pixe: data analysis what the data can (and cannot) tell us. larry lamm pixe seminar winter 2008
TRANSCRIPT
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PIXE: Data Analysis
What the data can(and cannot) tell us.
Larry Lamm
PIXE Seminar Winter 2008
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electronnucleusproton
Electron in orbit around the nucleus,
In quantized energy level.
Protons from the accelerator impinge upon the target.
Interaction with the passing proton excites the electron into a higher energy orbit.
The atom spontaneously de-excites, releasing the excess energy in the form of an X-ray.
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Things to think about
• Most (nearly all) of the X-rays produced are in directions such that they do not hit the detector!! (small solid angle).
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Things to think about
• Very rare – atom is mostly empty space – think of comets and our solar system, and how infrequently (thankfully!) a comet strikes Earth
• Most (nearly all) of the X-rays produced are in a direction such that they do not hit the detector!! (small solid angle).
• The detector is not perfectly efficient. Some X-rays that hit the detector will not be counted.
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Things to think about
• Detector efficiency varies with X-ray energy
• Some elements more easily detected than others
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There’s more
• Pileup – when too many X-rays hit the detector at once
• Escape peaks – when some of the energy from the X-ray is lost by the detector
• Absorption – when X-rays are lost between the target and the detector by absorption (scattering)
• Depth profiling in the sample
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PigmentGlaze
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There’s a lot going on here….
• Plenty of details to worry about…
• How to measure the number of protons hitting the target?– Results will depend on this number– Difficult to measure in air (easy to do in
vacuum)
• Plunger target?
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OK, but ….
• So, a lot of details to worry about, but how can we proceed from here?
• How do we get the data from the detector, and what information does it contain?
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Output from detector
Vo
ltag
e
Time
• X-ray hits detector, produces lots of charge, which is collected by detector over a short time.
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Conversion to digital (ADC)
• The voltage signal from the detector must be digitized before it can be stored in the computer. The curve is integrated to find the area.
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Conversion to digital (ADC)
• The area under the curve is measured and is converted to a digital number. This number is a measure of the energy of the X-ray seen by the detector.
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Histograms
• The number from the ADC is collected and stored in a histogram – a collection of bins (we use 2048) scaled to match the energy spectrum of the X-rays we want to measure.
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Histograms
• As the ADC gives the number for the X-ray energy, the count in the appropriate bin is incremented, and over time the shape of the distribution begins to develop.
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Typical Spectrum (INCO 625)• Here’s a histogram from a run on one of our standards,
INCO 625. There are lots of peaks here.
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INCO 625• Same spectrum as previous, but in log scale to
show low intensity peaks.
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INCO 625• The pileup, including double peaks, can clearly
be seen. Also visible are some escape peaks.
Pileup
Escape
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Fitting the data• A wealth of X-Ray data exists, see for example
the X-Ray Data Booklet from LBNL (http://xdb.lbl.gov/)
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X-Ray Energies
• Tabulated in many places, including the X-Ray Data Booklet
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X-Ray Intensities• Also tabulated are the relative intensities of
these X-Rays, listed for each line of each element – at least in the X-Ray Data Booklet
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Fitting Real Data to Theory
• Start with something simple to illustrate
• Consider a sample of pure silver (Ag)
• We often use this to set up the detector
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Ag X-Rays
• Expand the region near the peaks for detail.
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Ag X-Rays (Theory)• Calculate expected spectra based on data from
the X-Ray Data Booklet.
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Build the fit• Compare the theory to the data, with only a
simple scale factor involved.Ag X-Rays
0
50
100
150
200
250
300
350
20 21 22 23 24 25 26 27 28
X-Ray Energy (keV)
Inte
ns
ity
(A
rb. C
ou
nts
)
Data Fit
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The scale factor
• Getting this factor is the trick….
• GUPIX – a PIXE analysis software package from Guelph University, is the way most PIXE data is analyzed to determine the scale factor for the fits.
• This scale factor can be used to determine abundances.
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Fitting “by hand”
• GUPIX is not magic…
• We can do it all “by hand” – a lot of work, but very illustrative.
That sounds hard!
I can show you how…trust
me!