[GSAS-II] Extract number of formula units per unit cell

[Von Dreele, Robert B.]

Dear Ivo,
I’m not sure there is a generic solution; following your example Mn3O4 & Fe3O4 each have two different metal atom sites each with different multiplicities in a spinel structure. Since the script is made up of python statements, you could just tailor the math to fit your specific problem & calculate numbers of FUs you want.
Bob

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From: Ivo Alxneit via GSAS-II<mailto:gsas-ii at aps.anl.gov>
Sent: Monday, April 26, 2021 6:30 AM
To: gsas-ii at aps.anl.gov<mailto:gsas-ii at aps.anl.gov>
Subject: [GSAS-II] Extract number of formula units per unit cell

Dear all

I am a chemist that uses xrd-powder diffraction to follow the course of
reactions. Therefore, mass-fractions or number of atoms per unit cell
are not useful to me. I deal with mol fractions of formula units (FU).
To convert from the unit cell related values to FU related values I need
to know the number of FUs per unit cell (Z). How can I calculate this
based solely on the information stored in a gsas-II project (I want to
use scriptable to automate the task).


So far I seem to have a solution but I am not sure if it is really correct:

For each phase, the greatest common divisor (GCD) of the site
multiplicity of all atoms corresponds to Z. As example LaFeO3 (Pnma):
La      4
Fe      4
O1      8
O2      4
Formula per unit cell: La4Fe4O12
GCD=4 -> FU=LaFeO3

This also gives the correct FU for solid solutions like Ce0.1Ce0.9O2.

But there are cases where more than one atom form the basis as e.g.
graphite(P63/mmc):
C1      2
C2      2
Formulat per unit cell: C4
GCD=2 -> FU=C2
Here I miss the factor 2 due to the 2-atom basis. How do I identify a
n-atom basis? I assume that in this case I would find for each atom n
sets that have the identical multiplicity. In the case of the LaFeO3
example above a second set with La/4, Fe/4, O1/8, O2/4 would have to be
present.

So the question: Is my solution generic and correct?

Thanks for any help / suggestions

--
Dr. Ivo Alxneit
Applied Catalysis and Spectroscopy Group
Bioenergy and Catalysis Laboratory        phone: +41 56 310 4092
Paul Scherrer Institute                     fax: +41 56 310 2688
CH-5232 Villigen                      gnupg key: 0x515E30C7
Switzerland
https://www.psi.ch/acs/

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