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Standard Ionic Crystal StructuresSolid state chemistry involves the formation, motion, and interaction of defects within crystals. An appreciation of these factors involves, as a minimum requirement, a strong intuitive grasp of the structural relationships of the atoms and interstices of various crystal structures. Fortunately this minimum requirement can be readily acquired by limiting one's

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A computer investigation of the stability of clusters of substitutional xenon atoms in copper shows that xenon clusters are energetically unstable in the absence of adjacent vacancies in the surrounding copper lattice. The stability of various clusters increases as the ratio of vacancies to xenon atoms increases. The efficiency of the stabilization due to the vacancies is markedly affected by the geometrical distribution of the vacancies in the xenonvacancy clusters.Die Stabilitiit von substitutionellen Xenon-Atom-Clustern in Kupfer wurde mit Hilfe einer elektronischen Rechenanlage untersucht. Es ergab sich, daO die Xenon-Cluster ohne die gleichzeitige Anwesenheit von den Clustern angegliederten Leerstellen instabil gegen den Zerfall in isolierte Defekte sind. Die Stabilitiit der verschiedenen Cluster ist um so groOer, je groOer das Verhiiltnis von Leerstellen zu Xenon-Atomen ist. Die stabilisierende Wirkung der Leerstellen hiingt wesentlich von ihrer riiumlichen Verteiliing ab.

The foundation of an abstract algebra for the description of crystal structures is developed in terms of ideally closest-packed structures. All the spatial information of closest-packed structures can be derived in terms of (a) the geometry of the atoms (A positions) and the plane, triangular interstices (B and C positions) of a closest-packed p6mm monolayer, and (b) the permutations induced among these A, B, and C positions by translations from one monolayer midplane to another. The mathematical device used to correlate this information is a translation-permutation vector operator. Since this operator is closely related to the basic concept of a layer-by=layer crystal growth process, the algebra is readily extensible to crystal structures that are defective owing to many kinds of non-periodic elements of structure. Some examples are presented of the application of the algebra to closest-packed structures that are either ideal or exhibit one of two kinds of defect: classical stacking faults or point defects.

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