1. Ge 116 Module 2: Electron Probe
Part 1: instrument basics, WDS X-ray analysis and standardization

2. Electron Probe: Parts
(5 of these)

3. Electron Microprobe Instrumentation
What Makes a Microprobe?
High Stability Electron Source
Focussing WDS X-ray Optics
High Precision Stage
Reflected Light Optics
Beam Current (Faraday Cup)

4. Electron Probe: WDS spectro-meters

5. Proportional Counting Tube (note tubing for gas)
WDS Spectrometers
This is a Cameca spectrometer, but JEOL design is pretty similar
Crystals (2 pairs)
Proportional Counting Tube (note tubing for gas)
PreAmp

6. Electron Probe: WDS spectrometers
Rowland Circle: crystal moves in straight line away from sample focus point, detector must move along curve to remain on circle
With vertical Rowland circle, can pack lots of spectrometers around machine but X-ray counts very sensitive to Z focus

7. Electron Probe: diffracting crystals
E (eV)
K elements
LiF [lithium fluoride, (200)]
4.027 Å
Ca to Ge
PET [Penta-erythritol (001)]
8.742 Å
Si to Ti
TAP [Thallium acid phthalate (001)]
25.76 Å
O To Al
LDE1 (W-Si)
61.1 Å
C to F
LDE2
98.0 Å
B, C, N
LDEB
145.0 Å
Be, B, C

8. Electron Probe: diffracting crystals

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

10. Crystals in our probe SP1: TAP, PET, LDE1, LDEB SP2: PET, LIF
SP4: TAP, LDE2
SP5: PET-H, LIF-H
Example protocol:
SP1 TAP: Na, Mg
SP2 PET: Ca, Ti
SP3 PET-L: K, P
SP4 TAP: Al, Si
SP5 LIF-H: Mn, Fe

11. Electron Probe: gas proportional counters
With increasing bias, gas counters go from ionization chamber to proportional counting to Geiger cascade region (in proportional region, can use energy of X-ray to suppress counting of wavelength multiples)

12. Electron Probe: gas proportional counters
Trade-off between window thickness and gas pressure
Gas flow P10 vs. sealed Xe

13. Spectral Resolution
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.
Reed, 1995, Fig 13.11, in Williams, Goldstein and Newbury (Fiori volume)

14. Spectral Resolution

15. Electron Probe: wavelength scans and peaking
Al Ka Peaks
BaSO4
PbS
WDS has much higher spectral resolution than EDS, which is a big advantage, but peak shifts can be significant, so you have to check peak positions and match your standards well

16. Electron Probe: background correction
Low bkg
High bkg
Bkg under peak
Can use wavelength scans to find featureless regions near peak for background fitting.
For standard elements, this has already been done; for exotics you have to do it yourself

17. Quantitative Analysis
Background-corrected on-peak counting rate on standard (composition known), normalized to Faraday cup current: Iistd (counts/sec/nA)
Background-corrected on-peak counting rate on unknown, normalized to Faraday cup current: Iiunk (counts/sec/nA)
Ratio Iiunk/Iistd is called the ‘k-ratio’. To first order it equals the ratio of element concentration in unknown to that in standard.

18. Raw data needs correction
This plot of Fe Ka X-ray intensity data demonstrates why we must correct for matrix effects. Here 3 Fe alloys show distinct variations.

19. Absorption and Fluorescence
The Fe-Ni alloys plot above the 1:1 line (have apparently higher Fe), because Ni atoms present produce keV X-rays, above Fe K edge of keV.Thus, additional Fe K are produced by this secondary fluorescence.
The Fe-Cr alloys plot below the 1:1 line (have apparently lower Fe), because Fe atoms produce X-rays of keV, greater than the Cr K edge of keV. Thus, Cr K is increased while Fe K are “used up”.

20. Z A F
In addition to absorption (A) and fluorescence (F), there are two other matrix corrections based upon the atomic number (Z) of the material: one dealing with electron backscattering, the other with electron penetration (or stopping). These deal with corrections to the generation of X-rays. C is composition as wt% element (or elemental fraction).

21. Unanalyzed elements
The matrix corrections assume that all elements present (and interacting with the X-rays) will be included. There are situations, however, where either an element cannot be measured, or not easily, and thus the analyst must make explicit in the quantitative setup the presence of unanalyzed element/s -- and how they are to be input into the correction.
Typically oxygen (in silicates) is calculated “by stoichometry” (which requires valence of cations). Elements can also be defined in set amounts, or relative proportions, or “by difference” – although this later method is somewhat dangerous as it assumes that there are no other elements present.

22. Some remarks on standards
EPMA’s claim to fame as a microanalytical tool rests upon (1) faith in a correct matrix correction and (2) use of “good”, “correct”, “true” standards.
How do you know whether to trust a standard?

23. Standards
In practice, we hope we can start out using the “best” standard we have.* There have been 2 schools of thought as to what is the “best” standard is:
a pure element, or oxide, or simple compound, that is pure and whose composition is well defined. Examples would be Si or MgO or ThF4. The emphasis is upon accuracy of the reference composition.
a material that is very close in composition to the unknown specimen being analyzed, e.g. silicate mineral or glass; it should be homogenous and characterized chemically, by some suitable chemical technique (could be by epma using other trusted standards). The emphasis here is upon having a matrix that is similar to the unknown, so that (1) any potential problem with the matrix correction will be minimized, and (2) any specimen specific issues (i.e. element diffusion, volatilization, sub-surface charging) will be similar in both standard and unknown, and largely cancel out.
* This is based upon experience, be it from prior probe usage, from a more experienced user, from a book or article, or trial and error (experience comes from making mistakes!) It is commonly a multiple iteration, hopefully not more than 2-3 efforts.

24. Standards - Optimally “Round Robins”
Ideally the standard would be stable under the beam and not be altered (e.g., oxidizable or hygroscopic) by exposure to the atmosphere.
It should be large enough to be easily mounted, and able to be easily polished.
If it is to be distributed widely, there must be a sufficient quantity and it must be homogeneous to some acceptable level.
However, in the real world, these conditions don’t always hold.
“Round Robins”
On occasion, probe labs will cooperate in “round robin” exchanges of probe standards, where one physical block of materials will be examined by several labs independently, using their own standards (usually there will be some common set of operating conditions specified). The goal is to see if there is agreement as to the compositions of the materials.

25. Sources for standards :
Purchased as ready-to-go mounts from microscopy supply houses as well as some probe labs ($ )
Alternately, most probe labs develop their own suite of standards based upon their needs, acquiring standards from:
Minerals and glasses from Smithsonian (free)
Alloys and glasses from NIST (~$100 ea)
Metals and compounds from chemical supply houses (~$20-60 ea)
Specialized materials from researchers (synthesized for experiments, or starting material for experiments) – both at home institution as well as globally (some $, most free)
Swap with other probe labs
Materials from your Department’s collections, local researchers/ experimentalists, local mineral shop or national suppliers (e.g., Wards)

26. Thoughts on beam current
Is more beam current always better? No.
Detector saturation…too much deadtime
Sample heating (example: Mica at 50 nA, 1 m spot -> 514 °C of heating!)
Element migration (Na diffuses away from beam, especially in hydrous glasses)
Loss of spatial resolution (higher current = bigger beam)
T = max temp rise
E = accelerating potential in keV
I = beam current in A
k = thermal conductivity in W/mK
d = beam diameter in m

27. Reducing beam damage
For beam-sensitive samples (like hydrous, high-alkali glass…)
Reduce beam current (trade-off with counts)
Reduce counting time (trade-off with counts)
Defocus or raster beam over area (need homogeneous, clear spots); need to run standards in same geometry
Run sensitive elements in first pass
Examine counts vs. time experiments to see rate of damage; extrapolate to zero time?

28. Thoughts on temperature stability
Electron microprobes only operate well in very constant temperature rooms
Changing T causes thermal expansion of the diffracting crystals -> peak shifts
Changing T changes pressure in gas-flow proportional counters -> changes counting efficiency
Others?

29. Some tricks Normalization Secondary standards
With replicate data, can test which is more reproducible - raw or normalized data
Secondary standards
No physics here, just empirical adjustment for machine performance on a given day

30. X-ray mapping
Usually done in qualitative mode, that is not background corrected, normalized, or referenced to a standard
Can introduce empirical two-point calibration to semi-quantify maps
Map quality is a function of counting time, mostly

31. X-ray mapping

32. Statistics
Measurement is always a statistical process, and mature understanding of the statistics is essential to proper interpretation of data
There are several ways to look at the precision and sensitivity of electron probe analyses, depending on what question you are asking…

33. Counting Statistics
X-ray counts are quantized and the number of counts you get in an idealized experiment will always be a Gaussian distribution with standard deviation
Thus, 1% relative precision requires, in theory, counts. 0.1% relative precision requires 106 counts.

34. Real Statistics
The real standard deviation of a set of replicate measurements of the same spot is greater than or equal to the ideal value from counting statistics
Longer counting time leads to more instrument drift (source, column, stage, detector, etc.)
In practice, for a well-maintained instrument, if counting time ≤100 s then actual standard deviation Sc ~ 2sc

35. Real Statistics
Furthermore, quantification requires background correction
Hence, the estimated peak counting rate P is really based on 3 measurements: (P+B), Blow, Bhigh
These uncertainties add in quadrature and can increase Sc of the estimate (P+B) – B by a large factor if P/B is small

36. Statistical Tests 1. Sample homogeneity 2. Analytical Sensitivity
Based on multiple point analyses or mapping, is a phase homogeneous at some level of confidence?
2. Analytical Sensitivity
For (repeated?) measurements of two different concentrations, how different must they be before they can be distinguished at some level of confidence?
3. Detection Limit
What concentration of a trace element is necessary before its presence in a sample can be established at some level of confidence?

37. Statistical Tests 1. Sample homogeneity
Approximate formula: 99% confidence corresponds roughly to all n analyses falling within a range
So for 105 counts per point at C = 10%, W~0.1%. Obviously this can’t be very right since it does not depend on n
Better formula:

38. Statistical Tests 2. Analytical Sensitivity
How long should you count each point in a profile in order to get a smooth profile?
For a gradient from 5% to 4% over 25 mm, a profile of 25 points at 1 mm steps needs DC ≤ 0.04% to appear smooth, and this takes ≥85000 counts per step
The same gradient with 10 points at 2.5 mm spacing needs DC ≤ 0.1% to appear smooth, and this takes only ≥13600 counts per step -> not 2.5x but 15.6x faster!

39. Statistical Tests
3. Detection Limit