EPMA quantification on the chemical composition of retained austenite in a Fe-Mn-Si-C-based multi-phase steel

An electron probe X-ray microanalyzer (EPMA) is an essential tool for studying chemical composition distribution in the microstructure. Quantifying chemical composition using standard specimens is commonly used to determine the composition of individual phases. However, the local difference in chemical composition in the standard specimens brings the deviation of the quantified composition from the actual one. This study introduces how to overcome the error of quantification in EPMA in the practical aspect. The obtained results are applied to evaluate the chemical composition of retained austenite in multi-phase steel. Film-type austenite shows higher carbon content than blocky-type one. The measured carbon contents of the retained austenite show good coherency with the calculated value from the X-ray diffraction.


Introduction
An electron probe X-ray microanalyzer (EPMA) is a powerful equipment to characterize the distribution of the chemical composition in various materials (Rinaldi and Llovet 2015). EPMA determines the chemical composition accurately due to its high energy resolution (~ 10 eV) (Williams and Carter 2009). The elemental map confirms the relative intensity difference of individual elements in the various phases, including precipitate, inclusion, and matrix phases (Lee et al. 2022;Han et al. 2021). Although there was an effort to quantify the X-ray intensity without a standard specimen (Trincavelli et al. 2014), the obtained intensity is generally quantified by comparing it with the intensities of standard specimens where their chemical compositions have already been determined.
The calibration curves that show the correlation between X-ray intensity and absolute composition for the individual elements should have to be obtained from the standard specimens under the same analysis condition (beam diameter, beam current, accelerating voltage, and detecting crystals) to the observation condition for the actual specimen. Since the chemical compositions of the standard specimens are varied to obtain the correct calibration curve, repeated EPMA analyses on the multiple numbers of standard specimens are necessary. The calibration curve is generally expressed by a linear equation below (Rinaldi and Llovet 2015); where I i is the X-ray counts of element i, C i is an absolute composition of element i, k i is the proportional constant, and B is a background intensity or an intensity without element i in the matrix. X-ray emission depends on atomic number (Z), the absorption of X-rays (A), and the fluorescence of X-rays within the specimen (F) (Williams and Carter 2009;Trincavelli et al. 2014;Ziebold and (1) Ogilvie 2002). Therefore, the proportional constant k i is inversely proportional to the ZAF correction factor. k i and B values are varied with the corresponding element and measuring conditions (beam diameter, beam current, accelerating voltage, detecting crystals, and so on).
One of the typical difficulties in EPMA quantification is finding a proper standard specimen. Pure element is one of the candidates for the standard specimen. However, the absorption of X-rays and the efficiency of X-ray generation in multi-element materials are affected by the constituent elements. This brings the deviation from the exact composition when we study a diluted system using pure element standard. The proper standard specimens will be a form of a solid solution containing the compositions covering the range of interest. Since the chemical compositions of the standard specimens are diverse, the elemental distributions in the standard specimens are nonuniform. These compositional inhomogeneities in the standard specimens bring a significant deviation from the absolute composition of the target specimen because they make an uncorrected calibration curve. Since the chemical inhomogeneity of standard specimens is intrinsic and cannot avoid, the proper method to overcome it is necessary from a practical viewpoint.
The multi-phase steels are composed of diverse phases, including α-ferrite, α b -bainite, α′-martensite, pearlite, and retained austenite (γ) (Han et al. 2021;Kim et al. 2022a). Among them, γ controls the mechanical properties in the multi-phase steels. γ changes the work-hardening and ductility of the steel through the transformation-induced plasticity (TRIP) effect during mechanical deformation (Spencer et al. 2009). The TRIP phenomenon has a strong relationship with the mechanical stability of γ. The chemical compositions of γ that are specifically the contents of γ stabilizer (C, Mn, and so on) should be determined to evaluate the mechanical stability of γ (Heo et al. 2016). However, there are several difficulties to investigate γ in the multi-phase steels using transmission electron microscopy (TEM). Firstly, the volume fraction of γ is only a few % order. There is a limitation in finding the retained γ in a TEM specimen (Zhu et al. 2012). Rare distribution of γ is also an obstacle to fabricating TEM specimens using a focused ion beam. Secondly, statistical analysis is difficult in TEM analysis due to a limited observation of γ (Gutierrez-Urrutia et al. 2013).
In this study, we aim for the practical aspect of EPMA quantification of the chemical composition of retained γ in multi-phase steel. The accurate quantification method in EPMA analysis is suggested. Moreover, EPMA analysis's obtained carbon (C) content was compared to the calculated result from the X-ray spectrometry (XRD).

Preparation of EPMA quantification
The standard specimens were prepared, including a different amount of Mn, Si, and C. Except for 2.029Si alloy, the chemical compositions of all the standard specimens are verified by the National Institute of Standards and Technology. The details compositions are listed in Table 1. The standard specimens were mechanically polished with SiC papers. Then, micro-polishing was conducted using diamond suspensions holding 1, 3, and 9 μm particles. All the compositions of the standard specimens were also investigated by optical emission spectroscopy (OES) and confirmed finally (Table 1). EPMA (JXA-8530F, JEOL Ltd., Tokyo) mapping was conducted to obtain the accurate calibration curve. The condition for the EPMA mapping is given in Fig. 1.

Characterization of microstructure in a Fe-Mn-Si-C alloy
An alloy (Fe-1.5Mn-1.5Si-0.25C (wt.%)) was prepared by vacuum induction heating. First, the specimen was hot-rolled to a rod with a 20 mm diameter. Then, the intercritical annealing was performed at 800 °C for The retained γ is stabilized by the active C partitioning from α b to γ at 400 °C. The microstructure of the heat-treated multi-phase steel was investigated using a field emission-scanning electron microscope (FE-SEM, JSM-7900F, JEOL Ltd., Tokyo) equipped with an electron backscatter diffraction (EBSD, Aztec, Oxford, Abingdon) detector. The chemical compositions of the retained γ were investigated using EPMA. XRD spectrum of the specimen was also obtained to measure the precise lattice parameter of γ (Cullity and Stock 2001).

Effects of acquisition conditions on the calibration curves
As shown in Fig. 1a, OES analysis uses a large quantification area. Due to the large measuring areas, local compositional fluctuation is not sensitively affected by averaging the composition out. However, the compositional inhomogeneity in the standard specimen brings a critical error in constructing the calibration curve in EPMA. A few sampling points in a standard specimen give incorrect intensity values. As a result, there are significant deviations in X-ray intensities in a standard specimen, as shown in Fig. 2a to c. Since most standard specimens are carbon steels, the local difference in carbon intensity, which originated from different phases (cementite, carbide, retained γ or α′) in a standard specimen, is detected in Fig. 2a. This compositional inhomogeneity could be overcome by increasing the sampling area and averaging the obtained intensities. EPMA mapping was conducted using a relatively large area of a 500 μm × 500 μm area (Fig. 1b). All the intensities in a map are summed and then divided by the total number of pixels (455 pixels × 455 pixels).

The effect of probe current change on the calibration curves
The various probe currents are used for characterizing coarse and fine microstructures in EPMA. All through the fine probe is beneficial in spatial resolution, a small (3) I Mn, 100 nA, 3 0 ms = 55.5 × C Mn + 11.2, (4) and I Si, 100 nA, 3 0 ms = 50.2 × C Si + 11.7.  primary electron results in less X-ray emission. The optimum condition of the probe current is determined by the trade-off between special resolution and the output intensity of the X-ray signal. The effect of probe current change on the calibration curves was studied using the same standard specimens. Figure 4 shows the change in the calibration curves depending on the probe current. The obtained intensities at each standard specimen are almost three times higher when the probe current changes from 1 × 10 − 7 A to 3 × 10 − 7 A. The obtained calibration curves in 3 × 10 − 7 A are The experimental data and calculated intensities obtained from the three times the intensities in the probe current of 1 × 10 − 7 A condition were compared. As shown in Fig. 4a to c, the calculated intensities show coherency with the experimental data except for C in Fig. 4a. The probe current of 3 × 10 − 7 A shows higher intensity than the calculated one. C is frequently stacked on the specimen surfaces during observation in electron microscopy (Kim et al. 2022b). Higher current density provides more chances to dehydrogenize the hydrocarbon on the specimen (Toth et al. 2009). It results in more C contamination during the acquisition of the X-ray signal. Therefore, higher intensity in the probe current of 3 × 10 − 7 A is originated from the additional contribution of C-contamination. The increased k i in high probe current will be beneficial for the quantification by increasing the X-ray intensity gap between similar compositions.

The effect of dwell time on the calibration curves
To reduce the C-contamination, a short dwell time for mapping is recommended. The effect of dwell time on the calibration curve was investigated in Fig. 5. The X-ray intensity reduces by about half when the dwell time decreases from 30 ms to 15 ms. The experimental data was compared to the calculated intensities obtained from half of the intensities in the 30 ms condition. Both intensity values show good coherency. Decreased or increased dwell time directly contributes to X-ray generation. Figures 4 and 5 show that a calibration curve can be converted into the calibration curves for the different acquisition conditions. The empirical formulation was drawn as below; where p i is the probe current and t i is the dwell time for the measurement.

Quantification of the chemical composition of retained γ in a Fe-Mn-Si-C alloy
A Fe-1.5Mn-1.5Si-0.25C (wt.%) alloy shows a complex phase structure. Figure 6 shows a typical microstructure of the steel. A secondary electron (SE) image shows complex microstructures. The band contrast map reveals defect-lean α-ferrite(bright contrast) and defect-enriched α′-martensite or α b -bainite (dark contrast). The retained γ was also detected in the phase map in Fig. 6c. Since the alloy experienced intercritical annealing at 800 °C, the various orientations of α′/α b in a α grain originated from the γ to α′/α b transformation (Fig. 6d). The analysis was further performed to reveal the microstructure of γ. Figure 7a and b show the morphology of retained γ in high magnification. The retained γ shows protruding, clean, and elongated morphologies in SE and band contrast images ( Fig. 7a to c). EPMA analysis was performed to measure the chemical composition of the retained γ. Figure 8a and b show backscattered electron and SE images, respectively. The corresponding EPMA maps are displayed in Fig. 8c to e.
Two retained γ were selected, and the intensity profiles are extracted in Figs. 9 and 10. The X-ray intensities in the selected γ are listed in Table 2. The intensities are converted to the absolute composition using the obtained calibration curves in Fig. 5a to c. Interestingly, the thin γ film (site 2) shows higher C contents (1.39 wt.%) than that in blocky γ (1.29 wt.%).
The C contents are indirectly investigated by the lattice parameter of γ. The precise lattice parameter of γ was obtained from the XRD spectrum in Fig. 11a. Each lattice parameter obtained from specific planes of γ is plotted as a function of cos 2 θ/sinθ (Cullity and Stock 2001), and the precise lattice parameter (a γ ) is obtained to 3.6135 ± 0.0015 Å (Fig. 11b). The lattice parameter of γ and the individual chemical composition show the following relationship (Seol et al. 2012); where W i is the chemical composition (wt.%) of element i. Based on Eq. 9, the carbon contents in the (9) a γ (A) = 3.5720 + 0.033W C + 0.0012W Mn − 0.00157W Si , Fig. 9 Extracted intensity profiles from site 1 in Fig. 7c to e retained γ were calculated. Mn and Si contents were used as the average values in Table 2. The calculated C content is 1.26 wt.%. Considering the difficulty of C quantification in energy dispersive spectroscopy, the EPMA quantification of the C content (average value) is relatively accurate, with a deviation of 0.08 wt% from the XRD result. The slightly higher C content in EPMA results probably originates from the different C contamination amounts among the observed specimens.

Conclusion
The practical aspect of EPMA quantification was studied to evaluate the chemical composition of the retained γ in a Fe-1.5Mn-1.5Si-0.25C (wt.%) alloy. The followings are the conclusion obtained from this study; 1. The standard specimens show local inhomogeneity of chemical compositions. The EPMA calibration curves are successfully built by wide-range mapping and averaging the standard specimens.