On Wed, 30 May 2012 13:16:12 +0100 Ian Tickle <ianj...@gmail.com> wrote:
> 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. Possibly relevant here is a set of tables I put together for our free-electron laser experiments, where tens or even hundreds of thousands of patterns have to be indexed independently: https://www.desy.de/~twhite/crystfel/twin-calculator.pdf Underlying these tables is the same underlying information as everything else mentioned on this thread, but these ones tell you what the apparent symmetry would be if the intensities were mixed up according to all the available indexing ambiguities. So far, no-one has been able to reliably resolve these ambiguities in our case: the intensities are just obscured by too much noise, partiality, a spiky X-ray spectrum and so on. That's why we have to have so many patterns. For the time being, we just merge according to the higher symmetry, accept that the data may be (perfectly) "twinned", and handle it at the later stages. Later on when we've hopefully solved this problem, these tables will serve as a menu of options for doing the whole thing backwards. I agree that polarity isn't the right criterion. Point group "2" is polar but does not exhibit any indexing ambiguity. Point group 4/m, which is most definitely not polar, does. This paper, Le Page et al., has some similar tables but lists the actual ambiguity operators: http://scripts.iucr.org/cgi-bin/paper?S0108767384001392 Of course, all of this only covers "merohedral" ambiguities, not "pseudo-merohedral" ones which might arise by accident in special cases. Comments on and corrections to the tables are welcome! Tom
