Book: Intermetallic Chemistry
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3.6.1.3.2 Examples of alternative descriptions of the unit cell
In a number of cases, in order for instance, to compare a given atomic distribution and arrange-
ment with several others, it may be useful to use different descriptions of the same
structure (to refer to different, but obviously equivalent, unit cells). The transfor-
mations (of the unit cell constants and, consequently, of the coordinates of the atomic
positions) are described, for the general case, for instance, in the International Tables
(Hahn 2002). A few, frequently used, transformation formulae of the unit cell con-
stants are reported here.
Description of a rhombohedral unit cell in terms of the equivalent, triple-primitive,
hexagonal cell (see Fig. 3.9).
A detailed example of the alternative descriptions of a given compound, both in
terms of its hexagonal unit cell and of the corresponding rhombohedral primitive
cell is presented in Chapter 4: the rhombohedral compound Mo6PbS8 (the proto-
type of the family of the so-called Chevrel phases) is described and unit cell con-
stants and atomic positions are listed for its conventional hexagonal cell and for the
rhombohedral primitive cell.
The rhombohedral cell has a nearly cubic shape (αr 90°) when ch/ah
( 3/2) 1.2247…
Description of a hexagonal unit cell (ah, ch cell edges) in terms of an ortho-
hexagonal cell (equivalent orthorhombic cell a0, b0, c0) (see Fig. 3.10).
Description of a cubic (primitive, body centred or face centred) unit cell (ac) in
terms of the equivalent, primitive rhombohedral, (ar, ) and triple-primitive hexag-
onal, cells (ah, ch). See Fig. 3.11.
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