3.1. Optimization of Micro-Beam X-ray Fluorescence Test Conditions for IN718 Alloy
A typical XRF spectrogram of the IN718 superalloy is shown in
Figure 3. The spectral peak positions of Ti, Cr, Mn, Fe, and Ni are close to each other, and the Kβ peaks of some elements affect the Kα peaks of other elements. For example, the Kβ peak of Mn (
E = 6492 eV) is close to the Kα peak of Fe (
E = 6405 eV), which can cause an apparent higher concentration result for Fe. For Nb, the Kα line (
E = 16,615 eV) is far away from the spectral positions of the remaining elements and can be completely separated from the Kα line of Mo (
E = 17,480 eV), and thus it has fewer interferences.
Factors that affect XRF testing mainly include the tube voltage (kV), tube current (mA), pixel time (ms), filters, and vacuum. The operating voltage of the X-ray tube should be increased for heavier elements because of the higher critical excitation potential. The operating voltage is usually set at two to four times the critical excitation voltage. The corresponding excitation voltages for different elements are shown in
Table 3. When exciting the K-lines of Cr, Fe, Mo, Nb, and Ti, the tube voltage should be above 40 kV, as employed in this study.
Tube current is also a critical parameter in the testing of μ-XRF, as an insufficient intensity of the characteristic peaks can result from low tube currents. However, increasing the tube current also increases the spectrum background caused by scattering peaks, which may lower the PBR of the characteristic peaks. Therefore, the proper tube current must be chosen by considering both the fluorescence intensity and PBR.
Moreover, if a filter with
d (cm) thickness is used, the incident light intensity,
I0, will be attenuated to
I, according to the relationship [
38]:
where
μ is the filter mass attenuation coefficient (cm
2/g) and
ρ is the material density (g/cm
3). The absorption characteristics of the filter can be used to reduce the intensity of the primary radiation from the X-ray tube and weaken the intensity of the continuous spectral lines, thereby reducing the scattering background and, in particular, reducing the interference from the target characteristic X-ray spectrum and impurity lines, thus improving the PBR and reducing the dead time of the instrument. In the energy range from 5 to 10 keV, an aluminum filter is suitable to reduce the Rh L-series target line and increase the PBR. Several different thicknesses of Al filters are available for the M4 TORANDO instrument. In this study, a thinner filter was preferred to ensure a high intensity of the characteristic signals.
Pixel time is an important parameter when scanning an area. Extending the pixel time enhances the intensity of elemental peaks and makes it possible to detect elements with low atomic numbers or concentrations. However, a long pixel time means a longer scanning time and a decrease in productivity. In practice, the pixel time needs to be chosen to balance the accuracy and efficiency.
Finally, vacuum conditions are necessary for the detection of light elements to minimize the absorption of fluorescence by air. Additionally, vacuum conditions also prevent primary X-ray scattering from the air. The tests were conducted in a vacuum of 2000 Pa.
In spectroscopic analysis, the PBR is an important basis for assessing the quality of a fluorescence spectrum. PBR is the ratio of the characteristic X-ray peak intensity of an element,
Ip, to the background intensity,
Ib, and is related to the lower limit of detection (
LLD).
LLD is assumed to be the smallest amount of analyte in a specimen that can be detected in a given analytical context with the 95% confidence level [
39]. The relation is as follows:
where
SLP is the elementary sensitivity,
Ib is the background count under the characteristic X-ray peak, and
t is the measuring time [
40].
To optimize the test parameters for the IN718 superalloy and obtain a relatively optimum PBR for different elements, orthogonal tests were sequentially designed. The orthogonal test method (also called the Taguchi method) is a kind of design method used to study many factors and levels. It conducts tests by selecting a suitable number of representative test cases from many test data, which have evenly dispersed, neat, comparable characteristics [
41]. The Taguchi method is suitable for solving the stated problem with the minimum number of trials, as compared with a full factorial design. The experiments were designed according to an orthogonal array to show the effects of each potential primary factor. This method reveals which factors are most effective in achieving the goals and the directions in which these factors should be adjusted to improve the results. The control for achieving the goals will be best obtained by changes in these primary factors in the direction indicated by the analysis [
42,
43].
To shorten the test time, the voltage and current were pre-tested to determine the level ranges. The voltage was set to 40 kV, 45 kV, and 50 kV levels, and the current was set to 120 μA, 140 μA, and 180 μA. The results showed that the PBR of Nb, Mo, Cr, and Fe increased with the increase of the voltage and the decrease of the current. Therefore, the optimal voltage range fell between 45 kV and 50 kV, and the optimal current should not exceed 120 μA.
Four factors (voltage, current, pixel time, and filters) were numbered from A to D and set at two different levels. In addition to these four factors, two-factor interactions were considered. The factors are presented in
Table 4.
The PBR of four alloying elements (Nb, Mo, Cr, and Fe) were employed as test indicators.
Table 5 presents the L8(2
7) orthogonal array and corresponding results.
In order to study the results from the orthogonal tests, the range analysis was utilized in this study. Range analysis is a statistical method to determine the factors’ sensitivity to the experimental result according to the orthogonal experiment. Range is defined as the distance between the extreme values of the data. The greater the range is, the more sensitive the factor is. The calculation process of range analysis is as follows:
where
represents the average value of the experimental results that contain the factor
X with m level.
Y denotes the average value of all the test results, and
R indicates the degree of influence of factor
X.
The results of the range analysis are shown in
Table 6.
The range values reflect the extent to which changes in the level of factors affected the test results. According to
Table 6, voltage, filter, and pixel time are the main factors that affected the PBR. The PBR value increased as the operating voltage increased and the pixel time decreased under the experimental conditions. The addition of a 12.5 μm Al filter enhanced the spectra of the testing elements. Taking Nb as an example, the pivotal factor influencing its PBR value was the pixel time, with a PBR range of 3.13. Notably, voltage and current had an inevitable interaction in these tests.
Based on this optimization of the μ-XRF conditions, subsequent test conditions were set to 50 kV voltage, 120 μA current, 100 ms pixel time, and a 20 μm pixel step with a 12.5 μm Al filter to obtain better spectral results.
3.3. Concentration Distribution of Elements and Statistical Analysis
Area scanning was carried out on the S1 test area using a 20 μm pixel step. A 400 × 400 intensity matrix could be obtained by testing a rectangular area of 8 mm × 8 mm. The XRF intensity matrix was then converted to a concentration matrix using the calibration curves in
Figure 4. Following this, two-dimensional distribution maps of the elemental concentration were plotted, as shown in
Figure 5.
In
Figure 5, Cr, Fe, Nb, and Ti had obvious positive segregation regions on the S1 test area, where Cr, Fe, and Ti showed punctate segregation while Nb showed banded segregation. Ni mainly presented negative segregation in the test area, where the Nb concentration was often high. The content–frequency statistic distribution of six elements is plotted in
Figure 6.
If the distribution of an element is homogeneous, the content–frequency distribution can be described by a Gaussian function. There was a little tailing profile presented on the right side of the curve for Nb and Ti, as shown in
Figure 6, which indicated that a large amount of abnormally high concentration values of Nb and Ti existed on the scanning area. Therefore, obvious positive segregation of Nb and Ti took place on the scanning area, as shown in
Figure 5. However, the content–frequency distribution of Ni presented an opposite trend to that of Nb and Ti. It was found that a tailing profile occurred on the left side of the content–frequency distribution, which was caused by some lower concentration points of Ni; thus, severe negative segregation of Ni occurred on the scanning area, as shown in
Figure 5. To further characterize the degree of segregation in S1, an original position statistical distribution analysis was introduced [
44]. The maximum segregation degree,
M(
x,
y), is expressed as the ratio of the element maximum concentration,
, to the average concentration,
, on the scanning area:
The minimum segregation degree is similarly expressed as the ratio of the minimum to the average concentration of the element. The statistic segregation degree of the elements was calculated according to Formula (4):
where
C1 and
C2 are the lower and upper limits of the elemental concentration at the 95% confidence level, and
C0 is the median concentration value calculated from the whole concentration value matrix.
Table 7 shows the statistical results of elemental segregation on the scanning area.
The results for S1 showed that Nb and Ti had higher maximum segregation degrees and standard deviations than the other elements. The maximum segregation degrees of Nb and Ti on the test area were 3.88 and 6.86, and the statistical segregation degrees were 0.15 and 0.35, respectively. The concentration distributions of the six elements along the X direction of the scanning area when the value of coordinate Y was 5 mm are shown in
Figure 7. It was found that there were seven obvious high peaks in the line concentration distribution of Nb and similar high concentration peaks also appeared on the line distribution map of Ti. However, negative peaks appeared on the line distribution map of the nickel concentration at the same location where high concentration peaks of Nb occurred. Seven points with significant concentration fluctuations of Nb in
Figure 7 were selected for further study. The segregation degree was calculated by dividing the point concentration of the element by the average concentration within the scanning area, and the results are shown in
Table 8.
The segregation degrees of Nb and Ti on the seven chosen points all exceeded 1, especially for Nb, which suggests an enrichment of Nb and Ti at these positions. At the position of P2, the segregation degree of Nb was 1.666 and the concentration of Nb was higher than the average concentration of the entire scanning area, by more than 60%. At the positions of P1 and P6, the segregation degree of Nb was also high, reaching 1.535 and 1.504. Due to the positive segregation of Nb and Ti at the selected sites, the concentration of Ni as a matrix constituent was affected, resulting in a lower concentration than the average concentration, with a segregation value below 1. The concentration distribution of Cr, Fe, and Mo was relatively homogeneous, and the segregation degree values were generally close to 1, which indicates there is no obvious segregation trend for these elements.
3.4. Correlation between Elemental Segregation and Microstructure Distribution of IN718 Superalloy
It is widely acknowledged that the elemental distribution of materials is closely related to the composition and distribution of the microstructure. In order to further investigate the reasons for concentration segregation of Nb and Ti in IN718 superalloy, SEM-EDS was applied to characterize the morphology, size, composition, and quantity distribution of precipitates on the same test area of the S1 sample. Typical morphology and composition of precipitates by SEM-EDS are shown in
Figure 8. The analysis revealed that the precipitate in the S1 sample exhibited a bright white polygonal morphology, primarily comprising of Nb, Ti, and C. The mass fraction of Nb exceeded 75%, while a small amount of Ti dissolved in the white precipitate phase.
Figure 9 shows the elemental distribution of the precipitates, and it also indicates that the bright white area was enriched with Nb, Ti, and a small proportion of C, causing a decrease in the concentration of Ni, Cr, and Fe. The results had a good agreement with the segregation distribution characteristic results by μ-XRF.
The location and distribution of all bright white precipitate particles in the same test area were characterized by SEM-EDS, in combination with μ-XRF scanning analysis. This approach included advanced automatic analysis technology applied to multiple fields of view to ensure all white particles in the scanning area were identified and analyzed. A striped or banded distribution of the bright white precipitate particles in the test area is shown in
Figure 10. The distribution pattern closely resembled the concentration distribution of Nb, as shown in
Figure 5d. The locations of the Nb precipitates were consistent with the position where positive Nb segregation was observed. Furthermore, it was frequently observed that Ti is present in the Nb precipitates, indicating a tendency for Nb and Ti to have similar segregation behavior, as discussed in
Section 3.2. Therefore, it can be concluded that the Nb-containing precipitates led to the concentration segregation of Nb and Ti in the S1 sample.
The influence of precipitates’ size on the XRF intensity of Nb has been studied. To investigate the relationship between the XRF intensity of Nb and Nb precipitates, the 8 mm × 8 mm rectangular area on the test area was separated into 16 rectangular regions of 2 mm × 2 mm, as shown in
Figure 11a. An XRF intensity greater than three standard deviations of the mean (>
) was considered as an intensity threshold value for distinguishing the abnormal signals from all signals of Nb in the test zone. The sums of high XRF intensity from abnormal signals and the Nb precipitate area in each partition were separately counted.
Figure 11c displays the binary regression fitting curve of the high XRF intensity and the Nb precipitate area.
The curve shows a strong correlation between high XRF intensity and the area of Nb precipitates. With the increase of the high XRF intensity, the area of Nb precipitates also gradually increased, and the correlation coefficient, R, was close to 0.98. This implies that locations with a high XRF intensity for Nb are likely to indicate the existence of Nb precipitates, with the Nb precipitates being estimated based on the abnormally high intensity of Nb using μ-XRF.