1 PASI - Electron Microscopy - Chile Lyman - EDS Quant Quantitative X-ray Spectrometry in TEM/STEM Charles Lyman Lehigh University Bethlehem, PA Based on presentations developed for Lehigh University semester courses and for the Lehigh Microscopy School
Quantitative X-ray Spectrometry in TEM/STEM. Charles Lyman Lehigh University Bethlehem, PA. Based on presentations developed for Lehigh University semester courses and for the Lehigh Microscopy School. Quantitative X-ray Analysis of Thin Specimens. How much of each element is present?. - PowerPoint PPT Presentation
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1PASI - Electron Microscopy - Chile
Lyman - EDS Quant
Quantitative X-ray Spectrometry in TEM/STEM
Charles LymanLehigh UniversityBethlehem, PA
Based on presentations developed for Lehigh University semester courses and for the Lehigh Microscopy School
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Quantitative X-ray Analysis of Thin
Specimens Aim of quantitative analysis: to transform the intensities in the X-ray
spectrum into compositional values, with known precision and accuracy
Cliff-Lorimer method:
Precision: collect at least 10,000 counts in the smallest peak to obtain a counting error of less than 3%
Accuracy: measure kAB on a known standard and find a way to handle x-ray absorption effects
How much of each element is present?
€
CA
CB
= kAB
IA
IB
and CA + CB =1
CA = concentration of element AIA = x-ray intensity from element AkAB = Cliff-Lorimer sensitivity factor
What could be simpler?
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Assumptions in Cliff-Lorimer Method
Basic assumptions» X-ray intensities for each element are measured simultaneously» Ratio of intensities accounts for thickness variations» Specimen is thin enough that absorption and fluorescence can be ignored
– the “thin-film criterion”– We would like to handle absorption in a better way!
Cliff-Lorimer equation:
» CA and CB are weight fractions or atomic fractions (choose one, be consistent)» kAB depends on the particular TEM/EDS system and kV (use highest kV)
– k-factor is most closely related to the atomic number correction» Can expand to measure ternaries, etc. by measuring more k-factors
€
CA
CB
= kAB
IA
IB
and CA + CB =1
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Steps in Quantitative Analysis
Remove background intensity under peaks Integrate counts in peaks Determine k-factors (or -factors) Correct for absorption (if necessary)
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Calculate Background, the Subtract
Gross-Net Method» Draw line at ends of window
covering full width of peak» Impossible with peak overlap» Should work better above 2
keV where background changes slowly
Three-Window Method» Set window with FWHM (or even better
1.2 FWHM)
» Average backgrounds B1 and B2
» Subtract Bave from peak
» Requires well-separated peaks
Background Modeling» Mathematical model of background
as function of Z and E» Useful when peaks are close
together
from Williams and Carter, Transmission Electron Microscopy, Springer, 1996
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Digital Filtering
Convolute spectrum with “top-hat” filter
» Multiply channels of top-hat filter times each spectrum channel
» Place result in central channel
» Step filter over each spectrum channel
Background becomes zero
from Williams and Carter, Transmission Electron Microscopy, Springer, 1996
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Digital Filtering
Spectrum before filteringNote MgK, AlK, and SiK
Spectrum after filteringPositive lobes are
proportional to peak intensities
from Williams and Carter, Transmission Electron Microscopy, Springer, 1996
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Obtaining k-factors
Requirements for standard specimen for k-factor measurement» Single phase (stoichiometric composition helpful)» Homogeneous at the nanometer scale» Thinned to electron transparency without composition change (microtome)» Insensitive to beam damage
Measure k-factors on a known standard:
» Usually kASi or kAFe
» Measure k-factors at various thicknesses and extrapolate to zero thickness
Other ways» Calculate k-factors (when standards are not available)» Use literature values at same kV for x-rays 5-15keV (not recommended)» Use kAB = kAC/kBC (use only when necessary - errors add)
€
kAB =CA
CB
IB
IA
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Why Collect 10,000 Counts?
There is a 99% chance that a single measurement is within 3N1/2 of the true value
The relative counting error =
Thus, for 10,000 counts the relative counting error =
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Experimental k-factors
from Williams and Carter, Transmission Electron Microscopy, Springer, 1996
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Calculated k-factors
When suitable standard is not available» When a modestly accurate analysis is acceptable
Most EDS system software can calculate k-factors» But errors can be up to 20%
bfrom Williams and Carter, Transmission Electron Microscopy, Springer, 1996
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Spatial Resolution vs. Analytical Sensitivity
Conditions that favor high spatial resolution (thinnest specimen) result in poorer analytical sensitivity and vice versa. For example to obtain equivalent analytical sensitivity in an AEM to an EPMA, the X-ray generation and detection efficiency would have to be improved by a factor of 108
from Williams and Carter, Transmission Electron Microscopy, Springer, 1996
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Composition Profiles Across an Interphase Interface
The change in Mo and Cr composition across the interface can be used to determine the compositions of the phases either side of the interface which, in turn, give the tie lines on the Ni-Cr-Mo phase diagram.
Courtesy R. Ayer
from Williams and Carter, Transmission Electron Microscopy, Springer, 1996
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Measurement of Low T Diffusion Data
Measurement of composition profiles with high spatial resolution permits extraction of low- temperature diffusion data because the small diffusion distances at low T are detectable by AEM X-ray microanalysis. Here Zn profiles across a 200 nm wide precipitate-free zone in Al-Zn are used to determine values of the Zn diffusivity at T = 100-200°C. Courtesy A.W. Nicholls
Low-temp data
High-temp data
from Williams and Carter, Transmission Electron Microscopy, Springer, 1996
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Predicted Phase Separation Observed in Nanoparticles
Dotted misibility gap was predicted from other similar systems --> only observed in nanoparticles
Two phases observed
Pt-rich phase
Rh-rich phase
C. E. Lyman, R. E. Lakis, and H. G. Stenger, Ultramicroscopy 58 (1995) 25-34.
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Summary
Know the question you are trying to answer
Know the precision and accuracy required to answer the question
Accumulate enough counts in the spectrum to achieve the required precision (> 10,000 counts in the smallest peak)
Know the precision and accuracy of your k-factor
Measure zero-thickness k-factors and apply an absorption correction (need t at analysis point) or use -factors where t is not needed
Spatial resolution vs. detectability: » You cannot achieve the highest spatial resolution and the best analytical sensitivity