On Wed, Oct 12, 2011 at 1:35 AM, James Holton <jmhol...@lbl.gov> wrote:
> My list has 8 different allowed > shifts for I222, but I assume this is because the 0,0,1/2 shift is > part of a symmetry operator. I guess it is a matter of semantics as > to wether or not that is an "allowed shift"? > > James, the (0,0,1/2) shift is not "part of" any symmetry operator in I222, but I'm sure you knew that! - whereas the (1/2,1/2,1/2) shift _is_ a symmetry operator: the I centring operator in fact. This means that the lattice repeating units of the crystal structures (i.e. the set of atomic positions in the unit cell) will be identical in pairs, so in I222 (or indeed any I-centred space group) the crystal structure obtaining by shifting by (0,0,1/2) is identical in all respects to the one obtained from the (1/2,1/2,0) shift. In contrast, the structures obtained from all the other pairs, e,g, (0,0,0) and (0,0,1/2), are different in all respects, excepting that their sets of calculated amplitudes will be identical. In your terminology a "non-allowed" origin shift is one which would cause even the |Fc|s to differ, which is practice would mean that you would have to use a different space-group specific formula for the structure factor (so it's "non-allowed" only in the sense that you are "not allowed" to use the same structure factor formula, but you "are allowed" to use a different one). I prefer to call it "non-equivalent origin shift" (as opposed to equivalent origin or centring shift) - it's not really a question of whether it's "allowed" or not, it's whether it has any effect on the crystal structure. In practical terms of course it makes absolutely no difference to the result if you choose to do things that have absolutely no effect! Cheers -- Ian
