Fitting Quadrupolar spectra of Glasses
Example :
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^{ 27}Al^{ }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.

^{27}Al 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 50715079 (2004)
Example :
27Al 1D Spectrum of Glass with AlO4/AlO5/AlO6 sites
^{27}Al 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 nonsmooth 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