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Methods, Problems and Solutions

Overall temperature factor refinement and Quantitative Phase Analysis using Powder Diffraction and the Rietveld Method

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Via the Sci.techniques.xtallography Newsgroup

From: "Natale Perchiazzi" [natale@dst.unipi.it]
To: "rietveld" [rietveld_l@ill.fr]
Subject: overall temperature factor refinement
Date: Mon, 19 Nov 2001 12:36:45 +0100
Organization: Dipartimento di Scienze della Terra  Pisa


Dear All,

from what I understood, in QPA refinements is correct to leave 
untouched the literature structural (positional and thermal) 
parameters (assuming I have correct structural models for my 
analysis). About thermal parameters, is this always true or 
maybe correct in some case (what?) to refine an overall 
temperature factor for each phase of the mixture?

Best regards        Natale Perchiazzi


Date: Tue, 20 Nov 2001 11:21:15 +0000
To: rietveld_l@ill.fr
From: Lachlan Cranswick [l.m.d.cranswick@dl.ac.uk]
Subject: Re: overall temperature factor refinement


At 12:36 19/11/01 +0100, you wrote:
>Dear All,
>
>from what I understood, in QPA refinements is correct to leave untouched 
>the literature structural (positional and thermal) parameters (assuming 
>I have correct structural models for my analysis). About thermal parameters, 
>is this always true or maybe correct in some case (what?) to refine an 
>overall temperature factor for each phase of the mixture?
>
>Best regards        Natale Perchiazzi
>

(forwarded on behalf of Ian Madsen as the Rietveld listserver does not
love him at this point in time - and refuses to let him post out)

--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+

There are many and varied approaches being applied for QPA using
Rietveld based techniques (as evidenced in the recent IUCr CPD round
robin on QPA). Some seem to work better than others !!
 
The following is the approach that we take when accurate QPA is required
(but is not claimed to be the only valid procedure):-
 
(1) Start with the published values of crystal structure (including
thermal parameters). However, these values may only approximate the
structure found in the phase in your sample. This is especially true in
mineralogical materials where there may be variable composition (and
hence SOF's in specific sites).
 
(2) If some pure phase (or maybe a sample with very high concentration
of this phase) is available, then collect a "structure refinement"
quality data set (i.e. to very high upper limit of 2theta, good
resolution, good counting statistics etc...) and refine as much of the
structure as can be supported by the data (thermals, SOF's atom
coordinates as appropriate). Take these values and fix them for the
analysis of the 'real' sample - some parameters can still be refined at
lower concentrations, but in general we only refine the unit cell, peak
width/shape etc. At very low concentrations, even these values should be
fixed at the values determined from the high concentration sample (or at
least limited in the range over which they can vary) .
 
(3) For phases with variable composition (e.g. minerals) obtain
independent estimates of phase composition (e.g. electron probe
microanalysis) and adjust the SOF's accordingly.
 
(4) We have used the approach you suggested (refine an overall thermal
parameter), but have largely abandoned it in favour of the approach in
(2) above. Variations in the overall thermals can account for small
differences between the structure model used and the 'real' phase BUT,
the total thermal parameter should be checked for physical meaning - it
should be positive and have a value which is 'reasonable' for the type
of material being analysed. Large -ve or +ve values may indicate other
problems in the Rietveld model, or simply indicate you do not have
enough data to ensure stability. As with the refinement of any
parameter, you must be sure that the data you have supports the
parameter you are varying - a typical QPA data set (with high 2theta
cut-off say at 80-90 degrees) is unlikely to have enough data to support
refinement of thermal parameters, especially if the phase is not a major
component. 
 
Note also that the thermal parameters have a strong correlation with the
Rietveld scale factor - and hence on the determined phase abundances -
so do not vary them without good reason for doing so.
 
(5) Check your QPA against an independent measurement. The one we use
regularly is to calculate the expected elemental composition from the
QPA & the individual phase compositions and then compare this with
chemical analysis (e.g. XRF).
 
(6) In the recent QPA round robin, we used the approach in (2) above to
obtain our own estimates of QPA for verification of mixing Sample 1a
(95wt% fluorite) was used to refine details of the fluorite structure;
similarly, Sample 1b (95wt% corundum) for the corundum structure, Sample
1c (95wt% zincite) for the zincite structure - and then fixed these
values for the analysis of all 8 mixtures. 
 
I hope this helps - if not, feel free to contact me.
 
Cheers

o----------------------oo0oo---------------------------o 
     Ian Madsen 
        CSIRO Minerals 
        Box 312 
        Clayton South    3169 
        Victoria 
        AUSTRALIA 

     Phone      +61 3 9545 8785  direct 
                +61 3 9545 8500  switch 
                0417 554 935   mobile 
     FAX                +61 3 9562 8919 
     Email  Ian.Madsen@minerals.csiro.au 
o----------------------oo0oo---------------------------o 


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