Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1)...

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Oliver Bauer 1) , Sergey Subach 2) , Giuseppe Mercurio 2) , Frank Stefan Tautz 2) , Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry, University of Bonn, Wegelerstrasse 12, 53115 Bonn, Germany 2) Institute of Bio- and Nanosystems (IBN), Institute 3: Institute of Functional Nanostructures at Surfaces (IBN3), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany SimXSW / FitXSW ORIGIN C based routines for X-ray standing Waves data simulation and fitting Version 2.0 Bonn, 08.07.2009

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Page 1: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

Oliver Bauer1), Sergey Subach2), Giuseppe Mercurio2), Frank Stefan Tautz2), Moritz Sokolowski1)

1) Institute for Physical and Theoretical Chemistry, University of Bonn, Wegelerstrasse 12, 53115 Bonn, Germany2) Institute of Bio- and Nanosystems (IBN), Institute 3: Institute of Functional Nanostructures at Surfaces (IBN3), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany

SimXSW / FitXSW

ORIGIN C based routines for X-ray standing Waves data simulation and fitting

Version 2.0

Bonn, 08.07.2009

Page 2: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Outline

1. Manual / System Requirements

2. The Physics behind the Routine

3. Performance

4. Conclusions

Page 3: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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System Requirements

• Written and tested under OriginPro 8 SR4

– No downward compatibility to Origin 7.5 and lower …

• System currently in operation:

– Intel® Pentium® 4 CPU, 3.20 GHz

– 1.00 GB RAM

• The faster your computer, the better … !

Page 4: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

MANUAL

Page 5: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Manual

• The user is provided two *.c files:– SimXSW v2.0.c– FitXSW v2.0.c

• Both files have to be compiled with ORIGIN Code Builder (see below) every time ORIGIN is opened.

• Additionally two *.fdf files which contain the actual fitting routines for reflectivity and XSW absorption are provided:

– XSW_ReflectivityFit_v2_0.fdf– XSW_AbsorptionProfileFit_v2_0.fdf– XSW_AbsorptionProfileFit_Special_v2_0.fdf

• Add these files to your NLSF fitting engine (only once):– Make an arbitrary graph layer

(which actually shows data) active.– Go to Analysis > Fitting >

Nonlinear Curve Fit > Open Dialog.– Hit “Create/Edit Fitting Functions”

button.

Page 6: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Manual

– Get folder “--- User Defined ---” active and then click “New Category”. Choose a name for the folder which is to be created.

– Afterwards, click “Add” and browse for the three *.fdf files, then hit “OK”.

G. Brodén et al., Surf. Sci. 59, 593611 (1976).

Page 7: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Manual: SimXSW

• How to use SimXSW ?– Open ORIGIN 8.– Open “Code Builder”.

– Go to File > New Workspace, then open ”SimXSW v2.0.c”– Hit File > Add to Workspace, then click “Build”.

Page 8: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Manual: SimXSW

– After successful compilation the “output window” reads …

– Go back to ORIGIN and open the “Script Window” (Window > Script Window).– Type the name of the program (i.e. “SimXSW_v2_0”) and hit “Enter”.

Page 9: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Manual: SimXSW

– The program starts running and keeps the user updated in the Script Window.– The user will be asked to select a parameter file; for that purpose an input box

pops up:

– Choose a parameter file and click “Open”. The program continues…– An exemplary parameter file is provided with the source code of SimXSW. Do

NOT change the overall appearance of the parameter file !

Page 10: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Manual: SimXSW

– A second input box appears: Now you can decide on parameters such as coherent fraction, coherent position and non-dipolar parameters as well as the width of the Gaussian function (in eV) which is used to model the instrumental broadening and the substrate mosaicity:

– Choose the five parameters at your convenience and hit “OK”.– The program creates two workbooks and one graph:

• Book* - SimulationParameters: holds the default values for the above mentioned parameters (see screen print) and is updated to the values given by the user.

• Book* - SimulationData: houses energy scale (X axis) as well as calculated data, i.e. theoretical reflectivity, phase Phi and XSW absorption profile (Y data). Furthermore the theoretical curves are successively convoluted with the squared monochromator reflectivity (“ideal”) and a Gaussian function (“expected” in experiment).

• Graph* - SimulationPlot: displays the simulated reflectivity curves and the simulated XSW absorption profiles (“theoretical”, “ideal”, “expected”).

Page 11: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Manual: SimXSW

– This is what you get:

Page 12: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Manual: FitXSW

• How to use FitXSW ?– Open ORIGIN 8.– Open “Code Builder”.

– Go to File > New Workspace, then open ”FitXSW v2.0.c”.– Hit File > Add to Workspace, then click “Build”.

Page 13: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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– After successful compilation the “output window” reads …

– REMEMBER: Close “Code Builder” after successful compilation. Otherwise FitXSW will be significantly slowed down or ORIGIN might even be caused to crash!

– Go back to ORIGIN and open the “Script Window” (Window > Script Window).– Type the name of the program (i.e. “FitXSW_v2_0”) and hit “Enter”.

Manual: FitXSW

Page 14: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Manual: FitXSW

– The program starts running and keeps you updated in the Script Window.– The user will be asked to select a parameter file. For that purpose an input box

pops up:

– Choose a parameter file and click “Open”. The program continues…– An exemplary parameter file is provided with the source code of FitXSW. Do NOT

change the overall appearance of the parameter file! The parameter files for SimXSW and FitXSW are fully compatible.

Page 15: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Manual: FitXSW

– The program does some calculations. Then a 2nd input box appears: The user can select an input file which holds the experimental reflectivity data.

Page 16: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Manual: FitXSW

– In a 3rd dialog box the user is asked to decide on initial values for the fit parameters. The user can also decide to extend the convolution integral beyond the default setting (exp. photon energy range +/- 2.5 eV) and to decrease the integration stepsize (this is eqivalent to an increase in the convolution number of points, see screen print …) by a factor of 10 as compared to default settings.

Page 17: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Manual: FitXSW

– Please be patient, the fits may take a couple of minutes. After the fit is done, the fit results are pasted to the “Script Window” and to the Graph “ExpReflectivity” which holds the experimental data. Also the fit curve itself is copied to column 8 of Workbook “ExpReflectivity”.

– A 4th dialog box opens where you can select the input file for the experimental XSW absorption profile data:

Page 18: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Manual: FitXSW

– After the exp. data are read in, the user is asked - in a 5th dialog box - to decide on appropriate start values for the fit of the exp. XSW absorption profile. Further-more, the user may change the default settings (see screen print below) which parameters are fixed and which are free.

– Also a “special fit model” is offered: If chosen FitXSW will fit a linear combination of two XSW absorption profiles to the exp. data.

Enternon-dipolar parameters

here!

Page 19: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Manual: FitXSW

– Again, the fit to the exp. data may take a short while. After completion of the fit, the results are written to the Script Window. Also the results are plotted in Graph “Fit <n> – ExpXSWProfile - <input file>” and the fitted data points are stored in Workbook “Fit <n> - ExpXSWProfile - <input file>”.

Page 20: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Manual: FitXSW

– The following Workbooks and Graphes are created by FitXSW v2.0:• Workbook “ExpReflectivity”: holds the experimental data for the reflectivity and the fit

result as well as the normalised curves.

• Graph “ExpReflectivity”: displays exp. Reflectivity data and the respective fit curve incl. the fit parameters.

• Workbook “FitParameters - Reflectivity”: stores all parameters which were used / fitted during the Reflectivity curve fit, including the respective errors.

• Workbook “Fit <n> - ExpXSWProfile - <input file>”: holds the experimental data for the XSW absorption profile and the fit result as well as the normalised curves.

• Graph “Fit <n> - ExpXSWProfile - <input file>”: displays exp. XSW absorption profile data and the respective fit curve incl. the fit parameters.

• Workbook “Fit <n> - FitParameters – XSW Profile”: stores all parameters which were used / fitted during the XSW absorption profile fit, including the respective errors.

• Graph “Fit <n> - Result”: shows the normalised exp. curves and the normalised fit curves. The most interesting fit parameters are shown, too.

Page 21: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Manual: FitXSW

– This is the final “Fit <n> - Result” Graph:

Page 22: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Manual: FitXSW

– Finally the user is asked whether he would like to do another XSW absoprtion profile fit:

• If no, the program terminates.

• If yes (default), the user is asked again to choose an input file for the exp. XSW absorption profile (cf. page 17).

Page 23: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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 24: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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The Physics behind…

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

• where eta is (in terms of photon energy):

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

• Polarisation 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

Page 25: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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• The phase shift (named Phi in source code…) between the incoming and the outgoing X-ray plane wave is computed as (1-4):

• where is :

• and

The Physics behind…

conditions are inverted in source code:

() → (E)

Page 26: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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The Physics behind…

• 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).

= SR = |SI|

Page 27: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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The Physics behind…

• The 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 obeserved (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 0.15 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 …

Page 28: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

Performance

a) Test on experimental data

b) Test on synthetic data

Page 29: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Performance

• Fit of exemplary data sets for PTCDA / Ag(100):– C1s– O1s– Ag3s

• No weighting for reflectivity fit, instrumental weighting for XSW absorption profile fit (i.e. weighting coefficients gi = 1 / ( yi)2).

• Non-dipolar parameters are taken from theory.• Modification of the response function is NOT enabled during XSW profile fit.• BUT: apparent fit quality is significantly improved if response function parameters

(width wG, center xcG) are allowed to vary under the XSW profile fit.• Overview: Fit results in comparison to DARE (J. Zegenhagen, ESRF):

        DARE FitXSW

system Signal Q Delta CF Delta CF CP Delta CP CF Delta CF CP Delta CP

PTCDA /Ag(100)

C1s 0.275 -0.188  0.182 0.0354 0.575 0.0373 0.193 0.0356 0.557 0.0355

O1s 0.256 -0.251 0.245  0.0457 0.506 0.0378 0.255 0.0982 0.487 0.0368

Ag3s -0.019 -1.284 0.676 0.0010 0.029 0.0003 0.698 0.0010 0.043 0.0003

Page 30: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Performance

• Ag3s, PTCDA / Ag(100):

DARE vs. FitXSW

CF = 0.676, CP = 0.029 Version 2.0: CF = 0.698, CP = 0.043Version 1.0: CF = 0.705, CP = 0.040

Page 31: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Performance

• C1s, PTCDA / Ag(100):

DARE vs. FitXSW

CF = 0.182, CP = 0.575 Version 2.0: CF = 0.193, CP = 0.557Version 1.0: CF = 0.193, CP = 0.558

Page 32: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Performance

• O1s, PTCDA / Ag(100):

DARE vs. FitXSW

CF = 0.245, CP = 0.506 Version 2.0: CF = 0.255, CP = 0.487Version 1.0: CF = 0.255, CP = 0.487

Page 33: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Performance

• Fit of synthetic data sets for Ag(111):– 6 exemplary data sets were created by Giuseppe Mercurio with the EXCEL

simulation sheet written by Bruce Cowie.– Energy width: 3.76 eV, 52 points, energy stepsize: 0.074 eV.

(test with Jülich code v2.0 was done with 256 points, energy stepsize: 0.015 eV !)• No error weighting for reflectivity fit; also no error weighting for XSW absorption profile

fit in this case.• Non-dipolar parameters are chosen to be zero: Q = 0, = 0.• Modification of the response function is NOT enabled during XSW profile fit.• Overview: Fit results in comparison to simulation and Jülich code, version 2.0:

  simulation FitXSW v2.0 Jülich code v2.0

Data set CF CP CF CP CF CP

Test 1 0.5 0.5 0.513 0.496 0.530 0.482

Test 2 1.0 0.7 1.000 0.698 1.019 0.696

Test 3 0.3 0.7 0.300 0.696 0.286 0.687

Test 4 0.8 0.1 0.812 0.099 0.830 1.099

Test 5 0.8  0.8 0.809 0.799 0.817 0.799

Test 6 0.6 0.3 0.615 0.299 0.458 0.296

fit parameters in very nice agreement with simulation!

Page 34: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Performance

• Ag(111), Test 1:– Simulation: CF = 0.5 CP = 0.5– Fit: CF = 0.513 CP = 0.496

Page 35: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Performance

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

Page 36: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Performance

• Ag(111), Test 3:– Simulation: CF = 0.3 CP = 0.7– Fit: CF = 0.300 CP = 0.696

Page 37: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Performance

• Ag(111), Test 4:– Simulation: CF = 0.8 CP = 0.1– Fit: CF = 0.812 CP = 0.099

Page 38: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Performance

• Ag(111), Test 5:– Simulation: CF = 0.8 CP = 0.8– Fit: CF = 0.809 CP = 0.799

Page 39: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Performance

• Ag(111), Test 5:– Simulation: CF = 0.6 CP = 0.3– Fit: CF = 0.615 CP = 0.299

Page 40: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

CONCLUSION

Page 41: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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Conclusion

• FitXSW v2.0 employes the ORIGIN fitting engine NLSF for both, the reflectivity curve and the XSW absorption profile fit.

• FitXSW v2.0 provides convolution with a Gaussian as well as with the squared reflectivity of the monochromator.

• Upon test cases, FitXSW runs properly and gives reasonable results.• FitXSW v2.0 has been speed-up by about 30 % in comparison to FitXSW v1.0

(although another convolution is executed during the fits …).• The effect of the additional convolution with squared monochromator reflectivity on the

fit results is marginal as compared to the results of FitXSW v1.0.

Please report any bugs, remarks, critics etc. on SimXSW / FitXSW to:

[email protected]

Page 42: Oliver Bauer 1), Sergey Subach 2), Giuseppe Mercurio 2), Frank Stefan Tautz 2), Moritz Sokolowski 1) 1) Institute for Physical and Theoretical Chemistry,

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I am particularly grateful to…

• Prof. Dr. M. Sokolowski, Prof. Dr. F. S. Tautz, Dr. S. Subach and Giuseppe Mercurio for fruitful collaboration.

• Dr. C. Kumpf, I. Kröger and C. Stadler as well as Dr. Jörg Zegenhagen, Dr. Tien-Lin Lee and Dr.  Yanyu Mi for helpful discussions.

• DFG (trough SFB 624 and SFB 813) and ESRF.

Acknow-ledgement


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