Oliver Bauer, Moritz Sokolowski

Institute for Physical and Theoretical ChemistryUniversity of BonnWegelerstrasse 12, 53115 Bonn, Germanybauer@pc.uni-bonn.de

X-Ray Standing Waves experimentsand their evaluation

XSWAVES, version 2.x

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substrate / nominal Bragg energy: Ag(110) / 4294.597 eV XSW signal: Ag3d Reflectivity data file: Escan83_CC193_Ag3d_Irefl.txt XSW absorption profile data file: Escan83_CC193_Ag3d_raw.txt CF = 0.994 +/- 0.0016 CP = 0.032 +/- 0.0005 Q = 0.000 +/- 0.0000 Delta = 0.000 +/- 0.0000 Gaussian width wG = 0.251 +/- 0.0010 eV Gaussian center xcG = -5.437 +/- 0.0015 eV reduced chi-square = 1.747077e+001 date: Mon Feb 21 18:37:50 2011

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1) Introduction to X-Ray Standing Waves

2) Computation of XSW Data - XSWAVES

Outline

Introduction to XSW –

the Physics behind…

Literature:

(1) B.W. Batterman, H. Cole, Reviews of Modern Physics 36 (1964) 681-717.(2) J. Zegenhagen, Surface Science Reports 18 (1993) 199-271.(3) D.P. Woodruff, Progress in Surface Science 57 (1998) 1-60.(4) D.P. Woodruff, Reports on Progress in Physics 68 (2005) 743-798.

Introduction to XSW

• (NI)XSW = (Normal Incidence) X-ray Standing Waves– Absorption spectroscopy based on diffraction /

Photoemission spectroscopy at photon energies EBragg

– Determination of adsorption heights and adsorption geometries(molecular distortions upon adsorption?)

single-crystalline substrate

Introduction to XSW

• Within the finite width of the Bragg reflectionthere is interference between the incoming andthe Bragg-reflected wave standing wave field (phase (E)).

Bragg-reflectedx-ray plane wave

incoming x-rayplane wave

wavefronts

z

IXSW

dH

B

max IXSW

H

0k

Hk

dH

crystalsurface

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

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(a) zero absorption

(b) with absorption

refle

ctiv

ity R

(E)

relative photon energy (eV)

Ag - (200) reflection

J. Zegenhagen, Surf. Sci. Rep. 18 (1993) 199. / D.P. Woodruff, Rep. Prog. Phys. 68 (2005) 743. / B.W. Batterman, H. Cole, Rev. Mod. Phys. 36 (1964) 681.

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(d) 0.75

(c) 0.50

(b) 0.25

rela

tive

abso

rptio

n

relative photon energy (eV)

Ag - (200) reflection

(a) 0.00

• Typical NIXSW profiles

Bragg-reflectedwave

incomingwave

interference of incoming and reflected wave

FH: coherent fractionPH: coherent positionSR, |SI|, : non-dipolar parameters

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(a) zero absorption

(b) with absorption

refle

ctiv

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(E)

relative photon energy (eV)

Ag - (200) reflection

Introduction to XSW

• Non-dipolar contributions

Introduction to XSW

Bragg-reflectedwave

incomingwave

interference of incoming and reflected wave

FH: coherent fractionPH: coherent positionSR, |SI|, : non-dipolar parameters

The Physics behind XSW…

• The XSW absorption profile as a function of coherent fraction and coherent position is taken as (3,4):

• where and are :

p and l are the partial phase shifts for the outgoing p- and d-waves, respectively (photoemission from an s-state).

• Q and are tabulated.

= SR = |SI|

M.B. Trzhaskovskaya et al. , Atomic Data and Nuclear Data Tables 77 (2001) 97 and 82 (2002) 257.NIST Electron Elastic-Scattering Cross-Section Database 3.1 (June 2003)

• The reflectivity curve R is calculated as (1-4):

• where is (in terms of photon energy):

• is a complex number since the structure factors are complex.

• Polarisation factor P is taken as cos(2 * Bragg)(normal incidence => polarisation, P = 1).

• The above formula is only valid for centrosymmetric crystals since the pre-factor FH / F-H is omitted

= 1 for centrosymmetric crystals

The Physics behind XSW…

• The phase shift (or …) between the incoming and the outgoing X-ray plane wave is computed as (1-4):

• where is :

• and

The Physics behind XSW…

conditions inverted in XSWAVESsource code:

() → (E)

J. Zegenhagen, Surf. Sci. Rep. 18 (1993) 199. / D.P. Woodruff, Rep. Prog. Phys. 68 (2005) 743. / B.W. Batterman, H. Cole, Rev. Mod. Phys. 36 (1964) 681.

Computation of XSW data:

XSWAVES –

an XSW data evaluation routine for ORIGIN® 8

XSWAVES (open-source):

http://www.thch.uni-bonn.de/pctc/sokolowski/XSWAVES/XSWAVES_index.html

ORIGIN (commercial):

http://originlab.com/

• Requirements:– Open-source routine– Sophisticated, reliable fitting engine– Full access to fit parameters– Batch processing– User-friendly interface

Computation of XSW data

*.txt file input:• parameters• reflectivity• exp. XSW profile

NLSFfitting engine

numerical and graphicalresults output

XSWAVES

• Exemplary fit result

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substrate / nominal Bragg energy: Ag(110) / 4294.597 eV XSW signal: Ag3d Reflectivity data file: Escan83_CC193_Ag3d_Irefl.txt XSW absorption profile data file: Escan83_CC193_Ag3d_raw.txt CF = 0.994 +/- 0.0016 CP = 0.032 +/- 0.0005 Q = 0.000 +/- 0.0000 Delta = 0.000 +/- 0.0000 Gaussian width wG = 0.251 +/- 0.0010 eV Gaussian center xcG = -5.437 +/- 0.0015 eV reduced chi-square = 1.747077e+001 date: Mon Feb 21 18:37:50 2011

no

rm. R

efle

ctiv

ity /

rel.

ab

sorp

tion

yie

ld

photon energy (eV)

norm. Reflectivity norm. Reflectivity fit result norm. XSW absorption profile norm. XSW Profile fit result

Computation of XSW data

• Experimental broadening

Si(111) double-crystalmonochromator

alinstrumentmono GRidealII

II 2

00)(.exp

XSWAVES source code

alinstrumentmono GRidealII

II 2

00)(.exp

FFT convolution→ funtion F(E)

“step-wise“ convolution:trapezoidal rule

dttEGtFEGEFII

alinstrument

t

t

alinstrument

final

initial

.exp0

fitresult

XSWAVES benchmarking

• Fit of synthetic data sets for Ag(111):

– Exemplary data sets were created with EXCEL simulation sheet by Bruce Cowie.

– Neither error weighting for reflectivity fit nor for XSW absorption profile fit.

– Non-dipolar parameters : Q = 0, = 0.

– Modification of the response function is NOT enabled during XSW profile fit.

  simulation XSWAVES ver. 2.0

Data set CF CP CF CP

Test 1 0.5 0.5 0.513 0.496

Test 2 1.0 0.7 1.000 0.698

Test 3 0.3 0.7 0.300 0.696

Test 4 0.8 0.1 0.812 0.099

Test 5 0.8  0.8 0.809 0.799

Test 6 0.6 0.3 0.615 0.299

XSWAVES benchmarking

• Ag(111), Test 2:– Simulation: CF = 1.0 CP = 0.7– Fit: CF = 1.000 CP = 0.698

Summary

• XSWAVES – an XSW data evaluation routine for ORIGIN® 8:

– Open-source routine with user-friendly interface

http://www.thch.uni-bonn.de/pctc/sokolowski/XSWAVES/XSWAVES_index.html