A scanning electron microscope (SEM) is a type of microscope that creates images of a sample by scanning it with a focused beam of electrons. Chemical analysis can be carried out using wavelength dispersive X-ray Spectroscopy (WDS) or energy dispersive X-ray spectroscopy (EDS).
These techniques examine the characteristic X-rays produced from a sample when it is exposed to an electron beam. In the WDS technique, a single X-ray energy are counted at any given time, while in the EDS technique almost all X-ray energy lines are collected at the same time.
The original WDS spectrometers were designed by applying the Rowland circle technique. In advanced WDS spectrometers, a parallel beam wavelength-dispersive spectrometer was used that considerably enhanced the X-ray collection efficiency in the spectrum’s low energy range at the cost of X-ray collection efficiency in the moderate to higher energy ranges.
In the latest range of WDS spectrometers, a parallel beam spectrometer with a hybrid X-ray optic was used that facilitated high X-ray collection efficiency in high as well as low energy parts of the spectrum. This article examines the basic principles of WDS and analyzes the technical evolution of this method.
Principles of WDS
The principles of WDS are based on Bragg’s Law of diffraction:
nλ = 2d sinθ Equation 1
where n is an integer, λ(nm) is the X-ray wavelength of interest, d (nm) is the interplanar spacing of the diffractor, θ is the angle of X-ray incidence on the diffractor.
E(keV) = 1.2398/nλ Equation 2a
E(keV) = 1.2398n/2dsinθ Equation 2b
Thus, the hypothetical basis of WDS is fairly simple and straightforward. The material which is being studied produces characteristic X-rays, which are diffracted by a diffractor having a distinct 2d spacing.
A detector is used to count these diffracted X-rays. The geometry of the WD spectrometer is fine- tuned to choose the X-ray energy lines of interest. Such adjustments are done by altering the angle θ of the diffractor corresponding to the sample.
This angle established the X-ray energy, which satisfies Bragg’s Law. In this manner, WDS is often utilized to determine the elemental concentrations with a precision of approximately 0.1%.
Bragg’s Law enables for higher order reflections (n = 2, 3, 4...) in the WD spectrum. For instance, the Ag Lα1 X-ray has 2.984keV energy. Utilizing a PET crystal, this relates to an angle θ of 28.38°.
If the same Ag sample is studied and if the WD spectrometer is adjusted to count X- rays at 1.492keV, the WD spectrometer may determine a smaller amount of 2nd order (i.e. n = 2) Ag Lα1 X-rays, as shown in Figure 1.
Figure 1. ED spectrum (red) and WDS energy scan (blue) of the As L-line spectral region of freibergite ([Cu,Zn,Ag] 12 [Sb,As]4S13). 2nd order reflections of S K1,2 (1.154keV), S Kβ 1 (1.232keV), and Ag Lα1,2 (1.491keV) are present in this spectral region. In order to correctly quantify the As concentration or As Lα1,2 peak-to-background, these 2nd order reflections must be avoided when selecting off-peak measurement positions.
Conventional WDS and Rowland Circle Approach
Standard WDS systems include three basic parts such as an X-ray detector, a diffractor, and an X-ray source. Since gas is present in the detector, a window had to be utilized so as to separate the inside of the detector from the vacuum of the spectrometer and microscope. Two distinct types of detector are utilized in WDS systems.
Sealed proportional counters include Xe or Xe + CO2. Gas-flow counters normally include a P-10 gas which is a mixture of 10% CH4 and 90% Ar. In the Rowland circle WDS, the diffractor, the sample (X-ray source), and the detector must be placed on a Rowland circle of radius, R (Figure 2) to satisfy Bragg’s Law.
Figure 2. Diagrams of conventional WDS based on the Rowland circle using a Johansson diffractor (diffractor size is greatly exaggerated). The yellow area represents all X-rays emitted from the sample by the interaction of the electron beam with the sample. The blue area represents the subset of X-rays that will collide with the diffractor. The red area represents the X-rays that are reflected by the diffractor and are focused on the detector. From left to right, the spectrometer orientation changes to detect X-rays of lower energy. This change in orientation results in an increasing distance (L) between the sample (the X-ray source) and the diffractor. By increasing L, the X-ray intensity at the diffractor decreases because the X-ray intensity is proportional to 1/L2 The result of the Rowland circle orientation is that the collection of low energy X-rays (e.g., O Kα) is less efficient relative to high energy X-rays (e.g., Fe Kα).
In this geometry, the distances from the crystal to the detector and from the source to the crystal are similar (L). However, X-rays produced by a sample in a microprobe or SEM arise from a small interaction volume at the surface of the sample and deviate from the origin as a hemispherical wave front.
Since flat diffractors are not capable of converging or focusing the diverging X-rays, a flat diffractor produces a low count rate at the detector. This is because the X-ray intensity falls quadratically as a virtue of the distance between the actual X-ray counter and the sample. Therefore, a Rowland circle design having a flat diffractor does not present a practical solution (Figure 3).
Figure 3. The yellow area represents all X-rays emitted from the sample by the interaction of the electron beam with the sample. The blue area represents the subset of X-rays that will collide with the diffractor. The red area represents the X-rays that are reflected by the diffractor. When diverging X-rays contact a flat diffractor, they reflect but continue to diverge yielding a low count rate at the detector.
On the other hand, curved diffractors are utilized in Rowland circle WDS systems in order to converge or focus the deviating X-rays onto the detector. Figure 4, left shows a Johann diffractor that includes layers curved to radius, 2R. Thus diffractor does not actually focus the X-rays onto the detector, but can sufficiently converge the X-rays for practical application.
A Johansson diffractor, which also consists of layers curved to radius, 2R, can truly focus the X-rays and is then ground to radius, R – the same curvature as the Rowland circle on which the diffractor is placed (Figure 4, right).
Figure 4. Diagrams of the two diffractor geometries, Johann and Johansson, used in Rowland circle WDS. The yellow area represents all X-rays emitted from the sample by the interaction of the electron beam with the sample. The blue area represents the subset of X-rays that will collide with the diffractor. The red area represents the X-rays that are reflected by the diffractor.
However, it is not easy to manufacture layered diffractors with the Johansson geometry. Hence, standard Rowland circle WD spectrometers contain layered diffractors with crystalline diffractors and Johann geometry.
In fact, Rowland circle spectrometers perform the motion of the detector and the diffractor by forcing them to the required positions at the same time, thereby reducing the distance required to move the detector.
Rowland circle WDS particularly depends on the sample (X-ray source) positioned at the appropriate operating distance. In case the working distance is not accurate, the sample will not lie on the Rowland circle and the distance between the diffractor and the sample will not be equivalent to the distance between the detector and the diffractor.
The optical image is in focus when the sample is placed at the proper working distance and Z position. However, optical microscope is not interacted in most SEMs and care must be taken to make sure that the sample is placed at the right working distance.
Parallel Beam WDS
The main application of the Rowland circle method is to off-set the divergent nature of X-ray emission from the surface of the sample. In case of parallel beam WDS solutions, an X-ray optic is located close to the sample to change the divergent X-rays from the sample into a parallel beam.
As a result, a Rowland circle geometry is not necessary, thus reducing the complications of the spectrometer design and integration with the SEM. This approach ensures that the diffractor is flat and located at a semi-infinite distance from the sample sans affecting the X-ray intensity (Figures 6 and 7). Therefore, parallel beam WDS gives better sensitivity when compared to convention WDS systems, especially at low energies (Figure 5).
Figure 5. Expected intensities from a hybrid optic parallel beam WDS spectrometer (a) and a Rowland circle WDS spectrometer (b). Be, B, C, N, and O intensities were measured using layered diffractors with a 10 kV accelerating voltage. Al intensities were measured using a TAP crystal with a 20 kV accelerating voltage. Using a PET crystal, Si and Ti intensities were measured with a 20 kV accelerating voltage. Ti, Fe, Cu, and Ge were measured using LiF crystals with a 30 kV accelerating voltage. "LiF" refers to a LiF 200 crystal, and "LiF*" refers to a LiF 220 crystal. The difference between the two LiF crystals is that the LiF 220 has a smaller 2d spacing allowing it to be used for the analysis of higher energy X-rays compared to the more common LiF 200.
Figure 6. Schematic representation of a parallel beam spectrometer, showing a fixed L length movement of the detector, and diffractor turret.
Figure 7. The yellow area represents all X-rays emitted from the sample by the interaction of the electron beam with the sample. The blue area represents the subset of X-rays that will collide with the diffractor. The red area represents the X-rays that are reflected by the diffractor to the detector. This diagram of a parallel beam WDS includes a hybrid optic consisting of both polycapillary and grazing incidence optics that transforms the divergent X-rays into a parallel beam, which reflect off the detector and are counted by the detector. However, this diagram would also be accurate for grazing incidence and polycapillary optics.
Two X-ray optical technologies are available for collimating diverging X-rays: polycapillary optics and grazing incidence. At higher energies (> ~2.5keV), a polycapillary optic has greater efficiency (Figure 8) and at lower energies (< ~2.5keV), a grazing incidence optic has the greater efficiency. This option leads to two WDS spectrometer designs: one for low energy spectroscopy and one for high energy spectroscopy.
Figure 8. Expected intensities obtainable using parallel beam WDS spectrometers with (from left to right) a grazing incidence optic, a polycapillary optic, and a hybrid optic. Be, B, C, N, and O intensities are as would be obtained using layered diffractors with a 10kV accelerating voltage.
In case of parallel beam WDS systems, it is important to make sure that X-ray optic and the sample are aligned correctly, with the sample at the correct working distance. This would ensure that the parallel X-rays are incident on the diffractor. Any deviation from the correct working distance can decrease the detected X-ray intensity. This effect would be greater for higher energy X-rays (Figure 9).
Figure 9. Low magnification parallel beam WDS maps for C Kα (0.282keV) and Cu Kα (8.047keV) of carbon and copper standards. The maps are generated by rastering the electron beam over the mapped area in contrast to moving the stage and sample underneath a fixed electron beam. Even if the sample is physically at the proper working distance from the pole piece of the SEM, the X-ray geometry is only appropriate at the point immediately below the pole piece. X-rays generated some distance away from this point are effectively not at the correct working distance. Therefore, the detected X-ray intensity decreases as a function of distance from the point on the sample immediately below the pole piece.
Parallel Beam WDS with a Hybrid Optic
A hybrid optic incorporating a polycapillary optic and a grazing incidence eliminates the cost associated with low or high energy spectroscopy. This leads to intense X-ray detection between 65eV and 17.9keV.
Application 1: Tricky Overlaps (i.e., Identification of Elements Unresolved by EDS)
The energy resolution of WDS is comparatively better than the energy resolution of EDS spectrometers. WDS is used to establish the presence/absence of an element with characteristic X-ray lines, which obstruct with another element, particularly when one of the interfering elements is present at a trace concentration. This section provides three examples of typical EDS peak overlaps and how WDS gives clarity.
The P-Y-Zr-Nb Interference
Some accessory minerals include a mixture of P, Nb, Y, and Zr (for instance, zirconolite, (Ca,Fe,Y,REE)Zr(Ti,Nb)2O7; xenotime, (Y,HREE)PO4; yttrobetafite, (Ca,Fe,Y,REE)2 (Ti,Nb)2O7). These minerals hold significance for geochronology by electron-probe microanalysis as they may include wt%-level concentrations of U, Th, and radiogenic Pb.
The analyzed characteristic X-rays of these elements are P Kα1,2 (2.015keV), Y Lα1 (1.922keV), Zr Lα1 (2.042keV), and Nb Lα1 (2.166keV). Since these X-rays are 0.244eV apart, they are not suitably resolved in EDS (Figure 10).
Figure 10. Red: Zr L-line portion of an ED spectrum of zirconia (ideally, ZrO2) containing Y acquired using 15kV. Blue: WDS energy scan of the same spectral region.
A parallel beam WDS integrated with a hybrid optic was used to analyze a xenotime grain accruing in a rock sample. A WDS scan was then carried out from 1693.5 to 2128.5eV by means of a PET crystal as the diffractor, as shown in Figure 11.
Figure 11. Main: ED spectrum of xenotime ([Y,REE] PO4; REE = rare earth elements) acquired using 15 kV. Peaks, resolved and unresolved, are labeled. Inset: WDS energy scan (blue) and ED spectrum (red) of the same spectral region represented by the gray rectangle in the main image. Although partially resolved, P Kα1,2 is not completely resolved from Y Lβ1 and Y Lβ6 and should not be used for WDS quantitative analysis.
Upon inspection, the EDS spectrum of xenotime shows a strong peak in the P Kα1,2, Y Lα1, Zr Lα1, and Nb Y Lα1 part of the energy spectrum, but it proved complex to determine which of these elements contribute to the peak. The WDS energy scan easily resolves Y Lα1 from P Kα1,2 and partly resolves Y Lβ1 from P Kα1,2. Nb Lα1 and Zr Lα1 are not present in the WDS spectrum.
The Ti-V Interference
Z+1 interferences have often posed a problem for WDS and EDS quantitative analysis. The most notorious Z+1 interference is that of Ti Kβ1,3 on V Kα1,2, which makes it difficult to detect a small concentration of V in the presence of Ti.
A parallel beam WDS with a hybrid optic was used to examine a sample of Ti-6Al-4V alloy. Two WDS energy scans were carried out on V-poor and on V-rich phases in the alloy from 4850 to 5050eV by means of a LiF crystal as the diffractor.
The S-Mo-Pb Interference
The interferences of the Mo L-Lines, the S K-lines, and the Pb M-lines are often complex in the EDS system. Upon inspection of the EDS spectrum of galena, it is complex to establish which elements are present. The WDS energy scan easily resolves S Kα1,2 from Pb Mα1,2. Moreover, a small Mo Lβ1 peak is also detected. Without WDS, the presence of Mo in the sample would not have been easily detected.
The Ti-Ba Interference
In EDS, Ba Lα1 and Ti Kα1,2 are unresolved. Ti and Ba are common components in ceramics, metals, and minerals. In the WDS energy scan, Ba Lα1 and Ti Kα1,2 are virtually resolved from one another; however, hey are not resolved in the EDS scan.
Application 2: Quantitative Analysis
During WDS quantitative analysis, the X-rays on- and off-peak have to be measured to establish the peak intensity. To ensure that WDS quantitative results are precise, the peak that needs to be determined must be free of interferences and the off-peak measurement positions must represent the background.
In certain cases, a WDS energy scan does not resolve interferences, while in other cases, a WDS energy scan can partly resolve interferences. However, in case the low or high energy peak tails of the interfering X-ray line are not present at background levels of the on-peak position, the quantitative results will be not be accurate. In WDS, the peak height above the background is measured to determine the X-ray line Intensities.
Using a parallel beam WDS with a hybrid optic, quantitative WDS analysis of freibergite was carried out on an FESEM. The sample was carbon coated and polished. Analytical conditions were a beam current of 27 nA and an accelerating voltage of 15kV. Standardization was performed by applying synthetic and natural mineral standards.
Table 1 shows the results of the WDS quantitative analysis of freibergite. The composition matches to a mineral formula of (Cu,Ag) 102 (Zn) 19 (Sb,As) 42S13 and is in line with other reported analyses of the mineral freibergite perfumed using electron- probe microanalysis.
Table 1. Composition of freibergite determined by WDS quantitative analysis using a parallel beam WDS with a hybrid optic. Reported values are averages from 13 analyses.
Application 3: WDS Applications
Peak overlaps can also confound X-ray maps, leading to false positives or mapping of inaccurate elements. Mapping with WDS removes the effect of most of these overlaps. The low background of WDS enables trace elements to be mapped that otherwise it not possible to map with EDS due to their low concentration.
WDS maps of a Sn electrode having a layer of Ni insulating Cu from Sn were produced by rastering the beam across the sample. Since the Ni layer has a thin width, a low accelerating voltage was employed so as to reduce the electron probe interaction volume. X-rays were counted using a TAP crystal as the diffractor and a parallel beam WDS with a hybrid optic.
At the same time, a WDS map of a steel comprising B was created with an EDS image cube by rastering the beam across the sample. X-rays were then counted using a layered diffractor and an SDD (for EDS) and a parallel beam WDS with a hybrid optic.
Since the L-lines of Cu and Ni overlap significantly, the Cu and Ni EDS maps are identical. In the Ni EDS map, the Ni and Cu layers are not distinguished easily, but in the WDS maps, the Ni layer can be clearly detected from the Cu layer.
WDS provides superior resolution improvements when compared to EDS, and almost eliminates all the peak overlaps. Trace element detection is further improved by an order of magnitude enhancement in peak-to-background sensitivity.
Parallel beam WDS provides improvement in intensity in the low energy spectral region when compared to traditional WDS. Improved peak-to-background and removal of overlaps produce helpsa in achieving precise quantitative analysis for low concentration elements.
Since it is possible to place the WD spectrometer at the middle of the peak, where peak-to-background is maximized, WDS offers excellent X-ray maps, particularly for low concentration. Due to the serial nature of spectrum acquisition, qualitative analysis is slow in comparison to the EDS technique.
On the other hand, since WDS is operated by driving the crystal to the peak, counting time is focused only to the preferred points. For detection of minor elements, WDS is combatively fast than that of EDS, wherein most counted X-rays will arise from the major elements.
Thus, SEM users can use parallel beam WDS approach to perform quantitative studies with the same precision obtained in electron-probe microanalysis.
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