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Methods, Problems and Solutions

Errors and Rietveld R Factors

The CCP14 Homepage is at http://www.ccp14.ac.uk

[Problems and Solutions]
[Rietveld R and fit factors] | [Errors and Rietveld R Factors] | [ESDs, Probable Error and Rietveld Analysis]
[Calibration standards for Powder Diffraction] | [Diffconv - INEL PSD Spline based Data Calibration]

Relevant Papers

"ESDs and estimated probable-error obtained in rietveld refinements with local correlations" J.F. Berar and P. Lelann, Journal of Applied Crystallography, 1991, Vol.24, No.Pt1, pp.1-5.

McCusker, L. B., Von Dreele, R. B., Cox, D. E., Lour, D. & Scardi, P. (1999). J. Appl. Cryst. 32, 36-50.

Papers that can be referred to:

Hugo Rietveld - Rietveld Method Web-site


To: sdpd@egroups.com
From: Steve Maginn [maginn@ccdc.cam.ac.uk]
Date: Tue, 23 Jan 2001 10:41:11 +0000
Reply-To: sdpd@egroups.com
Subject: [sdpd] error measurements

Hi everyone,

With an increasing number of structures being determined ab initio from
powder data, the Cambridge Crystallographic Data Centre is beginning to
grapple with the problems of inclusion of these into the Cambridge
Structural Database.

There is no doubt that they should or will be included, but one problem is
that there appears to be little consistency or standard about which error
measurement is used to give a quality indicator for structures. There are a
plethora of different R-factors, chi squareds, etc. And the problem of
course is relating these to the standard R and weighted R used in
single-crystal structure determinations, with which powder structures will
be compared when they join the bulk of crystallographic data in the CSD. 

Are there any views as to which error measurement should be used ? And how
long will it be before reported powder structures are standardised using
this measurement, so database authors and more importantly users can
reliably judge the precision / quality of a structure ?

Views welcome ...

Cheers,

Steve Maginn,
CCDC, UK


=====================================================

Dr. Stephen J. Maginn,
Support and Marketing Manager,
Cambridge Crystallographic Data Centre (CCDC),
12 Union Road,
Cambridge CB2 1EZ, UK

phone +44 (0)1223 762534
FAX    +44 (0)1223 331116
e-mail   maginn@ccdc.cam.ac.uk

http://www.ccdc.cam.ac.uk

=====================================================


To: sdpd@egroups.com
From: Armel Le Bail [armel@fluo.univ-lemans.fr]
Date: Tue, 23 Jan 2001 14:45:40 +0100
Subject: Re: [sdpd] error measurements

>Are there any views as to which error measurement should be used ? And how
>long will it be before reported powder structures are standardised using
>this measurement, so database authors and more importantly users can
>reliably judge the precision / quality of a structure ?

That question is an endless controversy. However, see 11, page 47 in
McCusker, L. B., Von Dreele, R. B., Cox, D. E., Lour, D. & Scardi, P.
(1999). J. Appl. Cryst. 32, 36-50. 

The problem is that if you follow the recommendations, you will
have to give not only some R values, but also a plot of the observed 
and calculated data with a scale magnification at large angle for 
X-ray data ;-).

About R values, I prefer the conventional Rp and Rwp values
(background subtracted, peak only contributions) plus the Rexp
and the RB and RF values. The X**2 (goodness of fit) can be 
calculated from the Rwp/Rexp ratio. But you should not accept 
only X**2 without the Rwp and Rexp values, IMHO. A problem
can be that people give Rp and Rwp without background
subtraction, and without even saying it. 

And what about structures refined with many restraints and/or
constraints and with the (number of reflections)/(number of 
refined parameters) quite small (< 3 or even < 1) ? They
can give very good R values while being somewhat dubious.
At least, they are more dubious than structures refined with
such a ratio > 10. Thus, giving that ratio is an important
information too.

Hope this help.

Armel Le Bail
http://sdpd.univ-lemans.fr/course/

From: "Peter Y. Zavalij" [zavalij@binghamton.edu]
Date: Tue, 23 Jan 2001 09:40:31 -0500
Subject: RE: [sdpd] error measurements

I think the main 2 R-factors should be Rp and R(bragg) or R(F2) of course
with background subtracted.
>From my point these 2 values characterize Rietveld refinement similarly to
Rw and RF in single crystal refinement. The other R-factors especially Rwp
and Rexp should be taking into account as additional merits as well.
On the other hand Armel is right simple look on the difference plot and
other refinement parameters and restrictions can tell a lot about the
structure quality too.
It seems that some work on powder CIF is going on right now and it would be
also useful what are IUCr requirements for submission of the powder
refinement in Acta Cryst.

Dr. Peter Y. Zavalij  University Crystallographer
Materials Research Center, SUNY at Binghamton
Tel: (607)777-4298    Fax: (607)777-4623
E-mail:zavalij@binghamton.edu
http://materials.binghamton.edu/zavalij

From: cockcroft@gordon.cryst.bbk.ac.uk
Date: Tue, 23 Jan 2001 14:36:02 GMT
Reply-To: sdpd@egroups.com
Subject: Re: [sdpd] error measurements

I agree 100% with Armel about R-factors (and illustrate in particular
about the effect on background subtraction in our PD web course at
Birkbeck). I suspect the output of some programs are not very clear
concerning R-factors (or even weights - since I suspect there are still
many that use unit weights (i.e. non at all!)). I pointed out some
of these problems recently at CDCC, but as I said during my talk,
there will always be those who like to quote R-factors including
background because the numbers are lower, and there will always be
those who quote chi-squared values only becuase they wish to hide the
fact that the data is not of the highest quality.
Just the opinion of another powder crystalllographer,
         Jeremy Karl cockcroft.

From: cockcroft@gordon.cryst.bbk.ac.uk
Date: Tue, 23 Jan 2001 14:54:40 GMT
Reply-To: sdpd@egroups.com
Subject: Re: [sdpd] error measurements

To add to my recent comments, I disagree with quoting Rp (as used 
in the original JAC paper) - weights should be used - especially when
X-ray data is collected repeatedly at higher two-theta angles so
as to improve statistics. So I disagree with you, Peter Zavalij, re the
use of Rp. I would also add that R-factors based on both total peak
intensities and structure factors-squared are also useful, but they
should be treated with some caution if the data has been collected for
different time periods for different two-theta ranges (since they are
difficult to weight properly).
  Jeremy Karl Cockcroft
  School of Crystallography, Birkbeck College, UK.

To: sdpd@egroups.com
From: Jaap Vente [jaap@jade.mda.cinvestav.mx]
Date: Tue, 23 Jan 2001 10:02:28 -0600 (CST)
Reply-To: sdpd@egroups.com
Subject: Re: [sdpd] error measurements

The pain with background substraction CAN be that you have high values
with a further 'perfect' fit. In my experience this has often to do the
presence of a relative large amount of peaks with low intensity. You may
argue that you should measure longer under these circumstances, or reduce
the 2 theta angle you are using. Even so, the improvement is minor if you
have a low symmetry structure with atoms having very different scattering
factors (heavy metal oxides for instance). And yes your Rwp might than be
more an indication of how good the back ground has been fitted. High
background level gives a nice and low Rwp. With this in mind I think that
at the moment of writing there is no proper figure of merit for a Rietveld
refinement, and yes the diffraction pattern should be available. I am sure
that Steve Maginn is happy with this view :-).

By the way I assume that the background is never substracted in the Rwp
unless stated otherwise.

Best wishes

Jaap 

Jaap Vente
Cinvestav-IPN Unidad Merida
Departamento de Fisica Aplicada
Carretera Ant. a Progreso km 6
Apartado Postal #73 Cordemex
Merida, Yucatan, 97310
Mexico
Fax: +52 (9) 981 29 17
Tel: +52 (9) 981 29 60 ext 243/230
e-mail: jaap@mda.cinvestav.mx
web: http://www.mda.cinvestav.mx/  

To: sdpd@egroups.com
From: Steve Maginn [maginn@ccdc.cam.ac.uk]
Date: Tue, 23 Jan 2001 16:17:23 +0000
Reply-To: sdpd@egroups.com
Subject: Re: [sdpd] error measurements

This - and indeed those that have come before - is a very interesting point
of view. The storing of the whole diffraction pattern with a crystal
structure is of course impossible with the current file formats of the
Cambridge Structural Database, so I'm very happy with the view, but not
happy to have to say that at the moment it is impossible to realise it !
That's not to say that it won't be possible at some time in the future ...

This is all very valuable and helpful information for us - please keep it
coming.

Cheers,

Steve Maginn

To: sdpd@egroups.com
From: cockcroft@gordon.cryst.bbk.ac.uk
Date: Tue, 23 Jan 2001 16:22:26 GMT
Reply-To: sdpd@egroups.com
Subject: Re: [sdpd] error measurements

I think one point re background subtraction in Rwp is being missed. Background
count can be subtracted before the refinement process (as in the original
Rietveld) or after using the refinable background function, i.e. the calculated
background is subtracted. Both can easily be done. Also, in the summation
process, profile point should not be included where there is no diffraction
information.
   Jeremy Karl Cockcroft.

To: sdpd@egroups.com
From: Jaap Vente [jaap@jade.mda.cinvestav.mx]
Date: Tue, 23 Jan 2001 12:15:22 -0600 (CST)
Reply-To: sdpd@egroups.com
Subject: Re: [sdpd] error measurements


I agree with Jeremy Cockcroft that in THEORY you can substract the
background both before and after refinement. The first option is
actually rather difficult when you have peaks close to each other or with
overlapping peaks. Or you must assume a constant background or so. The
second option cause problems due to correlations between thermal and/or
displacement parameters and the background. 

I think we all would agree very quickly on how to treat SrO and get
reliable values, but life is not so easy with the more complicated
structures.


Jaap Vente
Cinvestav-IPN Unidad Merida
Departamento de Fisica Aplicada
Carretera Ant. a Progreso km 6
Apartado Postal #73 Cordemex
Merida, Yucatan, 97310
Mexico
Fax: +52 (9) 981 29 17
Tel: +52 (9) 981 29 60 ext 243/230
e-mail: jaap@mda.cinvestav.mx
web: http://www.mda.cinvestav.mx/  

From: cockcroft@gordon.cryst.bbk.ac.uk
Mailing-List: list sdpd@egroups.com; contact sdpd-owner@egroups.com
Delivered-To: mailing list sdpd@egroups.com
List-Unsubscribe: 
Date: Tue, 23 Jan 2001 18:46:25 GMT
Reply-To: sdpd@egroups.com
Subject: Re: [sdpd] error measurements

In reply to Jaap's last comment,
  You can subtract the background in PRACTICE too after refinement as 
long as you know the function used for the refinable background (e.g. 
the polynomial coefficients when a polynomial is used.) This can
be done each cycle of refinement (and is trivial to code). Whether
the peaks overlap or not is irrelevant - or even whether you can see
the background between peaks.
  After each cycle of refinement, simply do
     yi(calc. diffraction)' = yi(calc. total) - yi(calc. background)
and  yi(obs. diffraction)' = yi(obs. total) - yi(obs. background)
and then use yi' values for calculating Rwp, Rexp, etc. At least Rwp then
bears a better relationship to the structural side of the refinement.
  Whether the commonly used codes do this or not is another matter. But
just because some software doesn't calculate the "correct" numbers isn't
a justification (IMHO) for publishing "wrong" ones. (Obviously the
words in quotes are an my opinion only.)
  Jeremy

From: Jaap Vente [jaap@jade.mda.cinvestav.mx]
Date: Tue, 23 Jan 2001 14:06:40 -0600 (CST)
Reply-To: sdpd@egroups.com
Subject: Re: [sdpd] error measurements

Yes I understand all what Jeremy wants to say, even better, GSAS nowadays
does calculate the residuals with and without background substraction. And
what do I find, even with 'good' fits? A rather high number of nines for
the Rwp with background substraction. Of course this is not always the
case, but it does happen more often than desired.

Jaap

Jaap Vente
Cinvestav-IPN Unidad Merida
Departamento de Fisica Aplicada
Carretera Ant. a Progreso km 6
Apartado Postal #73 Cordemex
Merida, Yucatan, 97310
Mexico
Fax: +52 (9) 981 29 17
Tel: +52 (9) 981 29 60 ext 243/230
e-mail: jaap@mda.cinvestav.mx
web: http://www.mda.cinvestav.mx/  

From: "Peter Y. Zavalij" [zavalij@binghamton.edu]
Date: Tue, 23 Jan 2001 16:54:14 -0500
Reply-To: sdpd@egroups.com
Subject: RE: [sdpd] error measurements

>To add to my recent comments, I disagree with quoting Rp (as used
>in the original JAC paper) - weights should be used - especially when
>X-ray data is collected repeatedly at higher two-theta angles so
>as to improve statistics. So I disagree with you, Peter Zavalij, re the
>use of Rp. I would also add that R-factors based on both total peak
>intensities and structure factors-squared are also useful, but they
>should be treated with some caution if the data has been collected for
>different time periods for different two-theta ranges (since they are
>difficult to weight properly).
>  Jeremy Karl Cockcroft
>  School of Crystallography, Birkbeck College, UK.

Of course Rwp is very important as well as Rp. I do not insist on using Rp
only but it is "pure" R-factor while Rwp depends on what weight is used.

To: sdpd@egroups.com
From: Lachlan Cranswick [L.M.D.Cranswick@dl.ac.uk]
Date: Wed, 24 Jan 2001 17:22:07 +1100
Reply-To: sdpd@egroups.com
Subject: Re: [sdpd] error measurements - optimal weighting schemes?


At 14:36 23/01/01 GMT, you wrote:
>I agree 100% with Armel about R-factors (and illustrate in particular
>about the effect on background subtraction in our PD web course at
>Birkbeck). I suspect the output of some programs are not very clear
>concerning R-factors (or even weights - since I suspect there are still
>many that use unit weights (i.e. non at all!)). I pointed out some
>of these problems recently at CDCC, but as I said during my talk,
>there will always be those who like to quote R-factors including
>background because the numbers are lower, and there will always be
>those who quote chi-squared values only becuase they wish to hide the
>fact that the data is not of the highest quality.
>Just the opinion of another powder crystalllographer,
>         Jeremy Karl cockcroft.
>

In the Crystals single crystal suite - part of the guided refinement
option is to encourage the user to apply an optimal weighting 
scheme (near the end of the refinement process).

   http://www.xtl.ox.ac.uk/crystals.html

Which weighting schemes are considered optimal for Rietveld refinement
and at what point in the refinement should they be switched on (unit
weighting(?) turned off)?

(There have been a recent paper or two on this but the user tends to
use whatever is available in their Rietveld program of choice?)

Brian Toby could correct my flawed memory here: Ted Prince was mentioning
(in the aftermath of a CCP14 talk) about "Robust Resistent Weighting 
Schemes" that could be applied throughout the refinement process
(but in another context - single crystal refinement).   How relevant
and used are these by Rietveld software?

---

Also: for Le Bail fitting applied to Unit Cell refinement (where you 
may want to try and weight each HKL of significant intensity in a 
roughly  equal fashion - small to high intensity peaks would be
considered significant), what would be considered a good weighting
scheme to use here?  Log or Root weighting of the counts?

Lachlan.

Lachlan M. D. Cranswick

Collaborative Computational Project No 14 (CCP14)
    for Single Crystal and Powder Diffraction
Daresbury Laboratory, Warrington, WA4 4AD U.K
Tel: +44-1925-603703  Fax: +44-1925-603124
E-mail: l.cranswick@dl.ac.uk  Ext: 3703  Room C14
                           http://www.ccp14.ac.uk

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[Problems and Solutions]
[Rietveld R and fit factors] | [Errors and Rietveld R Factors] | [ESDs, Probable Error and Rietveld Analysis]
[Calibration standards for Powder Diffraction] | [Diffconv - INEL PSD Spline based Data Calibration]

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