Introduction to Quantitative XRF analysis Andreas - Germanos - PowerPoint PPT Presentation

Introduction to Quantitative XRF analysis Andreas - Germanos Karydas NSIL- Nuclear Science and Instrumentation Laboratory International Atomic Energy Agency ( IAEA ) IAEA Laboratories , A-2444 Seibersdorf, Austria A.Karydas@iaea.org A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

Outline • Basic mechanisms for ionization/fluorescence process • Primary XRF Intensity • Indirect enhancement processes of XRF intensity • XRF analysis in the real world: - Non-parallel exciting beams - Influence of surface topography - Geometrical considerations - Particle size effects A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

Interaction of X-rays with atoms  , x I I 0 Cross section              x I I e R C 0 Energy A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

Photoelectric cross sections K-shell Photoelectric cross sections 6 10 I onization Cross Section / barn 10 4 -10 5 b Na Photon ICS from Si 5 Cl 10 “Elam database” Ca V Fe Elam W.T. et al., Zn Rb Radiat. Phys. 4 Rh 10 Chem, 63, (2002) , 121 Photoelectric 3 10 cross section: � ~ Ε ��.� 2 10 � ~ Ζ � �� � 1 10 20 30 Energy / KeV A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

X-ray Scattering Interactions with atoms E 0 >>Binding Energy E i < E 0 : Incoherent E i =E 0 : Coherent (Rayleigh), (Compton), mostly with mostly with inner atomic outer, less bound electrons electrons A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

Scattering probabilities: Unpolarized excitation Z WF Coherent scattering (%) Al 8.4 Si 26.7 Ca 9.3 Fe 9.8 A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

Scattering probabilities: Unpolarized excitation Z WF Coherent scattering (%) Al 8.4 Incoherent Si 26.7 scattering Ca 9.3 Fe 9.8 A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

Scattering probabilities: Polarized radiation Scattering probability ~ sin 2 α α=angle between electric field vector of the incident radiation with the propagation direction of the scattered radiation Gangadhar et al. JAAS, 2014 A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

Working principle: X-Ray Fluorescence Analysis E 0 Working principle: Incident photon 1) Photo -Ionization Energy E 0 of atomic bound should be electrons Kα adequate to (K, L, M) ionize the / Photoelectric atomic L Κ M absorption bound Nucleus electrons 2) Electronic transition >= Electron amd emission Atomic shell of element Binding ‘ characteristic’ energy fluorescence radiation A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

De-excitation of atoms: Competitive processes Fluorescence emission f : Coster-Cronig (intra-shell)  Lij : K-shell fluorescence yield K transition probabilities from the i to the j L subshell A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

De-excitation: Fluorescence/Auger yield Auger probability 1.0 Fluorescence/Auger Yield 0.8 0.6 Fluorescence probability 0.4 0.2 0.0 0 20 40 60 80 Atomic Number A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

Emission of element ‘characteristic’ x-rays K - alpha lines: L shell e- transition to fill vacancy in K shell. Most frequent transition, hence most intense peak K - beta lines: M shell e- transitions to fill vacancy in K shell. L - alpha lines: M shell e- transition to fill vacancy in L shell. E Kα1 = U K - U L3 L 3 to K shell L - beta lines: N shell e- transition to fill vacancy in L shell. Each element has a unique set of emission energies A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

XRF cross sections: K- Emission  KX E ( ) XRF K-shell fluorescence cross section, o       ( E ) ( E ) F KX o K o K KX  K E ( ) : K-shell photoelectric cross section ( cm 2 /g or barns/atom ) o  : K-shell fluorescence yield K f : Transition probability for Kα emission KX A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

XRF cross sections: L- Emission Example: Incident energy E o >U L1       ( E ) ( E ) ( Z ) f ( Z ) L 1 X o L 1 o L 1 i L 1 X i          ( E ) ( f ) ( Z ) f ( Z ) L 2 X o L 2 L 1 L 12 L 1 i L 2 X i              ( E ) ( f f f ) ( Z ) f ( Z ) L 3 X o L 3 L 2 L 23 L 12 L 1 L 13 L 3 i L 3 X i f : Coster-Cronig (intra-shell) transition probabilities from the i to the j L subshell Lij A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

XRF cross sections: L- Emission L 3 M 5 (Au) Partial photoelectric cross L 2 M 4 (Au) sections versus jump ratio approximation L 1 M 3 (Au) KL 3 (Fe) A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

XRF cross sections: L- Emission Honicke et al, PRL 113, 163001 (2014) A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

Fluorescence Kα, Lα cross sections Optimization of Cross section (b) the exciting beam energy for maximizing the characteristic X- ray intensity 20 30 40 50 60 80 Atomic Number A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

Primary Fluorescence intensity: Assumptions • Parallel incident beam • D.K.G. de Boer, XRS, 19(1990) 145 • M. Mantler, in Handbook of Practical • Infinite surface for sample XRFA, Edited by B. Beckhoff et al . • Beam cross section infinite • Homogenous sample • Flat surface of the sample A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

Primary Fluorescence intensity: Assumptions • Parallel incident beam • D.K.G. de Boer, XRS, 19(1990) 145 • M. Mantler, in Handbook of Practical • Infinite surface for sample XRFA, Edited by B. Beckhoff et al . • Beam cross section infinite • Homogenous sample • Flat surface of the sample A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

Primary Fluorescence intensity  Number of I Solid angle of d : 0 incident 4  detection ( sr ) j=1,N number of elements Photons/s Intrinsic efficiency of  d E ( ) :   i X-ray detector; E i 1 2 e    ( E ) x / sin e    s i k 2 ( E ) x / sin x s o k 1 k d dx k     c ( E , E ) dx / sin i i o i k 1 (Concentration of i element) X (Fluorescence cross section; cm 2 /g) X (areal density; g/cm 2 )   s E ( ) :  c  ( E ) Sample mass attenuation coefficient for energy Eo o j j o  j 1 , N  dx           ( E ) x / sin     ( E ) x / sin   dI ( E ) I e c ( E , E ) k e d ( E ) s o k 1 s i k 2 i i o i i o i d i    sin 4 1       ( E , E ) ( E ) / sin ( E ) / sin  T o i s o 1 s i 2 A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

Primary Fluorescence intensity: Calibration     ( E , E ) d  1 e 1 T o i          I ( E ) I ( E , E ) c d ( E ) i i o i o i i d i     ( E , E ) sin 4 T o i 1 S ( E , E ) Sensitivity i o i 1 Thick target      d  I ( E ) S ( E , E ) c ( E , E ) 1 i i i o i i  T o i approximation ( E , E ) T o i      d  I ( E ) S ( E , E ) c d ( E , E ) 1 Thin target i i i o i i T o i Different approaches are followed depending on how well the set-up geometry and incident beam intensity are characterized:  Sensitivity calibration: certified pure element/compound targets  Solid angle calibration: Normalized beam intensity, detector efficiency known, well certified pure element/compound targets  Standard-less XRFA: Calibrated apertures, distances, detector response function versus energy, incident beam intensity A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

Indirect Enhancement Processes in Fluorescence Emission J. Fernandez et al ., X-Ray Spectrom. 2013, 42, 189–196 A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

Indirect Enhancement Processes in Fluorescence Emission J. Fernandez et al ., X-Ray Spectrom. 2013, 42, 189–196 A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014

Secondary Fluorescence Enhancement Exciting x-ray beam X-ray Detector Ε ο Ε i sample Ε i Sample j Ε j Energy condition: i Ε j >U x,i i Element j characteristic x-ray(s) can excite element i characteristic x-rays within the sample volume A.G. Karydas, ICTP-IAEA School, Trieste, 18 th November 2014