====== 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