Research Article | Open Access
Using Individual Spectra Simulation for the Study of Pole Figures Errors
Crystallographic texture is described by pole figures. In this paper, we continue to study experimental pole figure errors. In other words it can be named pole figure measurement errors. These errors are connected with the experimental procedure and do not depend on any further computations. In our previous works it was shown that the qualitative behaviour of pole figure measurement errors is similar to peak width determination errors. To check this conclusion a set of diffraction spectra were measured for Mg + 4.5%Al + 1%Zn sample on the spectrometer for quantitative texture analysis (SKAT) at FLNP, JINR, Dubna. Then we simulated the individual spectra and used these spectra for the pole figure extraction and the pole figure error determination. Such simulation enabled to confirm conclusions concerning the main role of the peak width determination error in the pole figure error. Additionally, we simulated individual spectra using model pole figures and extracted pole figures and pole figures errors from those spectra. For this case we also confirmed the same qualitative behaviour of pole figure measurement errors and peak width determination errors. The model pole figures were calculated on the basis of normal distributions.
- K. Ullemeyer, P. Spalthoff, J. Heinitz, N. N. Isakov, A. N. Nikitin, and K. Weber, “The SKat texture diffractometer at the pulsed reactor IBR-2 at Dubna: experimental layout and first measurements,” Nuclear Instruments and Methods in Physics Research A, vol. 412, no. 1, pp. 80–88, 1998.
- A. Mücklich and P. Klimanek, “Experimental errors in quantitative texture analysis from diffraction pole figures,” Materials Science Forum, vol. 157–162, pp. 275–286, 1994.
- V. V. Luzin and D. I. Nikolayev, “On the errors of the experimental pole figures,” Textures and Microstructures, vol. 25, no. 2–4, pp. 121–128, 1996.
- V. V. Luzin and D. Nikolayev, “The errors of pole figures measured by neutrons,” in Proceedings of the 11th International Conference on Texture of Materials (ICOTOM 11), pp. 140–145, International Academic Publishers, Xi'an, China, September 1996.
- V. V. Luzin, “Optimization of texture measurements. IV. The influence of the grain-size distribution on the quality of texture measurements,” Textures and Microstructures, vol. 31, no. 3, pp. 177–186, 1999.
- D. I. Nikolayev, T. A. Lychagina, A. V. Nikishin, and V. V. Yudin, “Study of error distribution in measured pole figures,” Solid State Phenomena, vol. 105, pp. 77–82, 2005.
- D. I. Nikolayev, T. A. Lychagina, A. V. Nikishin, and V. V. Yudin, “Investigation of measured pole figures errors,” Materials Science Forum, vol. 495–497, pp. 307–312, 2005.
- H. J. Bunge, Texture Analysis in Material Science, Butterworths, London , UK, 1982.
- S. Matthies, “On the reproducibility of the orientation distribution function of texture samples from pole figures (Ghost phenomena),” Physica Status Solidi B, vol. 92, no. 2, pp. K135–K138, 1979.
- S. R. Matthies, G. W. Vinel, and K. Helming, Standard Distributions in Texture Analysis, vol. 1, Akademie-Verlag, Berlin, Germany, 1987.
- M. Dahms and H. J. Bunge, “A positivity method for the determination of complete orientation distribution functions,” Textures and Microstructures, vol. 10, no. 1, pp. 21–35, 1988.
- M. Dahms and H. J. Bunge, “The iterative series-expansion method for quantitative texture analysis. I. General outline,” Journal of Applied Crystallography, vol. 22, no. 5, pp. 439–447, 1989.
- J. Imhof, “Texture analysis by iteration. II. Special cases of the general solution,” Physica Status Solidi B, vol. 120, no. 1, pp. 321–328, 1983.
- S. Matthies and G. Vinel, “On the reproduction of the orientation distribution function of texturized samples from reduced pole figures using the conception of a conditional ghost correction,” Physica Status Solidi B, vol. 112, no. 2, pp. K111–K114, 1982.
- K. Helming, Texturapproximation durch Modellkomponenten, Cuvillier, Göttingen, Germany, 1996.
- T. Eschner, Quantitative Texturanalyse durch Komponentenzerlegung von Beugungs-Polfiguren, dissertation, TU Bergakademie Freiberg, Göttingen, Germany, 1994.
- T. Eschner, “Generalized model function for quantitative texture analysis,” in Textures of Geological Materials, Proceedings of a Workshop, DGM Informationsgesellschaft, H. J. Bunge, S. Siegesmund, W. Skrotzki, and K. Weber, Eds., pp. 15–28, Oberursel, Germany, 1994.
- T. I. Savyolova, “Distribution function of grains with respect to polycrystal orientations and its. Gaussian approximation,” Zavodskaya Laboratoriya, vol. 50, no. 4, pp. 48–52, 1984 (Russian).
- K. G. van den Boogaart, R. Hielscher, J. Prestin, and H. Schaeben, “Kernel-based methods for inversion of the Radon transform on SO(3) and their applications to texture analysis,” Journal of Computational and Applied Mathematics, vol. 199, no. 1, pp. 122–140, 2007.
- R. Hielscher, The radon transform on the rotation group—inversion and application to texture analysis, Ph.D. thesis, TU Bergakademie Freiberg, Göttingen, Germany, 2007.
- P. H. Roberts and D. E. Winch, “On random rotation,” Advances in Applied Probability, vol. 16, no. 12, pp. 638–655, 1984.
- T. I. Bucharova, Izvestiya, Physics of the Solid Earth, vol. 6, pp. 59–67, 1993 (Russian).
- H. Schaeben and D. I. Nikolayev, “The central limit theorem in texture component fit methods,” Acta Applicandae Mathematicae, vol. 53, no. 1, pp. 59–87, 1998.
- S. Matthies, H. R. Wenk, and G. Vinel, “Some basic concepts of texture analysis and comparison of three methods to calculate orientation distributions from pole figures,” Journal of Applied Crystallography, vol. 21, no. 4, pp. 285–304, 1988.
- L. Lutterotti, S. Matthies, H.-R. Wenk, A. S. Schultz, and J. W. Richardson Jr., “Combined texture and structure analysis of deformed limestone from time-of-flight neutron diffraction spectra,” Journal of Applied Physics, vol. 81, no. 2, pp. 594–600, 1997.
- R. B. Von Dreele, “Quantitative texture analysis by Rietveld refinement,” Journal of Applied Crystallography, vol. 30, no. 4, pp. 517–525, 1997.
- S. Vogel, C. Hartig, L. Lutteroti, R. B. Von Dreele, H.-R. Wenk, and D. J. Williams, “Texture measurements using the new neutron diffractometer HIPPO and their analysis using the rietveld method,” Advance in X-Ray Analysis, vol. 47, pp. 431–436, 2004.
- S. Matthies, J. Pehl, H.-R. Wenk, L. Lutterotti, and S. C. Vogel, “Quantitative texture analysis with the HIPPO neutron TOF diffractometer,” Journal of Applied Crystallography, vol. 38, no. 3, pp. 462–475, 2005.
- S. Matthies, L. Lutterotti, K. Ullemeyer, and H. R. Wenk, “Texture analysis of quartzite by whole pattern deconvolution,” Textures and Microstructures, vol. 33, no. 1–4, pp. 139–149, 1999.
- K. Walther, J. Heinitz, K. Ullemeyer, M. Betzl, and H.-R. Wenk, “Time-of-flight texture analysis of limestone standard: dubna results,” Journal of Applied Crystallography, vol. 28, no. 5, pp. 503–507, 1995.
- C. G. Windsor, Pulsed Neutron Scattering, Taylor and Francis, London, UK, 1981.
- J. V. Bernier, M. P. Miller, and D. E. Boyce, “A novel optimization-based pole-figure inversion method: comparison with WIMV and maximum entropy methods,” Journal of Applied Crystallography, vol. 39, no. 5, pp. 697–713, 2006.
- E. Gill Philip, W. Murray, and M. Wright, Practical Optimization, Academic Press, New York, NY, USA, 1981.
- J. A. Nelder and R. Mead, “A simplex method for function minimization,” Computer Journal, vol. 7, no. 4, pp. 308–313, 1965.
- W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN. The art of Scientific Computing, Cambridge University Press, Cambridge, UK, 2nd edition, 1992.
- D. Nikolayev and K. Ullemeyer, “Note on preprocessing of diffraction pole-density data,” Journal of Applied Crystallography, vol. 27, no. 4, pp. 517–520, 1994.
- G. V. Vinel and S. Matthies, Communication of Zfk (Zenralinstitut fur Kernforschung Rossendorf bei Dresden), no. 391, 1979, Akademie der Wissenschaften der DDR.
Copyright © 2009 T. A. Lychagina et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.