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Radiation interaction with matterand energy dispersive x-ray fluorescence
analysis (EDXRF)
Giancarlo PepponiFondazione Bruno KesslerMNF – Micro Nano Facility
MAUD school 2018Caen, France
1Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi
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Radiation – x-rays (photons) , neutrons, electrons
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Wave – particle duality
De BrogliePlanck / Einstein
neutrons
electrons
charged particles
neutral particles
x-rays
photons
9.11E−31 kg511.0 keV/c2
939.6 MeV/c2
1.675E-27 kg
electromagnetic radiation
0 rest mass
protons
charged particles
1.673E−27 kg
938.27 MeV/c2
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Radiation – x-rays (photons) , neutrons, electrons
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neutrons
electrons
x-rays
photons
interactiontype
dipole
strong forcemagneticneutron capture
Coulomb force
interactionpartners
electronsatoms/electrons
nucleiunpaired electronsnuclei
electrons, nuclei
protons Coulomb force electrons, nuclei
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Radiation – x-rays (photons) , neutrons, electrons
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neutrons
electrons
x-rays
photons
wavelength
1.54 A0.71 A
1.8 A3.5 A
energy
8.048 keV17.479 keV
25 meV6.6 meV
20 keV200 keV
CuKa1MoKa1
thermalcold
SEMTEM
speed
2200 m/s1127 m/s
temperature
293.6 K77 K
0.122 A0.025 A 2.0845e+08 m/s
8.15033e+07 m/s
protonsPIXEProton therapy
1 MeV100 MeV
28.62 fm0.28 fm
1.38301e+07 m/s1.2837e+08 m/s
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Radiation – x-rays (photons) , neutrons, electrons
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40 eV
400 keV
1 keV
40 keV
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Radiation – attenuation - Beer Lambert law
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Au sheet
Calculated for X-Rays E = 17448eV
I0 I(x)
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Radiation – attenuation - Beer Lambert law
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?Scattering
(elastic, inelastic)Absorption
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Attenuation X-Rays : microscopic view
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Photoelectricabsorption
Inelastic (Compton)Scattering
Elastic Scattering
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X-ray elastic scattering
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Dipole emission
where
substituting
classical electron radius
Thomson cross section
In the X-Ray range: scattering from strongly bound electrons
Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi
is the angle subtended between the
direction of acceleration of the particle, and
the direction of the outgoing radiation
For unpolarized light calling now theta the angle between the direction of propagation of the incident light
and the direction of propagation of the scattered photon
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X-ray inelastic scattering (Compton)
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scattering from ‘free’ or loosely bound electrons
more important for light elements elements
inelastic scattering:
energy of scattered photon is less than
energy of incident photon
Relativistic quantum mechanical derivation
if
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X-ray inelastic scattering (Compton)
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Inelastic (Compton)Scattering
in a spectrum the Compton peak is broader due to the angle dependence (in the accepted solid angle there are different scattering angles) and due to Doppler broadening
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Compton shift
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angleenergy
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Doppler broadening in Compton scattering
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is the Compton profile and it is tabulated
Elastic
MoKα
Compton
peak
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Photoelectric effect - macroscopic
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e- e- e-
h h h
First observations:
1887 Heinrich Hertz
Ionisation of gases:
1900 Philipp Lenard
More detailed observations:
1899 Joseph John (J.J.) Thompson
- frequecy must be above a threshold- the higher the intensity the more
emitted photons
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Photoelectric effect – macroscopic - microscopic
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e- e- e-
h h h
- frequecy must be above a threshold- the higher the primary intensity on the material the more emitted photons
Photoelectricabsorption
e-
h
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X-Rays cross section magnitude
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data from:H. Ebel, R. Svagera, M. F. Ebel, A. Shaltout and J. H. Hubbell,Numerical description of photoelectric absorption coefficients for fundamental parameter programs,X-Ray Spectrometry, 32, 442–451 (2003)
Mg Au
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X-Rays
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Atomic binding energies, electron energy levels
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Absorption edgesElectron energy levelsShells
www.txrf.org/xraydata
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Photoelectric cross section – shell components
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Photoelectric cross section – shell components
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Between two absorption edges, τ decreases with the photon energy approximately following Bragg-Pierce law
r : jump ratio
J : jump factor
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X-Ray Absorption near edge fine structure
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The X-ray Absorption Fine
Structure (XAFS) of an iron foil
1000 10000
1E-4
1E-3
0.01
1
10
100
1000
10000
As
cro
ss s
ection
[cm
²/g]
energy [eV]
photoelectric
coherent
incoherent
sum
0.1
XAFS Spectroscopy
1000 10000
1E-4
1E-3
0.01
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1000
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cro
ss s
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[cm
²/g]
energy [eV]
photoelectric
coherent
incoherent
sum
0.1
1000 10000
1E-4
1E-3
0.01
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cro
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[cm
²/g]
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photoelectric
coherent
incoherent
sum
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0.01
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ss s
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[cm
²/g]
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incoherent
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XAFS Spectroscopy
XAFS Spectroscopy
Different phenomena for:
- ‘free’ atoms- molecules- condensed systems
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X-Ray Absorption near edge fine structure
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Eph ~ Eb
Core electron
unoccupied levels
Edge fine structure
(XANES or NEXAFS)
Eph > Eb
Core electron
continuum
Extended fine structure
(EXAFS)
XANES
EXAFS
outgoing wavefunction
Backscattering
from
neighbouring atomsincoming wavefunction
INTERFERENCE
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Transition energies
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www.txrf.org/xraydata
Can be obtained by difference from
Electron energy levels (electron binding
energies)Pb
As Kr
Pb L3-M5 13035.2-2484.0 = 10551.2
Pb L3-M4 13035.2-2585.6 = 10449.6
Pb L2-M4 15200.2-2484.0 = 12614.4
As K-L3 11866.7-1358.6 = 10508.1
Kr K-L3 14325.6-1674.9 = 12650.7
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Energy level widths
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www.txrf.org/xraydata
An atom with a vacancy is in an excited state. If Δt is the average time of relaxation, the Heisenberg's uncertainty principle tells us:
If Γ is the relaxation constant proportional to 1/ Δt we may write the probability for the atom to remain
in the excited state versus time is given by and hence
Taking the Fourier
transform to move
to the energy domain:
The energy
distribution is
a Lorentzian
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Energy level widths and transition energies
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www.txrf.org/xraydata
As
As K-L3 energy 11866.7-1358.6 = 10508.1
As K-L3 width 2.09+0.94 = 3.03
The line shape is a
Lorentz distrbution
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Transition families – As K
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www.txrf.org/xraydata
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Transition families – Pb L1
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www.txrf.org/xraydata
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Transition families – Pb L2
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www.txrf.org/xraydata
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Transition families – Pb L3
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www.txrf.org/xraydata
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Transition families – PbL - all
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www.txrf.org/xraydata
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Secondary effects – fluorescence vs Auger
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Incident photon
Photoelectron
Fluorescence
photon
Incident photonIncident photon
PhotoelectronPhotoelectronPhotoelectron
Fluorescence
photon
Fluorescence
photon
Fluorescence
photon
Incident photon
Photoelectron
Auger
electronIncident photonIncident photon
PhotoelectronPhotoelectronPhotoelectron
Auger
electron
Auger
electron
data from:M. O. Krause, J. Phys. Chem. Ref. Data 8 (1979) 307
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X-Ray Fluorescence – characteristic lines
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Germanium
IUPAC = International Union of Pure and Applied Chemistry
Siegbahn = Manne Siegbahn (swedish physicist)Nobel Prize in Physics in 1924
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The Auger effect
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The Auger electron emission process may be viewed as a radiation-lessdecay of a singly ionized X-ray level into a level described by two vacanciesand one electron in the continuum.
An Auger process in which the vacancy is filled by an electron from a highersubshell of the same shell is called a Coster–Kronig transition. If, in addition,the electron emitted (the "Auger electron") also belongs to the same shell,one calls this a super Coster–Kronig transition.
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Coster-Kronig transitions
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Electrons interaction with matter
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https://en.wikipedia.org/wiki/Electron_scatteringhttp://serc.carleton.edu/research_education/geochemsheets/electroninteractions.html
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Inner shell ionization cross section: x-rays vs electrons
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Inner shell ionization cross section: protons
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Neutrons interaction with matter
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http://www.uio.no/studier/emner/matnat/fys/FYS-KJM4710/h14/timeplan/neutron_chapter.pdf
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Cross section : x-rays vs neutrons
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https://www.psi.ch/niag/comparison-to-x-ray
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Cross section : x-rays vs neutrons
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https://www.psi.ch/niag/comparison-to-x-ray
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Neutron cross section
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Scattering (full line) and absorption (dotted) cross sections of light element commonly used as neutron moderators, reflectors and absorbers, the data was obtained from database NEA N ENDF/B-VII.1 using JANIS software
https://en.wikipedia.org/wiki/Neutron_cross_section
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Scattering - Differential cross section
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units: barn or cm2; 1b = 10-24cm2
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X-ray differential elastic cross section and the form factor
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Thomson cross section
Variable relatedto the momentum transfer
Atomic form factor (atomic scattering factor)
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X-ray differential elastic cross section and the form factor
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… but actually there is a further dependence on energy …
photoelectric absorption
corrections for photoabsorption (Kramers-Kronig dispersion)relativistic effects, nuclear scattering
Diffraction (structure factor)
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X-ray differential elastic cross section and the form factor
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forward scattering factors (x = theta = q = 0)
f1 and f2 are directly related to the index of refraction(reflection, refraction, XRR)
photoabsorption
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X-ray differential inelastic cross section (Compton)
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form factor elastic scattering
Inelastic scattering function
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X-Rays - Differential cross section – elastic scattering
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X-Rays - Differential cross section – inelastic scattering
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Electrons - Differential elastic cross section
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Data from: http://www.ioffe.rssi.ru/ES/Elastic/
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Cross section, mass/ linear absorption coefficient
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X-ray polarization – scattering as dipole oscillation/emission
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An oscillating charge emits dipole radiation.
Dipole radiation is not isotropic. Starting from
An harmonically oscillating electric dipole
and using Maxwell's equations you get the emitted
power calculating the time averaged Poynting vector
Scattering is based on a dipole interaction. The incident EM wave forces electrons to oscillate at the
same frequency and radiation is emitted at that frequency, but not in all directions.
There is no emission in the dipole oscillation direction.
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X-ray polarization - scattering
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http://pd.chem.ucl.ac.uk/pdnn/diff2/polar.htm
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Energy Dispersive X-Ray Fluorescence analysis (EDXRF)
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Incident photon
Photoelectron
Fluorescence
photon
Incident photonIncident photon
PhotoelectronPhotoelectronPhotoelectron
Fluorescence
photon
Fluorescence
photon
Fluorescence
photon
ADC
Pulse heightdiscriminator
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EDS detector
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detector efficiency + response
Modelling the response function of energydispersive X-ray spectrometers with silicondetectorsF. Scholze, and M. Procop
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Detector artefacts / ‘environmental’ artefacts
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sum / pile up
peaksescape
peak
Ar
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X-Ray Fluorescence analysis
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0 2 4 6 8 10 12 14 16 180
1000
2000
3000
4000
5000
6000
7000
8000
counts
/ c
hannel
photon energy [keV]
Sr
Ga
Zn
CuNi
Co
FeMn
Cr
KCa
Moscatter
TlPb
Bi
Tl BiPb
Sr
BaBa
Tl, Pb, Bi
Zn
Al
SiSr
Pb Bi
K
K
L
L
L
M
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X-Ray Fluorescence analysis
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0 1 2 3 4 5 6 7 8 9 100
1000
2000
3000
4000
5000
6000counts
/channel
photon energy [keV]
Zn
Cu
Ni
Co
FeMn
Cr
K CaBa
Ba
Tl, Pb, Bi
Al SiSr
K
K
L
L
M
CuNiAg
Cd
W Lscatter
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X-Ray Fluorescence analysis
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10 20 30 400
2000
4000
6000
8000 lines
LL
KKMultielement sample
10 ng Cd
W white spectrum
monochromatised at about 33 keV
load: 45 kV 20 mA; 500s
Tl
BiTl
Pb
Bi Pb
Cr
Mn
Fe
Co
Ni
Cu
Zn
Ga
Ca
K
Sr
In
Zr
ZrSr
Ag
Cd
Cd
In
Ag
W white spectrum
scattered radiation
counts
E (keV)
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X-Ray line families
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Sr-K lines
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X-Ray line families
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Pb L-lines
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X-Ray line families
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Sr-K lines
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X-Ray Fluorescence – intensity - Sherman equation
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1. attenuation to depth z
2. photoelectric absorption in
layer dz
3. fluorescence yield
4. transition probability
(relative intensity of lines in shell)
5. attenuation to the detector
6. detector efficiency
geometrical factors and
primary flux form the
element independent
proportionality constant
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X-Ray Fluorescence – intensity - Sherman equation
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1. attenuation to depth z
2. photoelectric absorption in
layer dz
3. fluorescence yield
4. transition probability
(relative intensity of lines in shell)
5. attenuation to the detector
6. detector efficiency
geometrical factors and
primary flux form the
element independent
proportionality constant
Integration over thickness
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X-Ray Fluorescence – intensity - Sherman equation
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Monochromatic
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Fluorescence enhancement, secondary fluorescence
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Incident photon
Photoelectron
Fluorescence
photon
Incident photonIncident photon
PhotoelectronPhotoelectronPhotoelectron
Fluorescence
photon
Fluorescence
photon
Fluorescence
photon
Cascade photon
Secondary
fluorescence
photon
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Fluorescence enhancement, secondary fluorescence
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200 nm of ZnSe on GeZnK
GeKa1
SeKa1
GeK
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Fluorescence enhancement, secondary fluorescence
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GaAs
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Fluorescence enhancement, secondary fluorescence
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GaAs solution deposited on silicon – Cascade – No Secondary Fluo
GaAs Wafer – No Cascade – No Secondary Fluo
GaAs Wafer – Cascade – Secondary Fluo
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Data analysis XRD vs XRF
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XRD : Rietveld
XRF : Fundamental parameters method
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Data analysis XRD vs XRF
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In MAUD:
the XRD definitions are obviously followed, since they are contain more
information:
from the XRD definition you can derive the XRF one, not the other way around
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Instrumental parameters
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XRF: energy, intensity fractionXRD: wavelength, intensity fraction
In MAUD:One or multiple wavelengths can be indicated with intensity fraction
Integration over different energies/wavelengths done numerically
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Primary radiation – x-ray tube
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Tube spectrum and filtered spectrum automatically calculated in MAUD
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Primary radiation – x-ray tube
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Tube spectrum and filtered spectrum automatically calculated in MAUD
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Primary radiation – x-ray tube
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sample
graphite monochromator
proportionalcounter
x-ray tube
filter
XRF and XRD signals related to different part of the X-ray primary beam
In MAUD: defined separately, hence taken into account
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X-Ray Fluorescence – intensity – filtered primary beam
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Thank you for your attention!
For any further question or doubt:[email protected]
Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi