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![Page 1: Oliver Bauer, Moritz Sokolowski Institute for Physical and Theoretical Chemistry University of Bonn Wegelerstrasse 12, 53115 Bonn, Germany bauer@pc.uni-bonn.de.](https://reader031.fdocuments.net/reader031/viewer/2022020105/55140468550346ec488b4a98/html5/thumbnails/1.jpg)
Oliver Bauer, Moritz Sokolowski
Institute for Physical and Theoretical ChemistryUniversity of BonnWegelerstrasse 12, 53115 Bonn, [email protected]
X-Ray Standing Waves experimentsand their evaluation
XSWAVES, version 2.x
4286 4288 4290 4292
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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
![Page 2: Oliver Bauer, Moritz Sokolowski Institute for Physical and Theoretical Chemistry University of Bonn Wegelerstrasse 12, 53115 Bonn, Germany bauer@pc.uni-bonn.de.](https://reader031.fdocuments.net/reader031/viewer/2022020105/55140468550346ec488b4a98/html5/thumbnails/2.jpg)
1) Introduction to X-Ray Standing Waves
2) Computation of XSW Data - XSWAVES
Outline
![Page 3: Oliver Bauer, Moritz Sokolowski Institute for Physical and Theoretical Chemistry University of Bonn Wegelerstrasse 12, 53115 Bonn, Germany bauer@pc.uni-bonn.de.](https://reader031.fdocuments.net/reader031/viewer/2022020105/55140468550346ec488b4a98/html5/thumbnails/3.jpg)
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.
![Page 4: Oliver Bauer, Moritz Sokolowski Institute for Physical and Theoretical Chemistry University of Bonn Wegelerstrasse 12, 53115 Bonn, Germany bauer@pc.uni-bonn.de.](https://reader031.fdocuments.net/reader031/viewer/2022020105/55140468550346ec488b4a98/html5/thumbnails/4.jpg)
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
![Page 5: Oliver Bauer, Moritz Sokolowski Institute for Physical and Theoretical Chemistry University of Bonn Wegelerstrasse 12, 53115 Bonn, Germany bauer@pc.uni-bonn.de.](https://reader031.fdocuments.net/reader031/viewer/2022020105/55140468550346ec488b4a98/html5/thumbnails/5.jpg)
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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0.8
1.0
(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.
![Page 6: Oliver Bauer, Moritz Sokolowski Institute for Physical and Theoretical Chemistry University of Bonn Wegelerstrasse 12, 53115 Bonn, Germany bauer@pc.uni-bonn.de.](https://reader031.fdocuments.net/reader031/viewer/2022020105/55140468550346ec488b4a98/html5/thumbnails/6.jpg)
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0
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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
-1.0 -0.5 0.0 0.5 1.0 1.5 2.0
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1.0
(a) zero absorption
(b) with absorption
refle
ctiv
ity R
(E)
relative photon energy (eV)
Ag - (200) reflection
Introduction to XSW
![Page 7: Oliver Bauer, Moritz Sokolowski Institute for Physical and Theoretical Chemistry University of Bonn Wegelerstrasse 12, 53115 Bonn, Germany bauer@pc.uni-bonn.de.](https://reader031.fdocuments.net/reader031/viewer/2022020105/55140468550346ec488b4a98/html5/thumbnails/7.jpg)
• Non-dipolar contributions
Introduction to XSW
Bragg-reflectedwave
incomingwave
interference of incoming and reflected wave
FH: coherent fractionPH: coherent positionSR, |SI|, : non-dipolar parameters
![Page 8: Oliver Bauer, Moritz Sokolowski Institute for Physical and Theoretical Chemistry University of Bonn Wegelerstrasse 12, 53115 Bonn, Germany bauer@pc.uni-bonn.de.](https://reader031.fdocuments.net/reader031/viewer/2022020105/55140468550346ec488b4a98/html5/thumbnails/8.jpg)
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)
![Page 9: Oliver Bauer, Moritz Sokolowski Institute for Physical and Theoretical Chemistry University of Bonn Wegelerstrasse 12, 53115 Bonn, Germany bauer@pc.uni-bonn.de.](https://reader031.fdocuments.net/reader031/viewer/2022020105/55140468550346ec488b4a98/html5/thumbnails/9.jpg)
• 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…
![Page 10: Oliver Bauer, Moritz Sokolowski Institute for Physical and Theoretical Chemistry University of Bonn Wegelerstrasse 12, 53115 Bonn, Germany bauer@pc.uni-bonn.de.](https://reader031.fdocuments.net/reader031/viewer/2022020105/55140468550346ec488b4a98/html5/thumbnails/10.jpg)
• 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.
![Page 11: Oliver Bauer, Moritz Sokolowski Institute for Physical and Theoretical Chemistry University of Bonn Wegelerstrasse 12, 53115 Bonn, Germany bauer@pc.uni-bonn.de.](https://reader031.fdocuments.net/reader031/viewer/2022020105/55140468550346ec488b4a98/html5/thumbnails/11.jpg)
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/
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• 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
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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
![Page 14: Oliver Bauer, Moritz Sokolowski Institute for Physical and Theoretical Chemistry University of Bonn Wegelerstrasse 12, 53115 Bonn, Germany bauer@pc.uni-bonn.de.](https://reader031.fdocuments.net/reader031/viewer/2022020105/55140468550346ec488b4a98/html5/thumbnails/14.jpg)
Computation of XSW data
• Experimental broadening
Si(111) double-crystalmonochromator
alinstrumentmono GRidealII
II 2
00)(.exp
![Page 15: Oliver Bauer, Moritz Sokolowski Institute for Physical and Theoretical Chemistry University of Bonn Wegelerstrasse 12, 53115 Bonn, Germany bauer@pc.uni-bonn.de.](https://reader031.fdocuments.net/reader031/viewer/2022020105/55140468550346ec488b4a98/html5/thumbnails/15.jpg)
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
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fitresult
![Page 17: Oliver Bauer, Moritz Sokolowski Institute for Physical and Theoretical Chemistry University of Bonn Wegelerstrasse 12, 53115 Bonn, Germany bauer@pc.uni-bonn.de.](https://reader031.fdocuments.net/reader031/viewer/2022020105/55140468550346ec488b4a98/html5/thumbnails/17.jpg)
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
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XSWAVES benchmarking
• Ag(111), Test 2:– Simulation: CF = 1.0 CP = 0.7– Fit: CF = 1.000 CP = 0.698
![Page 19: Oliver Bauer, Moritz Sokolowski Institute for Physical and Theoretical Chemistry University of Bonn Wegelerstrasse 12, 53115 Bonn, Germany bauer@pc.uni-bonn.de.](https://reader031.fdocuments.net/reader031/viewer/2022020105/55140468550346ec488b4a98/html5/thumbnails/19.jpg)
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