Radiation interaction with matter and energy dispersive x-ray fluorescence analysis (EDXRF)

Transcription

1 Radiation interaction with matter and energy dispersive x-ray fluorescence analysis (EDXRF) Giancarlo Pepponi Fondazione Bruno Kessler MNF Micro Nano Facility MAUD school 2017 Caen, France 1

2 Radiation x-rays (photons), neutrons, electrons Wave particle duality Planck / Einstein De Broglie x-rays photons electromagnetic radiation 0 rest mass neutrons neutral particles 1.675E-27 kg MeV/c2 electrons protons charged particles 9.11E 31 kg kev/c2 charged particles 1.673E 27 kg MeV/c2 2

3 Radiation x-rays (photons), neutrons, electrons interaction type interaction partners x-rays photons dipole electrons atoms/electrons neutrons strong force magnetic neutron capture nuclei unpaired electrons nuclei electrons Coulomb force electrons, nuclei protons Coulomb force electrons, nuclei 3

4 Radiation x-rays (photons), neutrons, electrons energy wavelength speed temperature x-rays photons CuKa1 MoKa kev kev 1.54 A 0.71 A neutrons thermal cold 25 mev 6.6 mev 1.8 A 3.5 A 2200 m/s 1127 m/s K 77 K electrons SEM TEM 20 kev 200 kev A e+07 m/s A e+08 m/s protons PIXE Proton therapy 1 MeV 100 MeV fm 0.28 fm e+07 m/s e+08 m/s 4

5 Radiation x-rays (photons), neutrons, electrons 400 kev 40 ev 40 kev 1 kev 5

6 Radiation attenuation - Beer Lambert law Au sheet I 0 I(x) Calculated for X-Rays E = 17448eV 6

7 Radiation attenuation - Beer Lambert law? Scattering (elastic, inelastic) Absorption 7

8 Attenuation X-Rays : microscopic view Elastic Scattering Photoelectric absorption Inelastic (Compton) Scattering 8

9 X-ray elastic scattering In the X-Ray range: scattering from strongly bound electrons Dipole emission where substituting classical electron radius Thomson cross section 9

10 X-ray inelastic scattering (Compton) Relativistic quantum mechanical derivation scattering from free or loosely bound electrons more important for light elements elements if inelastic scattering: energy of scattered photon is less than energy of incident photon 10

11 X-ray inelastic scattering (Compton) 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 11

12 Compton shift energy angle 12

13 Doppler broadening in Compton scattering Elastic MoKα Compton peak is the Compton profile and it is tabulated 13

14 Photoelectric effect - macroscopic h h h e - e - e - First observations: 1887 Heinrich Hertz More detailed observations: 1899 Joseph John (J.J.) Thompson Ionisation of gases: 1900 Philipp Lenard - frequecy must be above a threshold - the higher the intensity the more emitted photons 14

15 Photoelectric effect macroscopic - microscopic h h h e - e - e - Photoelectric absorption e - h - frequecy must be above a threshold - the higher the primary intensity on the material the more emitted photons 15

16 X-Rays cross section magnitude Mg Au 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, (2003) 16

17 X-Rays 17

18 Atomic binding energies, electron energy levels Absorption edges Electron energy levels Shells 18

19 Photoelectric cross section shell components 19

20 Photoelectric cross section shell components r : jump ratio J : jump factor Between two absorption edges, τ decreases with the photon energy approximately following Bragg-Pierce law 20

21 cross section [cm²/g] X-Ray Absorption near edge fine structure The X-ray Absorption Fine Structure (XAFS) of an iron foil photoelectric coherent incoherent sum XAFS Spectroscopy As 1E-3 1E energy [ev] Different phenomena for: - free atoms - molecules - condensed systems 21

22 X-Ray Absorption near edge fine structure E ph ~ E b Core electron unoccupied levels Edge fine structure (XANES or NEXAFS) XANES EXAFS E ph > E b Core electron Extended fine structure (EXAFS) continuum outgoing wavefunction INTERFERENCE incoming wavefunction Backscattering from neighbouring atoms 22

23 Transition energies Pb Can be obtained by difference from Electron energy levels (electron binding energies) Pb L3-M = Pb L3-M = Pb L2-M = As K-L = Kr K-L = As Kr 23

24 Energy level widths 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 24

25 Energy level widths and transition energies As As K-L3 energy = As K-L3 width = 3.03 The line shape is a Lorentz distrbution 25

26 Transition families As K 26

27 Transition families Pb L1 27

28 Transition families Pb L2 28

29 Transition families Pb L3 29

30 Transition families PbL - all 30

31 Secondary effects fluorescence vs Auger Photoelectron Incident photon Fluorescence photon Photoelectron data from: M. O. Krause, J. Phys. Chem. Ref. Data 8 (1979) 307 Incident photon Auger electron 31

32 X-Ray Fluorescence characteristic lines Siegbahn = Manne Siegbahn (swedish physicist) Nobel Prize in Physics in 1924 IUPAC = International Union of Pure and Applied Chemistry Germanium 32

33 The Auger effect The Auger electron emission process may be viewed as a radiation-less decay of a singly ionized X-ray level into a level described by two vacancies and one electron in the continuum. An Auger process in which the vacancy is filled by an electron from a higher subshell 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. 33

34 Coster-Kronig transitions 34

35 Electrons interaction with matter s/electroninteractions.html 35

36 Inner shell ionization cross section: x-rays vs electrons 36

37 Inner shell ionization cross section: protons 37

38 Neutrons interaction with matter KJM4710/h14/timeplan/neutron_chapter.pdf 38

39 Cross section : x-rays vs neutrons 39

40 Cross section : x-rays vs neutrons 40

41 Neutron cross section 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 Neutron_cross_section 41

42 Scattering - Differential cross section units: barn or cm 2 ; 1b = cm 2 42

43 X-ray differential elastic cross section and the form factor Thomson cross section Atomic form factor (atomic scattering factor) Variable related to the momentum transfer 43

44 X-ray differential elastic cross section and the form factor but actually there is a further dependence on energy photoelectric absorption corrections for photoabsorption (Kramers-Kronig dispersion) relativistic effects, nuclear scattering Diffraction (structure factor) 44

45 X-ray differential elastic cross section and the form factor forward scattering factors (x = theta = q = 0) photoabsorption f1 and f2 are directly related to the index of refraction (reflection, refraction, XRR) 45

46 X-ray differential inelastic cross section (Compton) Inelastic scattering function form factor elastic scattering 46

47 X-Rays - Differential cross section elastic scattering 47

48 X-Rays - Differential cross section inelastic scattering 48

49 Electrons - Differential elastic cross section Data from: 49

50 Cross section, mass/ linear absorption coefficient 50

51 X-ray polarization scattering as dipole oscillation/emission 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. 51

52 X-ray polarization - scattering 52

53 Energy Dispersive X-Ray Fluorescence analysis (EDXRF) Photoelectron Incident photon Fluorescence photon Pulse height discriminator ADC 53

54 EDS detector detector efficiency + response Modelling the response function of energy dispersive X-ray spectrometers with silicon detectors F. Scholze, and M. Procop 54

55 Detector artefacts / environmental artefacts Ar escape peak sum / pile up peaks 55

56 counts / channel X-Ray Fluorescence analysis Tl, Pb, Bi Al Si Sr K K L L L M K Ca Ba Ba Cr Fe Mn Co Cu Ni Zn Ga Tl PbBi Pb Tl Bi Zn photon energy [kev] Sr Pb Bi Sr Mo scatter 56

57 X-Ray Fluorescence analysis K K L Zn counts/channel L M Tl, Pb, Bi Cr Fe Mn Co Ni Cu W L scatter Sr Al Si Ag Cd K Ca Ba Ba Ni Cu photon energy [kev] 57

58 X-Ray Fluorescence analysis 8000 lines counts 6000 K Ni Co Fe Mn Cr K L K L Multielement sample 10 ng Cd W white spectrum monochromatised at about 33 kev load: 45 kv 20 ma; 500s Ca Cu Zn Ga Pb Tl Bi Pb Tl Bi Sr Sr Zr Zr Ag Cd In Ag Cd In W white spectrum scattered radiation E (kev) 58

59 X-Ray line families Sr-K lines 59

60 X-Ray line families Pb L-lines 60

61 X-Ray line families Sr-K lines 61

62 X-Ray Fluorescence intensity - Sherman equation geometrical factors and primary flux form the element independent proportionality constant 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 62

63 X-Ray Fluorescence intensity - Sherman equation geometrical factors and primary flux form the element independent proportionality constant 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 Integration over thickness 63

64 X-Ray Fluorescence intensity - Sherman equation Monochromatic 64

65 Fluorescence enhancement, secondary fluorescence Cascade photon Photoelectron Secondary fluorescence photon Incident photon Fluorescence photon 65

66 Fluorescence enhancement, secondary fluorescence 200 nm of ZnSe on Ge ZnK SeKa1 GeK GeKa1 66

67 Fluorescence enhancement, secondary fluorescence GaAs 67

68 Fluorescence enhancement, secondary fluorescence GaAs solution deposited on silicon Cascade No Secondary Fluo GaAs Wafer No Cascade No Secondary Fluo GaAs Wafer Cascade Secondary Fluo 68

69 Data analysis XRD vs XRF XRD : Rietveld XRF : Fundamental parameters method 69

70 Data analysis XRD vs XRF 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 70

71 Instrumental parameters XRF: energy, intensity fraction XRD: wavelength, intensity fraction In MAUD: One or multiple wavelengths can be indicated with intensity fraction Integration over different energies/wavelengths done numerically 71

72 Primary radiation x-ray tube Tube spectrum and filtered spectrum automatically calculated in MAUD 72

73 Primary radiation x-ray tube Tube spectrum and filtered spectrum automatically calculated in MAUD 73

74 Primary radiation x-ray tube x-ray tube filter graphite monochromator sample proportional counter XRF and XRD signals related to different part of the X-ray primary beam In MAUD: defined separately, hence taken into account 74

75 X-Ray Fluorescence intensity filtered primary beam 75

76 Thank you for your attention! For any further question or doubt: 76