Part 1

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Malzer. AXP. Our Current Activities. • 3D Micro-XRF. • 3D Micro-XANES. • High resolution X-ray emission spectroscopy. • Characterisation of X-ray optics and ...
AXP

Research group Analytical X-ray Physics

X-ray Fluorescence Spectrometry

Wolfgang Malzer

AXP and BLiX

AXP

Malzer

Team

AXP

Malzer

Our Current Activities

• • • • • • • •

AXP

3D Micro-XRF 3D Micro-XANES High resolution X-ray emission spectroscopy Characterisation of X-ray optics and sources Analytic for photovoltaics Laser-Plasma-Sources for the soft X-ray regime X-ray microscopy with laser-plasma-source Profesional courses

• fields of application: cultural heritage, solar cells, geology, bio-medical

Malzer

X-rays as a probe

AXP

Malzer

AXP

Selection rules and emission line energy shells

quantum numbers n l j 1 0 1/2

K Kα1

Kα2

Kβ1

Kβ2

2 2

0 1/2 1 1/2

LIII

2

1 3/2

MI

3 3 3

0 1/2 1 1/2 1 3/2

MV

selection rules ∆l=± 1 ∆ j = 0, ± 1 satellites

LI LII

Kα2: Siegbahn Notation K-L3: IUPAC Notation

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AXP

Outline

- Survey

on XRF Instrumentation and Methods

- Quantitative X-ray Fluorescence Analysis - An Application of Micro-XRF

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Scheme of a XRF-spectrometer

detector

source beam conditioner

geometry

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AXP

X-ray detectors

Wavelength Dispersive Spectrometer - Crystal or multilayer

source

- proportional counter, scintillation counter

detector

- Quantitative analysis - Light element analysis

beam conditioner

Energy Dispersive Spectrometer - Solid state detector (Si, Ge) - Small, leightweight detectors (SDD, PIN)geometry - Qualitative and quantitative analysis - Range: (B) – Na - U

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AXP

X-ray sources

Syncrotron radiation source

- High brillance - Mikro/Nano-XRF (< 1µm)

detector

X-ray tubes - Micro focus X-ray tubes

beam conditioner

beam conditioner - Brillance optimised - Miniature X-ray tubes

- Portable instrumentation (Handheld)

geometry Other - Radioactive sources

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Spectrometer geometry

source

AXP Standard: Ψ ≥ 45° detector Gracing Incidence XRF - Surface sensitive

Gracing Exit XRF beam conditioner - Surface sensitive

Total reflection XRF geometry

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AXP

Outline

- Survey

on XRF Instrumentation and Methods

- Quantitative X-ray Fluorescence Analysis - An Application of Micro-XRF

Malzer

Why is quantification an issue?

AXP Intensity plots for a 2-element sample

1. No matrix effects 2. Apsorption by matrix dominates 3. Absorption by analyte dominates 4. Analyte line is enhanced by matrix

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AXP

Routes and Steps of Quantification

• Primärintensität • Peakidentifikation

• Selbstabsorption

• Peaküberlagerung

• Leichte Matrix

• Untergrund

• Sekundärfluoreszenz

• Detektoreffekte

n e tr n k e Sp uatio l a v e Spektrum

Netto intensitäten

Fun d Par ament ame ale ter M.

Em p M. irische

Zusammensetzung der Probe

Malzer

Spectrum evaluation

AXP

Spectra of solid state det. And of wavelength systems detail

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Solid State Detectors spectrum fitting

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Enhanced uncertainty due to overlap with escape peak

AXP

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AXP

Routes and Steps of Quantification

• Primärintensität • Peakidentifikation

• Selbstabsorption

• Peaküberlagerung

• Leichte Matrix

• Untergrund

• Sekundärfluoreszenz

• Detektoreffekte

n e tr n k e Sp uatio l a v e Spektrum

Netto intensitäten

Fun d Par ament ame ale ter M.

Em p M. irische

Zusammensetzung der Probe

Malzer

AXP

X-ray fluorescence intensity of bulk samples

Complex radiation transport

is simplified to primary fluorescence intensity + secondary fluorescence intensity

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Sherman’s approach for intensity calculation

• Equation dI, • monochromatic

Ω dN i = wiε i 4 ⋅π

AXP

• Model for X-ray fluorescence production • Integration over sample thickness

 µ S ( E0 ) ρx µ S ( Ei ) ρx  τi  ρdx jiωi pi N I 0 exp − − sin Ψ0 sinψ 0 sinψ det  

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AXP

Sherman’s approach for intensity calculation

• Equation dI, • monochromatic

• Integration over excitation spectrum NIo • Sample is flat and homogeneous

τi N i = wi K i * N I 0 µi

with

µ = ∑w * i

j

(

µ0 j j sinψ 0

+

µ ij sinψ det

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AXP

Use of Sherman’s equation for quantification

wi =

K iτ i N I0

µ i*

Ni

(1 + S i )

but

µ = f (w ) * i

• Initial guess for w • Iterative solution

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AXP

Stratified materials

• Sketch primary intensity

(

)

1 − exp − µ Q N i = wi K i τ i N I0 * µi * i

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Stratified materials

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Primary fluorescence intensity + intra-layer enhancenment + inter-layer enhancenment Malzer

Use of Sherman’s equation

AXP

What is the information depth of my sample?

Is the homogeneity of my sample sufficient?

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Information depth

• Equation dI • Definition effective mass absorption coefficient • Example figures

AXP Definition of information depth: Half of the total intensity comes from above Simplifications: * Only consider attenuation of fluorescence line * 1/2 ≈ 1/e

Mean free path length 1/µρ is an estimate for the information depth Malzer

AXP

Information depth

• Equation dI • Definition effective mass absorption coefficient • Example figures Mean free path in µm

Fe

Sn

SiO2 (2 g/cm3)

70

3,500

O (1 g/cm3)

440

19,000 Malzer

Calculation of transmission

AXP

http://henke.lbl.gov/optical_constants/filter2.html

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Sample inhomogeneity

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• Respective LambertBeer equations exp( − ( wA µ A + wB µ B )Q ) • Use Q

=

exp( − wA µ A Q ) exp( − wB µ BQ ) ≠

exp( − wA µ A Q ) + exp( − wB µ BQ )

Q = ρd Malzer

Sample inhomogeneity

AXP

particle size « particle mean free path length information depth » sample mean free path length

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Routes and Steps of Quantification

• Primärintensität • Peakidentifikation

• Selbstabsorption

• Peaküberlagerung

• Leichte Matrix

• Untergrund

• Sekundärfluoreszenz

• Detektoreffekte

n e tr n k e Sp uatio l a v e Spektrum

Netto intensitäten

Fun d Par ament ame ale ter M.

Em p M. irische

Zusammensetzung der Probe

Malzer

Empirical methods for quantification

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• Standard addition, internal standard, etc. • Fingerprint • Influence coefficients method

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Influence coefficients

AXP

( ) + m N (1 + ∑ m I )

wi = w0i + mi N i 1 + ∑ j α ij w j

wi = w0i

i

i

j

ij

j

• Best precision achievable (< 1%) • Two reference materials per coefficient • Applied in analysis of steel, gold, concrete production

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Fin Part 1

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