Crystals Containing Finite Complexes

Many finite complex ions found in crystals may exist also in aqueous solution (although there are a few, such as the Cf ion, which may not). In a number of cases, the structures of crystals containing complex ions 

Often ions may rotate within the crystal and, if the rotation is completely free, the spinning ion will occupy a spherical space of diameter equal to the maximum cross section of the ion. The nitrate, ammonium, and cyanide ions may rotate in favorable cases, but such rotation becomes inhibited at lower temperatures. Thus, the high-temperature forms of both ammonium nitrate and cesium cyanide have the same structure as cesium chloride. 

In some cases, if the complex ion is not too far from spherical, the compound may assume a structure similar to the simple ones already described, hut with slight distortion. In calcium carbide, for example, the layout of positive and negative ions is the same as in sodium chloride, but the nonspherical Cl ions are lined up with their axes parallel, distending one dimension of the square units to form rectangles. In potassium nitrate, again similar to the sodium chloride structure, the unit cell has been even further distorted from a perfect cube, all faces becoming rhombuses rather than squares. 

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Class III. Crystals containing finite, 1-, or 2-dimensional complexes bonded through m-m bonds... 

Finite complex ions include the numerous oxy-ions and complex halide ions, the aquo-ions in some hydrates (e.g. A1(H2 0)6 ), and all finite charged coordination complexes, in addition to the very simple ions such as CN , C2 , O2, O , and many others. Crystals containing the smaller or more symmetrical complex ions... 

There is much experimental evidence for the formation of complex oxy-ions in solutions of vanadates, niobates, and tantalates. We describe in Chapters 12 and 13 the structures of some crystalline vanadates here we note only certain finite complex ions which exist both in solution and in crystalline salts. The ion of Fig. 11.3(a) has been shown to exist in the salts Na7H(Nb60i9). 15 H20. Light scattering from an aqueous solution of Kg(Ta60i9). I6H2O indicates that the anion species contains 6 Ta atoms and is presumably similar to the ion in the crystal. ... 

The X-ray crystal structures of the related, though less complex, anticrown mercury-containing macrocycles 45 and 46 have also recently been reported. Complex 45 may form either 1 1 complexes with Br or I" or a 3 2 complex with Cr. In the case of the bromo derivative, crystallographic results reveal an infinite chain of alternating Br and 45 with each halide bridging between six Hg atoms, Hg- Br 3.07-3.39 A. It is postulated that the related 3 2 chloride complex exhibits a similar, though finite layered structure. The related pentameric species 46 forms... 

Another classification is based on the presence or absence of translation in a symmetry element or operation. Symmetry elements containing a translational component, such as a simple translation, screw axis or glide plane, produce infinite numbers of symmetrically equivalent objects, and therefore, these are called infinite symmetry elements. For example, the lattice is infinite because of the presence of translations. All other symmetry elements that do not contain translations always produce a finite number of objects and they are called finite symmetry elements. Center of inversion, mirror plane, rotation and roto-inversion axes are all finite symmetry elements. Finite symmetry elements and operations are used to describe the symmetry of finite objects, e.g. molecules, clusters, polyhedra, crystal forms, unit cell shape, and any non-crystallographic finite objects, for example, the human body. Both finite and infinite symmetry elements are necessary to describe the symmetry of infinite or continuous structures, such as a crystal structure, two-dimensional wall patterns, and others. We will begin the detailed analysis of crystallographic symmetry from simpler finite symmetry elements, followed by the consideration of more complex infinite symmetry elements. 

An X-ray beam, of a finite width, samples a small volume of the polymer structure. The diffraction pattern gives no information about the location of crystals within that volume, but it gives information about the range of crystal orientations in the volume this can be used with optical microscopy to build up a picture of the microstructure. The crystal lattice model, used to interpret diffraction patterns, contains many sets of parallel planes. Polymer crystals often have lower lattice symmetry than metals, so the relationship between the interplanar spacing d and the Miller indices hkl) of the plane are complex (Kelly and Groves, 1970). The Bragg condition... 

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