Re: Ambiguity in atom_site.disorder_group value -1

Hi Bob,

 

My thinking is that the crystallographer might recognize "a" special symmetry element, but the application of symmetry creates n copies, not two, in a space group with n symmetry operations. Right?

 

Thus, fundamentally, there is no such concept of a "specific" symmetry element. All n copies symmetry related, but all are not "complementary".

 

There seems to be some mismatching terminology going on here. When I say “a symmetry element”, I mean a mirror plane, axis of rotational symmetry, etc. -- that is, an element of the relevant space group -- as realized in the particular structure.  I was under the impression that this usage was pretty conventional.  Surely you’ve listened to many talks and read many articles that discuss how a crystal structure contains a mirror plane here, or an inversion center there, or a rotation axis wherever?  I know I have.

 

In this sense, there are many symmetry elements in any crystal structure, and usually several distinct ones in or passing through each unit cell.  The International Tables present diagrams showing their types and locations.  So yes, in this sense there absolutely is a concept of a specific symmetry element.  But you seem to be using the term differently.

 

This group can be considered to be disordered about any of these symmetry elements.

 

Yes and no.  As a matter of terminology, when I say a group is disordered about a symmetry element, I am employing the typical reduction of the overall structure to a crystallographically unique unit, and looking at the symmetry elements that relate the chosen unit to a symmetry equivalent that overlaps that particular unit in space.  I think that this, too, is a relatively common usage in chemical and crystallographic jargon.  When I allow for the possibility of a group being disordered about multiple symmetry elements, I am talking about cases where the disorder occurs at a site where multiple symmetry elements intersect.  At such a site, multiple elements may generate images of the same unique unit that all overlap the original unit.

 

It is also true that when there is disorder, one can (always) find symmetry elements, sometimes of different kinds, that generate overlaps with a chosen unique unit from distinct symmetry copies of that unit.  But that’s not what I’m talking about, and I don’t think it’s very interesting because it follows as a necessary consequence of translational symmetry.

 

In addition to not being occupied simultaneously with sites belonging to different groups, the sites of such a group also are not occupied simultaneously with symmetry equivalents of sites belonging to the same group.  That is, the group's symmetry equivalents are among its disorder complements. 

 

I don't understand this statement. Why would it be true that sites related by symmetry are "not being occupied simultaneously"?

 

It took me embarrassingly long to work out what the problem was here.  Which is a great demonstration of why data dictionaries are valuable, and why collaborative development of them is important.  The point that is not adequately conveyed by my previous suggesting wording is that the bit about symmetry equivalents not being simultaneously occupied should be understood locally, not globally. 

Perhaps this refinement would be more acceptable:

 

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[...] Sites belonging to the same group are simultaneously occupied, but those belonging to different groups are not.

 

(paragraph break)

 

A minus prefix (e.g. '-1') is used to indicate that the group is disordered about one or more symmetry elements. In addition to not being occupied simultaneously with sites belonging to different groups, the atom sites of such a group are not occupied simultaneously with local symmetry equivalents of sites belonging to the same group.  That is, some of the group's symmetry equivalents are among its disorder complements.

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As far as I’m concerned, the three sentences in the latter paragraph are different ways of saying the same thing.