Structural Classification of Perovskites ‚ Nomenclature

Naming of Polytype Stacking

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The stacking sequence of a given structure is usually abbreviated by a notation of the form "hh" or "ccc". All layers of a unit-cell should be given in the sequence, unless repeated stackkings occur. E.g. in rhombohedral structures, the sequence is repeated three times, though the expression

hhc hhc hhc is identical to (hhc)₃.

A more symmetry-related, but rather unused notation has been worked out by

G.S. Zhdanov (Comptes Rendus de l'Academie des Sciences URSS 48, 39-42 (1945).

The general form of a sequence in this notation is:

p₁n₁p₂n₂...p_Nn_N

The characteristics of the Zhdanov-notation can be summarized as follows:

Every p or n stands for a number that represents a number of layers. As is indicated by the subscript, every p-symbol must be followed by an n-symbol, thus the nuber of symbol is never odd.
p represents a number of layers with a positive sequence; where positive means the sequence ABCA (or BCAB or CABC, respectively).
n represents the inverse seuqences i.e. ACBA (CBAC, BACB).
Symbols may be presented in brackets indicationg a symmetry-center in the center of the sequence (thus situated between two layers when the number of layers is even and sitauted on a layer when odd).
Symbols may be separated between a vertical slashes indicating a mirror plane in the center of the sequence.

Since all this is a bit confusing seeing nothing but the rules, I have inserted some examples here:

The BaRuO₃ 9R-Structure, Spacegroup: R 3b m

Zhdanov Notation

(2) (1) (2) (1) (2) (1) = (2) (1) (2) (1) (2) (1)

Layer Sequence

Katz & Ward Notation

Layer No.

A

h

0

+ B +

c

1

C ‚ B

h h

2 3

+ C +

c

4

A ‚ C

h h

5 6

+ A +

c

7

B ‚ A

h h

8 9

= chh chh chh = (chh)₃

A 12L-Structure, Spacegroup: P 3b m 1

Zhdanov Notation

(4) 3 (2) 3 = (4) 3 (2) 3

Layer Sequence

Katz & Ward Notation

Layer No.

A

h

0

+ B + C + A +

c c c

1 2 3

B ‚ A ‚ C ‚ B

h c c h

4 5 6 7

+ C +

c

8

A ‚ C ‚ B ‚ A

h c c h

9 10 11 12

= ccc hcc hch cch

For a more detailed introduction into the Zhdanov-Notation and referring tables, see the article of A.L. Patterson and J.S. Kasper on "Close Packing" printed in the International Tables for X-ray Crystallography, Vol. III, pp. 342.

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