In the $CHTML/twinning.html it tries to explain:
From the table:
# All *P2i3* and related *2i3* space groups:
(h,k,l) already equivalent to (-h,-k,l) so we only need to check:
real axes: (a,b,c) and (b,a,-c)
reciprocal axes: (a*,b*,c*) and (b*,a*,-c*)
/i.e./ reindex (h,k,l) to (k,h,-l).
# Twinning possible with this operator - apparent symmetry for two fold
perfect twin would be P43 (operator k,h,-l)
space group number space group point group possible twinning
operator
195 P23 PG23 k,h,-l
196 F23 PG23 k,h,-l
197 I23 PG23 k,h,-l
198 P213 PG23 k,h,-l
199 I213 PG23 k,h,-l
See if it all makes sense..
Eleanor
yanming Zhang wrote:
Dear 'old' crystallographers,
During one case of structure solution, the data processing programs output
incorrect space group-primitive cubic P4132, which later found out that the
correct one should be face centerd cubic f23. This problem was caused by
perfect twinning.
Now I'd like to invite you to help me understand, and explain in details,
WHY, IN CASE OF PERFECT TWINNING, THE LAUE GROUP m-3 WILL BE MIS-INDEXED TO m-3m by some data processing programs? I, sort of, understand the reason behind this is caused by the perfect twin operator which will emulate an additional 2-fold axis. But not fully understand the symmetry in details in this case. Your help and teaching are highly appreciated.
Yanming Zhang
