Crystal symmetry and X-ray diffraction

Dunitz, J.D. X-Ray analysis and the Structure of Organic Molecules, 1995, 2nd corrected reprint, Verlag Helvetica Chimica Acta, Basel, p. 25. 

Scatter, v.t. i.. 1. send, go, in different directions... 2. throw or put in various directions... 

Gatenby, E.V. Wakefield, H. The Advanced Learner s Dictionary of Current English, 1973, Oxford University Press, London. 

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Fluorapatite (FA) corresponds to the chemical formula Caio(P04)eF2 and crystallises in the hexagonal space group PGs/m, with Z = 1 and unit-cell parameters a = b = 9.367 A and c = 6.884 A [1] (Fig. 2). From a structural viewpoint, fluorapatite is often considered as a crystalline model for other apatites and is seen as a reference apatitic array [2]. It is one of the very first apatite structures to have been solved. It has been thoroughly studied since the 1930s [3] and is well documented in the literature. In particular, Sudarsanan et al. [1] reported the single crystal refinement of X-ray diffraction (XRD) data, and the detailed description of atomic positions and local symmetry is fully available [4,5],... 

Tetrachlorohydroquinone (45) is closely related to chloranil and might be expected to show overcrowding effects similar to those found in chloranil by Ueda. The crystal structure of tetrachlorohydroquinone has been investigated by Sakurai (1962) using nuclear quadrupole resonance and X-ray diffraction techniques. The crystal makes use of the molecular centre of symmetry and the asymmetric unit consists of half a molecule. The analysis shows that the C—O bond deviates by 0-9° from the aromatic plane and that the two adjacent C—Cl bonds are also bent out of the benzene plane, in the same direction, through 0-8°. (This is reminiscent of Harding and Wallwork s findings for chloranil in the hexamethylbenzene-chloranil complex.) Sakurai... 

Obviously, much of the development of crystallography predates the discovery of diffraction of X-rays by crystals. Early studies of crystal structures were concerned with external features of crystals and the angles between faces. Descriptions and notations used were based on these external features of crystals. Crystallographers using X-ray diffraction are concerned with the unit cells and use the notation based on the symmetry of the 230 space groups established earlier. 

In further comparing LEED and X-ray diffraction we recall that in X-ray diffraction one has ancillary information that is essential in structural analysis. One knows the density of the crystal, the chemical composition, the size of the unit cell and its symmetry. In LEED, comparable data are much more difficult to obtain. For example, the density of a surface structure is not measurable at all. The chemical composition after adsorption can often be inferred reliably from total gas exposure of a clean surface or from changes of symmetry of a LEED pattern, but it is never available as a separate datum. In X-ray diffraction, dimensions of the unit cell are easily found. In LEED, even the unit mesh size, as will be shown in Section IV, cannot in some cases be deduced with certainty. Multiple diffraction can sometimes cause beams which lead to a wrong assignment of unit mesh. 

It was reported recently, that polymeric can also form quasicrystals. Hayashida et al. [50] demonstrated that certain blends of polyisoprene, polystyrene, and poly(2-vinylpyridine) form starshaped copolymers that assemble into quaskrystals. By probing the samples with transmission electron microscopy and X-ray diffraction methods, they conclude that the films are composed of periodic patterns of triangles and squares that exhibit 12-fold symmetry. These are signs of quasicrystalline ordering. Such ordering differ from conventional crystals lack of periodic structures yet are well-ordered, as indicated by the sharp diffraction patterns they generate. Quasi-crystals also differ from ordinary crystals in another fundamental way. They exhibit rotational symmetries (often five or tenfold). There are still some basic questions about their stracture. 

However, while the crystal structure of [Cl3ln P(m-anis)3 2] determined by X-ray crystallography is in line with the solid-state NMR data, this is not the case for [Cl3ln P(p-anis)3 2]. Both compoimds have been found to have only one independent position for the phosphorus atoms, i.e. all P positions are related by symmetry. We should therefore expect one resonance as is seen for [Cl3ln P(m-anis)3 2]. So why are there two resonances for [Cl3ln P(p-anis)3 2] The single crystalline material contains solvent dichloromethane molecules, while the powdered samples do not (as was proven by elemental analysis). Despite the fact that both NMR and X-ray diffraction studies were of the solid state, they have actually been carried out with two chemically different materials with different structures. 

Newman projection in Figure 26. The prevailing form in the vapour phase is the same as the one found in the crystal phase by X-ray diffraction (Jordan, Smith, Lohr and Lispcomb, 1963) addition to form I, a smaller amount of form II was also detected by electron diffraction. Both forms have 0 symmetry and their ratio is 4 1. The corresponding radial distributions are also shown in Figure 26. The geometrical parameters determined by the two cited investigations are collected in Table 19 ... 

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