Fitting Quadrupolar spectra of Glasses
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
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
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]
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 :
: vertical scaling factor
: Istotropic average value
CS : Full Width at Half Maximum of the isotropic chemical shift gaussian
: 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
: Peak value of the quadrupolar coupling of the Czjzek/GIM distribution
(proportional to sigma values reported latest versions >2008)
: 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
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)
27Al 1D Spectrum of Glass with AlO4/AlO5/AlO6 sites
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.
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