Presentation on theme: "X-Ray Standing Waves experiments and their evaluation"— Presentation transcript:
1 X-Ray Standing Waves experiments and their evaluation Oliver Bauer, Moritz SokolowskiInstitute for Physical and Theoretical ChemistryUniversity of BonnWegelerstrasse 12, Bonn, GermanyXSWAVES, version 2.x
2 Outline Introduction to X-Ray Standing Waves Computation of XSW Data - XSWAVES
3 Introduction to XSW – the Physics behind… Literature:B.W. Batterman, H. Cole, Reviews of Modern Physics 36 (1964)J. Zegenhagen, Surface Science Reports 18 (1993)D.P. Woodruff, Progress in Surface Science 57 (1998) 1-60.D.P. Woodruff, Reports on Progress in Physics 68 (2005)
4 single-crystalline substrate Introduction to XSW(NI)XSW = (Normal Incidence) X-ray Standing WavesAbsorption spectroscopy based on diffraction / Photoemission spectroscopy at photon energies EBraggDetermination of adsorption heights and adsorption geometries (molecular distortions upon adsorption?)single-crystalline substrate
5 Introduction to XSWWithin the finite width of the Bragg reflection there is interference between the incoming and the Bragg-reflected wave standing wave field (phase (E)).Bragg-reflectedx-ray plane waveincoming x-rayplane wavewavefrontszIXSWdHlBmax IXSWcrystalsurfaceJ. Zegenhagen, Surf. Sci. Rep. 18 (1993) / D.P. Woodruff, Rep. Prog. Phys. 68 (2005) / B.W. Batterman, H. Cole, Rev. Mod. Phys. 36 (1964) 681.
6 interference of incoming and reflected wave Introduction to XSWTypical NIXSW profilesBragg-reflectedwaveincominginterference of incoming and reflected waveFH: coherent fractionPH: coherent positionSR, |SI|, : non-dipolar parameters
7 interference of incoming and reflected wave Introduction to XSWNon-dipolar contributionsBragg-reflectedwaveincominginterference of incoming and reflected waveFH: coherent fractionPH: coherent positionSR, |SI|, : non-dipolar parameters
8 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 D 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)
9 The Physics behind XSW… The reflectivity curve R is calculated as (1-4):where h is (in terms of photon energy):h 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
10 The Physics behind XSW… The phase shift (or F…) between the incoming and the outgoing X-ray plane wave is computed as (1-4):where is :andconditions inverted in XSWAVESsource code:() → (E)J. Zegenhagen, Surf. Sci. Rep. 18 (1993) / D.P. Woodruff, Rep. Prog. Phys. 68 (2005) / B.W. Batterman, H. Cole, Rev. Mod. Phys. 36 (1964) 681.
11 Computation of XSW data: XSWAVES – an XSW data evaluation routine for ORIGIN® 8 XSWAVES (open-source):ORIGIN (commercial):
12 Computation of XSW data Requirements:Open-source routineSophisticated, reliable fitting engineFull access to fit parametersBatch processingUser-friendly interface*.txt file input:parametersreflectivityexp. XSW profileNLSFfitting enginenumerical and graphicalresults outputNLSF = LabTalk object that can be called from ORIGIN C; robust, widely tested and documented fitting engineLabTalk = scripting language in ORIGINNLFitSession = ORIGIN C class; faster, but hardlay any documentation, no chance of error weighting (version 8.0) …
16 XSWAVES source codeThe theoretical curves (formulae given on pages 25 and 26) are convoluted with two further functions, namely a Gaussian and the squared reflectivity of the Monochromator, and then fitted to the experimental data employing the ORIGIN fitting engine NLSF.The Gaussian function (width wG, center xcG) resembles the instrumental broadening due to substrate mosaicity, e.g. The X-ray beam energy spread is explicitly mimiced by convolution with the squared reflectivity of the Si(111) double-crystal monochromator.The convolution of the squared monochromator reflectivity with the respective theoretical curve is done via FFT convolution which is an ORIGIN C global function. This results in an ideal curve named f which is then convoluted with a Gaussian g by explicitly solving the integral over (source code: integral over t from t_initial to t_final):If the Gaussian function is incorporated in FFT convolution, artefacts are observed (i.e. “wiggling” of the fit curve) which can be overcome by an increased convolution number of points. This is of course very time-consuming.Computational details:The integral is explicitly solved for the exp. photon energy range plus 2.5 eV (or more) in both directions (lower / higher photon energy); this avoids artefacts in the fit result on the boundaries of the exp. energy range.Stepsize d is chosen to be 0.1 eV or smaller (depending on exp. photon energy stepsize).Computation costs about 2 min in total for the template dataset (31 data points, 0.2 eV photon energy stepsize, default settings) on an Intel® Pentium® 4 CPU, 3.20 GHz, with 1.00 GB RAM.Allow the fit to a typical experimental data set (about 50 points, photon energy stepsize: 0.1 – 0.2 eV) to take around 5 to 10 min in total …ORIGIN C global functions : hirachy = global function <= header <= library
18 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.simulationXSWAVES ver. 2.0Data setCFCPTest 10.50.5130.496Test 21.00.71.0000.698Test 30.30.3000.696Test 22.214.171.12420.099Test 50.8 0.8090.799Test 60.60.6150.299Agreement within 1 – 2 % between synthetic data and XSWAVES fit result.