Determination of Space Group and Crystal Structure

As menhoned above, the unit cell of a crystalline specimen can be determined by SAED. However, the accuracy of the unit cell dimensions obtained is largely dependent upon the calibrahon of camera length, which is a funchon of specimen position and the conditions of the microscope. The procedure is complicated, and in most cases the unit cell parameters determined by SAED are less accurate than those obtained from XRD or neutron diffraction. Owing to the mulhple scattering problem, determination of space group by SAED is less reliable. Consequenhy, HRTEM is not an ideal technique for final determination of crystal structure. 

The crystal structures of hematite and corundum have been determined through the use of Taue and spectral photographs, interpreted with the aid of the theory of space groups. The unit of structure is a rhombohedron with a = 55° 17 and a = 5.420 = = 0.010 A. for hematite, and with a = 55° 17 and a = 5.120 = = 0.010 A. for corundum. The space group underlying the atomic arrangement is D. ... 

The result is that Factor III of 2.2.6. given above imposes further symmetry restrictions on the 32 point groups and we obtain a total of 231 space groups. We do not intend to delve further into this aspect of lattice contributions to crystal structure of solids, and the factors which cause them to vary in form. It is sufficient to know that they exist. Having covered the essential parts of lattice structure, we will elucidate how one goes about determining the structure for a given solid. 

Space lattices and crystal systems provide only a partial description of the crystal structure of a crystalline material. If the structure is to be fully specified, it is also necessary to take into account the symmetry elements and ultimately determine the pertinent space group. There are in all two hundred and thirty space groups. When the space group as well as the interatomic distances are known, the crystal structure is completely determined. 

A further report dealt with the synthesis, variable temperature magnetic susceptibility measurements, and crystal structure determination at various temperatures (115, 136, 140, 150 and 231 K space group P-1) of [Fe(isoxa-zole)6][Fe(isoxazole)4(H20)2](BF4)4 [73]. The molecular structure of this well-defined double salt consists of two mononuclear Fe(II) dications,... 

The structures of the radical cation salts of the TTF derivatives were determined by X-ray crystallographic analyses <1997SM1871>. The (CIO4) and (SbFs) salts of 45 presented, respectively, as monoclinic CZIm space group) and triclinic (FI space group) black single crystals. A coplanar 2-D network characterized by short intermolecular S- N (3.27 A) and S- S (3.58 A) contacts and a column structure formed by a dimer of the donor 45 with... 

During the last five years, a powerful new method of getting crystal structural information from powder diffraction patterns has become widely used. Known variously as the Rietveld method, profile refinement1, or, more descriptively, whole-pattern-fitting structure refinement, the method was first introduced by Rietveld (X, 2) for use with neutron powder diffraction patterns. It has now been successfully used with neutron data to determine crystal structural details of more than 200 different materials in polycrystalline powder form. Later modified to work with x-ray powder patterns (3, X) the method has now been used for the refinement of more than 30 crystal structures, in 15 space groups, from x-ray powder data. Neutron applications have been reviewed by Cheetham and Taylor (5) and those for x-ray by Young (6). 

In the X-ray analysis of a crystal structure the first step is the determination of the space group and the number of molecules in the unit cell. Occasionally it may be immediately apparent from such data that the molecule itself possesses certain elements of symmetry, and these may define or at least limit the possible molecular conformations. The elements most commonly found in aromatic molecules are centres of symmetry and twofold rotation axes. It might have been expected that the plane of symmetry would manifest itself in aromatic systems, but this is disappointingly rare. Indeed, amongst the structures reviewed here the only cases where a crystallographic symmetry plane coincides with that of a planar molecule occur in s-triazine and pyrazine (see Section V, A, 5). 

X-ray investigations of the structure of benzene began in 1923 when Broome took the first X-ray powder photographs of the molecule. Later, Cox (1928) determined the cell dimensions and space group and showed that the molecule was at least centrosymmetric. The development of the work on the benzene structure has been reviewed by Cox (1958). A more detailed paper on the crystal structure of benzene at — 3°C (Cox et al., 1958) has established that the benzene molecule does not deviate significantly from the 6jmmm symmetry predicted by chemical theory, the maximum deviation of the carbon atoms from the mean molecular plane being 0-0013 A. 

As part of a study of biscyclic dibenzacridines, the crystal structure of 1,2-8,9-dibenzacridine (72) has been investigated by Mason (1957, 1960). The space group was shown to be Pna2v thus, with four molecules in the unit cell, no molecular symmetry is required. The structure was determined from an examination of the weighted reciprocal lattice and trial and error methods, refinement being by two-dimensional least-squares procedures. At the conclusion of the analysis,... 

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