Aristotype structure

While all these structures derive from the elpasolite aristotype, the LisM Fe compounds (M = Al, Ga, Ti, V, Cr, Fe) exist at room temperature in two modifications. The Qf-form (e.g. Q -Li3AlF6 ) is still a strongly distorted variant of the elpasolite/cryolite family in which the coordination of all lithium ions is reduced to six. The jS-form, determined at -LiaVFe and confirmed by recent single-crystal work on the Al, Ga, Ti, and Cr compounds (Ref. 82 and literature cited... 

Table 1. List of structures derived from the rutile aristotype ordered by increasing values of a (see above figure). The coefficient f is a measure of the deformation of the octahedra.

Fig 7. Possible structures obtained from deformations of the perowskite aristotype by rotating the octahedra about the [111] direction. The patterns of the octahedra are characteristic of their respective height. 

Table 2. List of structures derived from the perowskite aristotype ordered by increasing values of(o.

This structure can be directly derived from the rutile aristotype with space group symmetry P42/mnm. From the data given above and in the appendix, sketch briefly the structure of CoRe04 and establish the group-subgroup diagram relating the two structures. 

Both structures can be derived from the a-Po aristotype. Their relationships can best be seen from a rhomboedral description of oc-Po wjth a cell volume three times the cubic cell and lattice parameters ar=4.75 and Cr=5.82 A. From the c/a ratio, it appears that the rhomboedral cell of y-Te is strongly compressed along the space diagonal whereas for a-Te it is slightly elongated relatively to the rhomboedral cell of a-Po. 

The structure of MgU04 can also be described from the rutile aristotype. The space group Imam is a ka subgroup of Cmmm, the space group of CoRe04. The I centering is a consequence of doubling the c-axis of a C-centered cell. 

According to the lUCr on-line dictionary, an aristotype is a high-symmetry structure type that can be viewed as an idealized version of a lower-symmetry structure. The lower-symmetry structure is called a hettotype." For example, CoRe04 crystallizes in the space group Cmmm, and the... 

If crystal structures are distorted and loose symmetry the description changes to another space group which may be a subgroup of the former space group. In such a way, interesting, mathematically well-defined relations can be demonstrated, which makes it possible to build structural family trees starting from an aristotype. ... 

Although the perovskite structure type is found for hundreds of compositions, most of these compounds are distorted from the aristotype cubic structure [1, 61, 62]. Octahedral tilting distortions are the most common type of distortion. They occur as... 

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