Crystal structures consisting of stacked layers can be described by Ramsdell notation. Thus, cubic-closed packed (ccp) is given by a sequence ABC....or 3C, whereas hcp (hexagonal-closed packed) is given as AB... or in Ramsdell notation 2H. Especially for SiC numerous polytypes are described where the Ramsdell notation only tells the number of layers in combination of the lattice metric.
It is prominent that odd numbers are combined with R (rhombohedral), and even number are combined with H (hexagonal). Only cubic is a special case and I've never seen another sequence than 3C.
Recently I've seen also an odd number combined with H. Was this a typing mistake, or is the correlation odd->R, even ->H simply wrong?
If the building layer a 2D closest packing (hexagonal symmetry) any sequence based on a string of A, B and C (without repetition of the same letter) is a polytype. All of them are based on either H or R lattice, except the sequence ABCABC... which is cubic. Example: ABABCABABC... is a polytype; ABBCABBC cannot exist. see http://www.mx.iucr.org/iucr-top/comm/cteach/pamphlets/5/node0.html
Hi Giovanni, maybe my explanation is not that clear as I thought. The close packing concept is also described very well in section 9.2 of Vol C in International Tables for Crystallography. Excellent description and more extended than the internet link!
I am only puzzled about the use of H and R. If you look in literature you "always" find 9R, 15R, 27R, 51R but 2H, 6H, 8H etc. so that it seems all odd stacked layers are R and all even stacked are H. But I've seen somewhere 27H. Is this possible, and is there some more extended paper which explains this?
Gert, here there are R polytypes with even number of layers http://scripts.iucr.org/cgi-bin/paper?S056774086800350X
What I suspect is that in R polytypes the number of layers must be a multiple of 3 because of the threefold rotation axis; instead in H polytypes only an even number of layers can occur because of the even sixfold rotaion axis.
A study of a silicon-carbide crystal containing a new polytype, 27H
Mitchell, R. S.; Barakat, N.; Shazly, E. M. El
Zeitschrift für Kristallographie, vol. 111, issue 1-6, pp. 63-70
& also in
Table 9.2.1.2 in International Tables for Cryst. Vol. C
"mysterious" :-|
I find that this 27H polytype is quoted in several papers but from hone I have no access to them. However I am skeptical about it. Has it been determined via solution of the crystal structure or via some undirect methods? Is it ordered or disordered?
Gert, I think that the mystery of H polytypes with odd number of layers is a consequence of the poorness of the Ramsdell symbols. Closest packing polytypes can belong only to cubic (only one: ABC), trigonal and hexagonal systems. Trigonal polytypes may be based either on R or P Bravais lattices; all hexagonal polytypes have H lattice. The crystallographic reference system for P trigonal polytypes is the same as for the hexagonal ones (a = b, c, gamma = 120°). According to Ramsdell symbols, H is used both for hexagonal and P trigonal polytypes; R is instead used for R trigonal polytypes. Whereas the presence of a sixfold rotation axis in hexagonal polytypes requires an even number of layers, the presence of a threefold rotation axis in P trigonal polytypes requires a number of layers that is multiple of 3, which can be either even or odd.
I wonder if one would use a 62... couldn't this fit to an odd number of stacking? In a paper I would not be surprised about a typing or a general mistake, but in International Tables?
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