Re: Rietveld refinement in TOPAS with parallel beam geometry

[Patrick Price]

Sorry about the confusion on the instrument configuration. I am new to
the field of x-ray diffraction. Hopefully this helps.
The Bruker D8 uses reflection geometry and a THETA : THETA goniometer,
where the x-ray source and detector can be move simultaneously on the
arms of the goniometer.  The x-ray source is Cu and is directed at a
Bruker multipurpose Si Gobel mirror which reflects a parallel beam of
Cu K-alpha (1&2) radiation at a 2-bounce Ge(022) analyzer crystal.  As
I understand it, the analyzer crystal filters our the K-alpha 2 peak,
producing monochromatic K-alpha 1radiation. There are no soller slits
on the primary side of the instrument. The beam is directed at the
specimen and the diffracted beam passes through a set of soller slits
and then to the point detector.
Thanks,
Patrick

On Fri, Dec 4, 2009 at 5:59 AM, Cline, James Dr.  wrote:
> Patrick,
>
> 
> From: Patrick Price [patrickpric...@gmail.com]
> Sent: Friday, December 04, 2009 6:30 AM
> To: Rietveld_l@ill.fr
> Subject: Rietveld refinement in TOPAS with parallel beam geometry
>
> Since this is my first post I will start with a brief introduction. My
> name is Patrick Price and I am in my second year of graduate school.
> My thesis work involves the investigation of phase equilibria in
> perovskites.
>
> I am using a Bruker D8 Discover diffractometer with parallel beam
> geometry. The diffractometer has a Cu K-alpha X-Ray source with a Si
> Gobel mirror and a Ge monochromator giving a parallel beam
> monochromatic x-ray source.
>
> This instrument description doesn't make sense.
>
> Regards,
>
> Jim
>
>
>  The receiving side has Soller slits and a
> Tl-doped NaI point detector. I am trying to teach myself how to use
> TOPAS to PROPERLY analyze my data using Rietveld refinement
> techniques.
>
> I have recently taken a scan of the NIST line profile 660 LaB6
> standard followed by scans of my perovskite powders using a step size
> of 0.02 degrees and scan time of 4 seconds.
>
> Most of the articles I have read are specific to convergent/divergent
> beam geometries and I do not know how much of that information
> transfers to parallel beam geometries. If anyone could help me answer
> the following questions I would greatly appreciate it. These questions
> mainly address which parameters should be refined with the LaB6
> standard when using parallel beam geometry.
> 1.      I need to use the scan of the LaB6 powders to characterize the
> contributions of the instrument to the diffraction profile. Starting
> with the emission profile, TOPAS asks for the wavelength, the Area,
> and the Lorentz Half Width. First, I assume the wavelength I should be
> the more recent Cu Ka wavelength of 0.154059 nm instead of 0.154056
> nm. Second, does Cu Ka have a definite Lorentz HW and “Area” or should
> these parameters be refined with the LaB6 diffraction pattern?
> 2.      Since I have a Ge monochromater I assume the Lorentz polarization
> factor should be fixed at 27.3 (Is this correct?). Obviously the
> lattice parameters and atomic positions would be fixed.
> 3.       I read that you should NOT refine both the zero shift error and
> sample displacement, and since it is parallel beam I only refine the
> zero shift error. Should I refine surface roughness, absorption, or
> sample tilt with the LaB6? (Currently I do not refine these)
> 4.      Am I correct in assuming that I do not have any EQUITORIAL
> convolutions (e.g. from slits, FDS, beam spill, VDS) since it is
> parallel beam geometry? What about TUBE TAILS?
> 5.      I am using the Finger_et_al  method to refine the AXIAL
> convolutions, however I often get a large error associated with the S
> value (sample length), even when my GOF is decent (<1.45). Do any of
> you know why this would happen?
> 6.      Should I refine the “Scale” or scale factor. (Currently I do)
> 7.      IMPORTANT: Originally I was refining the crystallite size but it
> always refined to a very small value (~300nm), where as NIST claims
> 660 LAB6 should have a mean grain size of a few microns or more. I
> assume this happens because the TOPAS is accounting for instrument
> caused peak broadening by making the crystallite size smaller than it
> actually is in the software. However, when I do refine the grain size
> I do get a better fit. Should I leave this unchecked, refine it, or
> fix it at a reasonable value of ~2500 nm.
>
> In summary, currently I am only refining the Lorentz HW and “Area” in
> the emission profile, zero shift error, the Finger parameters (S & H),
> the scale factor, and nothing else.
> I am unsure if I should be refining anything else such as the
> crystallite size, tube tails and other forms of equatorial
> convergence, or if there is something else that is important which I
> am disregarding completely. I am also unsure if I am correct in
> refining Lorentz HW and area in the emission profile.
> Sorry if I got a little long winded; I just wanted to give enough
> det

RE: Rietveld refinement in TOPAS with parallel beam geometry

[Cline, James Dr.]

Patrick,


From: Patrick Price [patrickpric...@gmail.com]
Sent: Friday, December 04, 2009 6:30 AM
To: Rietveld_l@ill.fr
Subject: Rietveld refinement in TOPAS with parallel beam geometry

Since this is my first post I will start with a brief introduction. My
name is Patrick Price and I am in my second year of graduate school.
My thesis work involves the investigation of phase equilibria in
perovskites.

I am using a Bruker D8 Discover diffractometer with parallel beam
geometry. The diffractometer has a Cu K-alpha X-Ray source with a Si
Gobel mirror and a Ge monochromator giving a parallel beam
monochromatic x-ray source.

This instrument description doesn't make sense.

Regards,

Jim


 The receiving side has Soller slits and a
Tl-doped NaI point detector. I am trying to teach myself how to use
TOPAS to PROPERLY analyze my data using Rietveld refinement
techniques.

I have recently taken a scan of the NIST line profile 660 LaB6
standard followed by scans of my perovskite powders using a step size
of 0.02 degrees and scan time of 4 seconds.

Most of the articles I have read are specific to convergent/divergent
beam geometries and I do not know how much of that information
transfers to parallel beam geometries. If anyone could help me answer
the following questions I would greatly appreciate it. These questions
mainly address which parameters should be refined with the LaB6
standard when using parallel beam geometry.
1.  I need to use the scan of the LaB6 powders to characterize the
contributions of the instrument to the diffraction profile. Starting
with the emission profile, TOPAS asks for the wavelength, the Area,
and the Lorentz Half Width. First, I assume the wavelength I should be
the more recent Cu Ka wavelength of 0.154059 nm instead of 0.154056
nm. Second, does Cu Ka have a definite Lorentz HW and “Area” or should
these parameters be refined with the LaB6 diffraction pattern?
2.  Since I have a Ge monochromater I assume the Lorentz polarization
factor should be fixed at 27.3 (Is this correct?). Obviously the
lattice parameters and atomic positions would be fixed.
3.   I read that you should NOT refine both the zero shift error and
sample displacement, and since it is parallel beam I only refine the
zero shift error. Should I refine surface roughness, absorption, or
sample tilt with the LaB6? (Currently I do not refine these)
4.  Am I correct in assuming that I do not have any EQUITORIAL
convolutions (e.g. from slits, FDS, beam spill, VDS) since it is
parallel beam geometry? What about TUBE TAILS?
5.  I am using the Finger_et_al  method to refine the AXIAL
convolutions, however I often get a large error associated with the S
value (sample length), even when my GOF is decent (<1.45). Do any of
you know why this would happen?
6.  Should I refine the “Scale” or scale factor. (Currently I do)
7.  IMPORTANT: Originally I was refining the crystallite size but it
always refined to a very small value (~300nm), where as NIST claims
660 LAB6 should have a mean grain size of a few microns or more. I
assume this happens because the TOPAS is accounting for instrument
caused peak broadening by making the crystallite size smaller than it
actually is in the software. However, when I do refine the grain size
I do get a better fit. Should I leave this unchecked, refine it, or
fix it at a reasonable value of ~2500 nm.

In summary, currently I am only refining the Lorentz HW and “Area” in
the emission profile, zero shift error, the Finger parameters (S & H),
the scale factor, and nothing else.
I am unsure if I should be refining anything else such as the
crystallite size, tube tails and other forms of equatorial
convergence, or if there is something else that is important which I
am disregarding completely. I am also unsure if I am correct in
refining Lorentz HW and area in the emission profile.
Sorry if I got a little long winded; I just wanted to give enough
detail so people could answer. Thank you in advance for your help.
Patrick




James P. Cline
Ceramics Division   
National Institute of Standards and Technology
100 Bureau Dr. stop 8520 [ B113 / Bldg 217 ]
Gaithersburg, MD 20899-8523USA
jcl...@nist.gov
(301) 975 5793
FAX (301) 975 5334

Re: rietveld refinement

[Leonid Solovyov]

>Going back to Leonid's question, well the answer is easy: check the 
>premises... the assumptions behind the use of the TCH function are
>not 
>compatible with he presence of a lognormal distribution of domains.

But the TCH function gave ALMOST PERFECT fit for the Size-Strain Round
Robin profiles. Where do we loose information applying THC in Rietveld
refinement? In this "ALMOST"? 
Or, maybe, the distribution dispersion was erroneously determined in
the SSRR and, actually, this information can not be unambiguously
derived solely from diffraction?

Leonid




__ 
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Meet the all-new My Yahoo! - Try it today! 
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Re: rietveld refinement

[Matteo Leoni]

just my 2 cents...

> Could I be so stupid to say that such kind of works, including mine, are
> nothing?
  
following Nicolae, I should also add to the list myself as well as most 
people participating to the four editions of the size-strain 
conference/meeting/workshop and all participants to Davor's size-strain  
round-robin.

I bet people should spend more time in the library... this is the point.
This is also a self criticism as I'm not the best library addict (though,  
online resources has simplified life enormously)... 

We should not try to use line profile analysis methods as a black box: 
it is easy to obtain numbers from measured data (with a proper software a 
computer can do it automatically), but then it is in the ability of the 
scientist to attach them a proper physical meaning.
What it is difficult (perhaps impossible?) is willing and pretending to do 
it in the general case as we're dealing with something that has no precise 
rules (domain size, shape and their distributions are not properties of 
the materials, nor they can be easily predicted in advance).
Some simple cases have been studied and some references already posted by 
several people in here, and in most of them the agreement between 
diffraction and alternative techniques is quite good: just in few cases, 
though, enough information is available to interpret the strain broadening 
fully in terms of physical defects present in the material, or to model 
the size term using a more or less complex distribution of (iso-shape) 
domains. But also in those cases the result is the one compatible with the 
model assumptions and does not pretend to be "God's truth".

So welcome the round robin on a more complex sample to test the maturity 
of the algorithms (they should be even tested on simpler examples, as 
concluded on the latest size-strain conference, but that's another 
story..), but beware that without any a priori info (or with a wrong 
one!), a vast set of odd results can be obtained. As a comparison, it 
would be like pretending to do a search match, a structure solution or,  
even worse, a Rietveld refinement on a material for which we don't know  
any chemical information... 

Going back to Leonid's question, well the answer is easy: check the 
premises... the assumptions behind the use of the TCH function are not 
compatible with he presence of a lognormal distribution of domains. It can 
be proven mathematically that the Fourier coefficients for a profile 
describing a lognormal distribution of domains have a hook at low Fourier 
number, hook that cannot be reproduced by any whatsoever voigtian or 
voigtian-like curve. This is a common problem in the use of Voigt and 
voigt-like curves in describing the peak profiles from nanocrystalline 
powders and is also the main source of the "superlorentzian" peak tails 
(they are a trick to get rid of the physical information contained in the  
profile ;) we are a bit masochist, aren't we?)

Best regards
Mat


-- 
Matteo Leoni
Department of Materials Engineering and Industrial Technologies 
University of Trento
38050 Mesiano (TN)
ITALY
Tel +39 0461 882416e-mail:   [EMAIL PROTECTED]
Fax +39 0461 881977Web:   www.matteoleoni.ing.unitn.it

Re: rietveld refinement

[Nicholas Armstrong]

Hi,
At the moment there is development of a NIST Nanocrystallite Size Standard 
Reference Material (SRM1979).

Jim Cline and I are working on this SRM. It will include two materials:
(1) CeO2 with spherical crystallite shape and size distribution in the ~20nm 
size range (isotropic shape);
(2) ZnO with cylindrical or hexagonal prismatic crystallite shape with height 
in the, H~60-80nm and diameter, D~20-30nm range (anisotropic shape).

This outlined in introduction of Armstrong et al (2004b) chapt.8, in 
"Diffraction analysis of the microstructure of materials", Springer-Verlag, 
pp.187--227.

In both cases the Bayesian/MaxEnt method will be used to determine the 
*physical* size distribution and shape. For example in the case of (1), the 
method tests the model for a spherical crystallite shape, while also testing 
various size distribution models i.e lognormal, gamma etc. For this case a 
lognormal size distribution has found to be the appropriate distribution. In 
the case of (2) the distributions are for H and D, respectively, while testing 
different shape models can also be carried out. This presently being developed.

The Bayesian/MaxEnt method is a general formulation which tests the underlying 
assumption of various models and determines the most probable size distribution 
and crystallite shape.

There is lots of working/development going on!!
Regards, Nicholas


- Original Message -
From: Nicolae Popa <[EMAIL PROTECTED]>
Date: Monday, November 22, 2004 7:12 pm

> 
> >
> > It is also true that no development has been done for anisotropy. 
> Not yet!
> >
> > Well, if all previous works about trying to take account of 
> size/strain> anisotropy in the Rietveld method are nothing yet, 
> this allows to
> > close the discussion. Let us wait for really serious developments to
> > come.
> 
> You not correctly understood me (I would like to believe that not
> ill-disposed).
> I said that no development for size anisotropy has been done including
> "physical" size distributions (like lognormal, etc.) as were done 
> for the
> isotropic case.
> For example: Langford, Louer & Scardi, JAC (2000) 33, 964-974 and 
> Popa &
> Balzar JAC (2002) 35, 338-346.
> Concerning previous (phenomenological) works trying to take account of
> strain/size anisotropy in the Rietveld method, I have myself a 
> contribution:"The (hkl) dependence of diffraction-line broadening 
> caused by strain and
> size for all Laue groups in Rietveld refinement, N. C. Popa, J. 
> Appl. Cryst.
> (1998) 31, 176-180."
> Could I be so stupid to say that such kind of works, including 
> mine, are
> nothing?
> 
> Best wishes,
> Nicolae Popa
> 
> 
> 
> 
> 
> 


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Re: rietveld refinement

[Daniel Chateigner]

At least the anisotropic formalism by Popa (J. Appl. Cryst.
(1998) 31, 176-180) has been used for anisotropic shape refinements using 
the MAUD Rietveld codes, on textured samples: Thin Solid Films 450, 2004, 
216-221.

daniel
  A 11:12 AM 11/22/04 +0300, vous avez écrit :
>
> It is also true that no development has been done for anisotropy. Not yet!
>
> Well, if all previous works about trying to take account of size/strain
> anisotropy in the Rietveld method are nothing yet, this allows to
> close the discussion. Let us wait for really serious developments to
> come.
You not correctly understood me (I would like to believe that not
ill-disposed).
I said that no development for size anisotropy has been done including
"physical" size distributions (like lognormal, etc.) as were done for the
isotropic case.
For example: Langford, Louer & Scardi, JAC (2000) 33, 964-974 and Popa &
Balzar JAC (2002) 35, 338-346.
Concerning previous (phenomenological) works trying to take account of
strain/size anisotropy in the Rietveld method, I have myself a contribution:
"The (hkl) dependence of diffraction-line broadening caused by strain and
size for all Laue groups in Rietveld refinement, N. C. Popa, J. Appl. Cryst.
(1998) 31, 176-180."
Could I be so stupid to say that such kind of works, including mine, are
nothing?
Best wishes,
Nicolae Popa


A Quantitative Texture Analysis Internet Course:
http://qta.ecole.ensicaen.fr/

The Crystallographic Open Database:
http://www.crystallography.net

Daniel Chateigner
Professeur
Co-Editor Journal of Applied Crystallography
CRISMAT-ENSICAEN, UMR CNRS n° 6508
Bd. Maréchal Juin, 14050 Caen FRANCE
Tel prof: 33 (0) 231452611
Fax:  33 (0) 231951600
http://www.ecole.ensicaen.fr/~chateign/danielc/

Re: rietveld refinement

[Nicolae Popa]

>
> It is also true that no development has been done for anisotropy. Not yet!
>
> Well, if all previous works about trying to take account of size/strain
> anisotropy in the Rietveld method are nothing yet, this allows to
> close the discussion. Let us wait for really serious developments to
> come.

You not correctly understood me (I would like to believe that not
ill-disposed).
I said that no development for size anisotropy has been done including
"physical" size distributions (like lognormal, etc.) as were done for the
isotropic case.
For example: Langford, Louer & Scardi, JAC (2000) 33, 964-974 and Popa &
Balzar JAC (2002) 35, 338-346.
Concerning previous (phenomenological) works trying to take account of
strain/size anisotropy in the Rietveld method, I have myself a contribution:
"The (hkl) dependence of diffraction-line broadening caused by strain and
size for all Laue groups in Rietveld refinement, N. C. Popa, J. Appl. Cryst.
(1998) 31, 176-180."
Could I be so stupid to say that such kind of works, including mine, are
nothing?

Best wishes,
Nicolae Popa

Re: rietveld refinement

[Nicholas Armstrong]

Hi,
With regards to size/shape/distribution analysis of  line profiles, the papers 
by Armstrong et al. (2004a,b,c) discusses a Bayesian/Maximum Entropy method, 
that determines these quantities from the line profile data. This can also 
resolve  bimodal distributions from  line profile data.

This method  tests models for shape/size distribution and modal properties 
using Bayesian analysis. The maximum entropy components is a generalisation of 
the approach presented in A. Le Bail and D. Lou?r. J. Appl. Cryst. (1978). 11, 
50-55. It preserves the positivity of the distribution, determines the most 
probable distribution give the line profile data, instrument profile and 
statistical noise.

Recent publications can be found at the following:
http://nvl.nist.gov/pub/nistpubs/jres/109/1/cnt109-1.htm;
Armstrong et al (2004b) chapt.8, in "Diffraction analysis of the microstructure 
of materials", Springer-Verlag, pp.187--227; 
WA5 Armstrong et al. (2004c), http://www.aip.org.au/wagga2004/.

Regards,Nicholas

Dr Nicholas Armstrong
Department of Applied Physics
University of Technology Sydney
PO Box 123 
Broadway NSW 2007

Ph: (+61-2) 9514-2203
Fax: (+61-2) 9514-2219
E-mail: [EMAIL PROTECTED]

- Original Message -
From: Armel Le Bail <[EMAIL PROTECTED]>
Date: Sunday, November 21, 2004 11:10 pm

> 
> It is also true that no development has been done for anisotropy. 
> Not yet!
> 
> Well, if all previous works about trying to take account of 
> size/strainanisotropy in the Rietveld method are nothing yet, this 
> allows to
> close the discussion. Let us wait for really serious developments to
> come.
> 
> Armel
> 
>   
> 
> 


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Re: rietveld refinement

[Whitfield, Pamela]

Title: RE: rietveld refinement





I'm afraid that you got the wrong end of the stick -I wasn't talking about the application of peak broadening to size distribution, I was commenting that determining crystallite shape is perfectly possible (some comments were flying that said otherwise), and I've done it myself.  For that purpose a sample approaching monodisperse is helpful.  It would be a bit pointless trying to determine the size distribution of a monodisperse sample !! :-)

I did send an email that I think only went to Armel by mistake making this clearer.  I was having a slow morning! :-)


Pam 


-Original Message-
From: Nicolae Popa
To: [EMAIL PROTECTED]
Sent: 11/21/2004 5:04 AM
Subject: Re: rietveld refinement


 


 Doesn't help with a size distribution, as it only works well for a
relatively monodisperse material - but it does work under some
circumstances.
Pam 
 
I disagree, it works also for large dispersion. One example you can find
in JAC (2002) 35, 338-346, "Sample 2". It is true that the specific peak
profile (that can be "superlorentzian") can not be found in no available
Rietveld code. It is also true that no development has been done for
anisotropy. Not yet!
 
Best wishes,
Nicolae Popa

Re: rietveld refinement

[Armel Le Bail]

It is also true that no development has been done for anisotropy. Not yet!
Well, if all previous works about trying to take account of size/strain
anisotropy in the Rietveld method are nothing yet, this allows to
close the discussion. Let us wait for really serious developments to
come.
Armel
  

Re: rietveld refinement

[Nicolae Popa]

Title: RE: rietveld refinement



 

   Doesn't help with a size 
  distribution, as it only works well for a relatively monodisperse material - 
  but it does work under some circumstances.
  Pam 
   
  I disagree, it works also 
  for large dispersion. One example you can find in JAC (2002) 35, 338-346, 
  "Sample 2". It is true that the specific peak profile (that can be 
  "superlorentzian") can not be found in no available Rietveld code. It is also 
  true that no development has been done for anisotropy. Not 
  yet!
   
  Best wishes,
  Nicolae 
Popa

Re: rietveld refinement

[Nicolae Popa]

> So I cannot let say that "Significantly different "physical"
> size distributions could describe equally well the peak profile".
> This is confusing. You may say that : significantly different
> crystallite shapes could describe equally well the peak profile
> in cubic symmetry. I am not sure that this sentence is
> valuable equally for other symmetries when looking at all

Sorry, it seems me that rather your sentence is confusing, not mine.

In the example with CeO2 the crystallites are quite spherical
(one shape) even seen by microscope. But two significantly different
distributions of the
sphere radius (6a1, 6a2) (lognormal & gamma, respectively) given quite the
same column length distribution
(6b1, 6b2) and practically the same peak profile. It is no matter here of
different crystallite shapes because the shape is unique (sphere). And also
the cubic symmetry has no relevance, this should happen for any symmetry (I
mean not an unique solution for the sphere radius distribution).
(By the way, the sample of CeO2 in discussion is just the sample used in the
round-robin paper that you co-authored; in this last paper we used only the
lognormal distribution, but doesn't mean that this is the unique solution
from powder diffraction).

Concerning the different crystallite shapes, this is another storry. I said
that even if the cristallites are not spherical, it is not obligatory to
observe an anisotropic size broadening effect. Not spherical crystallites is
only the necessary condition for size anisotropy effect, but not sufficient.
The anisotropic size broadening effect is observable only if the non
spherical shape is preferentially orientated with respect to the crystal
axes (don't confuse with the texture). It is the case of your nickel
hydroxyde in which the plate-like normal is preferentially oriented along
the hexagonal c axis. But, if the not spherical crystallite shapes are
randomly oriented with respect to the crystal axes (which is possible) the
size broadening effect is isotropic and, only from powder diffraction, we
can conclude erroneously that the crystallites are spherical.
On the other hand, if the anisotropy is observed, the crystallite shape (and
the distributions of specific radii) can not be uniquely determined only
from powder diffraction. What we can determine is an apparent shape (and
column lengths averages). Has any sense, in this case, to search for so
called "physical models", or we have to be content with "phenomenological"
findings (so much blamed, at least implicitely)? It is only a question,
valid also for the strain effect.


> So, let us have more fun with a size strain round robin on some
> complex sample  (or even a size-only round robin not on a
> cubic compound ;-).

I agree entirely.

Best wishes,
Nicolae Popa

Re: rietveld refinement

[Mutta Venkata Kamalkar (pBSc)]

can anyone send me a soft copy of the following paper
J. Appl. Cryst. (1978). 11, 50-55.


thanks 
venkat

+++
M Venkata Kamalakar
Junior Research Fellow,
S.N.Bose.National Centre for Basic Sciences,
Block-JD, Sector-3, Salt Lake,
Kolkata, Pin: 700 098.
Phone no: 033 23355705/6/7/8 Extn: 404, 104, 301.
+++

-- Original Message ---
From: Armel Le Bail <[EMAIL PROTECTED]>
To: [EMAIL PROTECTED]
Sent: Fri, 19 Nov 2004 08:43:11 +0100

> >It is a separate question to what extent those distributions are
> >"physical"...
> 
> Simple attempts to establish that at least the size distributions
> obtained from a mixture of two samples with same composition
> and two very different size distributions, are close to the
> expected result, establishing some self-consistency of the
> methodology, if not that they are "physical" (I believe they are
> "physical" in case of size-only effect).
> 
> See for instance J. Appl. Cryst. (1978). 11, 50-55.
> This can be found also (in french) in a thesis :
> http://tel.ccsd.cnrs.fr/documents/archives0/00/00/70/41/index_fr.html
> (self citation...;-). Things have not changed a lot since these
> old times.
> 
> Armel
--- End of Original Message ---

RE: rietveld refinement

[Mutta Venkata Kamalkar (pBSc)]

can you please send me the soft copy of the paper you referred to. We don't
have access to that journal...

very much sincerely yours
venkat

From: Armel Le Bail <[EMAIL PROTECTED]>
To: [EMAIL PROTECTED]
Sent: Fri, 19 Nov 2004 16:49:42 +0100

> >I'd have to disagree on this point - troublemaker I suppose!  I've 
> >followed the work by Langford and Louer closely, and have successfully 
> >applied their techniques
> 
> I do not understand on what point exactly you disagree.
> The cited paper about size effect in nickel hydroxyde
> is co-authored by D. Louer, and may still seem kosher to him ;-).
> The full reference is :
> 
> A. Le Bail and D. Louër. J. Appl. Cryst. (1978). 11, 50-55
> [doi:10.1107/S0021889878012662]
> Title: Smoothing and validity of crystallite-size distributions from 
> X-ray line-profile analysis Abstract: A smoothing procedure is 
> described which eliminates spurious details on crystallite-size 
> distribution functions deduced from X-ray line profiles. It is based 
> on a least-squares process with a stabilization scheme and is 
> applied to composite specimens prepared by mixing known quantities 
> of samples of nickel hydroxide, whose crystallite size-distribution 
> functions were previously determined. Calculated and observed 
> distributions and average sizes are compared. The results are 
> reasonably good and show the self-consistency of the method.
> 
> Best regards,
> 
> Armel
--- End of Original Message ---

Re: rietveld refinement

[Leonid Solovyov]

Let me put a more particular question on the size estimation from
Rietveld refinement.
If we refined the size-broadening parameters P and X of the
Thompson-Cox-Hastings function (as they are defined in J. Appl. Cryst.
(2004) 911) and corrected them for the instrumental contribution, then
can we say something about the coherent domain size DISTRIBUTION
assuming the domains approximately spherical?

Leonid Solovyov




__ 
Do you Yahoo!? 
Meet the all-new My Yahoo! - Try it today! 
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RE: rietveld refinement

[Armel Le Bail]

I'd have to disagree on this point - troublemaker I suppose!  I've 
followed the work by Langford and Louer closely, and have successfully 
applied their techniques
I do not understand on what point exactly you disagree.
The cited paper about size effect in nickel hydroxyde
is co-authored by D. Louer, and may still seem kosher to him ;-).
The full reference is :
A. Le Bail and D. Louër. J. Appl. Cryst. (1978). 11, 50-55
[doi:10.1107/S0021889878012662]
Title: Smoothing and validity of crystallite-size distributions from X-ray 
line-profile analysis
Abstract: A smoothing procedure is described which eliminates spurious 
details on crystallite-size distribution functions deduced from X-ray line 
profiles. It is based on a least-squares process with a stabilization 
scheme and is applied to composite specimens prepared by mixing known 
quantities of samples of nickel hydroxide, whose crystallite 
size-distribution functions were previously determined. Calculated and 
observed distributions and average sizes are compared. The results are 
reasonably good and show the self-consistency of the method.

Best regards,
Armel

RE: rietveld refinement

[Whitfield, Pamela]

Title: RE: rietveld refinement





 


>There was a strong size anisotropy. The X-ray study cannot
>gives the shape (you see that I agree with you on that point),
>an electron microscopy study showed that the coherently
>diffracting domains are plate-like crystallites aggregated along
>the c axis.


I'd have to disagree on this point - troublemaker I suppose!  I've followed the work by Langford and Louer closely, and have successfully applied their techniques to analyse anisotropic broadening to non-spherical (admittedly not very complex shapes - rods and octahedra) nanomaterials.  Doesn't help with a size distribution, as it only works well for a relatively monodisperse material - but it does work under some circumstances.

Pam

Re: rietveld refinement

[Armel Le Bail]

Small error, sorry,
three of the possible arrangement were :
   |--|
   |  |--|
   |  |  |--|--|
   |--|--|--|--|
   |--|
   |  | |--|
   |  |--|--|  |
   |--|--|--|--|
   |--|
   |  | |--|
   |  | |  | |--|  |--|
   |--| |--| |--|  |--|
Armel

Re: rietveld refinement

[Armel Le Bail]

What we see in diffraction is the column lengths (volume & area
averaged) and the classics were not full ignoring the shape and radius
(radii) distribution(s).
Nicolae Popa (Mister, Messieur, Don, Dom, etc.)
Of course I agree with you that completely different shapes
may correspond to the same distribution of column length.
For diffraction, and considering one direction, the columns of
cells look exactly as if they were separated. So, obviously :
   |--|
   |  |--|
   |  |  |--|--|
   |--|--|--|--|
gives the same column length distribution as :
   |--|
   |  | |--|
   |  |--|--|  |
   |--|--|--|--|
or as separated columns :
   |--| [--|
   |  | |  |
   |  | |  | |--|  |--|
   |--| |--| |--|  |--|
or etc, taking the columns in the bottum-up sense.
But, with these 3 different models (and more are possible), you
would not have the same distribution of column lengths in the
orthogonal direction...
My problem with most recent papers about size effect is that
they always consider cubic compounds, possibly spherical
crystallites etc. In such a case, all directions are gathered in
one.
Could you study something more complex sometimes ?
In my self-citation work, the study was made on nickel
hydroxyde, with hexagonal structure, looking for columns
exclusively in the direction of the c axis, using the Bertaut
formulations, with careful extraction of the column lenght
distribution after deconvolution from the instrumental effect.
There was a strong size anisotropy. The X-ray study cannot
gives the shape (you see that I agree with you on that point),
an electron microscopy study showed that the coherently
diffracting domains are plate-like crystallites aggregated along
the c axis.
So I cannot let say that "Significantly different "physical"
size distributions could describe equally well the peak profile".
This is confusing. You may say that : significantly different
crystallite shapes could describe equally well the peak profile
in cubic symmetry. I am not sure that this sentence is
valuable equally for other symmetries when looking at all
profiles. You would have maybe to restrain to the consideration
in one direction : if no change is produced in all other directions,
what is the degree of freedom for the crystallite shape now ?
Is it possible to organize the columns differently in one
direction without changing also the peak profiles in all other
directions for a triclinic compound ?
So, let us have more fun with a size strain round robin on some
complex sample  (or even a size-only round robin not on a
cubic compound ;-).
Best
Armel

Re: rietveld refinement

[Nicolae Popa]

>
> >The diffraction alone can not decide. Significantly different "physical"
> >size distributions could describe equally well the peak profile
> >(J.Appl.Cryst. v35 (2002) 338-346 - self citation too).
> >Nicolae Popa
>
> Looking at your figures 6b1 and 6b2, I measure how we
> differ on the sense of "significantly different". As you comment
> in the text, "The curves 1 and 2 differ in the position of the
> maximum by only 2 A and in height of the maximum by
> 9.76%".
>
> I would not call that "significantly different" but "very similar".
>
> Armel

Yes, but the figure 6b represents the COLUMN LENGTH distribution not the
CRYSTALLITE RADIUS distribution (in this case of spherical crystallites).
The crystallite radius distributions are given in 6a1 and 6a2 (lognormal and
gamma, respectively) and they are significantly different, what can be seen
also in the table 1: the average radius and the dispersions are completely
different. Nevertheless the profile of the diffraction peak is equaly well
described. And the column length distribution is quite the same (as
discussed in text and as you observed). But when we are speaking about the
"physical model" we understand in fact the distribution of the crystallite
radius (if spherical). Is that lognormal or gamma? Is the average radius
90(6) or 69(1) Angstroms, is the parameter c (determining the dispersion)
0.18 or 0.39?  We can not say only from diffraction that one is more
"physical" than other. On the other hand is the column length distribution a
full "physical" description of the crystallites, I mean of the shape and
radius (radii) distribution? I think not. You can imagine, for example, that
the crystallites are even not spherical, but ellipsoidal. It is easy to
understand that if the Euler angles representing the orientations of the
ellipsoidal principal axes with respect to the crystal axes are UNIFORMLY
distributed in their domains of definition, will be NO anisotropy effect.
Then we can think the crystallite are spherical with a certain distribution
of radius, when in fact they are ellipsoidal with other distributions of
(three) radii. But the column length distribution (and the peak profile) is
the same. What we see in diffraction is the column lengths (volume & area
averaged) and the classics were not full ignoring the shape and radius
(radii) distribution(s).

Nicolae Popa (Mister, Messieur, Don, Dom, etc.)

Re: rietveld refinement

[Armel Le Bail]

The diffraction alone can not decide. Significantly different "physical"
size distributions could describe equally well the peak profile
(J.Appl.Cryst. v35 (2002) 338-346 - self citation too).
Nicolae Popa
Looking at your figures 6b1 and 6b2, I measure how we
differ on the sense of "significantly different". As you comment
in the text, "The curves 1 and 2 differ in the position of the
maximum by only 2 A and in height of the maximum by
9.76%".
I would not call that "significantly different" but "very similar".
Armel

Re: rietveld refinement

[Nicolae Popa]

> methodology, if not that they are "physical" (I believe they are
> "physical" in case of size-only effect).

The diffraction alone can not decide. Significantly different "physical"
size distributions could describe equally well the peak profile
(J.Appl.Cryst. v35 (2002) 338-346 - self citation too).

Nicolae Popa

Re: rietveld refinement

[Armel Le Bail]

It is a separate question to what extent those distributions are
"physical"...
Simple attempts to establish that at least the size distributions
obtained from a mixture of two samples with same composition
and two very different size distributions, are close to the
expected result, establishing some self-consistency of the
methodology, if not that they are "physical" (I believe they are
"physical" in case of size-only effect).
See for instance J. Appl. Cryst. (1978). 11, 50-55.
This can be found also (in french) in a thesis :
http://tel.ccsd.cnrs.fr/documents/archives0/00/00/70/41/index_fr.html
(self citation...;-). Things have not changed a lot since these
old times.
Armel

Re: rietveld refinement

[Whitfield, Pamela]

This is where the real fun starts (if you're a masochist!).  I just finished
doing some work along those lines this afternoon, and managed to get it to
work(ish) eventually.  The double-Voigt analysis can give you Dv (volume
weighted domain size) and Ds (surface weighted domain size).  If you assume
a log-normal size distribution (not completely unreasonable) it is possible
to work backwards and derive the distribution from these values.  However,
you need really good data or you get complete rubbish because of the
correlations.  
Davor Balzar covers some of this in his recent J.Appl.Cryst. paper (page 911
latest issue) and Popa and Balzar, J.Appl.Cryst. v35 (2002) 338-346.  It
gave me a bit of a brain-ache but it does work!

Pam

Dr Pamela Whitfield CChem MRSC
Energy Materials Group
Institute for Chemical Process and Environmental Technology
Building M12
National Research Council Canada
1200 Montreal Road
Ottawa  ON   K1A 0R6
CANADA
Tel: (613) 998 8462 Fax: (613) 991 2384
Email: 
ICPET WWW: http://icpet-itpce.nrc-cnrc.gc.ca


-Original Message-
From: Maxim V. Lobanov [mailto:[EMAIL PROTECTED]
Sent: November 18, 2004 1:51 PM
To: [EMAIL PROTECTED]


What I remember is that "Breadth" outputs the distributions. What might
be the solution is to convert (write a program) Rietveld "peak output"
to "Breadth" input. However, I have never done this myself; I converted
Xfit-style
peak files only, which is pretty straightforward. 
It is a separate question to what extent those distributions are
"physical"...
Sincerely,
Maxim.
___
Maxim V. Lobanov <[EMAIL PROTECTED]>
Department of Materials Science and Engineering
University of Tennessee
101 South College
1413 Circle Dr.
Knoxville, TN 37996

Re: rietveld refinement

[Maxim V. Lobanov]

What I remember is that "Breadth" outputs the distributions. What might
be the solution is to convert (write a program) Rietveld "peak output"
to "Breadth" input. However, I have never done this myself; I converted 
Xfit-style
peak files only, which is pretty straightforward. 
It is a separate question to what extent those distributions are
"physical"...
Sincerely,
Maxim.
___
Maxim V. Lobanov <[EMAIL PROTECTED]>
Department of Materials Science and Engineering
University of Tennessee
101 South College
1413 Circle Dr.
Knoxville, TN 37996

RE: rietveld refinement

[Christopher Chervin]

Hi Venkat,

If you mean to use rietveld on X-ray data I don't think you can get 
particle size distributions.  X=ray data will give you an average 
crystallite size but this is not a distribution just an average.  Also, it 
is crystallite size and the actual particles size can be different if the 
crystallites are agglomerated.

Have you considered trying dynamic light scattering?  


Cheers,

Chris

will > 
> 
> I am a new user of rietveld softwares. Can anyone suggest me any program 
or
> software based on reitveld algorithm and giving the following results...
> 
> 1) size distribution of particles in a sample.
> 
> 
> yours sincerely
> venkat
> 

RE: Rietveld refinement and PDF refinement ?

[Radaelli, PG (Paolo)]

> do you really have the 
> resolution even on
> HRPD to see the diffuse scattering between Bragg peaks at 
> high Q ?

No we don't, but this is not the main point (by the way, we don't use HRPD
for PDF, it doesn't go to sufficiently short wavelengths).  The main reason
to go to high Q is to avoid truncation errors.  If you truncate S(Q), all
your G(r) peaks will be convoluted with the Fourier transform of a step
function, which is a sinx/x function.  The width of the central peak is
roughly 1/Qmax.  If you use a wavelength of 0.5 A, this corresponds to about
0.08 A, or an equivalent B of 0.5.  This in itself can be a problem when you
want to look at sharp correlation features.  Even worse, the "ripples" will
propagate to adjacent PDF peaks, generating unphysical features.  There are
ways to suppress the ripples by convoluting the data with an appropriate
smooth function rather than truncating them (these are extensively used in
disordered materials work), but they all tend to broaden the features.  You
can also fit a model including the ripples (as in PDFfit) but it is clearly
better not to have them if you are trying to exploit the model independence
of PDF.  Going to high Q does not solve all the problems. If the high-Q data
are noisy, your truncation function will have higher frequency but also
higher (and random) amplitude in the ripples, so there is always a
compromise Qmax, depending on statistics.  Finally, very high-Q data are
quite difficult to normalise, because of the epithermal background.   


> You may
> get better temperature factors with high-Q PDF refinement, 
> but you will
> also do that with high-Q Rietveld.

Generally, all crystallographic parameters come out worse from PDF
refinements than from Rietveld on the same data sets.  I think this is
because you are trying to fit an average structure to something that
contains correlations, so the fit is bound to be worse.  You could fit a
correlated model, but then you would not get "temperature factors" in the
usual sense. 

> I also doubt that just because PDF uses data between the 
> Bragg peaks, then
> it must be superior for seeing details not centered on atoms 
> in real space
> in a crystal, eg the split atom sites in (In/Ga)As). You 
> might do just as
> well with Bragg scattering if you use the result of Rietveld 
> refinement to
> construct a Fourier map of the structure. Happily, a sampling of
> reciprocal space (Bragg peaks) is sufficient to re-construct 
> the entire
> density of a periodic structure in real space, not just point 
> atoms, to a
> resolution limited only by Q.

You are right.  PDF is not always superior.  It is the interpretation of the
Fourier density in terms of correlated displacements that emerges uniquely
from PDF, although you can often guess it right from the Fourier map in the
first place.  The case of Jahn-Teller polarons in manganites (La,Ca)MnO3 is
quite illuminating.  Several groups noticed that the high-temperature phase
(above the CMR transition) has large DW factors for O.  We showed that this
affects primarily the longitudinal component along the Mn-O bonds, and
guessed that this was caused by an alternation of short and long Mn-O
distances.  Simon Billinge showed the same thing quite convincingly from PDF
data.  Only the latter can be considered "direct evidence" (with some
caveats).

> But you do agree that in a PDF experiment you integrate over 
> energy, so
> you only see an instantaneous snapshot of the structure...

Yes, I agree with this and the fact that inelasticity corrections are an
issue.  Sometimes they are exploited to obtain additional information, and
there is a claim that one can "measure" phonon dispersions with this method,
but the issue is quite controversial.

> 
> So while I am convinced of the interest of PDF for non-crystalline
> materials, with short or intermediate range order, I am not 
> yet convinced
> that you gain much from PDF refinement of crystalline 
> materials, where you
> can also apply Rietveld refinement.

I agree completely.  The directional information gained from phasing and the
fact of "locking in" to specific Fourier components is a major asset of
Rietveld analysis.  PDF is useful when correlated disorder is important (and
large), even if superimposed on an ordered structure.

Paolo Radaelli

Re: Rietveld refinement and PDF refinement ?

[Jon Wright]

Bob,
This exactly what is needed when the sample is a mixture of amorphous 
and crystalline components. But what happens when the material is a 
single crystalline phase with some coherent defects? Don't the defect 
<-> average structure correlations start to dominate, and separating 
components is no longer possible...? Thinking of all the different kinds 
of rods and streaks you can see from a single crystal and then 
projecting them into one dimension gives a lot of possibilities! The 
difficulty is finding a way to describe all of the possible kinds of 
defect so that either the PDF or equally the diffraction pattern can be 
computed. Probably one would have to follow the route in PDFFit of 
giving the user a Turing complete command language to use. I'm just glad 
that the proteins don't seem have coherent defects! Can you fit that 
broad bump in the second half of the pattern which always seems to turn 
up in protein data via the Debye equations? I have to admit I haven't 
tried yet...

See you in Prague,
Jon
Von Dreele, Robert B. wrote:
Jon & others,
Well, there is an attempt at this in GSAS - the "diffuse scattering" functions for fitting these contributions separate from  the "background" functions. These things have three forms related to the Debye equations formulated for glasses. The possibly neat thing about them is that they separate the diffuse scattering component from the Bragg component unlike PDF analysis. As a test of them I can fit neutron TOF "diffraction" data from fused silica quite nicely. I'm sure others have tried them - we all might want to hear about their experience.
Bob Von Dreele
 

RE: Rietveld refinement and PDF refinement ?

[Hewat Alan]

> Two very good points by Armel:
>>all the very good PDF studies ...are made by using synchrotron data or
>>neutron data from spallation sources

And he is modest as well :-) But do you really have the resolution even on
HRPD to see the diffuse scattering between Bragg peaks at high Q ? You may
get better temperature factors with high-Q PDF refinement, but you will
also do that with high-Q Rietveld.

I also doubt that just because PDF uses data between the Bragg peaks, then
it must be superior for seeing details not centered on atoms in real space
in a crystal, eg the split atom sites in (In/Ga)As). You might do just as
well with Bragg scattering if you use the result of Rietveld refinement to
construct a Fourier map of the structure. Happily, a sampling of
reciprocal space (Bragg peaks) is sufficient to re-construct the entire
density of a periodic structure in real space, not just point atoms, to a
resolution limited only by Q.

> What I am saying is that if this
> diffuse scattering is inelastic, then PDF will reflect istantaneous
> correlations in a way that is missed by Bragg scattering.

But you do agree that in a PDF experiment you integrate over energy, so
you only see an instantaneous snapshot of the structure, ie the spatial
correlations. If it is a periodic structure, you also average over unit
cells, even though the spatial correlations are different from one cell to
the next. (BTW, talk of inelastic scattering raises the question of
different inelastic cross-sections for the very different neutron energies
used on your TOF machine).

So while I am convinced of the interest of PDF for non-crystalline
materials, with short or intermediate range order, I am not yet convinced
that you gain much from PDF refinement of crystalline materials, where you
can also apply Rietveld refinement. A Rietveld refinement probably has
fewer correlations between parameters, and can be used to construct a
Fourier map of the complete scattering density, while PDF is only a
Patterson map of the pair correlations, and a lot more difficult to
interpret.

Alan.

RE: Rietveld refinement and PDF refinement ?

[Radaelli, PG (Paolo)]

Two very good points by Armel:

>all the very good PDF studies ...are made by using synchrotron data or
neutron data from spallation
>sources

This is because they are the only means to get to high Q (i.e., high
resolution in real space) and sufficiently high resolution (in reciprocal
space) simultaneously.  The RMC method is somewhat similar and does not
require such high Q, but it has the drawback of requiring a starting model
(arguably, there is also a uniqueness issue with RMC).  One nice feature of
the latest generation of TOF instruments is that one does not have to choose
in advance between PDF and crystallography, as long as one has appropriate
references (empty can, empty instrument etc.), which are collected as a
matter of course anyway.  PDF analysis requires better statistics, but, in
the context of a large phase diagram study, it is always possible to collect
a few data point to PDF accuracy.

>So, this PDF advantage does not impress me a lot

True, in most cases PDF=Rietveld + Common Sense.  However, there are some
exceptions.  For some nice cases see the work of Simon Hibble et al. (e.g.,
Hibble SJ, Hannon AC, Cheyne SM Structure of AuCN determined from total
neutron diffraction INORG CHEM 42 (15): 4724-4730 JUL 28 2003 and references
cited therein) and that by Simon Billinge (e.g. Petkov V, Billinge SJL,
Larson P, et al.
Structure of nanocrystalline materials using atomic pair distribution
function analysis: Study of LiMoS2 PHYS REV B 65 (9): art. no. 092105 MAR 1
2002 ).  Particularly, Simon Billinge makes the point that the future of PDF
is in the study of materials with short and intermediate-range order but no
long-range order ("nano-crystallography").  It is an interesting point of
view, although, at the moment, there are not very many examples of this in
the literature.

Paolo Radaelli

Re: Rietveld refinement and PDF refinement ?

[Von Dreele, Robert B.]

Jon & others,
Well, there is an attempt at this in GSAS - the "diffuse scattering" functions for 
fitting these contributions separate from  the "background" functions. These things 
have three forms related to the Debye equations formulated for glasses. The possibly 
neat thing about them is that they separate the diffuse scattering component from the 
Bragg component unlike PDF analysis. As a test of them I can fit neutron TOF 
"diffraction" data from fused silica quite nicely. I'm sure others have tried them - 
we all might want to hear about their experience.
Bob Von Dreele



From: Jon Wright [mailto:[EMAIL PROTECTED]
Sent: Sun 8/22/2004 6:13 AM
To: [EMAIL PROTECTED]




>Well, that is an old chestnut that Cooper and Rollet used to oppose to
>Rietveld refinement. I think Rollet eventually agreed that Rietveld was
>the better method. Has Bill really gone back on that ?
> 
>
The difference between the two approaches are just an interchange of the
order of summations within a Rietveld program. Differences in esds
should only arise through differences in accumulated rounding errors,
assuming you don't apply any fudge factors. Since most people do apply
fudge factors, the argument is really about which fudge factor you
should apply. I will only comment that the conventional Rietveld
approach (multiply the covariance matrix by chi^2) is often poor.

As for the PDF "versus" Rietveld - you should get smaller esds on
thermal factors if you were to write a program which treats the
background as a part of the crystal structure and has no arbitrary
degrees of freedom in modelling the background. This is just due to
adding in more data points that are normally treated as "background" but
which should help to determine the thermal parameters via the diffuse
scattering.

So, provided you were to remove the arbitrary background from the
Rietveld program and compute the diffuse scattering the methods ought to
be equivalent. Something like DIFFAX does this already for a subset of
structures, but I think without refinement. The real difficulty arises
with how to visualise the disordered component, decide what it is, and
improve the fit - hence the use of the PDF. Although no one appears to
have written such a program there does not seem to be any fundamental
reason why it is not possible (compute the PDF to whatever Q limit you
like, then transform the PDF and derivatives into reciprocal space).
Biologists already manage to do this in order to use an FFT for
refinement of large crystal structures!

In practice a large percentage of the beamtime for these experiments at
the synchrotron is used to measure data at very high Q which visually
has relatively little information content - just so that a Fourier
transform can be used to get the PDF. This is silly! The model can
always be Fourier transformed up to an arbitrary Q limit and then
compared whatever range of data you have. For things like InGaAs the
diffuse scatter bumps should occur mainly on the length scale of the
actual two bond distances. Wiggles on shorter length scales  are going
to be more and more dominated by the thermal motion of the atoms, and so
don't really add as much to the picture (other than to allow an
experimentalist to get some sleep!).

In effect it is like the difference between measuring single crystal
data to the high Q limit and then computing an origin removed Patterson
function and doing a refinement against that Patterson as raw data. No
one does the latter as you can trivially avoid the truncation effects by
doing the refinement in reciprocal space. The question then is whether
it is worth using up most of your beamtime to measure the way something
tends toward a constant value very very precisely? Could the PDF still
be reconstructed via maximum entropy techniques from a restricted range
of data for help in designing the model? Currently the PDF approach
beats crystallographic refinement by modelling the diffuse scattering.
As soon as there is a Rietveld program which can model this too then one
might expect the these experiments become more straightforward away from
the ToF source.

I'd be grateful if someone can correct me and show that most of the
information is at the very high Q values. Visually these data contain
very little compared to the oscillations at lower Q and seem to become
progressively less interesting the further you go, as there is a larger
and larger "random" component due to thermal motion. Measuring this just
so you can do one transform of the data instead of transforms of the
computed PDF and derivatives seems like a dubious use of resources?
Since the ToF instruments get this data whether they like it or not, the
one transform approach is entirely sensible there. For x-rays and CW
neutrons, it seems there is a Rietveld program out there waiting to be
modified.

August is still with us, Happy Silly Season!

Jon

RE: Rietveld refinement and PDF refinement ?

[Radaelli, PG (Paolo)]

>> I would argue that the Bragg &
>> diffuse scattering both reflect the average instantaneous atomic
>> structure.

>Yes. If you integrate over energy, the scattering function factors to a
>delta function in time, corresponding to an instantaneous snapshot of the
>spatial correlations. It is not a question of Bragg or or diffuse
scattering.

Your statement about integrating over energy is correct regardless of Bragg
or diffuse scattering, but Brian's statement is not, at least in the context
of the PDF/Bragg discussion, so "it is and it isn't" would have been a more
appropriate statement on my part.

It is true that in diffraction you measure the intermediate scattering
function S(Q,t=0), but this is not the same thing as saying that you can
then Fourier-transform any part of it you like to a G(x, t=0).  To get a
real-space function G(x) you have to integrate over the *whole* Q domain,
and in doing so for Bragg scattering you set to zero everything that is
outside the nodes of the RL.  However, it is easy to see that this can be
equivalent to setting an energy cut-off.  This is because fluctuations in
time and space are usually correlated, so by selecting an integration range
in Q for you Bragg peaks, you also effectively select an integration range
in energy.  Your superstructure example shows it clearly:  if you are far
from the phase transition and the correlation length of your tilt
fluctuation is 10 A,  you would not see a Bragg peak there and you would get
the time-average structure (without the superstructure).  Clearly there is
the limiting case of critical scattering very near the phase transition,
where the fluctuating regions are so large that you effectively take a
snapshot of each of them.  There could even be a deeper point here to do
with ergodicity, whereby you could show that coherent space average and
coherent time average are effectively the same (I am not positive about
this, though). 

The point I was trying to make is a different one. We are discussing about
the difference between Bragg and PDF.  If all the scattering is near the
Bragg peaks, so that you integrate it all in crystallography, there is and
there cannot be any difference between the two techniques.  I am sure we are
not discussing this case.  The interesting case is when there is additional
diffuse scattering. What I am saying is that if this diffuse scattering is
inelastic, then PDF will reflect istantaneous correlations in a way that is
missed by Bragg scattering. Let's look at the case of two bonded atoms
again, with a bond length L, and lets this time assume that they vibrate
harmonically in the transverse  direction, and that the semi-axis of the
thermal ellipsoid is a.  The possible istantaneous bond lengths range from L
to sqrt(L^2+4a^2) for an uncorrelated or anti-correlated motion, but is
always L for a correlated motion.  Bragg scattering will give you a distance
of L between the two centres, which is only correct for correlated motion.
It also provides information about the two ellipsoids, which is the same you
would get by averaging the scattering density over time, regardless of
correlations.  Istantaneous correlations are only contained in the diffuse
scattering, and are in principle accessible by PDF.

Paolo Radaelli

Re: Rietveld refinement and PDF refinement ?

[Jon Wright]

Well, that is an old chestnut that Cooper and Rollet used to oppose to
Rietveld refinement. I think Rollet eventually agreed that Rietveld was
the better method. Has Bill really gone back on that ?
 

The difference between the two approaches are just an interchange of the 
order of summations within a Rietveld program. Differences in esds 
should only arise through differences in accumulated rounding errors, 
assuming you don't apply any fudge factors. Since most people do apply 
fudge factors, the argument is really about which fudge factor you 
should apply. I will only comment that the conventional Rietveld 
approach (multiply the covariance matrix by chi^2) is often poor.

As for the PDF "versus" Rietveld - you should get smaller esds on 
thermal factors if you were to write a program which treats the 
background as a part of the crystal structure and has no arbitrary 
degrees of freedom in modelling the background. This is just due to 
adding in more data points that are normally treated as "background" but 
which should help to determine the thermal parameters via the diffuse 
scattering.

So, provided you were to remove the arbitrary background from the 
Rietveld program and compute the diffuse scattering the methods ought to 
be equivalent. Something like DIFFAX does this already for a subset of 
structures, but I think without refinement. The real difficulty arises 
with how to visualise the disordered component, decide what it is, and 
improve the fit - hence the use of the PDF. Although no one appears to 
have written such a program there does not seem to be any fundamental 
reason why it is not possible (compute the PDF to whatever Q limit you 
like, then transform the PDF and derivatives into reciprocal space). 
Biologists already manage to do this in order to use an FFT for 
refinement of large crystal structures!

In practice a large percentage of the beamtime for these experiments at 
the synchrotron is used to measure data at very high Q which visually 
has relatively little information content - just so that a Fourier 
transform can be used to get the PDF. This is silly! The model can 
always be Fourier transformed up to an arbitrary Q limit and then 
compared whatever range of data you have. For things like InGaAs the 
diffuse scatter bumps should occur mainly on the length scale of the 
actual two bond distances. Wiggles on shorter length scales  are going 
to be more and more dominated by the thermal motion of the atoms, and so 
don't really add as much to the picture (other than to allow an 
experimentalist to get some sleep!).

In effect it is like the difference between measuring single crystal 
data to the high Q limit and then computing an origin removed Patterson 
function and doing a refinement against that Patterson as raw data. No 
one does the latter as you can trivially avoid the truncation effects by 
doing the refinement in reciprocal space. The question then is whether 
it is worth using up most of your beamtime to measure the way something 
tends toward a constant value very very precisely? Could the PDF still 
be reconstructed via maximum entropy techniques from a restricted range 
of data for help in designing the model? Currently the PDF approach 
beats crystallographic refinement by modelling the diffuse scattering. 
As soon as there is a Rietveld program which can model this too then one 
might expect the these experiments become more straightforward away from 
the ToF source.

I'd be grateful if someone can correct me and show that most of the 
information is at the very high Q values. Visually these data contain 
very little compared to the oscillations at lower Q and seem to become 
progressively less interesting the further you go, as there is a larger 
and larger "random" component due to thermal motion. Measuring this just 
so you can do one transform of the data instead of transforms of the 
computed PDF and derivatives seems like a dubious use of resources? 
Since the ToF instruments get this data whether they like it or not, the 
one transform approach is entirely sensible there. For x-rays and CW 
neutrons, it seems there is a Rietveld program out there waiting to be 
modified.

August is still with us, Happy Silly Season!
Jon

RE: Rietveld refinement and PDF refinement ?

[Armel Le Bail]

Adding 2 cents to the discussion...
But I will try to convince myself otherwise :-)
Another reason which may preclude your self-convincing is the
fact that all the very good PDF studies of materials that are not perfectly
crystallized (producing diffuse scattering), though not being amorphous,
are made by using synchrotron data or neutron data from spallation
sources : not by using constant wavelength neutrons...
In the past, I have studied a few glasses at ILL by using the D4
instrument, at 0.5 A wavelength, allowing to attain modestly high Q
values. The fact that the instrument resolution was very poor was not
a problem for amorphous materials, but it was a problem for crystalline
or partially crystalline materials : they also look like amorphous in the
reciprocal space, due to the quite large instrumental contribution to the
peak broadening. Is that improved now ? If not, you would not be
able to apply both the Rietveld and the PDF methods from the
same data, raw or Fourier transformed. The raw data would
be too bad for applying the Rietveld method. So, no PDF at ILL ?-).
A different question is about size/strain effects, possibly
anisotropic, which may have effects on the peak shapes
and peaks broadening. We can more or less (progress are to
be made), take account of these effects reflecting the deviation
of the real sample from a model of infinite perfectly periodical
structure. All that peak shape information is lost in the PDF...
So, both PDF and Rietveld approaches may appear necessary
and complementary, sometimes - for ill-crystallized compounds.
However, is it really necessary to see on the PDF the difference
between the Si-O and Al-O distances in respectively SiO4 and AlO4 ?
This is already a well established fact (the same for any statistical
substitution of atoms with different radii like In and Ga in (In/Ga)As).
So, this PDF advantage does not impress me a lot (like opening an
already open door), EXAFS reveals the same. Apart from being able
to show such differences, I expect more from the PDF approach, but
the more an ill-crystallized sample is close to be amorphous, and the
more the structure hypothesis will be dubious...
Armel

RE: Rietveld refinement and PDF refinement ?

[Radaelli, PG (Paolo)]

>> I would argue that the Bragg &
>> diffuse scattering both reflect the average instantaneous atomic
>> structure.

>Yes. If you integrate over energy, the scattering function factors to a
>delta function in time, corresponding to an instantaneous snapshot of the
>spatial correlations. It is not a question of Bragg or or diffuse
scattering.

Your statement about integrating over energy is correct regardless of Bragg
or diffuse scattering, but Brian's statement is not, at least in the context
of the PDF/Bragg discussion, so "it is and it isn't" would have been a more
appropriate statement on my part.

It is true that in diffraction you measure the intermediate scattering
function S(Q,t=0), but this is not the same thing as saying that you can
then Fourier-transform any part of it you like to a G(x, t=0).  To get a
real-space function G(x) you have to integrate over the *whole* Q domain,
and in doing so for Bragg scattering you set to zero everything that is
outside the nodes of the RL.  However, it is easy to see that this can be
equivalent to setting an energy cut-off.  This is because fluctuations in
time and space are usually correlated, so by selecting an integration range
in Q for you Bragg peaks, you also effectively select an integration range
in energy.  Your superstructure example shows it clearly:  if you are far
from the phase transition and the correlation length of your tilt
fluctuation is 10 A,  you would not see a Bragg peak there and you would get
the time-average structure (without the superstructure).  Clearly there is
the limiting case of critical scattering very near the phase transition,
where the fluctuating regions are so large that you effectively take a
snapshot of each of them.  There could even be a deeper point here to do
with ergodicity, whereby you could show that coherent space average and
coherent time average are effectively the same (I am not positive about
this, though). 

The point I was trying to make is a different one. We are discussing about
the difference between Bragg and PDF.  If all the scattering is near the
Bragg peaks, so that you integrate it all in crystallography, there is and
there cannot be any difference between the two techniques.  I am sure we are
not discussing this case.  The interesting case is when there is additional
diffuse scattering. What I am saying is that if this diffuse scattering is
inelastic, then PDF will reflect istantaneous correlations in a way that is
missed by Bragg scattering. Let's look at the case of two bonded atoms
again, with a bond length L, and lets this time assume that they vibrate
harmonically in the transverse  direction, and that the semi-axis of the
thermal ellipsoid is a.  The possible istantaneous bond lengths range from L
to sqrt(L^2+4a^2) for an uncorrelated or anti-correlated motion, but is
always L for a correlated motion.  Bragg scattering will give you a distance
of L between the two centres, which is only correct for correlated motion.
It also provides information about the two ellipsoids, which is the same you
would get by averaging the scattering density over time, regardless of
correlations.  Istantaneous correlations are only contained in the diffuse
scattering, and are in principle accessible by PDF.

Paolo Radaelli

RE: Rietveld refinement and PDF refinement ?

[Hewat Alan]

> Another reason which may preclude your self-convincing is the
> fact that all the very good PDF studies of materials... are
> not by using constant wavelength neutrons...

You are right Armel :-) About the current advantage of SR and TOF for PDF,
I mean. That is why I am interested in being convinced.

> So, this PDF advantage does not impress me a lot (like opening an
> already open door), EXAFS reveals the same.

Open doors are good, and open minds are even better :-)

Alan.

RE: Rietveld refinement and PDF refinement ?

[Hewat Alan]

>> It is not a question of Bragg or diffuse scattering.
>
> Actually it is.  Bragg scattering is equivalent to projecting all the
> scattering density in the crystal onto a single unit cell divided by the
> number of unit cells in the crystal and replicate that average unit
> cell. In other words, you do a coherent configurational average (over
> the correlation length of the probe).

No it's not :-) What I said was that the crystal lattice has nothing to do
with Brian's  statement that if you integrate over energy you get an
instantaneous snapshot of the spatial correlations, which is true. More
precisely, if you write down the general expression for scattering S(Q,w)
it contains a term exp(iwt) so that if you integrate S(Q,w) over energy
you can factor out a delta function in time Integral[exp(iwt)]dt. This
applies to disordered materials as well as crystals - you don't need to
introduce a lattice here.

> Furthermore, because Bragg scattering is elastic, you also get a
> coherent time average.

This is not the way to look at it. Bragg scattering is simply all
scattering that peaks at points in the "reciprocal lattice" that
correspond to the long-range correlations called the "crystal lattice" in
real space. Take the superstructure example again. Suppose the
superstructure is condensing from a single zone-boundary soft mode eg a
simple octahedral tilt in a perovskite. This will produce a slightly
diffuse (in Q) and slightly inelastic, superstructure peak. A powder
experiment (and most others) will integrate over energy, so will see just
the spatial correlations, or an instantaneous snapshot.

If you do a Rietveld refinement restricted to the Bragg peaks, you can
either neglect the developing superstructure, in which case you won't see
the octahedral tilt except as an anisotropic DW factor, or else you can
double your unit cell to include the superstructure, in which case you
will correctly model the correlated tilts - i.e. your model will then
contain distances that are only present in the tilted structure.

In the PDF method, you don't have to decide anything about the lattice a
priori. This seems a strength, but it is also a weakness. The advantage is
that you will naturally see the distances (peaks) that are only present in
the tilted structure. The disadvantage is that you will have so many peaks
that you probably won't be able to interpret them all unless you also
(Rietveld) refine the structure :-)

The whole point of Rietveld refinement is to reduce correlations by
refining only parameters from a physical model. The fact that in
crystallography you constrain your data to the reciprocal space points
also helps :-) If you go to a more complex refinement without such
constraints, you can expect to have problems with correlations.

So I can see the interest of Fourier transforming the raw diffraction
pattern to look for peaks that should not be there with your periodic
model eg the split atom sites given as an example. But I am less sure that
you will get a better result by refining a model to fit the PDF function,
rather than modelling the split site or superstructure in Rietveld
refinement. But I will try to convince myself otherwise :-)

Alan.

RE: Rietveld refinement and PDF refinement ?

[Radaelli, PG (Paolo)]

>Yes. If you integrate over energy, the scattering function factors to a
>delta function in time, corresponding to an instantaneous snapshot of the
>spatial correlations. It is not a question of Bragg or diffuse scattering.

Actually it is.  Bragg scattering is equivalent to projecting all the
scattering density in the crystal onto a single unit cell divided by the
number of unit cells in the crystal and replicate that average unit cell.
In other words, you do a coherent configurational average (over the
correlation length of the probe).  Furthermore, because Bragg scattering is
elastic, you also get a coherent time average.  If you Fourier transform all
of the scattering function you get the instantaneous local pair-correlation
function averaged incoherently over time and space (actually, this is not
quite true because you can never measure Q in a diffraction experiment).

Paolo Radaelli

Re: Rietveld refinement and PDF refinement ?

[Hewat Alan]

Dear Brian,

It is 10:30 pm here, and I am supposed to be taking a day off tomorrow to
be with my new grand-daughter :-) But I find PDF so interesting that I
can't resist replying.

> I would argue that the Bragg &
> diffuse scattering both reflect the average instantaneous atomic
> structure.

Yes. If you integrate over energy, the scattering function factors to a
delta function in time, corresponding to an instantaneous snapshot of the
spatial correlations. It is not a question of Bragg or diffuse scattering.

> In the case where PDF shows split sites and the Rietveld
> gives the high symmetry site, this is really a failure of our
> crystallographic modeling techniques, as the split model should really
> do a better job with the Bragg-only data, too.

Yes. The Bragg-only data is perfectly adequate for periodic structures -
even those that contain two types of atoms disordered on the same site but
with different co-ordinates - a split atom model, as Bob said.

> As Paolo pointed out
> before I could finish this e-mail, the place where the PDF is different
> from "crystallographic" results is that the former will reflect
> correlation in interatomic distances.

Hmm. The diffuse (non-Bragg) scattering contains information about
short-range spatial correlations. Suppose we have a super-structure
condensing as short range islands. This will produce diffuse super-lattice
peaks that we will miss with Rietveld refinement. I suppose that PDF
refinement might pick that up.

> The other idea you raise, could one use the entire range of Q, up to
> 25 A-1 or even 50 A-1 in Rietveld to me raises a more profound question...
> Perhaps in the quest for fundamental parameters, someone should
> develop a Rietveld code that uses additional background & empty
> container scans (as is done to obtain the PDF) so that instrumental
> background is derived rather than fit in Rietveld. Then we could then
> have ADPs on an true absolute scale (something more important IMHO than
> relating every blip in peak shape to something intrinsic to the
> instrument or sample.)

I thought that had been done by people non-constrained by beam-time
allocation :-) So long as we are only looking for the periodic structure,
and we are prepared to take the same care with Rietveld and PDF
backgrounds, the methods should be equivalent.

> Simon and I just published a paper in Acta A on error analysis with
> models fit to PDFs.

I'll have to read that, because I don't quite understand how you do the
count statistics after the Fourier transform. I suppose it must be
possible, since the liquids and amorphous people :-) do it.

> The results: s.u. from models fit to PDFs (if done right) are equivalent
>  to those of Rietveld (for the same reasons why Bill David et al can do
> a  Pawley fit and then get the same esd's by fitting to the extracted
> I's).

Well, that is an old chestnut that Cooper and Rollet used to oppose to
Rietveld refinement. I think Rollet eventually agreed that Rietveld was
the better method. Has Bill really gone back on that ?

> However, s.u.'s from a PDF model fit values should be smaller,
> since it  typically uses more data.

Typically but not necessarily ? Alan.

Re: Rietveld refinement and PDF refinement ?

[Brian H. Toby]

Alan,
But if you refine the full data with the same model, can there really be any fundamental difference, if in one case you simply do a Fourier transform to real space ?
   

in Rietveld refinement we throw away the non-Bragg peak data, where-as with PDF all scattering is included. 

 

  It is funny to switch roles and "argue" this from your side w/r to 
the papers we each published on the disorder in the Tl2Ba2CaC2O8 
superconductor in the 80's (you worked on the problem with pretty much 
traditional methods while Takeshi Egami, Wojtek Dmowski and I developed 
methods for modeling the PDFs of crystals -- and we did come up with 
results in pretty good agreement). I would argue that the Bragg & 
diffuse scattering both reflect the average instantaneous atomic 
structure. In the case where PDF shows split sites and the Rietveld 
gives the high symmetry site, this is really a failure of our 
crystallographic modeling techniques, as the split model should really 
do a better job with the Bragg-only data, too. As Paolo pointed out 
before I could finish this e-mail, the place where the PDF is different 
from "crystallographic" results is that the former will reflect 
correlation in interatomic distances.

  The other idea you raise, could one use the entire range of Q, up to 
25 A-1 or even 50 A-1 in Rietveld to me raises a more profound question. 
In conventional use, the answer is probably no -- adding the "gentle 
wiggles" at high Q to a refinement provides almost nothing new. The 
reason for this is that Rietveld treats the background at high Q is an 
adjustable parameter. Thus, there are no termination errors in Rietveld, 
but the leverage of the high-Q data w/r to the ADPs is nearly zero once 
the peaks start to get quite broad due to extensive superposition -- 
where the computer (or user) draws the background curve is arbitrary. In 
"total scattering" the background is measured experimentally and 
"fixed." Perhaps in the quest for fundamental parameters, someone should 
develop a Rietveld code that uses additional background & empty 
container scans (as is done to obtain the PDF) so that instrumental 
background is derived rather than fit in Rietveld. Then we could then 
have ADPs on an true absolute scale (something more important IMHO than 
relating every blip in peak shape to something intrinsic to the 
instrument or sample.)

  Finally, in the shameless self-promotion department. Simon and I just 
published a paper in Acta A on error analysis with models fit to PDFs. 
The results: s.u. from models fit to PDFs (if done right) are equivalent 
to those of Rietveld (for the same reasons why Bill David et al can do a 
Pawley fit and then get the same esd's by fitting to the extracted I's). 
However, s.u.'s from a PDF model fit values should be smaller, since it 
typically uses more data.

Brian

Re: Rietveld refinement and PDF refinement ?

[Simon Billinge]

>  PDF requires exquisite data and a true passion
for data analysis.  If you have a good problem, you can get (probably) the
best PDF data worldwide "almost" routinely on my instrument GEM at the ISIS
facility (see also the cited paper by Billinge).
Paolo Radaelli
>
...on a final note, if you have a true passion for data analysis and 
want to have a go at PDF, either using x-rays or neutrons, but would 
like to be introduced more gently, we would be glad help however we can; 
please just drop me a line.

S
--
Prof. Simon Billinge
Department of Physics and Astronomy
4268 Biomed. Phys. Sciences Building
Michigan State University
East Lansing, MI 48824
tel: +1-517-355-9200 x2202
fax: +1-517-353-4500
email: [EMAIL PROTECTED]
home: http://www.totalscattering.org/

RE: Rietveld refinement and PDF refinement ?

[Radaelli, PG (Paolo)]

The only truly unique PDF information is about *correlations*.  Let's say
you have two bonded sites, both with anisotropic thermal ellipsoids along
the bond, and let's assume that the motion is purely harmonic.  A sharp PDF
peak will indicate that the atoms move predominanly in-phase, a broad PDF
peak that the atoms move predominantly out-of-phase.  The two scenarios will
give identical Fourier maps as reconstructed from the Bragg peaks, whatever
the Qmax, so the additional width (or additional narrowness) of the peak
with respect to an uncorrelated model arises purely from the non-Bragg
scattering.  You can make the same argument for static correlations.
Ga(1-x)In(x)As is a typical case.  It is not a split-site problem, in that
both Ga/In and As will be slightly displaced locally depending on their
surrounding, but the displacements are correlated in such a way as to give a
shorter bond length for Ga-As and a longer one for In-As.
Of course, PDF is also used to look at more general issues of static/dynamic
disorder that could also be examined using Bragg scattering, and in many
case it does quite well.  PDF is not (yet) very good for structural
refinements (so it is to be used only in desperate cases of highly
disordered systems) and is pretty hopeless for weak ordered displacement
patters, since the extra Bragg peaks in crystallography "lock-in" on the new
modulation even in the presence of large unrelated displacements.   For this
very reason, PDF tends to miss phase transitions, particularly at higher
temperatures, which led to some very wierd claims in the past literature.
There is a lot of controversy about PDF being able to say something about
weak disordered displacement patters (e.g., dynamic stripes), but I am
personally very skeptical.  PDF requires exquisite data and a true passion
for data analysis.  If you have a good problem, you can get (probably) the
best PDF data worldwide "almost" routinely on my instrument GEM at the ISIS
facility (see also the cited paper by Billinge).

Paolo Radaelli

Re: Rietveld refinement and PDF refinement ?

[Simon Billinge]

Hi Alan (et al.)
So my questions are naturally:
1) Could not the Rietveld refinement also be extended to the full data 
range ?
2) If that was done, would there be any fundamental difference between 
the two methods of fitting ?

(Yes, I know they also refined on a restricted d-spacing interval 
containing only Mn-O distances, and that there are other advantages to 
PDF analysis in identifying features that may not be included in the 
model).

But if you refine the full data with the same model, can there really be 
any fundamental difference, if in one case you simply do a Fourier 
transform to real space ? What am I missing here ?

There are answers to this question on a number of different levels.  The 
data are the same in real- and reciprocal-space and it is a matter of 
preference which one you work in, but to get the full story you have to 
analyze both the Bragg and diffuse components. We find the PDF function 
intuitive and easy to work with, especially when considering small 
deviations from well ordered crystals. A lot of RMC fits to more 
disordered materials these days are done directly to S(Q).

Stefan Breuner is correct; most Rietveld refinements remove diffuse 
scattering with an arbitrary background function.  In that case, a 
"value-added" of the PDF refinement is clearly the information that was 
in the diffuse component.  The InGaAs example is a nice example and 
there are many more in the Chem Comm review (Dr. Hewat, I will send you 
a copy under separate cover. Anyone else who wants one, pls drop me a 
line: [EMAIL PROTECTED]).

Even for a perfect crystal there is thermal diffuse scattering.  In the 
PDF this gives rise to an r-dependent PDF peak broadening which contains 
information about the lattice dynamics.  This can be usefully analysed 
(e.g., see Jeong et al., Phys. Rev. B 67, 104301 (2003)), and also 
overanalysed (Dimitrov et al., PRB 64, 14303 (2001)). However, the real 
value of the PDF is in probing aperiodic disorder when it is present.

The thermal factor argument is a bit tricky.  In general, better thermal 
factors will be obtained from data measured over a wider-Q range.  This 
can become difficult in Q-space when significant Bragg-peak overlap 
makes the background subtraction uncertain.  PDF doesn't suffer from 
this problem because there is no arbitrary background subtraction. 
However, Rietveld could be carried out on an explicitly corrected S(Q) 
and this problem would go away.  Thus, in principle, until Rietveld is 
done on fully corrected S(Q) data the PDF should give more reliable U's. 
  However, I would say that at this point, from a practical point of 
view, this is an overstatement.  We need to fine-tune some things like 
profile functions in the PDF refinements (currently Gaussians...remember 
Rietveld in the early '70's?) to fully exploit this.  We are working on it.

Thanks for bringing it up...I am delighted that PDF refinements are on 
the radar screen.

S
--
Prof. Simon Billinge
Department of Physics and Astronomy
4268 Biomed. Phys. Sciences Building
Michigan State University
East Lansing, MI 48824
tel: +1-517-355-9200 x2202
fax: +1-517-353-4500
email: [EMAIL PROTECTED]
home: http://www.totalscattering.org/

Re: Rietveld refinement and PDF refinement ?

[Von Dreele, Robert B.]

I'd only add that given the clue that the peak in GaInAs is split from the PDF then 
one should model it that way in a Rietveld refinement. It should agree. The thrown 
away info in a Rietveld refinement is also evident in the Bragg peak intensities - 
shows up as "funny" thermal parameters, low atom fractions, odd bond lengths, etc. in 
the results. I should also say that it isn't fair to compare truncated (in Q) Rietveld 
refinements with untruncated PDF refinements & say the latter is "better". Let's be 
even-steven about this.



From: Alan Hewat [mailto:[EMAIL PROTECTED]
Sent: Thu 8/19/2004 9:31 AM
To: [EMAIL PROTECTED]
Cc: [EMAIL PROTECTED]




>But if you refine the full data with the same model, can there really be any 
>fundamental difference, if in one case you simply do a Fourier transform to real 
>space ?

Thanks to Stefan Bruehne for providing an obvious (in retrospect :-) answer i.e. that 
in Rietveld refinement we throw away the non-Bragg peak data, where-as with PDF all 
scattering is included.

He quoted an example where PDF shows a split peak in Ga(1-x)In(x)As for Ga-As and 
In-As distances, where Rietveld refinement always gives the average (Ga,In)As 
structure.

Alan.

Alan Hewat, ILL Grenoble, FRANCE  <[EMAIL PROTECTED]> fax (33) 4.76.20.76.48
(33) 4.76.20.72.13 (.26 Mme Guillermet) http://www.ill.fr/dif/AlanHewat.htm
___

Re: Rietveld refinement and PDF refinement ?

[Alan Hewat]

>But if you refine the full data with the same model, can there really be any 
>fundamental difference, if in one case you simply do a Fourier transform to real 
>space ?

Thanks to Stefan Bruehne for providing an obvious (in retrospect :-) answer i.e. that 
in Rietveld refinement we throw away the non-Bragg peak data, where-as with PDF all 
scattering is included. 

He quoted an example where PDF shows a split peak in Ga(1-x)In(x)As for Ga-As and 
In-As distances, where Rietveld refinement always gives the average (Ga,In)As 
structure.

Alan.

Alan Hewat, ILL Grenoble, FRANCE  <[EMAIL PROTECTED]> fax (33) 4.76.20.76.48
(33) 4.76.20.72.13 (.26 Mme Guillermet) http://www.ill.fr/dif/AlanHewat.htm 
___