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!

Observed Specimen Instrument From Balzar (1993).  denotes a convolution A. THE PROFILES

1. Strain profile The peak shape is Gaussian (a specific shape from York’s model): H is full-width at half-maximum intensity and c =

2. Size profile involving size distribution parameter (  ) - derived using mean-field theory for normal and isotropic grain growth (York, 1999) Lognormal for small  and normal for large . For a size distribution function  :

Other types of (mathematical) functions  is mixing parameter, c=2.7724, and  denotes a convolution.

B. THE COMPILERS and LIBRARIES 1. Lahey ED4W Fortran Winteracter Starter Kit for Lahey Fortran Numerical Recipes in Fortran Numerical Recipes in Fortran 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 least- square calculation; - gaussj  matrix solution - covsrt  covariance matrix calculation - a function (Gaussian, as an example) - including its derivatives with respect to the refined parameters. (continued)

3. Pseudo-Voigt function is incorporated (simple and analytical) - also Lorentzian function 4. Incorporation of York-Gaussian function, i.e. the convoluted f strain  f size (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]

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 (continued)

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 York- Gaussian 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 instrument- specimen function - 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.

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