical. The cubic structure can be visualized as stacking of puckered planes of six-membered saturated carbon rmgs man EO EO sequence along (111) direction, referred to as 3C diamond (Fig. 1). All ofthe rings exhibit the chair... 

Fig. 3.58 SF formation a the FCC stacking of slip planes before removal of a plane b the stacking sequence of the 111 planes is modified at the region where the fault exists from the FCC to an HCP structure c the sequence before the insertion of an additional plane (indicating the place of insertion) d the re-insertion of the plane produces a thin FICP structure...

Partial dislocations can form not only by splitting a perfect dislocation, but also by inserting or partly removing a 111 plane. In Fig. 3.58a, the FCC stacking of slip planes is illustrated schematically before the removal of a plane. The sequence of the stacking of the 111 planes is modihed at the region where the fault exists from the FCC to a hexagonal closely-packed [henceforth HCP] structure, as seen in Fig. 3.58b. 

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...

The difference between the fee and hep structure is best seen if one considers the sequence of dose-packed layers. For fee lattices this is the (111) plane (see Figs. 5.1 and 5.3), for hep lattices the (001) plane. The geometry of the atoms in these planes is exactly the same. Both lattices can now be built up by stacking dose-packed layers on top of each other. If one places the atoms of the third layer directly above those of... 

For the evaluation of the response of the sensor, we selected several vapors of different polarity. The vapors included water (H20), acetonitrile (ACN), toluene, and dichloromethane (DCM). Solvent polarity and refractive index of tested vapors are listed in Table 4.346 47. The spectral range for the evaluation of the vapor responses of the colloidal crystal film was selected as 700 995 nm, which covered only the fundamental Bragg diffraction peak on the (111) planes of the colloidal crystal film to further reduce effects from possible stacking defects in the film as suggested in the literature44. 

A surface reconstruction containing the same structural elements as the one of Au(lll) has been recently found in Pt(lll) above 1330K [12] or under an excess of Pt adatoms at 400 K [13]. The reconstructed surface layer has an atomic density larger than a (111) plane in the bulk. Regions of fee and hep stacking are separated by bright double dislocation lines along [112], which, contrary to Au(lll), can meet and form a network structure with star-like features [13]. 

Another two-dimensional C60 polymer phase is the rhombohedral phase, in which the (111) plane of the original fee C60 lattice is the polymerized plane (Fig. 11). If the unit in the rhombohedral cell is spherical or, at least, has a six-fold symmetry along the axis perpendicular to the plane, the stacking sequence is unique. However, each polymerized C60 unit only has a three-fold symmetry along the axis, and there can be two different ways of stacking, ABC and ACB , where B and C correspond to the polymerized plane with the C60 positions above the B and C sites in Fig. Irrespectively [39]. 

The most common substrates for the growth of cubic P-GaN have been GaAs and 3C-SiC, discussed in Datareviews A7.7 and A7.8 respectively. There have been some structural studies of P-GaN films grown on Si (001) [8] and MgO [1]. The major defects in the cubic material are stacking faults along the 111 planes and perfect edge dislocations at the interface [1,8-11]. 

Figure 11.51 Schematic illustrating how intrinsic stacking faults along i.e. faults in the successive stacking of the ABC layers ( 111 planes) of an fee crystal, give rise to a hep region. The black dots represent atoms in the 110 plane while the grey dots represent atoms immediately below. Reproduced with permission from reference [128]. (2008) Wiley-VCH Verlag GmbH Co. KGaA.

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