Analysing the amorphous quantity in internal standards for a more accurate QPA

Ramon13

My XRD samples were spiked with a ZnO (zincite) standard. The crystallinity of this internal standard has been calculated to be 92%. How can I accommodate this for fully quantitative rietveld analysis? Should I add a degree of crystallinity parameter to the internal standard phase in JEdit or is there a better method that's locally specific for the internal standard structure?

I see in the GUI that there are Wt% of Spiked and Wt% in Spiked Sample parameters which I believe correlate to the spiked_phase_measured_weight_percent and spiked_phase_measured_weight_percent_wt in JEdit from the Topas Tech manual, however, I can't find the spiked_phase_measured_weight_percent_wt definition in the "Keywords"/dictionary part of the technical reference so I'm unsure. Right now I usually just assume the standard is 100% crystalline for ease, but I'd like to be more accurate. Could anyone please provide guidance here with accommodating amorphous quantities in the internal standard and, out of curiosity, explain how an internal standard with a large amorphous quantity would affect the diffractogram beyond added difficulty in refining the peak shapes?

Thanks and hello from Western Australia! 🙂

rowlesmr

You need to do the corrections/calculations manually.

I've written up some equations for the new vol G and another book chapter. They're on my other computer. When I get home, I can look them up.

In my experience, there is no issue with refining peak shapes for internal standards with higher levels of amorphous content.

Ramon13

rowlesmr Hey Matt, that would be fantastic thanks so much I'd love to have a read! Feel free to link here or send to my email, whatever is easier for you 🙂.

That's surprising regarding the amorphous content internal standards, although, in hindsight I remember from reading one of R. Williams' geopolymer papers that he used metakaolin as an internal standard for one of his reactivity XRD assessments so I guess it can be done. Perhaps I just had a misguided preconception in believing that the "ideal" internal standard is a fully crystalline one where it's structure can be completely quantified mathematically without too much difficulty.

rowlesmr

This is all assuming you're using internal standard, Hill&Howard quantification, and Rietveld. It probably works for other things, but that is the application I developed this for.

W - weight fraction (eg 0.5 = 50 wt%)
X - crystallinity (eg 0.92 = 92% crystalline)
p (subscript) - phase 'p'
s (subscript) - internal standard
a (superscript) - absolute
o (superscript) - original specimen before adding internal standard
k (superscript) - known
r (superscript) - relative

For a given phase, p, in the presence of an internal standard, s, the absolute weight fraction is given by

W^a_p = W^r_p (W^k_s X_s) / W^r_s

where W^k_s is the complete weight fraction of the standard in the specimen, and (W^k_s X_s) is the crystalline fraction.

The total amorphous fraction in the specimen with the internal standard is given by

W^a_amor = 1 - ((W^k_s X_s)/W^r_s)

But we're not normally interested in that; we want to know the weight fractions in the original sample, before the addition of standard. So we need to scale.

W^o_p = W^a_p/ (1 - W^k_s)
W^o_amor = ((1 - ((W^k_s X_s)/W^r_s)) - W^k_s (1-X_s )) / (1 - W^k_s)

(1 - ((W^k_s X_s)/W^r_s)): The absolute amorphous in the specimen with internal standard
W^k_s (1-X_s ): The amount of amorphous introduced by the internal standard
(1 - W^k_s): Scaling everything to remove the internal standard

Ramon13

rowlesmr Thanks for that, I'm just doing this for standard QPA using Rietveld, no unknown phases or crystal structures.

Thanks for the equations, I will study them and attempt to convert them to my JEdit template for my next QPA. 🙂

In your experience, does this modification make a big difference?

rowlesmr

If the standard is 99% crystalline, then not much difference. Once you get to 90% crystalline, you can be off by a lot!

Assume a three-phase sample 50% phase A, 30% phase B, 20% amorphous.

If you add 30% of a 99% crystalline internal standard and do the analysis assuming it is 100% crystalline, you results will come out as 50.5%, 30.3% and 19.2%, which is well within what I consider the precision of normal QPA to be.

If you add 30% of a 90% crystalline internal standard and do the analysis assuming it is 100% crystalline, you results will come out as 55.6%, 33.3% and 11.1%, which is well wrong.

Ramon13

rowlesmr Wow that's quite the impact. With something that significant on the outcomes of QPA, and because internal standards can't be 100% crystalline, I'm amazed that there's not already a built-in function for JEdit/TOPAS (unless I'm unaware of it).

My follow up questions are this:

Do you know if there is an in-built function(s) for JEdit/TOPAS that accommodates for this? If not I can manually insert them, all good.
Would you agree that it's safer to assume that, unless a value is given by the manufacturer, that the crystallinity value for the average internal standard is 95%?

Ramon13

rowlesmr Long story short, I tried replicating your numbers, even simply on excel so that I can extrapolate the logic to JEdit, but I seem to get different answers to you..

Just wondering if you could help me provide some perspective so that I can make the proper edits to my JEdit templates cheers.

rowlesmr

The built-in functions in TOPAS assume the standard is 100% crystalline.

I think that it is safer to assume 100% crystallinity, as this is more transparent to the end user, and makes it easier to calculate any other value if a standard crystallinity is measured later. But the best bet is to measure the crystallinity of your standard. Compare it to SRM676a (if you're lucky enough to have some) or purchase some IMS135 (https://imstandards.com.au/crm-standards-product-catalogue/)*

Happy QPAing!

*I was involved in its certification

Ramon13

rowlesmr I thought TOPAS would assume that. I think for the "end-user", you are correct, but for the purposes of research, publication and being as reasonably accurate as possible to get the most representative result from QPA; I'm going to go and implement these equations into my JEdit script. Thanks again for this 🙂.

rowlesmr

Ramon13

It's good to do the calcs with a low crystallinity std, as the alterations stand out more, but I think your relative column is wrong. You can't have any amorphous in a relative weight fraction, as that assumes everything is crystalline, and so you don't see any of it. That column should be, from the top, 34.7 40.8, and 24.5wt%, with 0% for amorphous.

You need to establish your original ground truth and your spiked ground truth. The relative then gets calced from the spike ground truth. Then you calc the amount of amorphous in the spiked specimen, and then correct that value to the original ground truth by removing the std content. When allowing for a non-crystalline std, you need to apportion the total amorphous between specimen amorphous and standard amorphous.

Here it is with 99% cryst std

rowlesmr

Hi Ramon

Hopefully this looks right for you?

Ramon13

Hey Matt,

Cheers for that! All seems to check out 🙂

In the absence of manufacturers having crystallinity parameters for their internal standard materials, would the best way of determining the crystallinity of a standard, or 2 if more than 1 phase is needed for QPA, be to make up a 50/50 sample of both standards and do a DOC method for the phases or an adjusted Rietveld?

rowlesmr

External standard against a material you trust. Make up a specimen of your unknown and a reference material. You know the answer for the reference material and can calculate the mass absorption. Now you can find the diffractometer constant.

Use that in the quantification of your unknown standard.

We had SRM 676 to act as a reference. That's out of stock now, but there is IMS135 available
https://imstandards.com.au/independent-mineral-standards-releases-ims135/
I was involved in its certification.

Ramon13

I was curious to see the knock-on effects of this in a bigger system with more phases as is usually encountered in practice. I did the following calculations for a 6-phase system and got the following result. A percentage difference of 5 wt.% amorphous when assuming a 100% Crystalline Internal Standard despite having an actual crystallinity of 90% (which isn't unreasonable). Note I used 30wt.% of internal standard as a modified approach from Westphal et al.

I would think this would be a focal point in all XRD labs or, in the case of TOPAS/JEdit, having some sort of function that works this error in? I also don't see many literature sources of people accommodating for this error, but perhaps I haven't read enough? Interesting stuff regardless, I've put my custom additions to JEdit (i.e. simplifying it to just the Int Std swmp = std_cryst_wt and using the std_wt (total) for the original portion calculations of the phases in the sample).

I'm surprised there's not a function for this already? Maybe something for the new update?

rowlesmr

New paper has just dropped

https://doi.org/10.1017/S0885715624000460

Have at it! 🙂

Ramon13

Nice! Would've been good to collab for this publication. Good piece of work for sure, I think a graph showcasing the differences would be impactful too, something along these lines which I just whipped up