Fitting Second order broadened Quadrupolar 1D spectrum...
With a distribution of Chemical Shift and Quadrupolar interaction

D.R. Neuville, L. Cormier, D. Massiot Geoch. Cosm. Acta 68 5071-5079 (2004)

 Example :  27Al 1D Spectrum of Glass with AlO4/AlO5/AlO6 sites  
References :

 Example :  27Al 1D Spectrum of Glass with AlO4/AlO5/AlO6 sites  

Step 1 : Follow explanation for fitting a  quadrupolar line shape... to position a second order broadened line-shape at the location of the distributed line.

Step 2 : Change Model to CzSimple, put d to 5, em to -200 (typical) and recompute the model spectrum.

  • Computation remains rapid until you put the FWHM CS value to non 0.

  • Adjust the em value to suppress spikes or wiggles

  • Optimise the physically relevant parameters : amplitude, Position, FWHM CS, nuQ

Step 3 : Reporting integrated intensities

  • The integrated intensities of the different lines cannot be computed analogically, go to the [Report] dialog and ask for the numerical integration.... Be very patient, this is a lengthy operation...

The "CZSimple" Model  :

The "CzSimple" model implements a rapid version of the Czjzek distribution of quadrupolar interaction for the distribution of the isotropic chemical shift (Gaussian Isotropic Model for d=5) with an uncoupled distribution of isotropic chemical shift. See our paper in Geochimica Acta or the following references for use of this model.

The CzSimple model takes the following parameters :

 Amplitude : vertical scaling factor
 Position : Istotropic average value
 FWHM CS : Full Width at Half Maximum of the isotropic chemical shift gaussian distribution.
 EM au : line broadening used to smooth the discontinuities issued from the sampling of nuQ/etaQ and diso, use she smallest possible value and do not allow optimisation. Take negative values for gaussian apodisation. This is just a cosmetic parameter.
 nuQ : Peak value of the quadrupolar coupling of the Czjzek/GIM distribution (proportional to sigma values reported latest versions >2008)
 d : critical exponent of the Czjzek distribution, take d=5 for GIM, other values do not have physical sense even if they give better rendering.