Transcript MOZAIX

Development of
MOZAIX
A Peak Profiling Software
Suminar Pratapa*
Materials Research Group Seminar
Curtin University of Technology
19 April 2002
* Currently on leave from Physics Department, Institute of Technology 10 November,
Surabaya, Indonesia
Outline
1. Introduction to Peak Profiling
2. Why MOZAIX?
3. Modelling and Programming
4. Structure of the Least-square Calculation
5. Structure of the GUI and LSq Calculation
6. Demonstration
7. Conclusion and Further Work
Peak profiling is a method to extract information from
a (single diffraction) peak by fitting a model to the
observed peak.
Traditionally, peak profiling is conducted using
mathematically-based formula, such as Gaussian, Cauchy
(Lorentzian), Voigt, pseudo-Voigt, or Pearson-VII (Young
and Wiles 1982).
Peak profiling using these function can be done using
commercial softwares such as SHADOW, TOPAS, etc.
MOZAIX is a peak profiling software for powder
diffraction data which is being developed for strain-size
evaluation by employing the physically-derived
expressions for strain and size profiles (York, 1999).
The new strain-size profile, namely the York-Gaussian
function, takes into account the full-width at half-maxima
(FWHMs) of the strain and size broadening as well as the
size distribution parameter. The latter is a controversial
regarding its incorporation in the peak profiling
procedures (see e.g. Langford et al., 2000) and is not
embraced in the mathematically-based functions.
(things behind the name)
1. Diffraction from mosaic blocks (Klug and Alexander)
2. ‘X’ to attrack people, particularly who use X-ray
diffraction data
3. I like it!
A. THE PROFILES
From Balzar (1993).
Observed
Specimen
Instrument
h(2 )       f 2   Bkg
 denotes a convolution
1. Strain profile
The peak shape is Gaussian (a specific shape from York’s
model):
f strain  f 0 e
 2  2 0
 c .
 H stra in




2
H is full-width at half-maximum intensity and c = 2.7724.
2. Size profile involving size distribution parameter () derived using mean-field theory for normal and isotropic
grain growth (York, 1999)
f0
f size 
  2
1  
  
 1
 2  2 0

 H size



2
 2


For a size distribution function :

 (u )  u e
 u
Lognormal for small  and
normal for large .
Other types of (mathematical) functions
f Gaussian  f 0 e
f Lorentzian 
 2  2 0
 c .
 H

2



f0
 2  2 0 
1  4

H


2
f pseudoVoigt    f Lorentzian  (1   )  f Gaussian
f Voigt  f Lorentzian  f Gaussian
 is mixing parameter, c=2.7724, and  denotes a convolution.
(continued)
B. THE COMPILERS and LIBRARIES
1. Lahey ED4W Fortran 95
2. Winteracter Starter Kit for Lahey Fortran 95
3. Numerical Recipes in Fortran 77
4. Numerical Recipes in Fortran 90
5. IMSL Fortran 90 Library
(all were available from Dr. Craig Buckley)
(continued)
C. STRUCTURE OF THE CALCULATIONS
1. Initially from modules and subroutines provided in the
Numerical Recipes books.
2. Original subroutines (run under DOS):
- mrqmin  Marquardt-Levenberg method for leastsquare calculation;
- gaussj  matrix solution
- covsrt  covariance matrix calculation
- a function (Gaussian, as an example) - including its
derivatives with respect to the refined parameters.
3. Pseudo-Voigt function is incorporated (simple and
analytical) - also Lorentzian function
4. Incorporation of York-Gaussian function, i.e. the
convoluted fstrain fsize (now include the convlv subroutine)
5. Incorporation of instrument profile on the refinement.
6. Calculation of uncertainties, figure-of-merits and
covariance matrix.
[run under DOS]
(continued)
D. STRUCTURE OF THE GRAPHICAL USER
INTERFACE (GUI) and THE CALCULATION
1. Initially from modules and subroutines provided in the
Winteracter Starter Kit.
2. Original subroutines:
- for plotting a simple graph
- for selecting options with radio buttons
- for making child windows and dialog boxes
3. Also available in Winteracter:
- Dialog Resource Editor
- Menu Resource Editor
4. Incorporation of the least-square calculation on the GUI
codes  dynamic display of the refinement.
5. Plot of the size distribution profile.
6. Report and save-on-disk the refined parameters, the
figure-of-merits of the refinement, the correlation matrix
between parameters and the output plot data.
- peak profile simulation using pseudo-Voigt or YorkGaussian functions
- peak profile refinement using Gaussian, Lorentzian,
pseudo-Voigt, Voigt or York-Gaussian functions
- displaying the size distribution plot after refinement using
York-Gaussian function
- peak profile refinement using the convoluted instrumentspecimen function
- report and save-on-disk the refined parameters, the figureof-merits of the refinement, the correlation matrix between
parameters and the output plot data.
1. Development of the home-made MOZAIX software is
being conducted and the progress so far includes the
least-square refinement using York-Gaussian function.
Further development is required prior to implementation.
2. Basic features for peak profiling have been covered in the
software.
3. The software has a GUI appearance makes it possible to
show the dynamic refinement.
4. Consistent results were obtained for the simulated data.
1. Implementation of the software for neutron and
synchrotron data.
2. Further development for strain profiles.
3. Development and implementation for data from
anisotropic materials.
4. Publications: modelling and simulation,
implementation to diffraction data and about the
software.
Acknowledgement
1. AusAID - for providing PhD scholarship
2. Prof Brian O’Connor - as supervisor
3. Dr Craig Buckley - as associate supervisor