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Crystallography in Russia

Computational mathematics and cybernetics at Moscow State University

Since the 1950s, research on the development of numerical methods and software for defining the structure of materials based on the data from diffraction experiments have been performed in the Inverse Problems Laboratory in the Computational Mathematics and Cybernetics Dept. of Moscow Statue University. Boris Shchedrin is head of the laboratory.

Within the last decade basic scientific efforts have concentrated on the following topics: the phase analysis of polycrystals; the numerical solution of autocorrelation functions; processing and interpretation of reflectometric data from thin multilayer organic films; and the development of numerical methods for interpretation of diffuse scattering from crystals with nanostructure inclusions.

The basic results are:

- Estimates of the agreement between spectra of probable phases in an alloy and the spectrum of the sample have been proposed and a dialogue for the intellectual phase analysis of polycrystals has been created[1];

- On the basis of previous theoretical work effective algorithms for the interpretation of the Patterson function of monocrystals have been developed. The uniqueness of solution of the restoration problem for spherically symmetric particles and two-dimentional finite axial distribution has been proven[2];

- Numerical methods and software packages for the restoration of structure of thin multilayer organic films from reflectometric data (small-angle scattering) have been developed;

- An effective multiresolution method for analysis of diffusive scattering from crystals with nanosized clusters has been developed[3,4].

Work on the highlighted topics was conducted in collaboration with employees of the Institute of Crystallography of the Russian Academy of Science (The Structural Analysis Laboratory, led by V.I. Simonov and the Small-angle Scattering Laboratory, led by L.A. Fejgin).

Contact: B. Shchedrin (

[1] Burova E.M, Shchedrin B.M. A windows application: the program for qualitative phase analysis of polycrystalline mixtures. (2000). Crystallography Report, 45, 340-342.
[2] Shchedrin B.M. On the existence of solution in the inverse problems of the substance structure restoration on the diffractional data. (2000). Applied Mathematics and Computer Science, Moscow: Max –press. N. 6, 67-71.
[3] Andrushevsky N.M, Shchedrin B.M., Malahova L.F., Simonov V. I. Diffusive scattering from crystals with dot defects. (2002). Crystallography (Russia), V. 47, N. 3, 518-521.
[4] Andrushevsky N.M., Shchedrin B.M., Simonov V.I. Restoring algorithm of atomic structure of nanosized inclusions in crystals on the base of diffuse scattering of X-rays or neutrons data. (2004). Crystallography (Russia).