Converting Quartz data from one (P3221) space group to another (P3121)

Ramon13

For my studies, I’ve done a lot of work on coal fly ash QXRD QPA which has been a fun and interesting challenge when trying to overcome the complexities of mullite solid solutions, different quartz phases and the sort. Apart from reviewing the foundations of crystallography and XRD instrumentation (etc.) a lot of my learning so far has come from a prior colleague of mine who had done an extensive amount of fly ash QPA. I started with the TOPAS GUI but I’ve recently been learning launch mode (shout out to John Evans’ great YouTube videos on this! 🙂 ).

One thing I’ve noticed in my prior colleague’s work is that he has occasionally gotten quartz .cif/.str files with a spacegroup of P3221 (left-handed quartz) and then, when loading it into a .inp file, seemingly changed the spacegroup to P3121 (right-handed quartz). Originally, I wasn’t sure why he would do this (and simplistically thought the simple right vs left-handed geometry would correct itself in a refinement) until I ran a refinement with the original .str file and had a big intensity error with my quartz. Since then, I’ve realised the massive difference alternate site positions can have which are seemingly mitigated when switching to the alternate space groups (which I presume are the quartz found in the original sample). From this, I’ve been trying to develop a model to easily convert between spacegroups as many quartz .cif/.str files I’ve seen have the former spacegroup and, obviously, I don’t want these refinement errors when I’m trying to get meaningful results out.

So, from the above, my questions are the following:

1. Apart from significant intensity errors, how can the suitability of left vs right-handed space groups (such as with quartz) be noticed during a refinement?

2. Is there a general rule when incorporating crystal enantiomorphs as to which ‘hand’ should be applied or should it be determined empirically when refining a given diffractogram?

3. Are the amended site positions correct? If so, or not, can anyone provide a reference so that I can create a model to do this conversion on Python (or JEdit) before doing a refinement?

a) The original .cif file (PDF database entry no. 000461045) had the following data:

Spacegroup: P3221

site Si_1   x 0.4723   y =0;   z =2/3;   occ Si+4 1.0   beq  0.59533
site O_1   x 0.416   y 0.2658   z  0.7881   occ O-2  1.0   beq  1.37938

b) The final .inp file used for analysis had the following information:

Spacegroup: P3121

site Si num_posns  3 occ Si+4  1 beq  0.46 x  0.4698 y  0 z =1/3; :  0.33333
site O num_posns  6 occ O-2  1 beq  0.46 x  0.4151 y  0.2675 z  0.2139

Ramon13

I'm also wondering for a similar conversion for magnetite from spacegroup R-3c (from original PFD) to R_-3_C_H in Jedit. It seems this conversion was made to get a better fit but I'm not sure how or what the logic was to go to this specific spacegroup.

johnsoevans

I may not have understood your question properly, but TOPAS/jEdit don't do anything clever with the space group when you read in a cif file - it basically just reads whatever is in the CIF file. For something like R-3c you can work with either hexagonal or rhombohedral axes. These are given symbols R-3c and R-3cr in TOPAS, respectively. Occasionally the space group symbol will be misinterpreted so you just have to set it by hand.

One lazy way of checking you probably have the right space group and setting is to use "view_structure" to visualise the structure and see if it make sense. One common problem with hexagonal/trigonal systems is that you need to have coordinates as "=1/3;" not "0.3333". You can spot this type of error by displaying atomic labels or calculating distances and angles. If you have multiple atoms close to a special position you'll get distances close to 0.0 Angstroms. You can also check your density is sensible.

With your quartz case you need to be careful that the coordinates and space group match.

You can see all the possible space groups in topas by looking in the "sgcom5.txt" file in your TOPAS directory (but be careful not to change anything). Or you can browse possibilities in the gui if you click the little "down arrow" in the structure/Spacegroup box.

If you want to convert between e.g. hexagonal and rhombohedral settings for R-3c you can use a tool like the isodistort suite (or many others).

Ramon13

Thank you for that John 🙂