Crystallography Reports

, Volume 63, Issue 6, pp 1051–1056 | Cite as

ASTRA 4.0 Program: Data Reduction for Obtaining Structure Results of Extreme Accuracy

  • A. P. DudkaEmail author


Unique methods for processing diffraction data, which guarantee extreme accuracy and reliability, have been implemented in the ASTRA 4.0 software package. The central (data-forming) element is a program for averaging intensities of repeated and equivalent reflections. The ASTRA averaging algorithm makes it possible to calculate the average intensity and its standard uncertainty, which correspond to normal distribution law for errors in data. Such data yield an unbiased estimate of the parameters of refined structural model at minimum reliability factors. To make the averaging program successfully operate, one must introduce all corrections for anisotropic effects into the reflection’s intensities. The following stages of investigation are considered: sample preparation; calibration of diffractometer; and correction for absorption, thermal diffuse scattering, and simultaneous reflections. A significant advantage of the proposed approaches is proven on several examples.



This study was supported by the Federal Agency for Scientific Organizations (contract no. 007-ГЗ/Ч3363/26) in the part of the development of algorithms and programming. Study of dodecaboride crystals and diffractometer calibration were supported by the Russian Foundation for Basic Research, project nos. 16-02-00171 and 17-53-45107, respectively. Some part of experimental data were measured using equipment of the Shared Research Center of the Federal Scientific Research Centre “Crystallography and Photonics” of the Russian Academy of Sciences.


  1. 1.
    M. Kendall and A. Stewart, The Advanced Theory of Statistics, Vol. 3, Design & Analysis, & Time-Series (Charles Griffin, London, 1968).Google Scholar
  2. 2.
    A. P. Dudka, Crystallogr. Rep. 47 (1), 152 (2002).ADSCrossRefGoogle Scholar
  3. 3.
    A. Dudka, J. Appl. Crystallogr. 40, 602 (2007).MathSciNetCrossRefGoogle Scholar
  4. 4.
    A. N. Tikhonov and V. Ya. Arsenin, Solutions of Ill-Posed Problems (Nauka, Moscow, 1979, 2nd ed.; Halsted Press, New York, 1977)Google Scholar
  5. 5.
    W. A. Paciorek, M. Meyer, and G. Chapuis, J. Appl. Crystallogr. 32, 11 (1999).CrossRefGoogle Scholar
  6. 6.
    J. W. Pflugrath, Acta Crystallogr. D 55, 1718 (1999).CrossRefGoogle Scholar
  7. 7.
    A. Dudka, J. Appl. Crystallogr. 43, 1440 (2010).CrossRefGoogle Scholar
  8. 8.
    A. P. Dudka, Crystallogr. Rep. 60 (4), 601 (2015).ADSCrossRefGoogle Scholar
  9. 9.
    A. P. Dudka, Crystallogr. Rep. 60 (6), 984 (2015).ADSCrossRefGoogle Scholar
  10. 10.
    A. P. Dudka and B. V. Mill’, Crystallogr. Rep. 56 (3), 443 (2011).ADSCrossRefGoogle Scholar
  11. 11.
    A. P. Dudka, A. M. Balbashov, and I. S. Lyubutin, Cryst. Growth Des. 16, 4943 (2016).CrossRefGoogle Scholar
  12. 12.
    A. P. Dudka, Crystallogr. Rep. 61 (2), 187 (2016).ADSCrossRefGoogle Scholar
  13. 13.
    T. K. Herman, S. C. Parks, and J. Scherschligt, J. Appl. Crystallogr. 46, 279 (2013).CrossRefGoogle Scholar
  14. 14.
    L. Ribaud, G. Wu, Yu. Zhang, and P. Coppens, J. Appl. Crystallogr. 34, 76 (2001).CrossRefGoogle Scholar
  15. 15.
    A. P. Dudka, I. A. Verin, and E. S. Smirnova, Crystallogr. Rep. 61 (4), 692 (2016).ADSCrossRefGoogle Scholar
  16. 16.
    B. T. M. Willis and A. W. Pryor, Thermal Vibrations in Crystallography (Cambridge Univ. Press, 1975).Google Scholar
  17. 17.
    X. Gonze, Phys. Rev. B 52, 1086 (2005).CrossRefGoogle Scholar
  18. 18.
    A. P. Dudka, M. Kh. Rabadanov, and A. A. Loshmanov, Kristallografiya 34 (4), 818 (1989).Google Scholar
  19. 19.
    A. P. Dudka, O. N. Khrykina, N. B. Bolotina, et al., J. Alloys Compd. 692, 535 (2017).CrossRefGoogle Scholar
  20. 20.
    R. H. Blessing, Acta Crystallogr. A 51, 33 (1995).CrossRefGoogle Scholar
  21. 21.
    A. P. Dudka, Crystallogr. Rep. 50 (6), 1068 (2005).ADSCrossRefGoogle Scholar
  22. 22.
    R. H. Blessing, Cryst. Rev. 1, 3 (1987).CrossRefGoogle Scholar
  23. 23.
    R. H. Blessing, J. Appl. Crystallogr. 30, 421 (1997).CrossRefGoogle Scholar
  24. 24.
    W. Härdle, Applied Nonparametric Regression (Cambridge Univ. Press, 1990).CrossRefzbMATHGoogle Scholar
  25. 25.
    S. C. Abrahams and E. T. Keve, Acta Crystallogr. A 27, 157 (1971).ADSCrossRefGoogle Scholar
  26. 26.
    M. Renninger, Z. Phys. 106, 141 (1937).ADSCrossRefGoogle Scholar
  27. 27.
    R. M. Moon and C. G. Shull, Acta Crystallogr. 17, 805 (1964).CrossRefGoogle Scholar
  28. 28.
    A. Dudka, J. Appl. Crystallogr. 43, 27 (2010).CrossRefGoogle Scholar
  29. 29.
    J. M. Zuo, P. Blaha, and K. Schwarz, J. Phys.: Condens. Matter 9, 7541 (1997).ADSGoogle Scholar

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© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Shubnikov Institute of Crystallography, Federal Scientific Research Centre “Crystallography and Photonics,” Russian Academy of SciencesMoscowRussia

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