Crystalline solids structural relationships

Crystalline solids display a very regular ordering of the particles in a three-dimensional structure called the crystal lattice. In this crystal lattice there are repeating units called unit cells. Figure 12.1 shows the relationship of the unit cells to the crystal lattice. 

Many crystalline solids can undergo chemical transformations induced, for example, by incident radiation or by heat. An important aspect of such solid-state reactions is to understand the structural properties of the product phase obtained directly from the reaction, and in particular to rationalize the relationships between the structural properties of the product and reactant phases. In many cases, however, the product phase is amorphous, but for cases in which the product phase is crystalline, it is usually obtained as a microcrystalline powder that does not contain single crystals of suitable size and quality to allow structure determination by single-crystal XRD. In such cases, there is a clear opportunity to apply structure determination from powder XRD data in order to characterize the structural properties of product phases. 

Using structural data obtained from neutron diffraction studies for 41 different crystalline solids, the following linear relationship was reported [70] ... 

The behaviour of crystalline solids is not always defined explicitly, because their properties depend on structure, size and shape of crystals and on the admixture of contaminating components. The following account is aimed mainly at the characteristic properties of pure substances (minerals) with reference to the effect of impurities, wherever the respective relationships are of more general validity. 

Furthermore, the driving force for the phosphorus enrichment on the CV0)2P20 surface is not clear yet. In the study of Arnold and Sundaresan [10] on the influence of water on the catalytic properties of a non-equihbrated VPO catalyst the hydrophilicity of phosphorus was supposed to be a reason for it but this assumption has not yet been proven. It was found that the addition of water vapour to the feed lowers the overall activity towards butane oxidation and enhances the selectivity towards partial oxidation products. The addition of steam accelerated the formation of (V0)2P207 in the solid structure which originally contained approximately equal amounts of a-V0P04 and (V0)2P207 crystalline phases [10]. However, the (V0)2P207 phase is the only crystalline phase in an equilibrated VPO catalyst with a P V ratio of 1.1 as used in [10]. Recently Cavani and Trifiro emphasized [2] that only a study of equilibrated catalysts provides precise information on the relationships between activity and selectivity and the structural properties of vanadylpyrophosphate catalysts. 

Ma, H.-S., A.P. Roberts, J.-H. Prevost, R. Jullien, and G.W. Scherer. 2000. Mechanical structure-property relationship of aerogels. Journal of Non-Crystalline Solids 277(2-3) 127-141. 

Ma, H.-S., J.-H. Prevost, R. Jullien, and G.W. Scherer. 2001. Computer simulation of mechanical structure-property relationship of aerogels. Journal of Non-Crystalline Solids 285(1-3) 216-221. Meador, M.A.B., A.S. Weber, A. Hindi, M. Naumenko, L. McCorkle, D. Quade, S.L. Vivod, G.L. Gould, S. White, and K. Deshpande. 2009. Structure-property relationships in porous 3D nanostructures epoxy-cross-linked silica aerogels produced using ethanol as the solvent. ACS Applied Materials and Interfaces 1(4) 894—906. 

Woignier, T., J. Reynes, A. Hafidi Alaoui, I. Beurroies, and J. Phalippou. 1998. Different kinds of structure in aerogels relationships with the mechanical jnoptaties. Journal of Non-Crystalline Solids 241(1) 45-52. 

A central tenet of materials science is that the behavior of materials (represented by their properties) is determined by their structure on the atomic and microscopic scales (Shackelford, 1996). Perhaps the most fundamental aspect of the structure-property relationship is to appreciate the basic skeletal arrangement of atoms in crystalline solids. Table 2.21 illustrates the fundamental possibilities, known as the 14 Bravais lattices. All crystalline structures of real materials can be produced by decorating the unit cell patterns of Table 2.21 with one or more atoms and repetitively stacking the unit cell structure through three-dimensional space. 

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