By M Ladd
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The crystallography of aperiodic crystals employs many recommendations which are frequently utilized to periodic crystals. the current textual content has been written lower than the belief that the reader understands options like area crew symmetry, Bragg reflections and vector calculus. This assumption is inspired by means of the popularity that readers attracted to aperiodic crystals will usually have a historical past within the strong country sciences, and by way of the truth that many books can be found that care for the crystallography of tronslational symmetric buildings at either introductory and complicated degrees.
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Additional resources for Crystal Structures: Lattices and Solids in Stereoview
45] based upon weighted cross-correlation (WCC) functions which are normalised and can be adapted to account for shifts in peak positions. The WCC procedure employs the concept of a ‘neighbourhood’, by which individual points in the profile are compared not just with exactly equivalent points in the reference profile, but also with points in the local neighbourhood, the scope of which is defined by a triangle function of specified width. Triangle functions that are narrow ignore the neighbourhood of the points in the profile, leading to strict requirements for similarity, while triangle functions that are broad lead often to uniformly high similarity values.
Taken to its extreme, cluster analysis can be made to show that each structure in a dataset is unique. At the other extreme, suitably liberal criteria will cluster all structures into a single group, without any discriminatory power. The most effective clustering level obviously lies somewhere between, and requires some level of input regarding how the results are to be interpreted. An effective procedure usually involves initial clustering into a small group of distinctly different clusters, which can then be sub-clustered to reveal more subtle differences.
4), together with a list of constraints on bond lengths, bond angles or bond torsion angles. 4 A generalised 3DSEARCH query containing three substructures (1–3) with four specified connections. ). The connections are defined between specified atoms in each substructure and can be constrained using a range of criteria (intra- or intermolecular, distance, angle, torsion). Reproduced from  by permission of the International Union of Crystallography criteria, such as particular interatomic distances.
Crystal Structures: Lattices and Solids in Stereoview by M Ladd