BGMN Models

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This page explains some of the special features in the BGMN software.

Peak model

Base of the BGMN program is the modelling of the peak profiles (fig. 1) by a deconvolution of wavelength distribution, instrumental profile and real structure profile (crystallite size and micro strain broadening, see fig. 1). For this purpose, the instrumental part of the profile can be simulated at different angular points 2T in accordance with the geometrical conditions by using a raytracing algorithm. Some examples of resulting instrumental profiles which can not be fitted by simple asymmetric functions like Pearson VII, are presented here. In BGMN this complex profiles are described by a number of Lorentzian functions (fig. 1). The parameters of these functions are interpolated over the whole angular range. These profiles are convolutable with wavelength distribution (experimentally determined, also described by sum of 4 Lorentzian functions) and the sample profiles to be determined.

peakmodel.gif
Fig. 1: Peak model in the BGMN program

Numerical algorithm

A special optimization algorithm permits the use of fixed upper and lower limits for the most parameters so that physically meaningless values can be prevented.

Modeling of preferred orientation

As preferred orientation models available, spherical harmonics of even order which can also describe multiple preferred orientation depending on Laue group with up to 66 parameters stand in addition to a simple ellipsoidal model. The determined PO correction factor is reported for every reflection. In that way it is possible to evaluate the success and meaning of the texture correction.

Anisotropic peak broadening

Crystallite size and micro strain broadening can be refined by anisotropic models in a simple manner. The program determines automatically the main axes of the broadening ellipsoides according to the symmetry of the Laue group.

Automatic refinement

It is the most important program feature that there is no necessity for controlling the refinement strategy by the user. All parameters to be refined can be unlocked in the starting model, any storing and managing of intermediate stages of refinement is needless. A solution will be always found without intervention of the user. The error calculation for the parameters and possible shift of a parameter to a limit defined in the starting model do allow a judgement whether the starting model was sufficient or not.

Reference

  1. J. Bergmann
    Beiträge zur Auswertung und Versuchsplanung in der Röntgenpulverdiffraktometrie
    (contributions to evaluation and experimental design in the fields of X-ray powder diffractometry)
    PhD thesis (in german), Dresden University of Technology 1984

  2. G. Querner, J. Bergmann, W. Blau
    A method for data reduction and optimal experimental design in XPD
    proceedings of the 1st European Conference on Powder Diffraction (EPDIC 1)
    Materials Science Forum 79–82 (1991) part 1 pp. 107–112

  3. J. Bergmann, R. Kleeberg, and T. Taut
    A new structure refinement and quantitative phase analysis method basing on predetermined true peak profiles
    Z. Kristallogr., Supplement issue No. 8, Europ. Cryst. Meeting 15 (1994), Book of Abstracts p. 580

  4. T. Taut, J. Bergmann, G. Schreiber, A. Börner, E. Müller
    Application of a New Rietveld Software for Quantitative Phase Analysis and Lattice Parameter Determination of AlN-SiC-Ceramics
    proceedings of the 4th European Conference on Powder Diffraction (EPDIC 4) held in Chester, UK, 1995
    Materials Science Forum 228–231 (1996) part 1 pp. 177–182

  5. J. Bergmann, D. Jehnichen, J. Tobisch, P. Friedel, M. Rillich, T. Taut
    Powder diffraction investigations on molecular ring system cyclo-tri(2,6-pyridyl formamidine)
    proceedings of the 4th European Conference on Powder Diffraction (EPDIC 4) held in Chester, UK, 1995
    Materials Science Forum 228–231 (1996) part 2 pp. 869–872

  6. R. Kleeberg, J. Bergmann
    Quantitative Röntgenphasenanalyse an schichtsilikathaltigen Gesteinen mit der RIETVELD-Methode — Probleme, Erfolge, Grenzen.
    Berichte der Deutschen Ton- und Tonmineralgruppe e.V. 4 (1997) pp. 127–137

  7. D. Jehnichen, P. Friedel, J. Bergmann, T. Taut, and D. Pospiech
    W.A.X.S. and force field RIETVELD modelling of meta-linked fully aromatic copolyesters: 1. poly(p-phenylene isophtalate).
    Polymer 39 (1998) pp. 1095–1102

  8. J. Bergmann, R. Kleeberg, and T. Taut
    Quantitative Phase Analysis Using a New Rietveld Algorithm — Assisted by Improved Stability and Convergence Behavior
    Poster at the 45th annual X-Ray conference in Denver 1996
    Advances in X-Ray Analysis, 40 (1998), 425 (published on CD-ROM)

  9. J. Bergmann and R. Kleeberg
    Rietveld analysis of disordered layer silicates
    Oral presentation at EPDIC 5
    proceedings of the 5th European Conference on Powder Diffraction (EPDIC 5) held in Parma, Italy, May 24–28, 1997
    Materials Science Forum, 278–281 (1998) part 1 pp. 300–305

  10. P. Friedel, D. Jehnichen, J. Bergmann, T. Taut, and A. Haase
    Application of Rietveld Refinement combined with Force Field Energy Minimization to Structure Investigations of Cyclo-tris-(2,6-pyridyl formamidine)
    Oral presentation at the 41th annual X-Ray conference in Denver 1997
    Advances in X-Ray Analysis, 41 (1999), pp. 593–600 (published on CD-ROM)

  11. R. Kleeberg, J. Bergmann
    Quantifizierung von fehlgeordneten Schichtsilikaten mit der Rietveld-Methode
    Berichte der Deutschen Ton- und Tonmineralgruppe e.V. 5 (1997) pp. 35–44

  12. T. Taut, R. Kleeberg, J. Bergmann
    The new Seifert Rietveld Program and its Application to Quantitative Phase Analysis
    Proceedings of the XVII Conference on Applied Crystallography,
    Wisla, Poland, Aug 31–Sep 4 1997
    Editors: Henryk Morawiec & Danuta Stroz
    World Scientific Singapore, New Yersey, London, Hong Kong 1998, 87–92

  13. P. Friedel, J. Tobisch, D. Jehnichen, J. Bergmann, T. Taut, M. Rillich, C. Kunert, F. Böhme
    Structure investigations of molecular crystals containing the ring system cyclo-tris(2,6-pyridyl formamidine) by means of XPD and force field constrained Rietveld refinement
    J. Appl. Cryst. 31 (1998), p. 874

  14. T. Taut, R. Kleeberg und J. Bergmann
    Vollautomatische Rietveld-Phasenanalyse mit dem Programm BGMN
    Poster, 6. Jahrestagung der Deutschen Gesellschaft für Kristallographie
    Z. Kristallog., Suppl. Issue No. 15 (1998) p. 153

  15. A. Herold, R. Kleeberg, J. Bergmann
    Vollautomatische Rietveld-Phasenanalyse mit dem Programm BGMN
    3. Symposium Technische und Angewandte Mineralogie 14.–16. Juni 1998 Halle (Saale)
    Institut für Geologische Wissenschaften und Geiseltalmuseum, Martin-Luther-Universität Halle/Wittenberg

  16. Jörg Bergmann, Peter Friedel & Reinhard Kleeberg
    BGMN — a new fundamental parameters based Rietveld program for laboratory X-ray sources, it's use in quantitative analysis and structure investigations
    CPD Newsletter No. 20, Summer 1998, pp. 5–8
    Commission of Powder Diffraction, International Union of Crystallography

  17. T. Taut, R. Kleeberg, J. Bergmann
    The new Seifert Rietveld program BGMN and its application to quantitative phase analysis
    Materials Science (Bulletin of the Czech and Slovak Crystallographic Association) 5 (1998) pp. 55–64

  18. R. Kleeberg, J. Bergmann
    Quantitative Röntgenphasenanalyse mit den Rietveldprogrammen BGMN und AUTOQUANT in der täglichen Laborpraxis
    Berichte der Deutschen Ton- und Tonmineralgruppe e.V. 6 (1998) pp. 237–250

  19. J. Bergmann, P. Friedel, R. Kleeberg
    Handling of unusual instrumental profiles by the BGMN Rietveld program
    Proceedings of the 6th European Conference on Powder Diffraction (EPDIC6)
    held in Budapest, Hungary, August 22–25, 1998.
    Materials Science Forum 321–324 (1999), pp. 192–197

  20. P. Friedel, J. Bergmann
    Molecular Modelling Features in XPD Rietveld Refinement of Organic Structures
    Proceedings of the 6th European Conference on Powder Diffraction (EPDIC 6)
    held in Budapest, Hungary, August 22–25, 1998.
    Materials Science Forum 321–324 (1999) pp. 34–39

  21. J. Bergmann, R. Kleeberg
    Standardfreie Size/Strain-Bestimmung mit dem Rietveld-Programm BGMN
    Poster, 7. Jahrestagung der Deutschen Gesellschaft für Kristallographie
    Z. Kristallogr., Suppl. Issue No. 16 (1999) p. 133

  22. J. Bergmann, R. Kleeberg
    EFLECH/INDEX — a program pair for peak search/fit and indexing
    CPD Newsletter No. 21, May 1999, p. 5
    Commission of Powder Diffraction, International Union of Crystallography

  23. T. Monecke, R. Kleeberg, P. Herzig, J. Bergmann, B. Gemmell
    Applications of quantitative X-ray diffraction analysis by the Rietveld method
    Proceedings of the fifth biennal SGA meeting and the tenth quadrennial IAGOD symposium, London, UK, Aug 22–25 1999
    published in: Mineral Deposits: Processes to Processing
    edited by C.J. Stanley et al.
    A.A. Balkema, Rotterdam & Brookfield 1999

  24. P. Friedel, J. Bergmann, T. Taut, J. Tobisch, D. Pospiech, D. Jehnichen
    Wide angle X-ray diffraction and force field constrained Rietveld modelling of m-linked fully aromatic copolyesters. 2. Poly(p-phenylene Terephthalate-co-p-phenylene isophthalate)
    Polymer 41 (2000) pp. 3791–3795

  25. J. Bergmann, R. Kleeberg
    Fundamental parameters versus learnt profiles im Rietveld-Programm BGMN
    Poster, 8. Jahrestagung der Deutschen Gesellschaft für Kristallographie
    Z. Kristallog., Suppl. Issue No. 17 (2000) p. 96

  26. P. Friedel, D. Pospiech, D. Jehnichen, J. Bergmann, C.K. Ober
    Polyesters with semifluorinated side chains: a proposal for the solid state structure
    J. Polym. Sci. Part B: Polym. Phys. 38 (2000) pp. 1617–1625

  27. J. Bergmann, R. Kleeberg, A. Haase, B. Breidenstein
    Advanced Fundamental Parameters Model for Improved Profile Analysis
    Proceedings of the 5th European Conference on Residual Stresses, Delft–Noordwijkerhout, The Netherlands, Sep 29–30 1999.
    Materials Science Forum 347–349 (2000) pp. 303–308

  28. J. Bergmann, R. Kleeberg
    Improved Size/Strain Accuracy/Detection limits by Advanced Fundamentals Method — A contribution to Line Profile Analysis and Rietveld Method: Crossing Paths?
    CPD Newsletter No. 23, July 2000, p. 5
    Commission of Powder Diffraction, International Union of Crystallography

  29. J. Bergmann, T. Monecke, R. Kleeberg
    Alternative algorithm for the correction of preferred orientation in Rietveld analysis
    J. Appl. Cryst. 34 (2001) pp. 16–19

  30. J. Bergmann, R. Kleeberg
    Improving the Accuracy of Size/Micro Strain Estimation by First Principles Monte Carlo Raytracing Fundamental Parameter Profiles
    unpublished

  31. B. Peplinski, R. Kleeberg, J. Bergmann, J. Wenzel
    Quantitative Phase Analysis Using the Rietveld Method — Estimates of Possible Problems Based on Two Interlaboratory Comparisons
    Materials Sience Forum 443–444 (2004) pp. 45–50

  32. K. Ufer, G. Roth, R. Kleeberg, H. Stanjek, R. Dohrmann, J. Bergmann
    Description of X-ray powder pattern of turbostratically disordered layer structures with a Rietveld compatible approach
    Z. Kristallogr. 219 (2004) pp. 519–527

  33. R. Kleeberg, K. Ufer, J. Bergmann
    The quantification of disordered clay minerals by the Rietveld method — some practical aspects. (2,6 MByte)
    Presentation at the 42nd Annual Meeting of the Clay Minerals Society, June 11–15, 2005, Burlington/Vermont

  34. J. Bergmann
    EFLECH/INDEX — Another try of whole pattern indexing
    poster at EPDIC 10, Geneve, Sep 2–4 2006
    Z. Kristallogr. Suppl 26 (2007) pp. 197–202

  35. K. Ufer, R. Kleeberg, J. Bergmann, H. Curtius, R. Dohrmann
    Refining real structure parameters of disordered layer structures within the Rietveld method
    Z. Kristallogr. Suppl. 27 (2008) pp. 151–158

  36. R. Kleeberg, K. Ufer
    Workshop "Rietveld analysis with BGMN" as held in Freiberg/Germany, Mar 25-26 2010
    Transparencies,
    comments to the exercises,
    exercises for Windows,
    exercises for Linux/Mac.
    Attention PowerMac-Users: you must regenerate all the *.geq files by calling MAKEGEQ on the appropriate *.sav files.