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II.2. Descriptive symbols: notation

In certain polytypic compounds a number of different polytypic structures may have an identical modified Gard symbol. A more detailed symbolism is hence desirable to allow specification of the exact stacking sequence of layers, if known. Such detailed symbols are necessarily complex, and the ideal goal is a symbol that gives the necessary information in a readily understandable format. Too complex a symbol will probably be used only by a few experts in the field.

In the present recommendation, the stacking sequence of two-dimensionally periodic building layers (BLs) in any polytype is described by a sequence of conventionally chosen characters (numbers, letters, signs, etc. ) which indicate the absolute orientation of each BL and the relative displacements of their origins. Before presenting the symbols for a given polytypic family, the choice of BLs, their origins, possible orientations and stacking possibilities are to be specified - e.g. by indicating the orientational and displacement vectors in diagrams of the normal projection of the structure onto the plane parallel to the BLs relative to a fixed coordinate system. The choice of orientational and displacement characters and other relevant items should also be given in this explanatory introduction .

The orientational characters should be in upper-case and the displacement characters in lower-case letters (denoting different kinds of BLs and structural displacements, respectively): both may have subscripts [integer numbers, sign (+, -), etc .], chosen by convention, to indicate respective orientation and displacement. The sequence of BLs is hence given by a corresponding sequence of orientational and displacement characters , as in (1).

$${\ldots}P_is_jQ_kt_lR_mu_n\ldots$$ (1)

If the BLs are all equivalent, or if their nature, orientation (and/or displacement) is fixed or otherwise obvious, the letters ${\ldots}P,Q,R,{\ldots} ({\ldots}s,t,u,{\ldots})$ may be omitted and only their subscripts used as orientational and displacement characters. These are generally written in a two-line form with orientation characters in the upper and displacement characters in the lower line. In this case, symbol (1) becomes

$${\ldots}i_{\textstyle j}k_{\textstyle l}m_{\textstyle n}\dots$$ (2)

If the orientations (displacements) are all alike, or if they follow unambiguously from displacements (orientations), the corresponding characters may be omitted. In such a case, sequence (1) may be reduced to

$${\ldots}s_jt_lu_n{\dots}({\ldots}P_iQ_kR_m{\dots}).$$ (3)

An analogous reduction is also possible for sequence (2):

$${\ldots}jln{\ldots}({\ldots}ikm{\ldots}).$$ (4)

Characters which are redundant may or may not be omitted, and accordingly we speak of non-redundant and redundant symbols , respectively. A symbol may also contain additional marks (dots, primers, etc .) for facilitating the recognition of relevant crystal-chemical features. The smallest repeating part of the periodic sequence of characters, placed between vertical bars ($\vert{\ldots}\vert$) indicates periodic polytypes. The number of BL-repeating units per symbol-repeating unit is represented by the corresponding subscript number.

When a polytypic structure consists of equivalent BLs and any BL may occupy only one of two alternative positions relative to the preceding BL, the polytypic symbol is reduced to the simplest form, i.e. a sequence of characters of two kinds, e.g. + and - in Häggs's (1943) symbolism, which in turn is simplified to the short-hand form of Zhdanov's (1945) symbolism, indicating the numbers m and n of the consecutive characters + and -, respectively.

Examples of recommended descriptive symbols are given in Appendix 2. Additional details may be found in Dornberger-Schiff, Durovic & Zvyagin (1982).

It is a pleasure to thank A. J. C. Wilson for improving this report by his critical comments.

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