[GSAS-II] Problem with intensities (my previous email)

[Leopoldo Suescun]

Dear Ivo,
Since intensities are a physical property, they do not depend on the
arbitrary selection of the origin of the unit cell used to calculate it. In
fact, there is no origin in a crystal, just interatomic vectors.
When the calculation of intensity is done based on the structure factor,
you need to define an origin in order to compute the calculated intensity.
If you define the origin, all atoms automatically have fixed coordinates
x,y,z. So when you use a set of coordinates to describe a structure they
must correspond to the same origin choice. It is possible to calculate the
intensities independently of the origin, but it is impossible to represent
a stucture using a computer algorithm without using an origin.

Since the origin choice is and will always be arbitrary (it is not a
physical property) you will need to use the right equations to compute your
structure/diffraction pattern respect to that arbitrary point. Usually the
point of maximum symmetry of the cell is selected as the origin (it is
called Origin Choice 1 in the International Tables of Crystallography Vol
A.). This may not be at all determined, for instance in many space groups
(P1, P21, Pc,P212121, etc) all points in the unit cell have the same
symmetry, the identity (or no symmetry at all). The origin choice,
therefore, is always a matter of convention and each piece of software is
written to handle structures expressed in some origin choice.

Most pieces of software choose the origin at a center of symmetry since
this simplifies calculations (usually called Origin Choice 2 also in the
ITA, where both origin choices are given), but this may not be the point of
maximum symmetry of the unit cell, therefore, the coordinates you get from
a cif file or a database may not refer to the same origin choice used by
the software.

When you want to represent (or do calculations with) a structure that is
described in one origin but the program assumes the origin is at a
different position you will have the wrong equations in place for the
structure and the result will have no physical sense.

There are only a few space groups where this happens, you have to be
vigilant in those cases.
I hope this helps,
Leo

El jue., 22 ago. 2019 a las 9:36, Ivo Alxneit via GSAS-II (<
gsas-ii at aps.anl.gov>) escribió:

> Dear all
>
> I could resolve my problem by selecting the other possible origin
> (translated by (1/4, 1/4, 1/4) for Cu2O. But (being not really a
> crystallographer) this confuses me a bit. In my understanding, origin 1
> or 2 give just two alternate description of the same structure. It may
> be more or less convenient to choose one or the other because both
> describe the identical structure. Intensities on the other hand are real
> physical properties. Why are they affected by the (free) choice of the
> origin? Also, VESTA gives me the opposite pattern than GSASII for the
> two different choices of the origin i.e. I get differing pattern for
> both choices of the origin.
>
> thanks for any clarification
> --
> Dr. Ivo Alxneit
> Catalysis for Energy 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/ceg/
>
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-- 
Prof. Agr. Dr. Leopoldo Suescun
Cryssmat-Lab/DETEMA, Facultad de Química, Universidad de la República.
e-mail: leopoldo at fq.edu.uy
Tel: (+598) 29290705
Fax: (+598) 29241906*
Mailing address:
Cryssmat-Lab./DETEMA
Facultad de Quimica
Av. Gral. Flores 2124
Montevideo 11800
Uruguay

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