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

SLIDE 1

A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

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

SLIDE 2

A.G. Karydas, ICTP-IAEA School, Trieste, 18th 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

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Interaction of X-rays with atoms

Energy Cross section

 

x

C R

e I I

    

 

   

x ,  I I

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Photon ICS from “Elam database” Elam W.T. et al.,

Radiat. Phys.

Chem, 63, (2002), 121

1 10

10

2

10

3

10

4

10

5

10

6

Ionization Cross Section / barn

Energy / KeV

Rh Rb Zn Fe V Ca Si Cl Na

Photoelectric cross sections 104-105 b

K-shell Photoelectric cross sections 20 30 Photoelectric cross section: ~ Ε. ~ Ζ

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

X-ray Scattering Interactions with atoms

Ei=E0 : Coherent (Rayleigh), mostly with inner atomic electrons Ei < E0: Incoherent (Compton), mostly with

uter, less bound

electrons E0>>Binding Energy

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Scattering probabilities: Unpolarized excitation

Coherent scattering

Z WF (%) Al 8.4 Si 26.7 Ca 9.3 Fe 9.8

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Scattering probabilities: Unpolarized excitation

Coherent scattering Incoherent scattering

Z WF (%) Al 8.4 Si 26.7 Ca 9.3 Fe 9.8

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Scattering probabilities: Polarized radiation

Scattering probability ~ sin2α α=angle between electric field vector of the incident radiation with the propagation direction of the scattered radiation Gangadhar et al. JAAS, 2014

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Κ L M

Nucleus

E0

Kα

Electron

Working principle: X-Ray Fluorescence Analysis

Working principle: 1) Photo-Ionization

f atomic bound

electrons (K, L, M) /Photoelectric absorption 2) Electronic transition amd emission

f element

‘characteristic’ fluorescence radiation Incident photon Energy E0 should be adequate to ionize the atomic bound electrons >= Atomic shell Binding energy

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014 Fluorescence emission

De-excitation of atoms: Competitive processes

: Coster-Cronig (intra-shell)

transition probabilities from the i to the j L subshell

Lij

f

K



: K-shell fluorescence yield

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

20 40 60 80 0.0 0.2 0.4 0.6 0.8 1.0

Fluorescence probability Auger probability

Fluorescence/Auger Yield Atomic Number

De-excitation: Fluorescence/Auger yield

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Emission of element ‘characteristic’ x-rays

Each element has a unique set of emission energies L3 to K shell EKα1 = UK- UL3 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. L - beta lines: N shell e- transition to fill vacancy in L shell.

SLIDE 13

A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014 KX K

K
KX

F E E       ) ( ) (

XRF cross sections: K- Emission

) (

K E



XRF K-shell fluorescence cross section,

K



KX

f

: K-shell photoelectric cross section (cm2/g or barns/atom) : K-shell fluorescence yield : Transition probability for Kα emission

) (

KX E



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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Lij

f

) ( ) ( ) ( ) (

1 1 1 1 i X L i L

L
X

L

Z f Z E E      

XRF cross sections: L- Emission

: Coster-Cronig (intra-shell) transition probabilities from the i to the j L subshell

Example: Incident energy Eo>UL1

) ( ) ( ) ( ) (

2 1 12 1 2 2 i X L i L L L L

X

L

Z f Z f E          ) ( ) ( ) ( ) (

3 3 13 1 12 23 2 3 3 i X L i L L L L L L L

X

L

Z f Z f f f E             

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

XRF cross sections: L- Emission

L1M3(Au) L2M4(Au) L3M5(Au) KL3(Fe)

Partial photoelectric cross sections versus jump ratio approximation

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

XRF cross sections: L- Emission

Honicke et al, PRL 113, 163001 (2014)

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Cross section (b) Atomic Number

20 60 80 30 50 40

Fluorescence Kα, Lα cross sections

Optimization of the exciting beam energy for maximizing the characteristic X- ray intensity

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

D.K.G. de Boer, XRS, 19(1990) 145
M. Mantler, in Handbook of Practical

XRFA, Edited by B. Beckhoff et al.

Primary Fluorescence intensity: Assumptions

Parallel incident beam
Infinite surface for sample
Beam cross section infinite
Homogenous sample
Flat surface of the sample

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

D.K.G. de Boer, XRS, 19(1990) 145
M. Mantler, in Handbook of Practical

XRFA, Edited by B. Beckhoff et al.

Primary Fluorescence intensity: Assumptions

Parallel incident beam
Infinite surface for sample
Beam cross section infinite
Homogenous sample
Flat surface of the sample

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Primary Fluorescence intensity

) ( 4 sin ) , ( ) (

2 1

sin / ) ( 1 sin / ) ( i d d x E k i

i

i x E

i

i

E e dx E E c e I E dI

k i s k

s

   

   

       

   

k

dx

1

sin / ) , (  

k i

i

i

dx E E c  

: 4

d



1

sin / ) (  

k

s

x E

e

I

k

x

d

2

sin / ) (  

k i s

x E

e

1



2



Number of incident Photons/s (Concentration of i element) X (Fluorescence cross section; cm2/g) X (areal density; g/cm2)

Intrinsic efficiency of X-ray detector; Ei

Solid angle of detection (sr)

: ) (

i d E



j=1,N number of elements Sample mass attenuation coefficient for energy Eo

) (

, 1

j

N j j

E c 







: ) (

s E



2 1

sin / ) ( sin / ) ( ) , (     

i s

s

i

T

E E E E 



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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Primary Fluorescence intensity: Calibration

) ( 4 sin 1 ) , ( 1 ) , ( ) (

1 ) , ( i d d i

T

d E E i i

i
i

i

E E E e c E E I E I

i

T

    



         

 

) , ( 1 ) , ( ) (

i

T

i i

i

i i

E E c E E S E I    

d c E E S E I

i i

i

i i

   ) , ( ) (

1 ) , (   d E E

i

T

 1 ) , (   d E E

i

T



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

) , (

i

i

E E S

Sensitivity

Thick target approximation Thin target

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Indirect Enhancement Processes in Fluorescence Emission

J. Fernandez et al., X-Ray Spectrom. 2013, 42, 189–196

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Indirect Enhancement Processes in Fluorescence Emission

J. Fernandez et al., X-Ray Spectrom. 2013, 42, 189–196

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

j i

sample

Secondary Fluorescence Enhancement

X-ray Detector Exciting x-ray beam

Element j characteristic x-ray(s) can excite element i characteristic x-rays within the sample volume

Εο Εj Εi

Energy condition: Εj>Ux,i

i

Sample

Εi

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Secondary enhancement calculation: Example

E



1

sin / ) , (  

j j

j

j

dx E E C  

1

sin / ) (  

j

s

x E

e

 

d

i

x

i

dx

j

x

j

dx

  cos / ) ( ) (

j i j s

x x E

e

  

2

sin / ) (  

i i s

x E

e

 

a dx E E C

i i j i i

cos / ) , (   i

E

        

2

4 1 ) ( ) sin 2 ( r d r r    

  d  sin 2 1

Number of photons emitted per unit area

f layer dxj that reach layer dxi within the

cones with aperture angles α, α+dα

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Sokaras et al, Anal. Chem. 2009, 81, 4946

Topology of secondary fluorescence

13 keV, excitation, SiO2 matrix, 5% Cu, 5% Fe

100 um

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

j k

sample

Tertiary Fluorescence Enhancement

X-ray Detector Exciting x-ray beam

The element j characteristic x-ray(s) can excite element’s k characteristic x-ray(s) which consequently can also excite element’s i characteristic x- rays

Εο Εj Εi

Energy conditions:Εj>Ux,kand Εk>Ux,i

i

Sample

i

Εk Εi Εο

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Type of Sample Secondary Fluorescence Mechanism Am-241 (59.6 keV) Source* Filtered Rh- tube excitation* Ag: 92.5% Cu: 7.5 % Ag-K to Cu 1.57 0.29 Au: 88.3 % Ag: 8.5 % Cu: 3.1 % (Ag-K+Au-L) to Cu 0.82 0.55 Ag-K to Au 6.6e-2 1.4e-2 Cu: 80 % Pb: 10 % Sn: 10 % (Sn-K + Pb-L) to Cu 0.22 7.8e-2 Sn-K to Pb 0.11 1.6e-2 * Including ternary contribution

SF Enhancement in Poly-Energetic excitation

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

i i

sample

Self-element SF Enhancement (special case)

X-ray Detector Exciting x-ray beam

Εο Εj Εi

Energy condition: Εj>UX,i

i

Sample

Element i characteristic x-ray(s) can excite different series of characteristic X-rays

f the same element i within the sample volume; for example K to L, L to M lines

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Self-element SF Enhancement (special case)

A.G. Karydas et al., X-Ray Spectrom. 2005; 34: 426–431

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Self-element SF Enhancement (special case)

A.G. Karydas et al., X-Ray Spectrom. 2005; 34: 426–431

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Self-element SF Enhancement (special case)

A.G. Karydas et al., X-Ray Spectrom. 2005; 34: 426–431

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

i

sample

Secondary Scattering Enhancement (Beam)

X-ray Detector Exciting x-ray beam

Εο Εs Εi

Energy condition: Εs>Ux,i

i

Sample

Incident beam after encountering elastic/inelastic scattering at one produces photoionization of an element i in another sample position volume

Εi

SLIDE 34

A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

i

sample

Secondary Scattering Enhancement (Fluo)

X-ray Detector Exciting x-ray beam

Element a characteristic x-ray after elastic/inelastic scattering within the sample volume are directed to the detector

Εο Εi,s

i

Sample

Εi

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Secondary Enhancement due to Scattering

Karydas, Paradellis, X-Ray Spectrom. 1993; 22: 208 Tirao, Stutz, X-Ray Spectrom. 2003; 32: 13–24

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Secondary Enhancement due to Scattering

Karydas, Paradellis, X-Ray Spectrom. 1993; 22: 208 Tirao, Stutz, X-Ray Spectrom. 2003; 32: 13–24

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Secondary Enhancement due to Scattering

Karydas, Paradellis, X-Ray Spectrom. 1993; 22: 208 Tirao, Stutz, X-Ray Spectrom. 2003; 32: 13–24

Effect on spectrum!

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

i

sample

Photo-/Auger/Compton e- Indirect Fluorescence Enhancement

X-ray Detector Exciting x-ray beam

Ejected electrons from the atoms of element j can ionize an inner shell of element i

Εο Εi

Energy conditions: Te, EΑ>Ux,b

i

Sample

j

e-

Electron spectrum: Discrete: Photo-e, Auger Continuous: Compton

Εi

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Ionization induced by electrons

Green and Cosslett expression for the number

f photons emitted by interaction with a single

electron of initial kinetic energy Eo Qi(E) and dE/ds are the inner shell ionization cross- section and the stopping power (energy loss function), respectively, of electrons in a material Love et al. expression for stopping power

f electrons

the mean ionization potential

10 20 30

10 10

1

10

2

10

3

10

4

Sokaras et al., Unpublished Penelope 2006 G4Penelope with Geant4.7.1 Casino

x-rays yield / cnts impact e- energy / keV Mg 3.08 m 45

/ 45
geometry

=

1
,
= 6.51 × 10 ,

,

= −
1

1.18 × 10

+ 1.47 × 10
= 0.0115 ()

Stochastic movement of electrons (20 keV on Fe)

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Ionization induced by electrons

Green and Cosslett expression for the number

f photons emitted by interaction with a single

electron of initial kinetic energy Eo Qi(E) and dE/ds are the inner shell ionization cross- section and the stopping power (energy loss function), respectively, of electrons in a material Love et al. expression for stopping power

f electrons

the mean ionization potential

10 20 30

10 10

1

10

2

10

3

10

4

Sokaras et al., Unpublished Penelope 2006 G4Penelope with Geant4.7.1 Casino

x-rays yield / cnts impact e- energy / keV Mg 3.08 m 45

/ 45
geometry

=

1
,
= 6.51 × 10 ,

,

= −
1

1.18 × 10

+ 1.47 × 10
= 0.0115 ()

Stochastic movement of electrons (20 keV on Fe)

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Photo e- Fluorescence Enhancement

N. Kawahara in Handbook of Practical X-Ray

Fluorescence Analysis, by B. Beckhoff B. Kanngiesser, N. Langhoff, R.Wedell, H.Wolff, (Eds.) Increases when exciting beam energy is far away from absorption edge of light elements

, = − , ∗

,
J. Fernandez et al., X-Ray

Spectrometry 2013, 42, 189–196

PENELOPE (coupled electron- photon Monte Carlo)

AlKα

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Monte Carlo calculations of phot-e enhancement: Al (4.54μm, 2.13μm, 0.76μm) and Si (4.22μm, 1.61μm) Casnati parameterization for electron ionization cross sections

D. Sokaras et al., unpublished

Photo e- Fluorescence Enhancement

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Important: When a light element analyte is embedded in

a heavy element matrix.

The Auger-electrons from the matrix elements can excite

light element fluorescence.

Example: When carbon in steel is analyzed, a Fe KLL

Auger-electron with a kinetic energy of 6.3 keV can excite multiple carbon K-shells

Auger e- Fluorescence Enhancement

, = 1 − ∑ ,

∗
,

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Secondary electron induced ionizations Example: Thick Fe target

2000 4000 6000 8000 10000

10

3

10

2

10

1

10

3

10

2

10

1

10 10

1

L2 L3

Ionization cross section (Mb)

Electron energy (eV)

L1

Auger e- emission probability

Auger-e

L-shell photoelectrons: Te=Eo-ULi,
Auger-electrons (when Eo>UK)

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

1 2 3 4 5 6 7 8 9

1.90x10

6

1.90x10

5

Auger-e

Secondary fluorescence

Fe-L

intensity (photon

1 sr
1)

Incident photon energy (keV)

photo-e

Fe 1s edge

Bulk metallic Fe, Unpolarized incident radiation

Relative e- enhancement to Fe-Lα excitation in the case of a Fe pure target

Sokaras et al., Phys. Review A 83, 052511 (2011)

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Thomas-Fermi model for the incoherent scattering function

K. Stoev, J. Phys. D: Appl. Phys. 25 (1992) 131-138

Exciting beam : 59.6 keV, Sample: Fe203 + ZnS

Eo to Fe-K to S Eo to Zn-K to S Eo to Zn-K to Fe-K to S Eo–scat to S Compton-e to S Photo-e to S (1): Photo-electrons (2), (3): Compton electrons (4): Direct Compton core hole creation Exciting beam : 59.6 keV, Sample: Pure element, Z

Compton electrons Fluorescence Enhancement

= , ,
, ,

= 1 − −4.88, = 2 3 137

2
=
= 2
+

− + 1 −

−

1 − −1.11766 ×

2 −

Energy distribution of Compton electrons

Compton electrons spectrum Karydas et al., XRS 32, 93 (2003)

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Thomas-Fermi model for the incoherent scattering function

K. Stoev, J. Phys. D: Appl. Phys. 25 (1992) 131-138

Exciting beam : 59.6 keV, Sample: Fe203 + ZnS

Eo to Fe-K to S Eo to Zn-K to S Eo to Zn-K to Fe-K to S Eo–scat to S Compton-e to S Photo-e to S (1): Photo-electrons (2), (3): Compton electrons (4): Direct Compton core hole creation Exciting beam : 59.6 keV, Sample: Pure element, Z

Compton electrons Fluorescence Enhancement

= , ,
, ,

= 1 − −4.88, = 2 3 137

2
=
= 2
+

− + 1 −

−

1 − −1.11766 ×

2 −

Energy distribution of Compton electrons

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

De-excitation processes for inner-shell ionized atoms. Diagram L-emission

Emission of a diagram line

Photo-ionization Fluorescence

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Cascade L X-ray emission

Cascade Emission: X-ray emission due to relaxation of an indirectly vacancy created by the relaxation of innermost shell and not due to a direct ionization. Satellite emission line by a multiple ionized atom

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Fe-L cascade effect

1 2 3 4 5 6 7 8 9

1.90x10

6

1.90x10

5

x0.83

E l a m + B a m b y n e k + R a

Present work

Fe-L

intensity (photon

1 sr
1)

Incident photon energy (keV) Fe 1s edge

x0.46

Bulk metallic Fe, Unpolarized incident radiation Sokaras et al., Phys. Review A 83, 052511 (2011)

T. Schoonjans et al, SAB, B66, (2011) 776

Fluorescence cross sections include full cascade effect due to radiative and non radiative probabilities

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Secondary fluorescence enhancement

Z WF (%) Ipr (%) Isec (%) Iter (%) Iscat (%) Al 8.4 1 21.2 1.17 1.2 Si 26.7 1 18.1 0.64 1.23 Ca 9.3 1 13.8

1.64

Fe 9.8 1

2.44
45

2 1

  

) ( 44 . 17

a

K Mo keV E  

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Geometrical considerations: Non-parallel x-ray beams

Sokaras et al., Review of Scientific Instruments 83, 123102 (2012);

θin=45.2◦ and θout=44.7◦

SLIDE 53

A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Malzer, Kanngiesser, X-Ray Spectrom. 2003; 32: 106–112

The divergent angle ˛ is 20° and the trajectories are distributed isotropically

Fluorescence intensities for non-parallel x-ray beams

=

⃗ −

⃗

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

A polycapillary lens, with a divergent angle of 10°, pointing perpendicular towards the sample surface. Detector angle of 20°.

Fluorescence intensities for non-parallel x-ray beams

=
⃗

⃗ 1 − −

+ 1 −
+ 1 −
⃗

⃗ cos = cos = = + =

The divergent angle of the excitation is

60°, inclined to 20°. The detector again covers 20°, inclined to 30°. XRF and micro-XRF spectrometers which employ Bragg optics

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Geometrical considerations in XRF intensities

De Boer, XRS, 18, 119, 1989

2 1 2 2

sin sin 4        a wd G

1 2 sin

4   a wd G

s

  

2

4 a wd G



  

1

sin  G

2 1

sin sin    G

const G 

Incident flux Io is expressed in number of photons/s/cm2 do d2 =ds

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Geometrical considerations in XRF intensities

Weblin Ll, Rev. Sci. Instrum. 83, 053114 (2012); doi: 10.1063/1.4722495

Geometry under GI conditions

B. Beckhoff et al Anal. Chem. 2007

2 2 /

) ( R r r d    

ab f h r d / ) 2 / ( ) (     



  

   dx x d x I ) ( ) (

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Geometrical considerations in XRF intensities

Sample Volume effect in milli- beam size XRF set-ups

Orlic et al. XRS, 16, 125-130 (1987)

                           

2 3 3 2

1 1 1 arccos ) ( h d h d h d R R R z P

j



Sr 1400 ppm in H3BO3

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

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T. Trojek, J. Anal. At. Spectrom., 2011, 26, 1253

Effect of Surface Topography in XRF intensities

=

sin +
,

,

+ ,
+
, × ,

,

+ ,
,

,

=

, sin + ,

=

, sin −

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

10-12-10

Effect of Surface Topography in XRF intensities

E. C. Geil and R. E. Thorne, J. Synchrotron Rad. (2014), 21, 1358-1363
+
= 0

= −

≡

= − +

=
+

= cos + tan sin ∝ 1 1 +

cos + tan sin

θ is the rotation of the surface normal around the z axis; θ = 0 for a surface parallel to the xz plane

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

μf/μi = 20

The angle effect vanishes as the detector position approaches the incident beam, and it is maximal when the detector is perpendicular to the beam. CaCO3 matrix, with incident beam energy 16.5keV

Effect of Surface Topography in XRF intensities

Hints: The objects should be mounted so that their dominant surface curvature runs perpendicular to the detector–incident beam (x-y) plane

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

10-12-10

Map of surface angle θ computed from the Ca − Kα fluorescence

Effect of Surface Topography in XRF intensities

Rendering of the scanned area and shaded as if obliquely illuminated from the right side by a light source. Photograph of the scanned area, adjusted to enhance contrast and brightness.

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Sample effects – Particle size

Example: Fe2O3 50% of 8 -12 keV from 30μm – 60μm 90% of 8 -12 keV from 100μm – 200μm Information originates only from the first two layers

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Particle size correction models

 Berry et al (Adv. X-ray Anal. 12, 612 1969)

Dependence of fluorescence intensity on:
=2/3 diameter of sphere
η =packing ratio,

   

   

) exp( ) exp( 1 ) exp( ) exp( 1 ) ( exp 1 ) ( exp 1

' '

d m d D m D D d P

nf nf f f nf nf f f f f f f f f ja

                                                      nm D 10 





f f f f

E c

1

sin ) (   



   

f 2 j f f ' f

sin ) E ( c





nf nf nf nf

E c

1

sin ) (   



   

nf 2 j nf nf ' nf

sin ) E ( c

f nf

c c m 

d

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A.G. Karydas, ICTP-IAEA School, Trieste, 18th November 2014

Overview - Conclusions

The quantitative XRF analysis is currently supported by a well-defined

mathematical formalism based on the so-called fundamental parameters approach

The majority of second/third order phenomena that affect the

analyte fluorescence intensity are described by analytical formulas Obstacles:  Enhancement due to electrons ionization requires verification and currently is not taken into account routinely  Accuracy of fundamental parameters (soft energy region) and for L, M characteristic X-rays Perspectives  Monte Caro methods it is the most comprehensive tool to account for all high-order phenomena and assess their contribution in fluorescence intensities  FP re-evaluation by means of metrological SR experiments

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Acknowledgements

 Charalambos Zarkadas, PANalytical B.V. , The Netherlands  Dimosthenis Sokaras, Stanford Synchrotron Radiation Lightsource, USA  Vasiliki Kantarelou, INPP, NCSR “Demokritos”, Greece