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Radiation interaction with matter and energy dispersive x-ray fluorescence analysis (EDXRF) Giancarlo Pepponi Fondazione Bruno Kessler MNF – Micro Nano Facility [email protected] MAUD school 2018 Caen, France 1 Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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Page 1: Radiation interaction with matter and energy dispersive x ...chateign/formation/course/... · 16 X-Rays cross section magnitude data from: ... (2003) Mg Au Radiation interaction with

Radiation interaction with matterand energy dispersive x-ray fluorescence

analysis (EDXRF)

Giancarlo PepponiFondazione Bruno KesslerMNF – Micro Nano Facility

[email protected]

MAUD school 2018Caen, France

1Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

Page 2: Radiation interaction with matter and energy dispersive x ...chateign/formation/course/... · 16 X-Rays cross section magnitude data from: ... (2003) Mg Au Radiation interaction with

2

Radiation – x-rays (photons) , neutrons, electrons

2

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

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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3

Radiation – x-rays (photons) , neutrons, electrons

3

neutrons

electrons

x-rays

photons

interactiontype

dipole

strong forcemagneticneutron capture

Coulomb force

interactionpartners

electronsatoms/electrons

nucleiunpaired electronsnuclei

electrons, nuclei

protons Coulomb force electrons, nuclei

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

Page 4: Radiation interaction with matter and energy dispersive x ...chateign/formation/course/... · 16 X-Rays cross section magnitude data from: ... (2003) Mg Au Radiation interaction with

4

Radiation – x-rays (photons) , neutrons, electrons

4

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

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

Page 5: Radiation interaction with matter and energy dispersive x ...chateign/formation/course/... · 16 X-Rays cross section magnitude data from: ... (2003) Mg Au Radiation interaction with

5

Radiation – x-rays (photons) , neutrons, electrons

5

40 eV

400 keV

1 keV

40 keV

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

Page 6: Radiation interaction with matter and energy dispersive x ...chateign/formation/course/... · 16 X-Rays cross section magnitude data from: ... (2003) Mg Au Radiation interaction with

6

Radiation – attenuation - Beer Lambert law

6

Au sheet

Calculated for X-Rays E = 17448eV

I0 I(x)

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

Page 7: Radiation interaction with matter and energy dispersive x ...chateign/formation/course/... · 16 X-Rays cross section magnitude data from: ... (2003) Mg Au Radiation interaction with

7

Radiation – attenuation - Beer Lambert law

7

?Scattering

(elastic, inelastic)Absorption

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

Page 8: Radiation interaction with matter and energy dispersive x ...chateign/formation/course/... · 16 X-Rays cross section magnitude data from: ... (2003) Mg Au Radiation interaction with

8

Attenuation X-Rays : microscopic view

8

Photoelectricabsorption

Inelastic (Compton)Scattering

Elastic Scattering

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

Page 9: Radiation interaction with matter and energy dispersive x ...chateign/formation/course/... · 16 X-Rays cross section magnitude data from: ... (2003) Mg Au Radiation interaction with

9

X-ray elastic scattering

9

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

Page 10: Radiation interaction with matter and energy dispersive x ...chateign/formation/course/... · 16 X-Rays cross section magnitude data from: ... (2003) Mg Au Radiation interaction with

10

X-ray inelastic scattering (Compton)

10

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

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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11

X-ray inelastic scattering (Compton)

11

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

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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12

Compton shift

12

angleenergy

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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13

Doppler broadening in Compton scattering

13

is the Compton profile and it is tabulated

Elastic

MoKα

Compton

peak

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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14

Photoelectric effect - macroscopic

14

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

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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15

Photoelectric effect – macroscopic - microscopic

15

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

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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16

X-Rays cross section magnitude

16

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

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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17

X-Rays

17Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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18

Atomic binding energies, electron energy levels

18

Absorption edgesElectron energy levelsShells

www.txrf.org/xraydata

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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19

Photoelectric cross section – shell components

19Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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20

Photoelectric cross section – shell components

20

Between two absorption edges, τ decreases with the photon energy approximately following Bragg-Pierce law

r : jump ratio

J : jump factor

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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21

X-Ray Absorption near edge fine structure

21

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

1

10

100

1000

10000

As

cro

ss s

ection

[cm

²/g]

energy [eV]

photoelectric

coherent

incoherent

sum

0.1

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

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

XAFS Spectroscopy

Different phenomena for:

- ‘free’ atoms- molecules- condensed systems

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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22

X-Ray Absorption near edge fine structure

22

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

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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23

Transition energies

23

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

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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24

Energy level widths

24

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

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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25

Energy level widths and transition energies

25

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

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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26

Transition families – As K

26

www.txrf.org/xraydata

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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27

Transition families – Pb L1

27

www.txrf.org/xraydata

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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28

Transition families – Pb L2

28

www.txrf.org/xraydata

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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29

Transition families – Pb L3

29

www.txrf.org/xraydata

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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30

Transition families – PbL - all

30

www.txrf.org/xraydata

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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31

Secondary effects – fluorescence vs Auger

31

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

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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32

X-Ray Fluorescence – characteristic lines

32

Germanium

IUPAC = International Union of Pure and Applied Chemistry

Siegbahn = Manne Siegbahn (swedish physicist)Nobel Prize in Physics in 1924

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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33

The Auger effect

33

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.

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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34

Coster-Kronig transitions

34Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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35

Electrons interaction with matter

35

https://en.wikipedia.org/wiki/Electron_scatteringhttp://serc.carleton.edu/research_education/geochemsheets/electroninteractions.html

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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36

Inner shell ionization cross section: x-rays vs electrons

36Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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37

Inner shell ionization cross section: protons

37Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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38

Neutrons interaction with matter

38

http://www.uio.no/studier/emner/matnat/fys/FYS-KJM4710/h14/timeplan/neutron_chapter.pdf

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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39

Cross section : x-rays vs neutrons

39

https://www.psi.ch/niag/comparison-to-x-ray

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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40

Cross section : x-rays vs neutrons

40

https://www.psi.ch/niag/comparison-to-x-ray

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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41

Neutron cross section

41

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

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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42

Scattering - Differential cross section

42

units: barn or cm2; 1b = 10-24cm2

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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43

X-ray differential elastic cross section and the form factor

43

Thomson cross section

Variable relatedto the momentum transfer

Atomic form factor (atomic scattering factor)

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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44

X-ray differential elastic cross section and the form factor

44

… but actually there is a further dependence on energy …

photoelectric absorption

corrections for photoabsorption (Kramers-Kronig dispersion)relativistic effects, nuclear scattering

Diffraction (structure factor)

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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45

X-ray differential elastic cross section and the form factor

45

forward scattering factors (x = theta = q = 0)

f1 and f2 are directly related to the index of refraction(reflection, refraction, XRR)

photoabsorption

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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46

X-ray differential inelastic cross section (Compton)

46

form factor elastic scattering

Inelastic scattering function

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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47

X-Rays - Differential cross section – elastic scattering

47Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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48

X-Rays - Differential cross section – inelastic scattering

48Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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49

Electrons - Differential elastic cross section

49

Data from: http://www.ioffe.rssi.ru/ES/Elastic/

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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50

Cross section, mass/ linear absorption coefficient

50Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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51

X-ray polarization – scattering as dipole oscillation/emission

51

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.

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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52

X-ray polarization - scattering

52

http://pd.chem.ucl.ac.uk/pdnn/diff2/polar.htm

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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53

Energy Dispersive X-Ray Fluorescence analysis (EDXRF)

53

Incident photon

Photoelectron

Fluorescence

photon

Incident photonIncident photon

PhotoelectronPhotoelectronPhotoelectron

Fluorescence

photon

Fluorescence

photon

Fluorescence

photon

ADC

Pulse heightdiscriminator

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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54

EDS detector

54

detector efficiency + response

Modelling the response function of energydispersive X-ray spectrometers with silicondetectorsF. Scholze, and M. Procop

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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55

Detector artefacts / ‘environmental’ artefacts

55

sum / pile up

peaksescape

peak

Ar

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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56

X-Ray Fluorescence analysis

56

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

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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57

X-Ray Fluorescence analysis

57

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

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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58

X-Ray Fluorescence analysis

58

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)

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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X-Ray line families

59

Sr-K lines

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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X-Ray line families

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Pb L-lines

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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X-Ray line families

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Sr-K lines

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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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

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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X-Ray Fluorescence – intensity - Sherman equation

63

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

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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X-Ray Fluorescence – intensity - Sherman equation

64

Monochromatic

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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Fluorescence enhancement, secondary fluorescence

65

Incident photon

Photoelectron

Fluorescence

photon

Incident photonIncident photon

PhotoelectronPhotoelectronPhotoelectron

Fluorescence

photon

Fluorescence

photon

Fluorescence

photon

Cascade photon

Secondary

fluorescence

photon

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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Fluorescence enhancement, secondary fluorescence

66

200 nm of ZnSe on GeZnK

GeKa1

SeKa1

GeK

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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Fluorescence enhancement, secondary fluorescence

67

GaAs

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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Fluorescence enhancement, secondary fluorescence

68

GaAs solution deposited on silicon – Cascade – No Secondary Fluo

GaAs Wafer – No Cascade – No Secondary Fluo

GaAs Wafer – Cascade – Secondary Fluo

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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Data analysis XRD vs XRF

69

XRD : Rietveld

XRF : Fundamental parameters method

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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Data analysis XRD vs XRF

70

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

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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Instrumental parameters

71

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

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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Primary radiation – x-ray tube

72

Tube spectrum and filtered spectrum automatically calculated in MAUD

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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Primary radiation – x-ray tube

73

Tube spectrum and filtered spectrum automatically calculated in MAUD

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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Primary radiation – x-ray tube

74

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

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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X-Ray Fluorescence – intensity – filtered primary beam

75Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi

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7676

Thank you for your attention!

For any further question or doubt:[email protected]

Radiation interaction with matter and XRF – MAUD school 2018 – Giancarlo Pepponi