Oliver Bauer , Moritz Sokolowski Institute for Physical and Theoretical Chemistry University of Bonn Wegelerstrasse 12, 53115 Bonn, Germany [email protected]X-Ray Standing Waves experiments and 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 su b stra te / n o m ina lB ra g g en e rg y: A g(110) / 4 2 9 4 .5 9 7 e V X S W sig n a l: A g3d R eflectivity d a ta file : E scan83_C C 193_A g3d_Irefl.txt X S W a b so rp tio n p ro file d a ta file: E sca n 8 3 _ C C 1 9 3 _ A g 3 d _ ra w .txt C F = 0 .994 + /- 0.0 01 6 C P = 0 .03 2 + /- 0.0 00 5 Q = 0 .0 0 0 + /- 0 .0 0 0 0 D elta = 0.0 00 + /- 0.0 000 G a u ssia n w id th w G = 0 .2 5 1 + /- 0 .0 0 1 0 eV G a u ssia n cen te r xcG = -5 .4 3 7 + /- 0 .0 0 1 5 e V reduced chi-square = 1.747077e+001 d ate: M on Feb 21 18:37:50 2011 no rm .R e fle ctivity /re l.ab so rp tion yie ld p h oto n e ne rg y (e V ) norm .R eflectivity norm .R eflectivity fitresult norm .XS W absorption profile norm .XS W P rofile fitresult
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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
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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)).
• 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):