Understanding Electron Probe Microanalysis: Theory and Applications

1. UofO- Geology 619 Electron Beam MicroAnalysis- Theory and ApplicationElectron Probe MicroAnalysis -(EPMA) WDS (Wavelength Dispersive Spectrometry): (Parameters) Modified from Fournelle, 2006

2. Generic EMPA/SEM WDS Electron gun Column/ Electron optics Optical microscope EDS detector Scanning coils SE,BSE detectors WDS spectrometers Vacuum pumps Faraday current measurement

3. Key points • X-rays are dispersed by crystal with only one wavelength (nl) reflected (=diffracted), with only one wavelength (nl) passed to the detector • Detector is a gas-filled (sealed or flow-through) tube where gas is ionized by X-rays, yielding a massive multiplication factor (‘proportional counter’) • X-ray focusing assumes geometry known as the Rowland Circle • Key features of WDS are high spectral resolution and low detection limits

4. WDS Spectrometers An electron microprobe generally has 3-5 spectrometers, with 1-4 crystals in each. Here, SP4 (spectro #4, LF) with its cover off. Crystals (2 pairs) Proportional Counting Tube (note tubing for gas) PreAmp

5. Key points X-rays are dispersed by a crystal with only one wavelength (nl) reflected (=diffracted), with that one wavelength (nl) passed to the detector.This is a monochrometer. Recall that n can be >1, so other elements can cause interference if their wavelengths are at an integral fraction of the desired wavelength. The detector is a gas-filled (sealed or flow-through) tube where gas is ionized by X-rays, yielding a massive multiplication factor (‘proportional counter’) X-ray focusing assumes geometry known as the Rowland Circle Key features of WDS are high spectral resolution and low detection limits

6. The typical electron microprobe has vertically mounted spectrometers (a), i.e. the Rowland circle is vertical. This orientation permits up to 5 spectrometers to be mounted around the column, as well as having room for an EDS detector. In this orientation, X-ray intensities are susceptible to small differences in the Z position of the sample (= X-ray defocusing, not good). We use polished planar samples, and focus the sample Z with reflected light. Spectrometers- Orientation There are some applications (e.g., industry) where the probe is utilized in production, and samples are rough surfaces. For this specialized situation, the spectrometer can be inclined(b), which then permits X-ray diffraction from a range of heights, all now on the inclined Rowland circle. However, only 2 inclined spectrometers will then fit around the column. Reed, 1993, Fig. 6.9, p. 70.

7. Inclined Spectrometer

8. Focussing Geometry • The point source of X-rays in the electron microprobe is not optimally diffracted by a flat crystal, where only a small region is “in focus” for the one wavelength of interest. • X-ray intensities are improved by adding curvature to the crystals: • Johann geometry: the crystal is bent/curved to a radius 2r (=diameter of Rowland circle); • Johansson geometry: the crystal is curved to 2r, and the surface is ground to r. This is a difficult process, so most crystals have Johann geometry. Reed, 1993, p. 67.

9. C B A Rowland Circle • For most efficient detection of X-rays, 3 points must lie upon the focusing circle known as the Rowland Circle. These points are • the beam impact point on the sample (A), • the active central region of the crystal (B), and • the detector -- gas-flow proportional counter (C).

10. Rowland Circle The loci of 3 points must always lie on the Rowland Circle. Starting at the top position (blue), there is a shallow angle of the X-ray beam with the analyzing crystal. To be able to defract a longer wavelength X-ray on the same spectrometer, the crystal travels a distance further out, and effectively the (green) Rowland Circle “rolls”, pinned by the beam-specimen interaction point.

11. Bragg defocussing

12. BSE detectors alternate X-ray path Only a small % of X-rays reach the spectrometer. They first must pass thru small holes (~10-15 mm dia; red arrows) in the top of the chamber (above, looking straight up), then thru the column windows (below, SP4).Thus, in our EMP, there are different vacuum regimes in the chamber vs the spectrometer.

13. BA’ = A’C = d sinq for constructive reinforcement of a wave, the distance BA’ must be one half the wavelength. Thus, 2d sinq = l and by similar geometric construction = nl Wavelength Dispersion Of the small % of X-rays that reach the crystal, only those that satisfy Braggs Law will be diffracted out of the crystal. nl = 2d sinq Note that exact fractions of l will satisfy the conditions for defraction. Thus, there is a possibility of “higher order” (n=2,3,...11,?) interference in WDS (but there also is the means electronically to discriminate against the interference).

14. Lots of Analyzing Crystals Over the course of the first 30 years of EPMA, ~50 crystals and pseudocrystals have been used.

15. Temperature Dependence • We attempt to keep a constant temperature in the probe lab, around 68°F (20°C). This is also the temperature of the chilled water that circulates both through the electronic cabinet as well as the column (and outer jacket of diffusion pump). • Two aspects of the instrument are sensitive to temperature changes – the spectrometer crystals, and the detector P10 gas. • Spectrometer crystals have a linear expansion coefficient, and expansion will change the 2d. The effect upon PET is 4x worse than upon LIF, and increases rapidly with increasing sin q. • P10 gas pressure must be constant, as this is critical to having reproducibility in counting rates between the standards and the unknowns, both over short time spans as well as longer (e.g. 24 hour) durations. (Loss of air conditioning on very hot summer days precludes probing.)

16. WDS provides roughly an order of magnitude higher spectral resolution (sharper peaks) compared with EDS. Plotted here are resolutions of the 3 commonly used crystals, with the x-axis being the characteristic energy of detectable elements. Note that for elements that are detectable by two spectrometers (e.g., Y La by TAP and PET, V Ka by PET and LIF), one of the two crystals will have superior resolution. When there is an interfering peak and you want to try to minimize it, this knowledge comes in very handy. Spectral Resolution Reed, 1995, Fig 13.11, in Williams, Goldstein and Newbury (Fiori volume)

17. The intensity of a WDS spectrometer is a function of the solid angle subtended by the crystal, reflection efficiency, and detector efficiency. Reed (right) compared empirically the efficiency of various crystals vs EDS. However,the curves represent generation efficiency (recall overvoltage) and detection effeciency. Spectrometer Efficiency Reed suggests that the WDS spectrometer has ~10% the collection efficiency relative to the EDS detector. How to explain the curvature of each crystal’s intensity function? At high Z, the overvoltage is presumably minimized (assuming Reed is using 15 or 20 keV). Low Z equates larger wavelength, and thus higher sinq, and thus the crystal is further away from the sample, with a smaller solid angle. Reed, 1996, Fig 4.19, p. 63

18. Crystals and PC/LSMs • Consider the order of 2d in Braggs Law: sin q varies from .2-.8, and l varies over a wide range from hundreds to fractions of an A. Thus, we need diffractors that cover a similiar range of 2d, from around 1 Å to hundreds of Å. In our SX50/100, we utilize TAP, PET and LIF crystals for the shorter wavelengths. For longer wavelengths, there are 2 options: • Pseudocrystals (PCs), produced by repeated dipping of a substrate in water upon which a monolayer (~soap film) floats,progressively adding layer upon layer, or • Layered synthetic microstructures (LSMs; also LDEs, layered diffracting elements), produced by sputtering of alternating light and heavy elements, such as W and Si, or Ni and C. • Both these are periodic structures that diffract X-rays. The LSMs yield much higher count rates; however, peaks are much broader, which have good/bad consequences, discussed later. • In reality, people interchange the words PC, LSM, LDE, etc. Cameca uses PC and JEOL uses LDE, for same things.

19. Crystals and PCs on the UofO SX50/100 There is a more accurate form of Braggs Law, that takes into account refraction effects, which are more pronounced in the layered synthetic diffractors (why?), nl = 2d sinq(1-k/n2) k is refraction factor, n is order of diffraction

20. Crystals and PCs: Which to use? • The EPMA user may have some control over which crystal to use; some element lines can be detected by either of 2 crystals (e.g. Si Ka by PET or TAP, V Ka by PET or LIF), whereas other elements can only be detected by one (e.g. S Ka by PET). Each probe has its own (unique?) set of crystals and the user has to work out the optimal configuration, taking into account concerns such as • time and money (resolution vs. count rate) • interferences vs counting statistics (sharper peaks usually have lower count rates) • stability (thermal coefficient of expansion) • sensitivity to de-focussing, peak shape/shift

21. Pseudocrystals/LSMs Goldstein et al, p. 280

22. The class project in 2002 was to collect data that will be put in a chart to compare the efficiency of different crystals/ PCs for certain elements. Crystal comparison Å Å TAP gives a higher count rate, and wider peak for Si Ka vs. using PET Si Ka on TAP sin q = 27714 P/B= 4862/40=122 FWHM=0.038Å Si Ka on PET sin q = 81504 P/B= 207/1.3=159 FWHM=0.006Å

23. Max 4862 cts Peak (spectral) resolution is described by FTWM Full Width Half Max Full Width Half max 2431 cts counts Si Ka on TAP sin q = 27714 P/B= 4862/40=122 FWHM=0.038Å Å

24. P10 gas (90% Ar - 10% CH4) is commonly used as an ionization medium. The X-ray enters through the thin window and 3 things can occur: (1) the X-ray may pass thru the gas unabsorbed (esp for high keV X-rays); (2) it may produce a trail of ion pairs (Ar+ + e), with number of pairs proportional to the X-ray energy; and (3) if the X-ray is >3206 eV it can knock out an Ar K electron, with L shell electron falling in its place. There are also 3 possibilities that can result from this new photon: WDS detector (3a) internal conversion of the excess energy with emission of Auger electron (which can produce Ar+ + e pairs); (3b) Ar Ka X-ray itself can knock out electron of another Ar molecule, producing Ar+ + e pair; or (3c) the Ar Ka X-ray can escape out thru a window, reducing the number of Ar+ + e pairs by that amount of energy (2958 eV)

25. Nominally, it takes 16 eV to produce one Ar+- electron pair, but the real (effective) value is 28 eV. For Mn Ka (2895 eV), 210 ion pairs are initially created per X-ray. However, there is a multiplier effect (Townsend avalanching). For our example of Mn Ka, all 210 electrons are accelerated toward the center anode (which has a positive voltage [bias] of1200-2000v) and produces many secondary ionizations. This yields a very large amplification factor (~105), and has a large dynamic range (0-50,000 counts/sec). Detector amplification

26. Detector windows Thin (polypropylene) windows are used for light X-rays (e.g. those detected by TAP and PC crystals). Since the windows are thin, the gas pressure must be low (~0.1 atm). And being thin windows, some of the gas molecules can diffuse out through them -- so the gas is replenished by having a constant flow. For thicker windows (mylar), 1 atm gas pressure is used (with higher counts resulting). Sealed detectors with higher pressure gas (e.g. Xe) are also used by some.

27. WDS detector The bias on the anode in the gas proportional counter tube needs to be adjusted to be in the proportional range. Too high bias can produce a Geiger counter effect. Too low produces no amplification.

28. WDS pulse processing The small electron pulses (charges) generated in the tube are first amplified in the pre-amp (top) located just outside the vacuum on the outside of the spectrometer, then sent to the PHA board where they are amplified (center) and shaped (bottom). Each figure is for one (the same) pulse. Goldstein et al Fig. 5.10

29. Ar-escape peak There is a probability that a small number of Ar Ka X-rays produced by the incident X-ray (here, Fe Ka) will escape out of the counting tube. If this happens, then those affected Fe Ka X-rays will have pulses deficient by 2958 eV. Fig 7.8 is an unusual plot of this (for teaching purposes); what is normally seen is the Pulse Height distribution where the pulses are plotted on an X-axis of a maximum of 5 or 10 volts. Reed, 1993, p. 90

30. Actual PHA plot for Si Ka: there is no Ar-escape peak. WHY?

31. Higher order reflections Recall nl = 2d sinq. Higher order reflections are possible in your specimens, and must be avoided to prevent errors in your analyses. Reed (1993) reports that LIF can show a strong second order peak, up to 10% of the first order peak. In 1999, the 777 class examined the higher order reflections of Cr Ka lines. On PET, 2nd and 3rd order peaks were present, and decreased ~an order of magnitude with increasing n. On LIF, up to the 8th order peak was present. Here, the intensity of the odd numbered orders was less than the following even order, e.g. the 5th order Ka had 30% fewer counts than the 6th order line. Differential mode of pulse height analysis (PHA) may be used to ignore counting higher order X-rays.

32. Integral vs Differential PHA Analysis of ‘light elements’ such as C is complicated because of the long wavelength (44 Å) which means that higher order reflections of many elements can interfere. At top, where the PHA is set to the “count everything” integral mode, the 3rd order reflection of Ni La1 falls very close to C Ka and adds some to C peak counts. Note also the 2 and 3 order Fe L lines. By setting the detector electronics to the discrimination mode (“differential”), bottom, the higher order lines are strongly (but not totally) suppressed. Spectrometer scans Goldstein et al, p.507-8

33. Bkg under peak High bkg Low bkg Spectrum =Characteristic + continuum Recall that the X-rays generated by electron bombardment are both characteristic of each element present in the specimen, as well as the broadband “continuum”. And recall that the background level increases with increasing mean atomic number of the specimen. In EPMA, several steps must occur. First, the peak position must be precisely found. Then, trustworthy background positions must be found in order to model the background level at the peak position. Above, the Mg ka peak position is at the white (center) line and we need to determine where adjacent to it would be the best places to measure the background level, in order to calculate (model) the continuum level under the peak..

34. Bkg under peak High bkg Low bkg Probe for EPMA Peak and Background displays Our software provides handy ways to store wavescans. The standard procedure is to peak the elements of interest and use either default background positions or ones previously chosen. The displayed wavescans have a central line that is white. This is the peak of interest (here, Mg Ka).Background positions are shown by yellow lines. If a background position has been changed, the old position is shown in magenta.The “background model” is a line, here red (normally yellow).

35. Curved background-1 There are some cases where the background has a curvature, particularly at low sin theta A linear model (below) results in too high calculated background. .

36. Curved background-2 An exponential curved background, however, provides a better result. Note the presence of several other background models in the right box.

37. In some (many) cases, adjacent peaks can interfere with either high or low background position, requiring same side backgrounds: here, average of 2 measurements on the high side. Highest peak is 3rd order Ca Ka. Congested backgrounds

38. Background Offsets How far away from the peak should the background offsets be? Reed demonstrates mathematically (adjacent figure) that a small overlap on the tails of the peak ends up making no significant difference. However, he warns (and it is my experience) that being too close to the peak is not good practice, and should only be done in extreme cases where it is impossible to find a ‘free area’ in the adjacent background. Reed, 1993, p. 150

39. This is an EDS view of the absorp;tion edge. To translate to WDS (wavelength or sin q), just reverse the axes. Backgrounds and Absorption Edges You need to be aware of potential for error if you position your low background too far to the left (low sinq, short wavelength), below the absorption edge of the element you are measuring. For the K edges, this is at the Kb position. The background level to the low sinq (=higher energy) side of the edge will be depressed because these continuum X-rays have energies great enough to be “used up” causing secondary fluorescence of the element in question, and thus produce a misleadingly low background. If a low background position between the peak and absorption edge can’t be taken, then only measurements on the high side should occur. “These considerations do not apply to small peaks for which the associated absorption step is negligible.”–Reed, 1993, p. 151

40. Analysts need to understand the possible implications of the Ar absorption edge (recall Ar is in the detector P10 gas). A certain fraction of X-rays with energy lower than the argon K edge (3.202 keV) will pass through the gas without interaction. However, for X-rays with energies > 3.202 keV, approximately twice as many will interact with the gas and be detected. Ar Absorption Edge From Paul Carpenter’s talk at April 2002 NIST-MAS EPMA workshop • Lines of the same family that fall on either side will have ‘abnormal’ proportions–normally the La > Lb, but for Cd, it is reversed due to this. • Trace element studies utilizing the U Ma line must utilize only background offsets on the high sinq side of the peak (see figure above).

41. Au La peak position Holes in the Background-1 In 1987, Bruce Robinson (Australia) reported on a phenomenon uncovered during examination of arsenopyrite for trace amounts of gold. After looking at unknowns, he checked a reference arsenopyrite that should have had no Au in it – but it showed 100 ppm. High resolution scan of the background near the Au La peak on the LIF crystal showed a distinct drop (trough) by ~10% relative to the adjacent background. With an incorrect (artifically “low”) background, zero Au had become 100 ppm Au. From Remond et al, 2002, NIST Journal of Research

42. Au La peak position Holes in the Background-2 These holes or ‘negative peaks’ are caused by reflections of the continuum X-rays from planes in the crystal other than the correct plane (the 200 in LIF). These X-rays do not reach the counter. The point is that when you are looking for very low detection levels, it pays to pay very close attention to the shape of the background and to try to understand it well. And to have some well characterized secondary standards to evaluate your procedure with.

43. On Peak Interferences Users must be vigilant for interferences upon the peaks being measured, both in the unknowns and in the standards. The figure to the right shows an interference type seen where peak B overlaps peak A. For elements whose wavelengths can be diffracted by a choice of 2 crystals, one will be better for spectral resolution (the lower 2d, with higher sin theta position). Reed, 1993, p. 153

44. On Peak Interference-Slight REE analysis is particularly tricky, since there are so many elements present and there are so many L lines.Here the high side tail of Ce Lb1 interferes with Nd La.

45. Interference Correction We must correct for interferences, by software options, if we have standards that have the interfering element (here Ce) but none of the interfered with element (here Nd). During count acquisition (“calibration” or “standardization”) on the Ce standard (356), we also acquire interference counts at the Nd La peak position. Then during analysis of unknowns, an appropriate correction is made for the overlap.

46. Peak Centering-1 Quantitative analysis requires knowledge of the peak intensity, which is a function of the composition of the specimen.We could also use the integrated area of the peak, but that is time-consuming. The peak position is first determined upon either the specimen or the standard, with the general assumption that the position is the same (with important exceptions!). Then that position (and user-determined background offsets) are utilized in the automated movement of the spectrometers during analysis.

47. Peak Centering-2 There are several methods possible to find the peak center. In times past, manual searching was done (aided by an audio device whose pitch increased as counts increased). Today we have automated peaking routines. We have developed a routine of (1) using one of the top 3 methods (usually the fast ROM) to get pretty close to the peak, and then (2) a “post-scan” across the top of the peak that allows the operator the final decision of picking the optimal peak position. (This option was added based upon detailed peak scans done by 777 students in the Fall of 2002.)

48. It is very important to start with the “best” peak position, which means the center of the peak (usually the highest counts – though not necessarily). At the right are two “post-scans” where the red vertical line is the position selected by the ROM automation—very good for the Si Ka position, but about 7 units too high for Al Ka. The “post-scan” option gives the operator the freedom to over-ride the computer’s best guess with an intelligent decision. Best operating practice calls for picking the center of the peak centroid, because there may be slight offsets developed over a probe session due to mechanical drift and there is also the question of real peak shifts; by starting in the dead center, these variables should be minimized. Peak Centering-3

49. X-ray Peaks - Poisson Distribution X-ray peaks follow a Poisson distribution, which describes the counting of events that occur at random but at a definite average rate. “It can be shown” that for a Poisson distribution, the standard deviation is the square root of the counts. The Poisson distribution is similar to, but different from the Gauss distribution. The Gauss distribution is bell shaped and symmetrical about its mean value, while the Poisson distribution has neither of these properties in general. John R. Taylor, An Introduction to Error Analysis, 2nd Ed., 1997. p. 245-256

50. PbS BaSO4 Al Ka Peaks Shifts in peak shape of certain elements can occur due to difference in chemical bonding, between different samples/standards. Some well understand examples are Al Ka and S ka, as well as P ka, and the “light” element K lines. Articles have been published that show evidence of peak shifts of Si and Al kb as well as Fe La/Lb in relation to valence/bonding. Peak Shifts-1