Polytype notations

Bailey (1984c) recommended a notation system for structural sites in micas. However, there is no agreement to the labeling of these sites e.g., either an italic or roman font is used with or without parentheses to separate the alphanumeric parts. Following recent papers (Nespolo et al. 1999c Nespolo 2001) and in agreement with the chapter of Nespolo and Durovic (this volume), the nomenclature of the OD theory of polytypes (Domberger-Schiff et al. 1982 Durovic 1994) is here adopted to label sites. 

From the examples above it is evident that 1) the homo-octahedral approximation corresponds to applying to a polytype the relation of homomorphy 2) in micas, the classical Ramsdell notation rigorously applies to homo-octahedral polytypes only. 

The technique of Raman scattering (RS) to study vibrational spectra in the numerous polytypes of SiC will be described. An explanation of the various notations used to describe the stacking sequences in these polytypes will then be given. Section C discusses the various optical phonons studied by RS and the concept of a common phonon spectrum for all polytypes will be introduced. Raman studies are also used to assess crystalline structure and quality of epitaxial layers of SiC on Si and SiC substrates. Section D outlines several other excitations of interest, e.g. polaritons, plasmons, and electronic RS, as well as impurity and defect recognition in irradiated and ion implanted material. 

The stacking sequence of these polytypes can be described by the ABC notation, where A, B and C represent the three sites available in one sublattice. For example (...ABCABC...) and (...ABABAB...) stand for cubic (3C or p-SiC) and simple hexagonal (wurtzite) respectively. The intermixing of these two simple forms can also occur, generating a large number of... 

Zhadanov [7] visualised the SiC stacking sequences by considering the sequence of non-basal tetrahedral planes. The observed zig-zag of layers ([111] direction for cubic, and [0001] direction for hexagonal and rhombohedral) was represented by a notation which denotes the number of consecutive layers without rotation, the total stacking sequence, and a subscript indicating the sequence repetition. A detailed discussion of polytypism, polytypic transformation and notations has been reported by Jepps and Page [8]. 

TABLE 1 Seven of the most simple SiC polytypes with four notations (R = Ramsdell notation, J = Jagodzinski notation, Z = Zhadanov notation). They are listed by increasing percent hexagonality. 

TABLE 1 Principal phonon energies (meV) in six polytypes derived from the luminescence spectrum (from [26]). The notation (TA) for transverse acoustic, (LA) for longitudinal acoustic, (TO) for transverse optical, and (LO) for longitudinal optical phonons is accurate for the cubic polytype, but not for the hexagonal and rhombohedral polytypes. For details see Datareview 2.2. 

Polytype Jagodzinski notation Hexagonality h Minimum bandgap eV dEgin/dT... 

The Zhdanov notation specifies the stacking sequence in yet another way. The translation between an A layer and a B layer or a B layer and a C layer can be represented by a rotation of +60° or a translation of + K. Reverse transformations, C to B or B to A, are then represented by -60° or The stacking sequence of any polytype can then be written as a series of + and - signs. This, itself, does not result in a compact notation, and this is addressed by the Zhdanov symbol of the poly type, which gives the number of signs of the same type in the sequence. Thus the cubic... 

Ramsdell Numbers. A shorthand notation for labelling polytypes (q.v.) of crystal structures The numbers are of the form /iR or nH were n is the number of layers in the unit cell (q.v.) necessary for the arrangement of the layers to repeat itself. R, H stand for rhombohedral or hexagonal crystal form respectively. Originally devised to classify silicon carbide polytypes, the system has been applied to other carbides and nitrides. (L.S. Ramsdell, Amer. Miner 32, 147, p64). 

Verma and Krishna (1966) have reported the main properties of polytypic materials. Different notations have been used to describe the stacking sequence of successive packed layers in the hexagonal unit cell. This has been chosen as the basic lattice because it... 

Alloys about AujCd have the M = 2 antiphase domain structure (AujZr type). With increasing Cd content (increasing electron concentration) modulated structures (polytypes of the M = 2 structure) are obtained in the order 1R , 4H , 6H , and 3R (12R, 4H, 6H, and 36R in Ramsdell s notation), in agreement with estimates from the electron diffraction patterns of the order of increasing volumes included within their Brillouin zones. ... 

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