Hi,
this is explained in details in table 2.2.4.1 of vol A of International
Tables of Crystallography (p 18 in my edition).
For trigonal/hexagonal, the primary direction is along c, along the
3-fold (6-fold axis). It's the same in tetragonal (obviously for the
4-fold axis !)..
The secondary directions for trigonal/hexagonal are [100], the a vector,
[010], the b vector, and [-1-10] the diagonal direction between -a and
-b vectors (and therefore of between the a and b vectors).
In tetragonal, the secondary directions are only [100], a, and [010], b.
The tertiary direction for trigonal/hexagonal are [120] and [-2-10]
which are directions perpendicular to a and to b, respectively, and
[1-10]. None of these directions are the diagonal of a and b vectors.
In tetragonal, the tertiary directions are [110], the diagonal of the a
and b vectors, and [1-10], the diagonal of the a and -b vectors.
laurent
Le 18/02/2015 17:04, Kay Diederichs a écrit :
Hmm, "placeholder" for me does not seem to emphasize enough the role that this
number plays in the space group names. My understanding (but I fail to remember where I
read this ...) is that the first number is the order of the rotation (i.e. 6,4,3,2 or 1)
of the unique unit cell axis (often the one with the highest symmetry), the second number
is the rotation order of a secondary axis, and the third number gives the rotation order
of a tertiary axis - which is the third axis in the orthorhombic system, but a diagonal
at least in the trigonal and tetragonal (and I think cubic) systems.
This makes it clear that each (baseline) letter in the spacegroup name has its
specific role, and tells you about the order of the rotation axis. On top of
that comes the screw axis information which is much easier to read when using
subscripts. But obviously the naming scheme was chosen such that even if screw
axes are not indicated with subscripts, the resulting names are unambiguous.
best,
Kay
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Laurent Maveyraud laurent.maveyraud AT ipbs DOT fr
P I C T --- Plateforme Intégrée de Criblage de Toulouse
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Département Biologie Structurale et Biophysique
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