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Inorganic Materials

, Volume 54, Issue 15, pp 1477–1482 | Cite as

Restoration of Orientation Distribution Function Using Texture Components with Radial Normal Distributions

  • T. M. IvanovaEmail author
  • V. N. SerebryanyiEmail author
THE STUDY OF STRUCTURE AND PROPERTIES PHYSICAL METHODS FOR STUDY AND CONTROL
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Abstract

The methods for restoration of the orientation distribution function (ODF) from experimental pole figures have been compared for materials possessing a low symmetry of specimen (by example of the median section of the hot-pressed band from Mg–4.5% Nd magnesium alloy), namely, the method of texture components using radial normal distributions on SO(3) with different spreading and the method of superposition of a large number of normal distributions with equivalent small spreading. Both approaches have demonstrated similar ODFs. In this case, the former method, which is less sensitive to measurement errors of pole figures, is based on nonlinear optimization with a complex choice of initial approximations of the parameters of the model. The latter approach is more sensitive and easier to use.

Keywords:

orientation distribution function method of texture components method of superposition of a large number of radial normal distributions pole figure Mg–4.5% Nd magnesium alloy 

Notes

REFERENCES

  1. 1.
    Savelova, T.I., Ivanova, T.M., and Sypchenko, M.V., Metody resheniya nekorrektnykh zadach teksturnogo analiza i ikh prilozheniya (Methods of the Solution of Ill- Posed Problems of Texture Analysis and Their Applications), Moscow: Mosk. Inzh.-Fiz. Inst., 2012.Google Scholar
  2. 2.
    Savelova, T.I. and Ivanova, T.M., Methods of recovery of orientation distribution function by pole figures (a review), Zavod. Lab., Diagn. Mater., 2008, vol. 74, no. 7, pp. 25–33.Google Scholar
  3. 3.
    Ivanova, T.M. and Savelova, T.I., Robust method of approximating the orientation distribution function by canonical normal distributions, Phys. Met. Metallogr., 2006, vol. 101, no. 2, pp. 114–118.CrossRefGoogle Scholar
  4. 4.
    Kurtasov, S.F., Quantitative analysis of the texture of rolled materials cubic symmetry of crystal lattice, Zavod. Lab., Diagn. Mater., 2007, vol. 73, no. 7, pp. 41–44.Google Scholar
  5. 5.
    Serebryanyi, V.N. and Shamrai, V.F., The experimental study of the textured materials in the Laboratory of crystal and structure study of Baikov Institute of Metallurgy and Materials Science, Russian Academy of Sciences. Part II. The textures of materials from the magnesium alloys, Tsvetn. Met., 2011, no. 5, pp. 65–73.Google Scholar
  6. 6.
    Serebryany, V.N., Rokhlin, L.L., and Monina, A.N., Texture and anisotropy of mechanical properties of the magnesium alloy of Mg–Y–Gd–Zr system, Inorg. Mater.: Appl. Res., 2014, vol. 5, no. 2, pp. 116–123.CrossRefGoogle Scholar
  7. 7.
    Ivanova, T.M. and Serebryanyi, V.N., Recovery of orientation distribution function of MA2-1hp magnesium alloy exposed to equal-channel angular pressing, Inorg. Mater., 2016, vol. 52, no. 15, pp. 1472–1477.CrossRefGoogle Scholar
  8. 8.
    Serebryanyi, V.N., Kurtasov, S.F., and Litvinovich, M.A., Investigation of errors of ODF upon inverse of pole figures using statistical method of ridge estimates, Zavod. Lab., Diagn. Mater., 2007, vol. 73, no. 4, pp. 29–35.Google Scholar
  9. 9.
    Matthies, S., Wenk, H.R., and Vinel, G.W., Some basic concepts of texture analysis and comparison of three methods to calculate orientation distributions from pole figures, J. Appl. Cryst., 1988, vol. 21, pp. 285–304.CrossRefGoogle Scholar
  10. 10.
    Kahaner, D., Moler, C., and Nash, S., Numerical Methods and Software, NJ: Prentice-Hall, 1989.Google Scholar
  11. 11.
    Brandt, S., Data Analysis. Statistical and Computational Methods for Scientists and Engineers, New York: Springer-Verlag, 1999.Google Scholar
  12. 12.
    Bunge, H.J., Texture Analysis in Materials Sciences. Mathematical Methods, London: Butterworths, 1982.Google Scholar
  13. 13.
    Vasilenko, G.I., Teoriya vosstanovleniya signalov (The Theory of Signal Restoration), Moscow: Sovetskoe Radio, 1979.Google Scholar
  14. 14.
    Huang, T.S., Barker, D.A., and Berger, S.P., Iterative image restoration, Appl. Opt., 1975, vol. 14, no. 5, pp. 1165–1168.CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.National Research Nuclear University MEPhIMoscowRussia
  2. 2.Baikov Institute of Metallurgy and Materials Science, Russian Academy of SciencesMoscowRussia

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