5Proportional Counting Tube (note tubing for gas) WDS SpectrometersThis is a Cameca spectrometer, but JEOL design is pretty similarCrystals (2 pairs)Proportional Counting Tube (note tubing for gas)PreAmp
6Electron Probe: WDS spectrometers Rowland Circle: crystal moves in straight line away from sample focus point, detector must move along curve to remain on circleWith vertical Rowland circle, can pack lots of spectrometers around machine but X-ray counts very sensitive to Z focus
7Electron Probe: diffracting crystals E (eV)K elementsLiF [lithium fluoride, (200)]4.027 ÅCa to GePET [Penta-erythritol (001)]8.742 ÅSi to TiTAP [Thallium acid phthalate (001)]25.76 ÅO To AlLDE1 (W-Si)61.1 ÅC to FLDE298.0 ÅB, C, NLDEB145.0 ÅBe, B, C
11Electron 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)
12Electron Probe: gas proportional counters Trade-off between window thickness and gas pressureGas flow P10 vs. sealed Xe
13Spectral ResolutionWDS 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)
15Electron Probe: wavelength scans and peaking Al Ka PeaksBaSO4PbSWDS 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
16Electron Probe: background correction Low bkgHigh bkgBkg under peakCan 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
17Quantitative 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.
18Raw 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.
19Absorption 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”.
20Z A FIn 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).
21Unanalyzed elementsThe 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.
22Some 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?
23StandardsIn 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.
24Standards - 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.
25Sources 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 labsMaterials from your Department’s collections, local researchers/ experimentalists, local mineral shop or national suppliers (e.g., Wards)
26Thoughts on beam current Is more beam current always better? No.Detector saturation…too much deadtimeSample 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 riseE = accelerating potential in keVI = beam current in Ak = thermal conductivity in W/mKd = beam diameter in m
27Reducing beam damageFor 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 geometryRun sensitive elements in first passExamine counts vs. time experiments to see rate of damage; extrapolate to zero time?
28Thoughts on temperature stability Electron microprobes only operate well in very constant temperature roomsChanging T causes thermal expansion of the diffracting crystals -> peak shiftsChanging T changes pressure in gas-flow proportional counters -> changes counting efficiencyOthers?
29Some tricks Normalization Secondary standards With replicate data, can test which is more reproducible - raw or normalized dataSecondary standardsNo physics here, just empirical adjustment for machine performance on a given day
30X-ray mappingUsually done in qualitative mode, that is not background corrected, normalized, or referenced to a standardCan introduce empirical two-point calibration to semi-quantify mapsMap quality is a function of counting time, mostly
32StatisticsMeasurement is always a statistical process, and mature understanding of the statistics is essential to proper interpretation of dataThere are several ways to look at the precision and sensitivity of electron probe analyses, depending on what question you are asking…
33Counting StatisticsX-ray counts are quantized and the number of counts you get in an idealized experiment will always be a Gaussian distribution with standard deviationThus, 1% relative precision requires, in theory, counts. 0.1% relative precision requires 106 counts.
34Real StatisticsThe real standard deviation of a set of replicate measurements of the same spot is greater than or equal to the ideal value from counting statisticsLonger 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
35Real StatisticsFurthermore, quantification requires background correctionHence, the estimated peak counting rate P is really based on 3 measurements: (P+B), Blow, BhighThese uncertainties add in quadrature and can increase Sc of the estimate (P+B) – B by a large factor if P/B is small
36Statistical 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 SensitivityFor (repeated?) measurements of two different concentrations, how different must they be before they can be distinguished at some level of confidence?3. Detection LimitWhat concentration of a trace element is necessary before its presence in a sample can be established at some level of confidence?
37Statistical Tests 1. Sample homogeneity Approximate formula: 99% confidence corresponds roughly to all n analyses falling within a rangeSo for 105 counts per point at C = 10%, W~0.1%. Obviously this can’t be very right since it does not depend on nBetter formula:
38Statistical 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 stepThe 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!