On the Importance of Including All Elements in the EPMA Matrix Correction

Electron probe microanalysis (EPMA) labs do not always measure all the elements present in certain samples due to limitations in acquiring low energy X-ray lines, or simply to save some analysis time. These missing elements are then added through stoichiometric apportionment and post-processing, often outside of the matrix correction procedure. However, not including them in the matrix correction calculations may lead to inaccuracies in the obtained concentrations. We present here a careful evaluation of the matrix correction procedures for several mineral specimens with complex elemental compositions to demonstrate the importance of including all elements into the matrix correction to produce a fully accurate quantitative result. The matrix correction determines the concentrations of elements in a sample by comparing the intensity of characteristic X-rays emitted by the sample and a standard. The correction algorithm accounts for physical effects such as X-ray generation by electron beam interactions and X-ray absorption. The ZAF nomenclature refers to the three factors that are considered to obtain the correction: atomic number correction factor Z, absorption correction factor A, and fluorescence correction factor F. The concentration Ci in the unknown, for an element i, is given by (Pouchou and Pichoir, 1991): where ki is the k-ratio, Cistd is the concentration of element i in the standard and the terms Z, A and F are the compositionally dependent correction factors. The atomic number correction factor Zunk for the unknown (and Zstd for the standard) is calculated from the product of the deceleration factor (i.e., the electron deceleration in the atomic electric field, also called stopping power) and the backscattering factor. Generally, we observe that for geological samples, when a light element is added to the matrix correction, the relative decrease of the deceleration factor is larger than the relative increase of the backscattering factor, leading to an overall decrease of the Zunk factor. By adding a missing element to the matrix, the variation of the absorption correction factor Aunk (and Astd for the standard) depends on the variations of both the ionization depth distribution ϕ(ρz) and the mass absorption coefficients (MAC). For the addition of a light element, the variation of ϕ(ρz) has a negligible effect on Aunk, thus the main variation is caused by the modification of the absorption factor through the MAC. The MAC will increase if the product of the new element concentration by its MAC is higher than the original MAC of the material. This increase of the MAC will decrease the number of the emitted X-rays because more X-rays are absorbed, which results in a decrease in the Aunk factor. The factor Funk describes the enhancement of the emitted X-ray intensity by fluorescence effects. The characteristic fluorescence only varies substantially if the newly added element emits X-rays that have an energy higher than the ionization threshold of the recorded X-ray lines. Generally, when adding a light element, the factor Funk remains globally unchanged. Because both factors Zunk and Aunk decrease, the concentration Ci must increase to keep the product constant in Eq. 1. Hence, adding a missing light element in the matrix generally increases the calculated concentrations of the other elements. One important example of this effect is the analysis of hydrous phases such as zeolite group minerals [2], which are characterized by aluminosilicate framework structures with open cavities. These cavities are often occupied by H2O molecules and/or large ions. Examples of these minerals include stilbite and natrolite which contain about 9.5 wt.% and 16 to 19 wt.% H2O, respectively. When analyzing zeolite minerals, there are several options for including water in the analysis, e.g., "water by difference" in the correction software; using an experimentally determined amount of water, stating a theoretical stoichiometric proportion of H2O, or by explicitly measuring oxygen. Inclusion of "water by difference" in the matrix correction can yield accurate results, but it can also hide problems in the analysis (such as a low analytical total). Inputting the theoretical amount of water based on the specific zeolite structural formula can also be problematic as the real water content may differ from the theoretical value. The last method is to explicitly measure O, stoichiometrically apportion it to the different cations, and calculate the remaining (“excess”) O as OH or H2O, all this being done in the matrix correction loops. Table 1 shows that there are significant errors when water is not included in the analysis of a heulandite-family zeolite: SiO2 is 1.70 wt.% too low and Al2O3 is 0.44 wt.% too low. BaO and other minor elements also show errors, although the change remains within the analytical uncertainty. This analysis was performed using the mean atomic number (MAN) background modeling method [3], which is useful for minimizing the total analysis time and thus the problem of beam damage in sensitive materials such as zeolites. However, the MAN method relies on an accurate determination of all the elements present in the sample. The absence of H2O causes the MAN to be overestimated and thus the calculated background intensity is also overestimated, leading to an underestimation of the net X-ray intensity. This significant source of error is often overlooked when quantifying hydrous minerals with MAN technique. Exclusion of other, non-light elements from the matrix correction can also lead to inaccuracies. For example, analyzing apatite without including minor elements, such as REEs, can lead to inaccurate values for F, P2O5, and CaO. This can be seen on the Durango apatite (Table 2), where not including minor elements such as REEs in the matrix correction can result in F being 0.08 wt.% too high, CaO being 0.14 wt.% too high, and P2O5 being 0.21 wt.% too low. Additionally, apatite grains that contain high concentrations of REEs, such as those from the Mineville district, Essex County, NY, can cause even greater discrepancies when REEs and other elements are not included in the matrix correction. There is also an issue with F measurements due to an interference from the Ce Mz X-ray line with the F Kα X-ray line. Table 2 shows two sets of results for F, one without correction for the Ce Mz interference and one with proper correction. While negligible for the Durango apatite, this correction decreases the F value by almost 0.5 wt.% in the REE-enriched Mineville apatite. Our results demonstrate that it is necessary to consider the effects of all elements on the matrix correction procedure for accurate quantification with EPMA. EPMA analysis of a heulandite-family zeolite. A low total is obtained when H2O is added by difference post-processing, i.e., when water is not taken into account in the matrix correction. EPMA analysis of two apatite crystals. Errors are observed when REE and other elements are not accounted for in the matrix correction. Two values are given for F: the first ignores the Ce Mz interference upon F Kα, whereas the second takes in into account.

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