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--- documentation:fitting_maps [2011/10/13 02:28] – 142.103.140.43
+++ documentation:fitting_maps [2013/04/03 22:21] (current) – external edit 127.0.0.1
@@ Line 1: / Line 1: @@
+====== 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
+	0.143709769837871	8.0612174367649	        v
+	0.143709858415225	8.05128038331844	v
+	0.143711236888019	8.03961449049679	v
+	0.143710416540384	8.03067803567478	v
+.
+.
+.
+.6	0.213303345314291	0.630505341022796	h
+.7	0.213302538170217	0.625630243774844	h
+.8	0.213303561368094	0.618766907338261	h
+.
+.
+.
+.5	0.172127894406649	5.64570582534484	h
+.5	0.175902024999232	6.58121875884301	h
+.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