Planar tilings

Consider tile free radicals CHj and CFj. One is planar, the other pyramidal. Which is which Why ... 

The crucial hypothesis is the fourth one. It excludes hyperbolic tilings of the plane, like those which we can see in some of Escher art (planar ones but we cannot draw them with given metric constraints). 

Tile diulkylgold halides are dimeric, having die planar structure ... 

Compound 6-XXVII can be obtained from xylene, toluene or benzene as superb, long, very dark blue-black needles with metallic lustre . A brilliant scarlet form can be obtained from polar solvents such as acetic acid, DMF or DMSO. The black form can be converted to the red form both photophysically and thermally (abruptly at 139-142°C) (Begley et al. 1981). The two structures are shown in Fig. 6.14. In the black form, the molecules form infinite stacks ( in the manner of roof tiles ) in the ac plane with intermolecular contacts of 3.31 A which the authors attribute to charge-transfer interactions. The stacking is absent in the scarlet form, and the molecular conformation is considerably more non-planar, making this pair of structures also conformational polymorphs. No mechanism for the conversion or colour difference has been proposed. 

Various approaches to the enumeration of connectional isomers have been discussed folding and gluing of a planar lattice section in every possible way, the application of tiling mles,3i,32 the application of hexagon matrix rules, and oth-erg 12,38 appears to have been only one report giving explicit enumeration... 

Tile - Agn and Aig - > Em transitimis are allowed, with the Aig - > Em tmhdtion expected to have consukrably greater intendty. Thus a three-band charge tiansfer spectrum, with an intendfy order - Em > A A m > A g - Bia, should be tyincal oi square planar complexes with cas 2 type figands. 

Question If tile triphenylphosphine molecule were planar, what would be its point group ... 

This is the first time that the name unit cell has been used, a name that seems innocuous enough. In fact, some care is needed in its use because there is no unique definition of unit cell for any crystal structure. For any crystal structure there is an infinity of acceptable choices of unit cell—the only requirement on it is that it contains one primitive structural unit and that it generates the entire crystal by translation operations alone. A unit cell need not have six faces and its faces need not be planar (just as tiles with curved edges can cover a surface). It is often convenient to choose as unit cell a volume defined by the primitive translation vectors themselves but, equally, for other purposes this can be an inconvenient choice. 

The assembly of hexagonal molecules is a good method for obtaining well-defined supramolecular architectures, and is known as molecular tiling. However, the concept has mainly been applied to planar polyaromatic... 

Fig. 38. Metadislocation in Al72.oPd22,8Fe5,2 associated with three planar defects in a -host structure, (a) TEM micrograph, (b) Corresponding idealized tiling representation.

Fig. 43. High-resolution HAADF micrograph of a (100) planar defect in edge-on orientation located between the dashed hnes, and superposed tilings for the T- and R-phases.

Fig. 44(a) shows a HAADF micrograph of a metadislocation in T-Al-Mn-Pd. The planar defect at the right-hand side, that is the slab of R-phase, is visible between the dashed lines. The metadislocation core is indicated by a polygon, which directly corresponds to the predicted polygon representing a metadislocation core [cf. Fig. 42(d)]. In addition three phason defects are visible at the left-hand side of the metadislocation core. Fig. 44(b) shows a full tiling representation of the defect. 

It is obvious that the core structure of the experimental [Figs 44(a) and 44(b)] and predicted [Fig. 42(d)] metadislocation are represented by the same tile. Hence they both have the same Burgers vector. However, they are connected to different types of planar defects. While the metadislocation in Fig. 42(d) is associated with six phason planes, the metadislocation in Fig. 44(b) is associated with a slab of R-phase. The phason elements on the left-hand side of the metadislocation core change the stacking sequence of the ideal T-phase structure A,B,A,B,A to a sequence A,A,A,B,B. These additional defects are required to accommodate the symmetrical metadislocation core into the structure and have to move along with the latter. In other words, the three phason lines act as escort defects to the metadislocation core, which move ahead and clear the way for the latter. Upon movement, the metadislocation locally transforms the T-phase structure, leaving a slab of modified R-phase in its wake. Different types of metadislocations in T- and R-phase structures and their modes of motion are discussed in Section 6.4. 

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