Internal standards with FP - necessary or not?

djurdjijadzodan

Dear crystallographers,

May I kindly ask you to tell me your opinion(s) whether the use of an internal standard is necessary for correcting zero-(and height) displacement(s) errors when using Fundamental Parameters (FP) approach for accurate determination of unit cell parameters of powders of interest? Based on the [1]: "An inherent advantage of the present technique is that the fitted 2th peak positions are automatically corrected for all instrument aberrations except zero error and surface displacement" ( the page 119), I have understood that the use of internal standard is still necessary. However, the paper is from 1991, maybe the FP technique "has improved" in the meantime?

I wish to determine as more accurately as possible the unit cell parameters of different Prussian Blue Analogues from their XRDs (collected at the D8 diffractometer in BB geometry) and I am wondering if it would be better to first re-collect all the data including an internal standard?

Thanks so much in advance.

Kind regards,
Djurdija

[1] Cheary, Robert W., and Alan Coelho. "A fundamental parameters approach to X-ray line-profile fitting." Journal of Applied Crystallography 25.2 (1992): 109-121.

johnsoevans

If I really want to be sure of accurate cell parameters I use an internal standard. If you have a well cared for, well understoond reliable instrument it might not be needed. However if it's a multi-user instrument where you can't be 100% sure of alignment, sample mounting, etc on a given day an internal standard means you always have a fixed reference point. If you find one sample in a series is "unusual" an internal standard will help you pin down whether it was a sample or other effect.
You could always try a few samples with/without internal standards with your set up to see if any differences in cell parameters you extract are significant.

rowlesmr

I would use an internal standard. FP helps with instrumental things, but you can still have issues with specimen displacement which you may not realise because your PBA might be a little funky; that might ruin your whole day.

Addint an internal std helps to mitigate those issues. You can also use your internal standard as an intensity calibrant, too. This might help you monitor crystallinity in your PBAs, as long as you always know how much std you've added, and have ensured that it is well-mixed.

.
We have issues with specimen-displacement at work, and an internal standard helps tie down our peak position corrections for phase ID.

djurdjijadzodan

Dear John and Matthew,

Thank you so much, I am having only one additional question regarding the Zero_Error(c,v) Specimen_Displacement(c,v) corrections in general.

1a) Do you have any suggestions in which order to try to refine the two parameters in respect to one another and all other parameters upon Lebail/Pawley and Rietveld refinements? After reading the [1] I have started being worried how to refine the two terms in order to get minimal possible uncertainties/errors?

1b) With the use of an internal standard, I assume that the zero shift and sample displacement terms I would first refine on the standard and then keep them fixed upon refinement of PBA powders? Or are there any additional macros to be used instead of the two mentioned above to address the two type of displacements when using internal standard?

Kind regards,
Djurdjija

[1] De Campos, Marcos F., et al. "Uncertainty estimation of lattice parameters measured by X-Ray diffraction." XVIII IMEKO WORLD CONGRESS Metrology for a Sustainable Development September. 2006.

johnsoevans

1a) I think this is used as an example in the YouTube video of correlated parameters. The parameters are very highly correlated (particularly if you have a narrow 2-theta range) so my advice would be to never refine both. For a well aligned lab system it's usually the sample height that is in error. If you have to worry about the order in which you refine parameters in TOPAS you're generally doing something dodgy.

1b) The traditional way of doing this was to make a graph of e.g. 2-theta error (expected - experimental) vs 2-theta experimental for each peak in your internal standard and then fit a simple function to the data which allows you to correct the 2-theta experimental values of the peaks in your phase of interest. Normally a simple polynomial did a pretty good job.

You can do this directly in TOPAS with a 2-phase refinement:

Fix the Si cell parameter to its (NIST) certified value and use a 2-theta correction polynomial to adjust experimental peak positions of Si to those expected for the fixed cell parameter. The Si can be refined either as a Rietveld phase (perhaps with a spherical harmonic intensity correction as you're just after fitting the peaks well) or as a Pawley phase.

You'll need to add the following lines in your input file in the xdd section:

prm zero 0.000
prm step_error 0.06584
prm square 0.00598
prm !data_middle 50 'this is average 2-theta value e.g. for a 10-90 degree scan
th2_offset = (Xo-data_middle)^2*(square/1000) + (Xo-data_middle) (step_error/1000) + zero;

By refining zero, step_error and square you should get a good fit to the Si peaks. The same correction will be applied to your sample so its refined cell parameters should be accurate. The th2_offset polynomial coefficients can be highly correlated so check the matrix. You may need to e.g. fix the square term. The !data_middle value helps stabilise the least squares and is the "average" value of your start_X and end_X.

As a check, I would then fix !zero, !step_error and !square and refine the Si cell parameter. It shouldn't change significantly from the NIST value. If it does something is wrong with your calibration (wrong th2_offset function, Si weighting not high enough to calibrate well).

rowlesmr

Have a look at (the quite excellent paper, if I say so myself 🙂) https://doi.org/10.1107/S160057672100371X. If you refine both zero error and specimen displacement together, they'll correlate 100% and give you what ever answer you want. I general leave ZE at 0 and refine SD.

You can do 1b John's way, or you could also just refine SD and ZE together - it all depends on if you want "real" numbers, or values that make the cell edges correct. There is no way to refine the peak shift prms separately when you've got an internal standard, as it's all one specimen. As long as all of your reference material peaks cover a wide range of 2Th and are fit well, then it should be OK for the unknowns.

djurdjijadzodan

Dear John and Matthew,

Thank you so much, I explored many different refinement scenarios following your advices in this post and I have managed to eliminate most of my doubts.

I am having an additional question regarding the John's 1b approach. After having confirmed how the 2-theta error (expected - experimental) vs 2-theta experimental plot of my Si standard looked like (something like the figure 5a from the [1]), I managed to successfully apply the John's th2_offset code lines keeping the fixed Si cell parameter at the value of 0.5431073nm (since the experimental temperature was about 25deg, or at least it was the temperature value that I read from the .raw file using the Eva software). After completing the Lebail fitting of the Si standard, I fixed the !zero, !step_error and !square to the refined values of:

                       prm !zero  0.01855_0.00152
                       prm !step_error -0.14595_0.03451
                       prm !square -0.00154_0.00028

and managed to refine the a parameter of Si to the value of 0.5431066nm, which I assume can be considered as a satisfying result.

However, I didn't additionally include the Specimen_Displacement correction in that case, was it still needed?
In my next trial I then included the Specimen_Displacement correction after fixing the previously refined !zero, !step_error and !square parameters and after the first refinement cycle, the following was retrieved:

                     Specimen_Displacement(@height, 0.00000`_0.00025 min -0.5 max 0.5).

Unfortunately, as soon as I have included the LVol_FWHM_CS_G_L and e0_from_Strain code lines, in the next refinement cycle the following was displayed:

                     Specimen_Displacement(@height, 0.00160`_0.00018 min -0.5 max 0.5)

and then during the check, a parameter of Si was refined to the value of 0.5431063nm. Maybe in this specific case the inclusion of the specimen displacement correction beside the polynomial function didn't make a significant impact on the refined unit cell parameter of Si in the end, but considering that I can't know for sure the exact value of a parameter to the accuracy of it's each decimal number (considering the st deviations, temperature variations and similar) and that zero and height displacement errors could vary from measurement to measurement, I don't feel confident to conclude based only on my refinement trials that the specimen displacement correction don't ever need to be used with the polynomial zero correction. Hence, it would really mean a lot to me to hear what you think about it & know from your experience.

I really have to emphasize once again that I am extremely grateful to you on your extensive help, no way I could have figured out everything myself following only the literature available online.

Looking forward to hearing from you.

Kind regards,
Djurdjija

[1] Stinton, Graham W., and John SO Evans. "Parametric rietveld refinement." Journal of Applied Crystallography 40.1 (2007): 87-95.

johnsoevans

You shouldn't refine the height correction with this method. The philosophy you are using is that the polynomial takes care of all the possible 2theta abberations (height, zero, absorption, goniometer issues, etc, etc.

You can see in your example that it (correctly) remained at essentially zero.

djurdjijadzodan

Dear professors Evans or Rowles,

I need to perform LeBail fitting also on some of the "old" XRDs of our PBA powders that I hadn't mixed with the internal NIST640b standard prior to collecting those XRDs and I am wondering how to determine the zero and sample displacement parameters without having any reference point in the XRDs. I have several questions:

Question 1. From [1 and 2] I have understood that I should fix the zero-point error to the value determined using the external standard. From the appropriate plot retrieved using the XRD of an external standard, I have understood that the zero-point error in my case should be lower than an absolute value of 0,01. Does it mean that I then only "constrain" the zero-point error to min value of -0.1 and max value of 0.1 and not fix the parameter upon the refinement:

Zero_Error(@zero, 0.1 min -0.1 max 0.1)

I am concerned that in that case I will still be refining the zero error together with the unit cell parameters of the PBA powders decreasing any chance of retrieving reliable unit cell parameters of the PBA powders? How do I address the issue?

Question 2. Regarding the "Specimen_Displacement(@height, 0.1 min -0.5 max 0.5)" correction, I assume that in this case have no other choice, but to let the parameter to be refined together at the same time with the unit cell parameters of the PBA?
I collected those XRDs long time ago when I knew much less about how to do a proper sample preparation procedure and I suspect that I introduced a "large" (just a feeling I have no reference point) height displacement error. Would it be better in that case not to constrain the height parameter upon the refinements, but to let the parameter to take any value?

Thank you in advance.

Kind regards,
Djurdjija

[1] Dinnebier, Robert E., and Simon JL Billinge, eds. Powder diffraction: theory and practice. Royal society of chemistry, 2008 (page )
[2] Rowles, Matthew R. "The effect of data quality and model parameters on the quantitative phase analysis of X-ray diffraction data by the Rietveld method." Journal of Applied Crystallography 54.3 (2021): 878-894.

johnsoevans

As in some of the earlier posts, 2th zero point errors and height errors are highly correlated (close to 100% with normal data). You probably can't refine them independently, If you've got a well maintained and well aligned diffractometer then it's probably better to assume it's a height error and keep the zero point error fixed at 0. If the height differs significantly from 0 then your cell parameters might be affected. I'd be concerned if my height correction was more than +/- 0.1 mm. You shouldn't constrain the value. If it refines to a large or unreasonable value it's telling you something.

Unless you've run an external standard immediately before or after your sample you can't be sure of the instrumental zero point so you shouldn't fix it to an arbitrary value or put limits on it as you suggested. Good commercial diffractometers might specify peak positions to +/- 0.01 degrees over the whole 2-theta range on a standard material, but that only holds if the instrument is well aligned and the user before you didn't knock the detector!

djurdjijadzodan

Dear professor Evans,

Thank you so much for the detailed explanation, I feel now very comfortable to proceeding further with the refinements.

Wish you a nice day.

Kind regards,
Djurdjija

djurdjijadzodan

Dear professor Evans.

I am sorry for an additional question in this post, but I really need to ask.

My hopefully last concern is regarding finding the optimal (minimal) NIST640b internal standard amount to be used with the Prussian Blue Analogues. Considering that there are overlapping peaks of the NIST640b powder and concretely the Prussian White(PW) powder in the XRD of the NIST640b-PW mixture and that I have access to a very limited amount of the NIST640b powder, I performed some basic experiments in order to determine the minimal amount of the NIST640b powder to be used with the PW powder so that the first few peaks of the NIST 640b standard are well distinguished in regards to the peaks of the PW in the XRD of the NIST640b-PW mixture. My experiments had shown that using perhaps around 10wt% of the NIST640b powder would be enough, which I decided to increase to 15wt% in order to "leave space" for not efficient mixing of the powders. However, I then found a publication (not related to the PBA powders) where it was written that the amount of an internal standard was chosen in a way that the intensity of the strongest peak of the standard would be about equal to the intensity of the strongest peak of the main phase [1] - in my case it would mean that I needed to use much more NIST640b powder than 10wt%. What is a common practice in the field regarding the issue?

I had an idea to try to investigate the issue further using an additional standard in powder form such as the LaB6 powder (since the unit cell parameters of the PW powder I need to determine I can't use it as a reference point). However, I haven't managed to get access at my department to any additional standard in powder form. I am also wondering if it is "enough" to do the check only by refining the a parameter of Si for the previously determined and then fixed polynomial parameters as you suggested in one of the replies above (I never miss to do that check upon the LeBail fitting procedure and I always get the a parameter refined to the standard value at experiment temperature with a small variation under the standard deviation)?

Kind Regards,
Djurdjija

[1] McMurdie, Howard F., et al. "Methods of producing standard X-ray diffraction powder patterns." Powder Diffraction 1.1 (1986): 40-43.

johnsoevans

I don't think there's any hard and fast rule about how much internal standard to add. You want enough that its peaks are sufficiently strong that their positions can be reliably determined. We typically do the same as suggested in the paper of having the strongest Si peak roughly comparable to the strongest peak in the sample. That's already a very rough definition as the peak heights from the sample depend on composition, symmetry, etc, etc.

NIST standards are expensive (I hope Jim isn't reading this!). Many years ago we bought a large bottle of 99.5% purity Si from Alfa and use that for everyday work. We calibrated it in the lab against NIST 640c and it's indistinguisable. Over the years we've also measured it at various synchrotrons and reached the same conclusion.

If you're measuring a series of samples you could do something similar. Your derived cells would then be directly comparable with each other. You could check one sample with NIST Si if you want to verify the absolute values.

One warning: we intially bought some very expensive 99.99+% Si for this purpose but it was amorphous!

rowlesmr

1: Don't use NIST SRMs in your daily samples. Use them to calibrate a set of (cheaper) secondary materials. An exception to this is where you're just prepping a specimen of pur SRM, then just go for it.

2: Is a corroloary (sp?) to 1. NIST SRMs go out of production. There are currently no quant stds available for purchase from NIST, so our lab is running on fumes, and hoping no-one drops the sample holders with our last few grams of SRM in them.

3: How much to add... It depends on what you wnat to do. If it's a line position, then you only need enough to see the lines. For quant, well, that is another kettle of fish. I'll add [1] to the pot, and say that you may need anywhere between 10- 50 wt% internal std.

[1] Westphal, T., Füllmann, T. & Pöllmann, H. (2009). Powder Diffr. 24, 239-243.