> It does, at least my edition (Vol. A: 5th ed., 2002, Table 10.2.1.2,
> p.806) does - ITC has everything you need to know about space groups
> (and a lot more besides)!
Actually, as the aforementioned table indicates, it's not correct to
talk about "polar and non-polar space groups", but only about "polar
and non-polar directions" in space groups. Many space-groups have
both polar and non-polar directions, which would seem to imply that
these space groups are both polar and non-polar at the same time!!!
For example, P3 has a polar direction parallel to the 3-fold and no
non-polar directions, whereas P321, even though it's classed as a
non-polar space group, nevertheless has 3 polar directions [100],
[010], [-1-10] parallel to the 3 2-folds in the xy plane, plus 4
non-polar directions (including the 3-fold). Note that any direction
perpendicular to an even-fold rotation axis is always non-polar: these
'trivial' cases are not shown explicitly in the above table.
From the point of view of deciding which are the alternate settings I
don't think it's helpful to consider polar directions anyway. What
matters is which symmetry axes of the lattice are not present in the
point group. So in the case of P321 the hexagonal lattice has a
6-fold parallel to c which can be thought of as the product of a 3-
and a 2-fold both || c, and also 2-folds perp to the 6-fold. The
3-fold and the perp 2-folds are all present in P321 but the 2-fold ||
c is not, so that is what gives rise to the 2 alternate settings
(h,k,l) and (-h,-k,l). In P3 all 2-folds are missing so you get 4
alternate settings. The same missing symmetry can also give rise to
merohedral twinning, so it's nice to "kill 2 birds with 1 stone"!
Cheers
-- Ian
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