TOPAS with synchrotron powder diffraction data

originlab1

Hello there!
I have a question regarding performing structure refinement using TOPAS with synchrotron powder diffraction data. Explained below is my situation and I am hoping to receive a quick response from one of the experts here. Please help!
Situation: I have collected powder diffraction data using a flat image plate detector in a synchrotron beamline. The incident X-rays are 100 um in diameter, gets diffracted from the sample and then the diffracted data is collected by the image plate detector placed behind the sample. I have data for both the sample and a calibrant (a NIST standard for which I have information regarding the lattice parameter and crystallite size). From the collected data, I have generated the "I vs. 2-th" plots to be input into the TOPAS (commercial version) program. Regarding the incident beam/ instrument parameters, I know the following:
Beam size: 100 um in diameter at the source. I also have an estimate of the beam divergence along equatorial and axial direction at the point the beam hits the detector ( 2-th =0). Beam size is approx. 600 um in equatorial and 300 um in axial direction at the point it hits the detector. Also, I know the distance (D) between the sample and the detector (at the point where 2-th=0).
In order to perform Rietveld refinement in TOPAS, I need to setup the correct "Instrument parameters" for synchrotron data but there is not much information available in TOPAS user manual. My idea is to obtain the instrument parameters (especially the contribution from beam divergence in both axial and equatorial directions) by using the calibrant as a standard and then keep these fixed while analyzing my sample. Which instrument convolution function I may use and how to account for the incident beam divergence in TOPAS? Should I use Finger et al. model or any other defined model in TOPAS or should I go for the “additional convolution” feature?
My question is similar to the one in this thread: http://topas.dur.ac.uk/unb/forum.php?req=thread&postid=66.
But I do not understand the need to use “simple axial model” and why

lam ymin_on_ymax 0.0001 la 1.0 lo 0.354134 lh 0.1

is chosen by the user.
My aim is to obtain the emission profile and the instrument broadening by using the NIST standard. Then, I want to keep these FIXED for my sample(s). The above thread also talks about using the additional convolution feature by using:

lor_fwhm = pr1 Tan(Th) + pr2/Cos(Th) ;
 gauss_fwhm = pr3 Tan(Th) + pr4/Cos(Th) ;

But then the users agreed on instrument broadening being negligible. But, I want to device a way in TOPAS to separate out the instrument broadening, if possible -- in addition to obtaining the correct emission profile, if possible. I am almost convinced about using the emission profile as "lam ymin_on_ymax 0.0001 la 1.0 lo 0.354134 lh 0.1" (as given in the above thread), but the instrument broadening part is a mystery to me! Could any of you please help me in this regard? Thanks in advance.
--
AB

rowlesmr

Best attempt at a reply.

For equatorial divergence, just use the Divergence macro. If you know the sizes and distances, you can calc the angle.

For axial divergence, I think I've always used the Finger model, but that assumes a parallel incident beam. If you've got an idea of the incident divergence, then you could use the full model and use the incident divergence as the incident soller slit, leaving the diffracted soller out of it.

With regards

lam 
   la 1.0 lo 0.354134 lh 0.1 lg 0.1
ymin_on_ymax 0.0001

If you've got a single wavelength, the la should be 1 (by definition)
lo is the wavelength in angstroms
lh is the lorentzian halfwidth of the incident radiation
lg is the gaussian halfwidth of the incident radiation

To refine those parameters, you need to set the cell parameter, crystallite size and strain in your standard to their known values, and then refine the lam prms until you get a good fit. FOr my last go at synchrotron data, lh was negligible, but lg was quite big.

Once you've done them on your standard, fix them, and then you can refine cell prms and xstal size/strain on your unknowns.

Hope this makes sense

Matthew

johnsoevans

There's also a step-by-step description of a literature-based empirical approach to this type of problem at: http://community.dur.ac.uk/john.evans/topas_workshop/tutorial_ceo2_sizestrain.htm. The philosophy is similar to that in Matthew's response.

originlab1

Hi Matthew and John:
Thanks a lot for your prompt reply. I really should have asked here earlier! But better late than never! All of these make perfect sense and are very helpful in directing me to the right directions. Thanks to both of you.

I have a few more questions and as you may have already guessed, I am relatively new to using TOPAS. Please pardon me if I ask silly questions. No way I want to use this forum and your valuable time for educating myself in TOPAS (and Rietveld refinement therein) .... I have gone through and still going through the tutorials available in Durham websites and elsewhere (in TOPAS help files). Still, I have a few very basic questions regarding the TOPAS macros, and if you can answer some of these, it will help me immensely.

All my questions arise from the following considerations:
1) Typically, the synchrotron experiment geometry is more like a parallel beam geometry where the diffracted intensities are collected via an image plate detector placed behind the the sample -- which is different then the Bragg Brentano geometry used in conventional lab diffractometers.

2) Having said that, am I wrong in assuming that all the existing models and macros in TOPAS are written based on BB geometry and as such, the macros can not be used "directly" for performing Rietveld analysis in TOPAS? If so, how should these be modified in a very simple manner to be used with data collected at synchrotron? The tutorial link (and links therein) given by John touches on that and I am still going through understanding its full worth.

3) Still the idea remains same -- which we all agree - -first obtaining the instrument emission profile and divergence by using a NIST standard. Then keep those values "FIXED" in the analysis process. That way, Matthew's suggestion is very close to what I want to do. I think the tutorial (posted by John) also goes in the same line. But both talk about using one of the axial models (Simple/Full/Finger) as the instrument convolution function which, I suspect, is incorporated in TOPAS with BB geometry in mind.

Nevertheless, below is the text copied from TOPAS technical reference manual (in quotes):

Simple_Axial_Model
Syntax Simple_Axial_Model(c, v)
Description Simple model for describing peak asymmetry due to axial divergence of the beam.
[c, v]: Parameter name, receiving slit length [mm].

Full_Axial_Model, Sollers
Syntax Full_Axial_Model(filament_cv, sample_cv, detector_cv, psol_cv, ssol_cv)
Description Accurate model for describing peak asymmetry due to axial divergence of the beam.
[filament_cv]: Tube filament length in [mm].
[sample_cv]: Sample length in axial direction in [mm].
[detector_cv]: Length of the detector (= receiving) slit in [mm].
[psol_cv, ssol_cv]: Aperture of the primary and secondary Soller slit in [°].

Finger_et_al
Syntax Finger_et_al(s2, h2)
Description Simple model for describing peak asymmetry due to axial divergence of the beam
according to Finger et al., 1994.
[s2, h2]: Sample length, receiving slit length.

Suppose I want to go with the full axial model as suggested by Matthew. I have information about the width of the direct beam (say beam_size_source) at the source and also at the point the direct beam hits the detector (say beam_size_detector_horizontal and beam_size_detector_vertical). Also, I have an estimate of the distance between the source and the detector (say d_source_detector). Using these three parameters, I can calculate the angular divergence ( in degrees) in both equatorial (or horizontal here) and axial (or vertical here) directions. This angle (as an approximation) comes at 10 deg and 3 deg respectively in equatorial and axial directions. How to use the axial divergence value (3 deg) in the full_axial_model? Should I use the beam_size_source as the filament length? Should I use my sample's length in axial direction ( do have an estimate) or leave that alone? If I want to leave that alone, should I just leave it blank in the macro? In other words, how do I write the full_axial_model macro if I do not know some of the essential parameters in the macro?

If I want to use simple_axial_model macro, it asks for receiving slit length (in mm). This macro is used in the tutorials in the link posted by John. Which number should go here? Should I refine it or leave it alone?

Same question for Finger model, what values I should use for sample length and receiving slit length? Should I use beam_size_detector_vertical or beam_size_source for the receiving slit length? Should I use an estimate of the sample length for using the Finger model or is there a way to use it with only one parameter?

4) As discussed in the blog link I posted in my first post and also somewhere in the tutorial links (that John posted) and in Durham's website, they mention about using the additional convolution functions for synchrotron geometry instead of using the default TCHZ peak types in TOPAS. Then they use tan_th and 1/cos_th functions as the convolution. I am not very familiar with the correct definition of these functions (in TOPAS) for separating the effect of instrument broadening and physical broadening (size and strain) in the diffraction data. Any help in this regard will be much appreciated. Also, if I decide to use these convolution functional forms (instead of the default TCHZ peak type in TOPAS), I still need to obtain the instrument broadening part. Any suggestions on how to do that. The tutorial link posted by John uses TCHZ peak type for obtaining the instrument convolution part and then keeps it fixed during subsequent size/strain broadening analysis. I would want to avoid using the TCHZ peak type if it is implemented for BB geometry in TOPAS by default. But again, I may be wrong and I shall value the suggestions by experts like you more than anything here.
Thanks again. Am really sorry for the long post.
--
AB

PS: I came across this post just now:
https://community.dur.ac.uk/john.evans/topas_workshop/tutorial_joyofconv.htm

Question is: can I just use the HAT type convolution function for obtaining the instrument convolutions from the NIST standard? Makes sense to me as I think the direct beam can be assumed as one with finite width (in both horizontal and vertical directions) so only the HAT convolution should be applied to obtain the contribution from direct beam in the collected diffraction data. Please correct me if I am wrong. I am inclined toward making this assumption for obtaining the incident beam convolution function.

alancoelho

originlab1

Best to read a paper like:

J. Res. Natl. Inst. Stand. Technol. 109, 1-25 (2004)
Fundamental Parameters Line Profile Fitting in Laboratory Diffractometers

e-mail me if you want a copy.

Also, it’s often not always possible to completely separate Sample aberrations from Instrument aberrations. Axial divergence assumes randomly orientated crystals; when there's a lot of texture (partial diffracting cones) then peaks tend to have varying degrees of axial divergence. The low angle Brucite peak is a good example.
Additionally the aberration due to penetration of x-rays into the sample is a function of the thickness of the sample. Even when the thickness can be considered infinite then the density of the sample (how it was packed) plays a part in how severe the absorption aberration is. In parallel geometry the angle allowed by the analyser slits in the equatorial plane becomes important and the aberration becomes a function of the sample as well as the slits.

Basically the idea of separating sample and instrument is nice and possible to a large degree but not completely. Sometimes therefore one or two sample/instrument parameters are refined even when the sample is not a standard.

cheers
alan

rowlesmr

I'll have a go at this.

That said, all my files are at work, and I'm not, so this is from memory...

originlab1:1404674254 wrote Hi Matthew

Hi!

originlab1:1404674254 wrote 1) Typically, the synchrotron experiment geometry is more like a parallel beam geometry where the diffracted intensities are collected via an image plate detector placed behind the the sample -- which is different then the Bragg Brentano geometry used in conventional lab diffractometers.

Are you using capillaries at the synchrotron? If so, there aren't that many differences between BB and synch data, even with the parallel v divergent beam.

originlab1:1404674254 wrote 2) Having said that, am I wrong in assuming that all the existing models and macros in TOPAS are written based on BB geometry and as such, the macros can not be used "directly" for performing Rietveld analysis in TOPAS? If so, how should these be modified in a very simple manner to be used with data collected at synchrotron? The tutorial link (and links therein) given by John touches on that and I am still going through understanding its full worth.

Things like the Divergence macro should work, but things like Absorption won't. Sample offset corrections for fixed incident beam are not included in Topas. If you're doing a flat plate sample with a fixed incident beam angle, then you'll want to correct for the beam width. I've got a nice correction paper on that.

So, in short, if you're not doing BB, approach each correction with care, and check that the assumptions in the macro are correct for your geometry.

originlab1:1404674254 wrote 3) ...
Suppose I want to go with the full axial model as suggested by Matthew.
...
Using these three parameters, I can calculate the angular divergence ( in degrees) in both equatorial (or horizontal here) and axial (or vertical here) directions. This angle (as an approximation) comes at 10 deg and 3 deg respectively in equatorial and axial directions. How to use the axial divergence value (3 deg) in the full_axial_model? Should I use the beam_size_source as the filament length? Should I use my sample's length in axial direction ( do have an estimate) or leave that alone? If I want to leave that alone, should I just leave it blank in the macro? In other words, how do I write the full_axial_model macro if I do not know some of the essential parameters in the macro?

If I want to use simple_axial_model macro, it asks for receiving slit length (in mm). This macro is used in the tutorials in the link posted by John. Which number should go here? Should I refine it or leave it alone?

Same question for Finger model, what values I should use for sample length and receiving slit length? Should I use beam_size_detector_vertical or beam_size_source for the receiving slit length? Should I use an estimate of the sample length for using the Finger model or is there a way to use it with only one parameter?

Are you diffracting in the vertical plane or the horizontal? I've only ever worked in the vertical, so if I give a direction, it is with that in mind.

Filament length is the width of the beam in the axial direction, which in your case is ~100 um.
Sample length is the length of the sample illuminated by the beam. ie how big is the beam at the sample?
You have an estimate of the axial divergence, so use that value as the incident soller setting. THere is nothing on the diffracted side to constrain the beam, so leave that alone.

I don't know how the simple model works, I've never used it. THe slit length is the length of the detector in the axial direction. In my lab system my detector is 0.075 mm high and 16 mm wide, so "16" would go there.

The Finger model assumes a parallel incident beam, so the sample length is the length of the sample illuminated by the beam. The slit length is the size of the receiving slit in the axial direction. I normally use this model in my synchrotron modelling. The sample length is normally ~3-5 mm and the slit length is ~ 5-10 (I think)

originlab1:1404674254 wrote 4) As discussed in the blog link I posted in my first post and also somewhere in the tutorial links (that John posted) and in Durham's website, they mention about using the additional convolution functions for synchrotron geometry instead of using the default TCHZ peak types in TOPAS. Then they use tan_th and 1/cos_th functions as the convolution. I am not very familiar with the correct definition of these functions (in TOPAS) for separating the effect of instrument broadening and physical broadening (size and strain) in the diffraction data. Any help in this regard will be much appreciated. Also, if I decide to use these convolution functional forms (instead of the default TCHZ peak type in TOPAS), I still need to obtain the instrument broadening part. Any suggestions on how to do that. The tutorial link posted by John uses TCHZ peak type for obtaining the instrument convolution part and then keeps it fixed during subsequent size/strain broadening analysis. I would want to avoid using the TCHZ peak type if it is implemented for BB geometry in TOPAS by default. But again, I may be wrong and I shall value the suggestions by experts like you more than anything here.
Thanks again. Am really sorry for the long post.

TCHZ, I don't think is BB specific. I've only ever used FP modelling in Topas. If you want to learn more about convolutions, read Alan's paper in the NIST Journal. I've based a lot of my corrections on that paper.

Whether or not you use FP or TCHZ, the same routine of fixing the sample with the standard and refining the instrument, then fixing the instrument to refine the unknowns should be followed.

originlab1:1404674254 wrote Question is: can I just use the HAT type convolution function for obtaining the instrument convolutions from the NIST standard? Makes sense to me as I think the direct beam can be assumed as one with finite width (in both horizontal and vertical directions) so only the HAT convolution should be applied to obtain the contribution from direct beam in the collected diffraction data. Please correct me if I am wrong. I am inclined toward making this assumption for obtaining the incident beam convolution function.

Well yes, normally, but the beam also degrades towards the edges, so you'll also need to include a gaussian/lorentzian component, and there is also interactions with the sample, and absorption type things that may change it.

I found that I couldn't assume a hat-shaped beam in this paper http://scripts.iucr.org/cgi-bin/paper?hx5099

Hope all of this makes sense.