Axial set

We may describe the centrosymmetric structure in Scheme 10c in terms of the alternative, left-handed axial system by choosing the reverse vectors —a, -b, -c as the axial set, as shown in Scheme lOg. The whole arrangement remains unchanged, the only difference being that the molecules S and R are now described by coordinate sets x y z, and —x —y —z respectively. By symmetry the same applies to the nonisometric arrangement (Schemes IQf and h). 

Finally, if setting proves difficult, it is quite possible (and without inordinate difficulty) to index the diffraction pattern of a crystal in a completely random setting, by a procedure (Turner-Jones and Bunn, 1944) based on the same principle as the tilted crystal method described on p. 174. This may be useful for crystals grown in sealed tubes, when the orientation taken up by the crystal happens to be inconvenient for axial setting. 

In the example of the regular tetrahedron, (Figures 4.5a, 4.6), the principle symmetry element is the 4 axis, which is put in the primary position in the point group symbol, and defines the [100] direction of the cubic axial set. The rotation triad (3) lies along the (111) directions... 

Nespolo M, Takeda H, Kograe T, Ferraris G (1999c) Periodic interrsity distribntion (PID) of mica polytypes Symbohsm, stmctural model orierrtation and axial settings. Acta Crystallogr A55 659-676 Newrrham RE (1961) A refinement of the dickite stmcture and some remarks on polymorphism of the kaolin minerals. Minerd Mag 32 683-704... 

Figure 13. Definition of the S, and axial settings of mica polytypes.

Subclass must be taken into account. OD and Z symbols for non-orthogonal polytypes always correspond to (1/3, Q) (fflass a) or (0, 1/3) Class b). The PID is most conveniently expressed in the axial setting, which corresponds to c = (1/3, 0) or... 

Finally, in Class b the axes exchange a b expresses PID in the F axial setting. 

Mechanical circulation can be accomplished internally by plug fans (usually in the roof) with the driving motor outside the furnace and a drive shaft extending through the roof to an axial set of blades within the furnace. Materials limitations restrict this method to rather low temperature furnaces. 

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