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documentation:fitting_maps [2011/10/17 18:40]
142.103.140.43
documentation:fitting_maps [2013/04/03 22:21] (current)
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 +====== Sample Characterization ====== ​
 +
 +{{ :​documentation:​sample.png?​direct&​ |}}
 +
 +PNO: PrNiO<​sub>​3</​sub>​ \\
 +LSAT: 0.29(LaAlO<​sub>​3</​sub>​):​ 0.35(Sr<​sub>​2</​sub>​AlTaO<​sub>​6</​sub>​) (3.8735 Angstrom unit cell)
 +((La<​sub>​0.3</​sub>​Sr<​sub>​0.7</​sub>​Al<​sub>​0.65</​sub>​Ta<​sub>​0.35</​sub>​O<​sub>​3</​sub>​))
 +\\
 +
 +Interesting peaks: \\
 +
 +substrate: \\
 +La M5: 836 eV\\
 +La M4: 853 eV\\
 +\\
 +film:  \\
 +Ni L3: 852.7 eV\\
 +Ni L2: 870.0 eV\\
 +
 +
 +====== Optical Constants ====== ​
 +
 +The TEY signals were fitted to chantler tables by the formula
 +
 +beta(e) = alpha * TEY(e) / e + gamma + delta*e
 +
 +e: energy \\
 +beta: imagninary part of the optical constant n as function of energy \\
 +TEY: measured TEY signal as function of energy \\
 +alpha, gamma, delta: fit parameters \\
 +
 +== PNO ==
 +
 +{{ :​documentation:​pno.png?​direct&​ |}}
 +
 +== LSAT ==
 +The TEY signal from a LAO film was measured and fitted. (no LSAT TEY data measured)
 +{{ :​documentation:​lsat.png?​direct&​ |}}
 +
 +====== Reflectivities ======
 +
 +At the REIXS beamline reflectivities,​ energy scans (const qz), and reflectity maps were measured. ​
 +Putting all valid points together one can create a unsorted list
 +
 +<​file>​
 +#energy qz                      Reflectivity ​           polarization
 +800 0.143709769837871 8.0612174367649  ​       v
 +801 0.143709858415225 8.05128038331844 v
 +802 0.143711236888019 8.03961449049679 v
 +803 0.143710416540384 8.03067803567478 v
 +.
 +.
 +.
 +856.6 0.213303345314291 0.630505341022796 h
 +856.7 0.213302538170217 0.625630243774844 h
 +856.8 0.213303561368094 0.618766907338261 h
 +.
 +.
 +.
 +870.5 0.172127894406649 5.64570582534484 h
 +870.5 0.175902024999232 6.58121875884301 h
 +870.5 0.17967280667221 7.14328792593677 h
 +.
 +.
 +.
 +</​file>​
 +
 +Writing a program to sort the data one can end up with very many reflectivies or escans
 +== Reflectivities for both polarizations==
 +{{ :​documentation:​all_reflectivities.gif?​direct&​ |}}
 +== Energy scans for both polarizations==
 +{{ :​documentation:​all_escan.gif?​direct&​ |}}
 +
 +== Energy scans on Ni (pi correction)==
 +To show the asymmetry between sigma and pi polarization one can multiply the pi-polarization by <m> cos(2theta)^2 </m>
 +{{ :​documentation:​all_escan_corrected.gif?​direct&​ |}}
 +
 +
 +====== Fitting: An overview ======
 +
 +Each of the reflectivities were fitted independently. The fit procedure was done with the simplex algorithm ​
 +up to 500 iterations. For delta and beta, the tabulated values were taken.
 +
 +
 +
 +==== Fitting thickness, interface roughness, surface roughness and multiplicator together ====
 +
 +== Thickness ==
 +{{ :​documentation:​fit_thickness.png?​direct&​ |}}
 +  - thickness around 90 to 100 Angstrom
 +  - off resonant: thickness is constant (98 Angstrom)
 +  - off resonant: thicker film of around 1 Angstrom for pi polarization
 +  - La M5: left side of peak reduced thickness, right Ok
 +  - La M4: left side of peak reduced thickness, right seems Ok
 +  - Ni L3: reduced thickness, strong polarization dependent (vice versa to off-resonant)
 +  - Ni L2: reduced thickness
 +
 +== Multiplicator ==
 +{{ :​documentation:​fit_multiplicator.png?​direct&​ |}}
 +  - off resonant: factor around 3e-5
 +  - strong influence on the number of points (peaks and noise effects). => Muliplicator can have a large error.
 +  - almost a factor of 5 difference between off and on resonance
 +
 +== Interface roughness ==
 +{{ :​documentation:​fit_sigma1.png?​direct&​ |}}
 +  - roughness varies between 0 and 10 Angstrom. ​
 +  - off resonance: not constant
 +  - off resonance: increasing with higher energy
 +  - on resonance: sigma is often zero. 
 +  - depends on the number of points +- 2 Angstrom  ​
 +
 +== Surface roughness ==
 +{{ :​documentation:​fit_sigma2.png?​direct&​ |}}
 +  - off resonance: surface roughness around 3-5 Angstrom
 +  - on resonance: roughness can drop to zero
 +  - depends on the number of points +- 1 Angstrom
 +
 +
 +== Error of fit ==
 +{{ :​documentation:​fit_error2.png?​direct&​ |}}
 +  - error is small off resonance, large on resonance
 +
 +
 +====== Fitting: Refining ======
 +
 +  - Set multiplicator. This must be constant in that range. Off resonant fit very well, so choose 3e-5 as multiplicator.
 +  - set maximum roughness of the surface to 7 Angstrom
 +
 +==== Fitting thickness, interface roughness, surface roughness together ====
 +
 +This gives almost the same results as the first fit. But the error changes especially on resonant on the La-edges,.
 +
 +{{ :​documentation:​fit2_refl.png?​direct&​ |}}
 +
 +  - the top two curves are the measurement,​ the bottom two curves are the fit.
 +
 +
 +====== Fitting: Optical constants ======
 +
 +  - Fixed thickness to 98.5 Angstrom
 +  - Fit delta and beta of substrate independently ( no Kramers-Kronig relation)
 +
 +==== Fitting interface roughness, surface roughness and delta, beta of LSAT ====
 +
 +
 +== delta and beta ==
 +{{ :​documentation:​fit_delta_substrate.png?​direct&​ |}}
 +{{ :​documentation:​fit_beta_substrate.png?​direct&​ |}}
 +
 +  - huge underestimate of the size of peaks. (The La peak of LAO is not really a good replacement)
 +  - almost no difference between sigma and pi
 +  - off resonant fits very well with chantler tables ​
 +
 +
 +==== Apply Kramers-Kronig ====
 +
 +  - Because of the disturbance of the Ni L3 edge  one has to fit a lorentzian to the La M4 edge and take this values for the higher energies (850-860 eV).
 +
 +== Fit Lorentzian to the M4 peak ==
 +{{ :​documentation:​kk_fit_lorentz.png?​direct&​ |}}
 +
 +
 +
 +  - take the new values for delta and beta and put them to chantler. ​
 +  - calculate Kramers-Kronig ​  ​beta->​delta and delta->​beta
  
documentation/fitting_maps.txt ยท Last modified: 2013/04/03 22:21 (external edit)