This I believe is a critically important topic in EPMA (and SEM) science, that has been neglected for far too long in our field. I will attempt to summarize the issues in this post. Please read it carefully. What exactly is meant by "Intra and Inter Laboratory Reproducibility and Accuracy"? Two things:
1. Intra Laboratory Reproducibility and Accuracy: the ability to obtain k-ratio consensus for all WDS and EDS spectrometers on a single instrument. Because there's little point in comparing results from one instrument to another if we can't even get all the spectrometers on a single instrument to agree with each other! And by utilizing k-ratios instead of concentrations we remove any matrix specific issues such as mass absorption coefficients.
As a reminder, we know that for a given element emission line, measured using the same beam energy, and the same detector take-off angle and measuring the same two materials, we should obtain a net intensity k-ratio within statistics for all spectrometers on our instrument. This is sometimes referred to the "simultaneous" k-ratio test.
An example comparing multiple WDS and EDS spectrometers is given here:
(https://smf.probesoftware.com/gallery/395_18_11_23_8_16_55.png)
For more details on testing for intra (internal) laboratory consistency see this topic
https://smf.probesoftware.com/index.php?topic=1569.0
and also these posts:
https://smf.probesoftware.com/index.php?topic=1535.msg11937#msg11937
https://smf.probesoftware.com/index.php?topic=1239.0
Note that spectrometer k-ratios that fall outside statistical consensus of your other spectrometers (which only proves that some or all may have problems), can results from a number of causes:
A. Spectrometer alignment problems. That is, is the effective take off angle of your various spectrometers actually close to the nominal value? For SEM instruments, this could include sample tilt issues. For WDS spectrometers, this could also include whether your Bragg crystals are diffracting symmetrically (god help you if your electron beam column is not centered in the spectrometer housing!). One way to test individual WDS spectrometer alignment problems is using the Bragg order k-ratio test as described here:
https://smf.probesoftware.com/index.php?topic=1739.msg13382#msg13382
But first try measuring k-ratios on as many spectrometers as you can as the same time (e.g., Si Ka on TAP and PET, Ti Ka on LiF and PET) to see the magnitude of the problem. Of course just because all your spectrometers all agree with each other doesn't mean they will agree with other labs, but it's the first place to start.
B. Dead time calibration problems. If your different spectrometers produce different count rates for a given material and condition, then dead time calibration issues could be part of the problem. See this post for a summary of how to test WDS dead time calibration accuracy using the "constant" k-ratio tests:
https://smf.probesoftware.com/index.php?topic=1466.msg11102#msg11102
C. Background modeling problems. That is, is our background modeling and fitting accurate and avoiding interferences from secondary peaks? Always (unless you are using the MAN background correction method!), scan the area around your peak and make sure your background model is accurately producing net intensities for the k-ratio calculations:
https://smf.probesoftware.com/index.php?topic=68.0
Next we will discuss inter-laboratory reproducibility and accuracy.
For the purposes of intra laboratory testing on a single instrument, the constant k-ratio and Bragg order k-ratio tests described in the previous post above, can be performed using any two materials that are homogeneous and beam stable. They don't even need to be standards (see the links for a few more helpful tips on selecting suitable materials). However, for the inter laboratory testing described below in the post, we must utilize homogeneous and beam stable materials that are shared globally to all laboratories that we wish to compare reproducibility and accuracy.
2. Checking inter laboratory reproducibility and accuracy: the immediate concern here is that we already know that there is a problem as demonstrated in the "Barometers Behaving Badly" paper by Wieser et al.:
Wieser, Penny E., et al. "Barometers behaving badly I: Assessing the influence of analytical and experimental uncertainty on clinopyroxene thermobarometry calculations at crustal conditions." Journal of Petrology 64.2 (2023): egac126.
as shown in this figure from the paper:
(https://smf.probesoftware.com/gallery/395_05_01_26_9_03_57.png)
And the one thing we also know is that different labs tend to use different primary standards for their analyses. And even if these labs using natural standard materials (e.g., Kakanui augite, etc.) are ostensibly using the same primary standard material, we know that these labs are definitely not using the same grain, and we also know that many of these natural standard materials are not homogeneous, as shown in this figure by Will Nachlas and John Fournelle:
(https://smf.probesoftware.com/gallery/395_24_01_26_11_10_29.png)
So, the first problem (in addition to the spectrometer alignment (effective takeoff angle) and dead time accuracy problems described in the previous post), are our choices of primary (and secondary) standards. Standard choice is critically important is obtaining agreement with other EPMA (and SEM) laboratories and we will discuss this first:
A. The first problem is primary (and secondary) standards as mentioned already, but we can test this inter-laboratory reproducibility and accuracy through round robin k-ratio tests. One could utilize natural standard materials for such tests, but again, due to known issues of compositional variability and grain to grain variation as shown above, we should instead use mounts of high purity, stoichiometric, homogeneous synthetic globally distributed standard materials, where each laboratory utilizes the same primary and secondary standards in the performance of these k-ratio tests.
This same globally distributed standard mount could then also be used to check the composition of each laboratory's internal standards. In an ideal world, we would utilize the same primary synthetic standards in all laboratories for a given unknown composition.
Once we are using such a globally distributed mount of homogeneous synthetic materials, any variation between laboratories is then due to individual instrument/spectrometer alignment and calibration issues. As mentioned in the previous post, these issues can be tracked down and corrected by careful measurements of constant k-ratios over a range of beam currents for dead time calibrations and multiple Bragg order k-ratios for spectrometer alignments using any homogeneous and beam stable materials.
B. Once we obtain k-ratio consensus from inter laboratory measurements, then we can turn to the question of of matrix corrections and mass absorption coefficient accuracy. Some compositions will yield very similar results with different matrix corrections and some materials (usually highly absorbing matrices) will yield very different compositions. Then there is the Z (atomic number) correction, which I believe is the key to many remaining quantitative accuracy problems remaining today. Specifically, the use of mass based averaged backscatter corrections in quantitative analysis, when we should be using a Z based correction for compounds. See here for details on this issue:
Donovan, John, et al. "An improved average atomic number calculation for estimating backscatter and continuum production in compounds." Microscopy and Microanalysis 29.4 (2023): 1436-1449.
and also this post here:
https://smf.probesoftware.com/index.php?topic=1809.msg13858#msg13858
We can fix this problem of systematic differences between various laboratories, we just need a few tools such as the constant k-ratio test, the Bragg order k-ratio test and also a suite of homogeneous, high purity, inclusion free synthetic minerals, which are globally distributed.
These are important issues and ones we need to address in the coming years to remain credible.
For EDS, there is another elephant in the room - software. We have never demonstrated that the various different vendors of EDS software produce similar (correct) k-ratios given similar standard and unknown spectra. It can be hard to know what the "correct k-ratios" are given that most EDS measurements reflect multiple lines and may or may not be directly comparable to single line WDS measurements. (There is a similar issue with WDS when we assume the peak intensity is a good proxy for the peak integral.)
Quote from: Nicholas Ritchie on January 28, 2026, 10:54:06 AMThese are important issues and ones we need to address in the coming years to remain credible.
I am hoping that as these constant k-ratio and Bragg order k-ratio WDS spectrometer alignment tests become more familiar to everyone and these documents provide clear instructions:
https://smf.probesoftware.com/index.php?topic=1739.msg13873#msg13873
they will be utilized by more labs. Just for internal (intra) laboratory consistency if nothing more!
As for inter laboratory consistency that will require global cooperation with globally distributed standards. I am very hopeful that the efforts being led by Will Nachlas will continue to be supported by MAS (EMAS/AMAS?).
Quote from: Nicholas Ritchie on January 28, 2026, 10:54:06 AMFor EDS, there is another elephant in the room - software. We have never demonstrated that the various different vendors of EDS software produce similar (correct) k-ratios given similar standard and unknown spectra. It can be hard to know what the "correct k-ratios" are given that most EDS measurements reflect multiple lines and may or may not be directly comparable to single line WDS measurements.
Interesting.
Would you be willing to lead a study on this? It seems to me that it should be pretty straight forward to get EMSA spectra from every vendor and process with both DTSA2 and the OEM software. The problem being once again, global standards.
But we do already have a number of mounts already distributed by Will Nachlas with high purity synthetic Al2O3, MgO and MgAl2O4. Here are the EDS results from various labs that Will obtained:
(https://smf.probesoftware.com/gallery/395_29_01_26_8_41_25.png)
See here for the full paper:
https://academic.oup.com/mam/article/29/Supplement_1/225/7228643
Would you be willing to contact Will and see what raw data he has for these EDS measurements?
Quote from: Nicholas Ritchie on January 28, 2026, 10:54:06 AM(There is a similar issue with WDS when we assume the peak intensity is a good proxy for the peak integral.)
Yes, this is a well known problem for low Z K line emissions. Well, for any x-ray shell transition that involves the valence band.
But fortunately we have some decent tools for this, primarily integrated intensity measurements on both the standard and unknown:
https://smf.probesoftware.com/index.php?topic=733.msg4660#msg4660
which is slow but accurate, and compound or specified area peak factors (APFs) which are fast but subject to proper calibration of the peak shape factors:
https://smf.probesoftware.com/index.php?topic=536.0