# Ways to Improve EDS Quantitative Results Accuracy: FSQ and SmartStandards

### Introduction

To achieve the most accurate quantitative results, reducing the correction needs of raw measured data by physical models is beneficial. The model and fundamental parameter uncertainties also influence the final quantitative results less; the less the original measured raw intensities are corrected. One way to reduce correction needs is to measure standards or use measured standards libraries. EDAX has developed the Full Standards Quant (FSQ) for eZAF.

But this method also puts some responsibility into the analysts’ hands, who are decisively in charge of reasonably selecting standards and carefully performing the measurement processes. And one should not forget that the standards need to be available with reliable known certified compositions (even with homogeneity in micron scales) at the lab site, at least in the classical approach. But using EDS offers you the ability to use previously measured standards libraries and even a central database source [1].

### Results and Discussion

The first question is always which of the available standards one should use to evaluate an unknown sample spectrum. The FSQ presents the k-ratios (measured unknown counts divided by the counts of the standard) in relation to the actual measured standard values. This is different from earlier standards- based quantitative solutions by EDAX, where the k-ratio was always presented in relation to the pure standard (which was then calculated if a pure one was not measured). This now makes it clear which corrections are actually applied. Also, all error calculation is based on the applied corrections. If no correction is needed or it is minimal, then practically no systematic error influence comes from the model.

Figure 1 demonstrates how the standard selection will influence the final correction needs. With example 1b, the Z correction is reduced for Fe due to the standard being closer to the unknown sample Fe composition. But the final goal is reached using the Magnetite standard (1c), where the corrections needed with the eZAF model are finally below 2%. In theory, this means the original raw data are required to correct the differences between measured standards and unknown specimen data by about 2%. The interesting point with the example is that even the standard with the lowest correction needs is not the same as the best-measured k-ratios.

**Figure 1. a) FSQ evaluation of a Hematite specimen based on measured standard SiO _{2} for Oxygen and based on pure Fe standard for Fe. b) The same sample but a FeSi compound is used as a standard for Fe determination. c) The same sample using a Magnetite standard for both elements is much closer in composition than with examples a and b.**

The benefits are visible compared to the pure standardless eZAF results (Figure 2). Although Fe-K correction needs are still moderate, the oxygen R and A corrections are enormous, reaching almost 60% absorption correction by theory with the standardless case. This is always less in all cases where measurements are supported via standards. Corrections reduced when the SiO_{2} standard was used, only about 36%, despite its composition still being far from the unknown sample.

**Figure 2. eZAF standardless evaluation of the Hematite specimen**

The benefit of using standards (measured with your own instrument) is that it cancels out the detector efficiency uncertainties (September 2021 issue of EDAX Insight). This especially influences the oxygen result in the example. The standardless unnormalized Fe result is pretty good already, but oxygen is still overestimated.

However, one can see that choosing which standards to use is in the operator’s hands. The new EDAX software supports this by presenting the applied correction needs with the applied ZAF-factors, which vary much depending on which standard composition is used. Additionally, the error % value includes the systematic error estimations. For example, the oxygen standardless evaluation starts with an error of 7%. It will be improved to about 5%, even with non-ideal standard selection, and finally, it is reported to be a 1.6% error for oxygen with the magnetite standard. Therefore, one can optimize the standards selection with the software’s support. But without previous experience, it can get to be trial and error work. Smart application software may support you with best-guessed standards based on standardless results expectations about the unknown sample. But the FSQ based algorithm still needs a preselection of the standards data, which must be provided.

Shouldn’t it be possible to provide all relating available and measured standards for the algorithm, then automatically select the best matching standards that require as few corrections as possible? The SmartStandards was developed with the ability to access all provided standard data, and the algorithm optimizes the standards that should be considered for evaluation during the iteration process [2] (Figures 3 and 4).

**Figure 3. Hematite evaluation with SmartStandards, which picks the closest standards with the least correction need. The Err% are almost only statistical fluctuations with the measurements (unknown and standard), with practically no systematic error part. The curve shows the eZAF model adjusted by standards (the diamonds) for Fe with k-ratios (in relation to the pure element) vs. Fe concentrations.
**

**Figure 4. Using the same standards data, a FeSi specimen spectrum was evaluated with SmartStandards. Again, the closest standard to use is automatically picked by the algorithm iteration process. The correction factors and Err% are close to the ideal case. The curve shown used the eZAF model adjusted by standards (the diamonds) for Fe with k-ratios (in relation to pure element) vs. Fe concentrations.
**

The curve using the repeated reference example with the Al/Si standards chain is improved in the ideal case. There are only <2% relative deviations over the entire concentration range (Figure 5).

**Figure 5. a) Calculated concentration results by SmartStandards for the binary Al/Si example specimen (blue Al; red Si) over the Si nominal concentration, all in % units, MACC is used for Si-K in Al. The broad light-red line is the Si net-count raw data curve, arbitrary units, not yet ZAF corrected. b) FSQ plot with net counts vs. concentrations of all the used standards (diamonds); calculated eZAF curve with the standards adjustments and some estimation of the smooth changing matrix composition (red Al; broad light red Si but for inverse X-axis 100%-CAl%). The crosses are the measurement points with the 40% Si/60% Al sample spectrum evaluated.
**

A parallel and alternative way to measure standards at your instrument is to create a growing global standards library that includes measured data with standards measured elsewhere [1]. This universal standards library can then inherit the customers’ local measurements based on SmartStandards. At a minimum, one reference measurement must be applied, which bridges the gap between other measured standards and your instrument operation. The reference measurement is already known from the eZAF standardless, not normalized (September 2021 issue of EDAX Insight).

If the SmartStandards is applied, providing as many standards as possible, which cover all concentrations quite closely (e.g., ideal case 100 standards can have 1% step to cover all concentrations tightly), then the eZAF model is completely outsmarted. Then, it only deals with the remaining tiny deviations (e.g., between 31% and 32% standards of the element, if the unknown is 31.3%). It can be imagined that the standards chain provided is supported by or even only provided by Monte Carlo (MC) calculations. It is a first step to completely replacing ZAF or Φ(ρz)-models with a large and automatically associated standards database that is available for continued access or is always calculated in advance by MC for given compositions. The pure-element specimen reference measurement can be the bridge between the different systems measured standards and the MC calculation model world. But this requires detector efficiency to be under control. Alternatively, one can use simple standards local measurements to bridge to a much bigger central standards library. The hope is that the big remote standards library contains standards closer to the locally measured unknown specimen in the SEM than one’s own simple standards [1]. If a local standard measurement can be applied for each element, then the detector efficiency uncertainty will cancel out.

### References

[1] Ritchie N et al. (**2020**) “Let’s Develop a Community Consensus K-ratio Database” *Microscopy and Microanalysi*s **26** Suppl 2 (2020) 1774

[2] Eggert F (**2021**) “Abilities Towards Improved Accuracy in EPMA” *Microscopy and Microanalysis ***27** Suppl 1 (2021) 2021