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**Up:** Notations Used for Representing Close-Packed Structures
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If the layers in a close-packed structure are projected on to one of the close-
packed planes, the atoms fall into one of the three possible positions A, B and
C with *xy* coordinates 00, and
respectively. The passage from A B
C A involves a vector translation of in
the basal plane, whereas the passage from A C
B A involves a vector translation of , =
, (fig. 1). Hgg^{9} therefore denoted the
former by a plus sign (+) and the latter by a minus sign (-). A structure
such as ABCB is thus represented as ++-. The relationship between the three
orientations, A, B and C of the close-packed layers may also be visualized in
terms of clockwise or anticlockwise rotation about [00.1] through 60.
Frank^{10} used the symbols and for the
two rotations. Thus the symbol implies a cyclic change
A B C A and the symbol
implies an anticyclic change. No compactness results from the use of these +
and - or and symbols for representing a
close-packed structure because their number remains the same as the number of
layers in the ABC sequence of the structure. Zhdanov^{11} therefore suggested
summing up the consecutive + (or ) and - (or )
signs and putting them down in numeral figures. Thus the 6*H* SiC
structure having the ABC sequence ABCACB and a Hgg^{9} sequence +++-- is denoted by the symbol (33) in the Zhdanov notation.

Ramsdell^{8} interpreted the Zhdanov symbols in terms of the zig-zag sequence
of Si and C atoms in the (110) planes of SiC structure. These
planes contain all the atoms of the structure since the three symmetry axes
parallel to [001] all lie in this plane. Figure 10 illustrates the meaning of
the zig-zag sequence, taking the 6*H* (33) structure of SiC as example. If
a Si or C atom lies on A in one layer, the next must be either to the right on
B, or to the left on C. If to the right, the third layer may have its atom
continue to the right or it may change direction and go to the left. Because of
these repeated changes, a zig-zag pattern results. Such an arrangement can be
described in terms of the number of layers added in each direction in succession
and has been called the `zigzag sequence` by Ramsdell. The unit cell is
completed after arriving at an identical atom having the same environment as the
atom from which one started. Thus in Fig. 10 the unit-cell of 6*H* is
completed at 2 and not at 1. The Zhdanov notation is by far the most convenient
and concise notation to describe close-packed structures.

**Copyright © 1981, 1997 International Union of
Crystallography**