Introduction
Recently, we reported on the improvement in quantitative analysis of energy dispersive x-ray spectroscopy (EDS) measurements performed in the EDAX APEX™ 3.0 EDS Standard and Advanced software suites using the normalized standardless eZAF correction [1]. Based on the analysis of more than sixty certified standards, we reported a three-fold improvement in the accuracy of standardless quantitative evaluation using APEX 3.0. However, it is difficult—if not impossible—to rely on a single figure of merit to understand the performance of the analytical algorithm used for quantitatively evaluating EDS spectra. In this article, we examine the analytical accuracy of APEX EDS Advanced software for samples with a range of mean atomic numbers between 6 and 70.
For many years, there has been accepted wisdom amongst microanalysts that standardless evaluation provides acceptable results for many applications when the elements present within the sample are of atomic number 12 and higher. In these materials, the effects of changes in excitation efficiency, self-absorption of x-rays generated in the sample, and secondary x-ray fluorescence for each element present in the sample (commonly referred to as ZAF corrections) are understood with reasonable certainty. However, for materials consisting of or containing low-Z elements (Z <12), standardless analytical methods have been used with trepidation due to the possibility of significant errors in analytical measurements driven by uncertainty in the correction values applied.
Results and discussion
We performed quantitative analysis of 34 alloy and compound certified standards provided by MAC Micro-Analysis Consultants Ltd, 50 % of which contained elements with atomic number <12, including boron nitride, lanthanum hexaboride, silicon carbide, and 12 oxides, including quartz, magnesium oxide, albite, almandine garnet, and yttrium aluminum garnet. EDS spectra were captured at a count rate of 10,000 cps with a live time of 40 s, and the mean atomic number was calculated using the modified electron fraction model [2]. For each analysis, we determined the absolute error per element by summating the absolute difference between the measured and known composition for each element, i, present in the sample (Equation 1).
Equation 1.
Figure 1 summarizes the variation in sum absolute error per element as a function of mean atomic number. In accordance with common wisdom, for samples that did not contain light elements (blue circles), the elemental composition was determined with great accuracy—the mean error per element was just 1.0 at. % and 13 of the 17 samples analyzed exhibited a negligible error (<1 at. %). However, excellent results were also achieved for the samples that contained one (or more) light elements (orange triangles); the mean error was only slightly larger at 1.4 at. % and 11 of the 17 samples analyzed exhibited a negligible error. Furthermore, for the 12 oxide samples, the mean error was only 1.2 at. %—an improvement of close to 3x compared to APEX 2.5 EDS Advanced. The outstanding accuracy of standardless normalized analysis using eZAF correction in APEX 3.0 EDS Advanced makes standardless analysis practical for many more samples.
Figure 1. A plot of the error in quantitative evaluation of materials of certified composition using APEX 3.0 EDS Advanced using a Bremsstrahlung background model and correction for the thickness of the carbon coating. All composition values are provided in atomic percent.
Figure 2 shows a plot of the absolute error per element plotted against the variance in atomic number (calculated from DZ = Zmax – Zmin) and reveals that the error in analytical results is largest for samples of widely differing elements. The primary reason for this is the large—and sometimes uncertain—correction factors for absorptions and secondary fluorescence in widely dissimilar materials. Any calculation of the net counts is subject to a large correction, meaning that uncertainty in the net counts or correction factors leans to an analytical result with larger errors. Nevertheless, even in the cases of thallium bromide iodide (DZ = 76) and lanthanum hexaboride (DZ = 52), the error per element was only 2.1 and 0.3 at. %, respectively.
Figure 2. A plot of the error in quantitative evaluation of materials of certified composition as a function of the maximum difference in atomic number. They were analyzed using APEX 3.0 EDS Advanced software using a Bremsstrahlung background model and correction for the thickness of the carbon coating.
These results reveal significant improvements in the accuracy of compositional analysis by normalized standardless analysis using eZAF correction in EDAX APEX 3.0 Advanced software versions for almost all samples, particularly for samples containing one or more light elements. An improvement of 3x was observed for oxide samples analyzed and >5x for other light elements containing, e.g., boron, carbon, or fluorine.
Conclusion
These results show that exceptional accuracy can be achieved for light and heavy elements using normalized standardless analysis using EDAX’s eZAF correction model using the APEX 3.0 EDS Advanced software, making standardless analysis practical for a much wider range of materials than previously considered.
References
- Evaluation of the accuracy of standardless EDS analysis in APEX EDS software. EDAX Insight Vol. 21, Issue 4. December 2023.
- J. Donovan et al., (2003) Microsc. Microanal. 9, p202. DOI: 10.1017/S143192760030137