Fitting Quadrupolar spectra of Glasses

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 :

The spectrum of a quadrupolar nucleus in a disordered solid involves :

 Distribution of isotropic chemical shift (characterized by FWHM CS)
 Distribution of quadrupolar interaction leading to distribution of 2nd order shift and shape (characterized by its average quadrupolar coupling nuQ and a critical exponent d).

The Czjzek distribution and its d=5 Gaussian Isotropic Model (GIM) case are defined as follows :

    the probability P of a nuQ/etaQ pair is given by the formula below where from two parameters : sigma and d. Sigma is related to the intensity of the quadrupolar coupling and d is a critical exponent typically 3<=d<=5.

The Gaussian Isotropic Model (GIM, d=5), discussed by Le Caer and coworkers correspond to a statistical distribution of charges around the observed nucleus and accounts very well for 27Al spectra of glasses.

Important remark : Sigma hardly makes sense in terms of quadrupolar coupling and we use a modified version of the Czjzek expression where the nuQ parameter displayed in dmfit is the average quadrupolar coupling over the P probability.

Main reference [Geochimica Acta 2004] or the following references for use of this model

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.

27Al GIM distributions of quadrupolar interaction
Example Files...
D.R. Neuville, L. Cormier, D. Massiot 'Al environment in tectosilicate and peraluminous glasses: a NMR, Raman and XANES investigation'
Geochimica Cosmochimica Acta 68 5071-5079 (2004)

 Example :  27Al 1D Spectrum of Glass with AlO4/AlO5/AlO6 sites  
27Al GIM distributions of quadrupolar interaction

First become familiar with the fit of a quadrupolar line shape...

Important parameters to be checked before beginning :

[Menu/Models/Compute Param] or [Menu/Decomposition/Compute Param]
    Size of computed spectrum : good rendering for 2048, better with 8192 is the prefered value
    Number of steps for a_b (integration of powder pattern) : do not go to less than 32, 64 is the prefered value.

[Menu/Models/Disperse Param]
    Step CSA : step for sampling isotropic CSA distribution for Amorphous model : typically 50, depending on apodization factor, see below (lowering this number yields quicker computation but can introduce non-smooth model.
    Step nuQ : step for sampling gaussian distribution of Quadrupolar interaction in Amorphous or int2Q typically 21 give decent results depending upon the final apodization factor (see below)
    Sw mult : sweep width multiplier should be set to 4 in principle

The exemple files have been computed using the above mentioned typical values