Topas course

3 types of fitting

  • Peak fitting (individual peaks)
  • Structure-less fitting (Pawley fitting, from space group)
  • Ritveld fitting, from crystal structure and composition.

These can be used together in TOPAS

Least squares fitting

  • \(R_{wp} = \frac{\Sigma_i}{}\)

  • Are you overfitting your data?

  • Balance of observables vs variables

  • Chi\(^2\), (\(\chi\)) (GOF in TOPAS)

  • \(\chi^2 = [\frac{R_{wp}}{R_E}]^{1/2}\)

  • R\(_E\) is the expected R-factor

    • Basically the best fit the data statistics can support

  • Visual inspection of fit and variables is important

    • Many variables can correlate - watch for this
    • Look for the software doing stupid things
      • e.g. fitting background into broad peaks

Full pattern fitting

  • Link the peaks using some crystallographic knowlende

Rietveld fitting

  • Data quality determines analysis limitations
    • Sample prep is important (Flat surface, enough material)
    • Choise of divergence slits (all X-ray beams must hit sample at all angles if not: can makes some peaks larger or smaller)
    • Wider collection windows (up to at least 90 deg 2-theta for most samples)
    • Choose step-size to properly describe peak shapes
    • Rotation of samples on Si-holders: Take 20x1h scans in stead of 1x20h scan
    • Longer collection times -> lower noise
    • Capillary measurements can be an advantage, especially when preferred orientation is possible. This eliminates sample height errors as well.
  • Pitfalls:
    • Preferred orientations: Random orientation is assumed for powder diffraction.
    • Can be avoided by:
      • capillaries (spinning it)
      • roughened sample holder (or grease method with powder sprinkle)
    • Peaks and valleys, just ensure flat top of sample.

Quantitative Phase Analysis

  • \(w_i = \frac{s_i \cdot V_i \cdot M_i \cdot Z_i}{\Sigma_{j=1}^n s_j \cdot V_j \cdot M_j \cdot Z_j}\)
  • s is the scale factor of the phase
  • V is the volume of unit cell
  • M is the mass of one formula unit
  • Z is the number of formula units
  • Need to know the correct composition
  • Amorphous phases of you material can throw off the results.

Settings

LP factor

  • Only needs to be used when ??

Fundamental parameters (FP)

  • Used to tell topas about the instrument
  • Instrument
    • Primary/secondary radius
    • Linear PSD
      • Angular range = 4.1deg (for Lynxeye detector)
      • FDS Angle = 0.1 (for 0.2mm slit)
    • Full axial model
      • Source length = 12
      • Sample Length = 15
      • RS Length = 12
      • Primary/secondary soller slits = 2.5

L often means Lorentian type peak G often mean Gaussian type peak Lvol-IB is easiest/best for finding crystallite sizes. LVol-FWHM is basically Scherrer equation., which isnt as nice because it has a k-factor which can be different for people, making Scherrer sizes almost pointless in the litterature. Standard k-value is 0.89, but not all use it.

Judging fit

  • Tricky
  • R_wp-dash is better than R_wp
    • -dash does not include contribution from background fitting. Makes huge meaning when you have low signal-to noise ratio. You can spend many parametres doing the fitting of the background, while the peak fitting is bad. R_wp-dash ignores background fitting and is therefore better.

Capillaries

  • Glass can give broad background peak at around 30\(^\circ\) 2 \(\theta\) which can be solved by just fitting a single phase with really small (2nm) crystallite size to. By fitting and locking that peak you can better refine other parameters more directly connected to your crystal.
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