Enhancing EDS Quantitative Accuracy with FSQ and SmartStandards

Reducing the correction needs of raw measured data by physical models is beneficial for receiving the most accurate quantitative results. When the original measured raw intensities are corrected, the model and the fundamental parameter uncertainties have less influence on the final quantitative results. One method for reducing correction needs is measuring or using measured standards libraries. EDAX has developed the Full Standards Quant (FSQ) for eZAF.

This method places some responsibility onto the analysts, who are tasked with reasonably selecting standards and performing the measurement processes carefully. It is essential not to forget that the standards must be available with reliable, known, certified compositions (even with homogeneity in micron scales) at the lab site, at least in the traditional approach. Using EDS allows for utilizing previously measured standards libraries and a central database source.¹

Results and Discussion

The initial query typically regards which available standards should be used to evaluate an unknown sample spectrum.

The FSQ offers the k-ratios (measured unknown counts divided by the counts of the standard) relative to the real measured standard values. This is a step away from EDAX’s previous standards-based quantitative solutions, where the k-ratio was always presented relative to the pure standard (which was subsequently calculated if a pure option was not measured). This makes it apparent which corrections are applied. Error calculations are based on the applied corrections. If corrections are unnecessary or minimal, then there is essentially no systematic error influence coming from the model.

Figure 1 shows how the standard selection influences the final correction needs. In example 1b, the Z correction was reduced for Fe because the standard was closer to the unknown sample Fe composition.

The goal is reached using the Magnetite standard (1c), where the corrections required with the eZAF model are less than 2%. Theoretically, this means the original raw data must correct the differences between measured standards and unknown specimen data by approximately 2%. Even the standard with the least correction needs does not equal the best-measured k-ratios.

Figure 1. a) FSQ evaluation of a Hematite specimen based on measured standard SiO₂ 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. Image Credit: Gatan, Inc.

The advantages are visible compared to the pure standardless eZAF results (Figure 2). The Fe-K correction needs to remain moderate. However, the oxygen R and A corrections are huge, at nearly 60% absorption correction by theory with the standardless case. This is reliably less in all cases where measurements are supported through standards. The required corrections were reduced to 36% when the SiO₂ standard was used, even though the composition remained far from the unknown sample.

Figure 2. eZAF standardless evaluation of the Hematite specimen. Image Credit: Gatan, Inc.

The advantage of using standards (measured with your instrument) is that the detector efficiency uncertainties are canceled out (see the September 2021 issue of EDAX Insight). This influences the oxygen result in the example. The standardless unnormalized Fe result is already decent, but oxygen remains overestimated.

Selecting which standards to use is at the operator’s discretion. The new EDAX software supports this through the presentation of the applied correction needs with the applied ZAF factors, which can alter significantly depending on the standard composition used. Furthermore, the error percentage includes systematic error estimations. For example, the oxygen standardless evaluation begins at a 7% error. It will improve to around 5%, even with less than ideal standard selection, and eventually, reports a 1.6% error for oxygen with the magnetite standard.

The software can support the optimization of standards selection. However, without previous experience, it can become trial-and-error work. Smart application software can support best-guessed standards based on standardless results expectations about the unknown sample. The FSQ-based algorithm requires a pre-selection of the standards data, which needs to be provided.

Ideally, it would be possible to offer all relevant standards for the algorithm and then automatically select the best matching standards that demand the fewest corrections. SmartStandards were developed with the potential to access all provided standard data, with an algorithm capable of optimizing the standards to be considered for evaluation throughout the iteration process (Figures 3 and 4). ²

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. Image Credit: Gatan, Inc.

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. Image Credit: Gatan, Inc.

The curve that uses the repeated reference example with the Al/Si standards chain is improved in the ideal situation. 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. Image Credit: Gatan, Inc.

A similar yet alternate method of measuring standards at your instrument is creating an evolving global standards library that includes measured data with standards measured elsewhere.¹

This universal standards library could adopt the customers’ local measurements using the SmartStandards as a baseline. At least one reference measurement must be applied, bridging the gap between other measured standards and instrument operation. The reference measurement is known from the eZAF standardless, not normalized (September 2021 issue of EDAX Insight).

When SmartStandards are applied, incorporating as many standards as possible to cover all concentration ranges closely—for example, in an ideal scenario, 100 standards with 1% increments—the eZAF model is effectively minimized. At that point, it only needs to account for minor deviations, such as distinguishing between a 31% and 32% standard when the unknown sample falls at 31.3%.

The chain of provided standards is supported—or even entirely generated—by Monte Carlo (MC) calculations. This marks an initial step toward replacing traditional ZAF or Φ(ρz) models with an extensive, automatically associated standards database. Such a database could be continuously accessible or precomputed using MC simulations for given compositions.

Using pure-element specimen reference measurements is a key element in bridging measured standards with the MC model. However, this approach requires precise control over detector efficiency. Alternatively, localized standard measurements could connect with a much larger central standards library. The advantage of this method is that a well-developed remote library may offer standards more closely aligned with the unknown specimen analyzed in an SEM than locally available reference materials.¹ If a local standard measurement is performed for each element, uncertainties related to detector efficiency could be effectively canceled out.

References

1. Ritchie, N., et al. (2020). Proposal: Let’s Develop a Community Consensus K-ratio Database. Microscopy and Microanalysis, 26(S2), pp.1774–1776. https://doi.org/10.1017/s1431927620019303.
2. Eggert, F. (2021). Abilities Towards Improved Accuracy in EPMA. Microscopy and Microanalysis, 27(S1), pp.1108–1110. https://doi.org/10.1017/s1431927621004165.

This information has been sourced, reviewed and adapted from materials provided by Gatan, Inc.

For more information on this source, please visit Gatan, Inc.