Oliver Bauer, Moritz Sokolowski Institute for Physical and Theoretical Chemistry University of Bonn...
-
Upload
elijah-ramsey -
Category
Documents
-
view
220 -
download
0
Transcript of Oliver Bauer, Moritz Sokolowski Institute for Physical and Theoretical Chemistry University of Bonn...
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
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
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
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
0.0
0.2
0.4
0.6
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.
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
(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
0.0
0.2
0.4
0.6
0.8
1.0
(a) zero absorption
(b) with absorption
refle
ctiv
ity R
(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
4286 4288 4290 4292
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
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