Stacking relations in the hexagonal ferrites and a new series of mixed-layer structures*

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Abstract
The six complex hexagonal and rhombohedral layer structures known as hexagonal ferrites can be derived by stacking three building-block types, S, R, and T, having 2, 3, and 4 anion layers, respectively. The anion framework of R and T contains stacking reversals after each layer; the stacking sequence of R is 1·1·1, T is 1·1·1·1. S has a spinel-like configuration; its stacking is designated 2. Larger structural units, RS and TS, have sequences of 1·1·3 and 1·1·1·3, respectively. The six known hexagonal ferrites consist of one or two of the stacking sequences 1·1·3, 1·1·1·3, and 1·1·5. The family is thus similar to a polytypic system; it involves, however, the stacking of chemically different layers. Single-crystal x-ray studies have disclosed four new structures which, together with three of the original phases, form a series of mixed-layer structures, RS…TS. The new structures are derived from the so-called Z phase, (RS TS)2 or (113 1113)2, by adding TS (1113) units, giving (RS TS)2 (TS)n or (113 1113)2 (1113)n. Weissenberg patterns have shown many syntactically intergrown crystals with n = 1, 2, 3, or 4, corresponding to the structures 84R, 102R, 40H, and 138R, respectively. Dimensions along c reach 331 Å. One-dimensional structure-factor and electron-density calculations confirmed the stacking model. Permutation of structural units within a given stacking sequence gives rise to additional phases, one of which has been observed. The remaining three original hexagonal ferrites comprise a second series, RS…S. Other series, combinations, and permutations may exist, giving a vast number of possible structures.

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