Not violating symmetry restrictions you may either have the sphere with the terms 11=22=33 and 12=13=23=0 or something else allowing the 12=13=23 terms to be equal but different from 0. These two possibilities are all you can do in cubic symmetry with h,k,l permutable. If I am not wrong.
The (111) and (-111) come out with different widths if the {12=13=23} != 0, but the quartic's have declared this blasphemous as they are symmetry equivalents... perhaps you should go into hiding before they burn you at the stake[*]. There would be an equivalent "solution" with (-12=13=23, etc), so the "something else" is an ellipsoid along the 111 direction, and you can find the same "solution" if you put the ellipsoid along any of the 111 directions. Same solutions, but some have the crystal upside down or on it's side. Sometimes happens if you drop your crystal.
So if (111) and (-111) do not need to be equal in width, someone is hopefully about explain to me why (100) and (010) do need to be equal in width in cubic symmetry. I don't understand why they do, and for a single crystal I have a vague memory of seeing them measured as being different (it is a very vague memory and I might have been mistaken). In a powder you don't know which direction is which anymore, but squash some cubic grains and then shake them up, and each grain will probably remember which way was up when you squashed it. If you use a subgroup of your crystal spacegroup for the peak widths then you'll find the same solution moved by the symmetry operators you threw out to make the subgroup. Nothing surprising there. I wouldn't generally expect the crystal defects to have the full crystal symmetry, but some people seem to be insisting they should have. I am curious as to how that comes about, especially if the defects interact with each other and eventually gather themselves up into a full blown symmetry breaking small distortion. If I were to implement this stuff in PRODD, should I force the users to apply the symmetry or not? If not it means taking care internally to sum over the equivalents when computing the peakshape. If that sum is not carried out, then I can see why problems could arise, but otherwise it seems unreasonable to insist that everyone use the full crystal symmetry?
So can someone just tell me why the symmetry is not optional?
Jon
[*] Please excuse my sense of humour.
