Abstract
A new program for the refinement of models of atomic structures by the X-ray, neutron, and electron diffraction data has been described. The program is based on a special form of the goal function including the term responsible for minimizing the difference between the normalized measurements [the interexperimental minimization (IEM) method] and the adaptive nonlinear algorithm of minimization based on the Lavrent’ev-Levenberg-Marquardt regularization. As a result, it became possible to determine a new solution to the problem different from that obtained by the classical least squares method. To a large extent, the program allows one to overcome the effect of parameter correlations on the procedure of refinement and the results obtained. The test of the program on 17 experimental data sets showed the fast and stable convergence in all the cases. Under the identical initial conditions, the new program provided lower reliability factors for most of the crystals studied.
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A. P. Dudka, A. A. Loshmanov, and B. A. Maksimov, Kristallografiya 43, 613 (1998) [Crystallogr. Rep. 43, 565 (1998)].
A. P. Dudka and A. A. Loshmanov, Kristallografiya 46, 565 (2001) [Crystallogr. Rep. 46, 511 (2001)].
A. P. Dudka and A. A. Loshmanov, Kristallografiya 46, 1135 (2001) [Crystallogr. Rep. 46 (6), 1049 (2001)].
A. P. Dudka, Kristallografiya 47(1), 156 (2002) [Crystallogr. Rep. 46 (1), 145 (2002)].
A. P. Dudka, A. A. Loshmanov, and B. A. Maksimov, in Proceedings of the 2nd National Conference on Application of X-rays, Synchroton Radiation, Neutrons and Electrons for Study of Materials (RSNE), Moscow, 1999, p. 33.
A. P. Dudka, A. A. Loshmanov, and B. A. Maksimov, Poverkhnost, No. 2, 2833 (2001).
D. Schwarzenbach and H. D. Flack, Acta Crystallogr., Sect. A: Found. Crystallogr. 47, 134 (1991).
A. N. Tikhonov and V. Ya. Arsenin, Solutions of Ill-Posed Problems (Nauka, Moscow, 1979, 2nd ed.; Halsted Press, New York, 1977).
J. E. Dennis, D. M. Gay, and R. E. Welsch, ACM Trans. Math. Softw. 7(3), 348 (1981).
J. E. Dennis, D. M. Gay, and R. E. Welsch, ACM Trans. Math. Softw. 7(3), 369 (1981).
B. M. Shchedrin, I. N. Bezrukova, and E. M. Burova, in Library of Programs for Study of Structure and Properties of Materials by Diffraction Methods (Mosk. Gos. Univ., Moscow, 1987).
U. Zucker, E. Perenthaler, W. F. Kuhs, et al., J. Appl. Crystallogr. 16, 398 (1983).
V. Petriček, SDS94 (Institute of Physics, Prague, 1994).
A. K. Kulygin, G. G. Lepeshov, and A. S. Avilov, in Proceedings of the Russian Conference on Electron Microscopy, Chernogolovka, 1998, p. 105.
W. H. Zachariasen, Acta Crystallogr. 23, 558 (1967).
P. J. Becker and P. Coppens, Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr. 30, 129 (1974).
P. Coppens, T. N. Guru Row, P. Leung, et al., Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr. 35, 63 (1979).
B. M. Shchedrin, N. V. Belov, and N. P. Zhidkov, Dokl. Akad. Nauk SSSR 170(5), 1070 (1966) [Sov. Phys. Dokl. 11, 833 (1967)].
A. P. Dudka and V. A. Strel’tsov, Kristallografiya 37, 517 (1992) [Sov. Phys. Crystallogr. 37, 269 (1992)].
É. M. Galeev and V. M. Tikhomirov, Optimization: Theory, Examples, Problems (Éditorial URSS, Moscow, 2000).
International Tables of Crystallography (Kluwer, Dordrecht, 1992), Vol. C, p. 609.
D. Schwarzenbach, S. C. Abrahams, H. D. Flack, et al., Acta Crystallogr., Sect. A: Found. Crystallogr. 51, 565 (1995).
B. M. Shchedrin, Lectures for Students of Faculty of Physics of Moscow State University: Mathematical Aspects of Processing of the Data of Physical Experiments (Mosk. Gos. Univ., Moscow, 1996).
M. Kh. Rabadanov, I. A. Verin, Yu. M. Ivanov, et al., Kristallografiya 46(4), 703 (2001).
T. S. Chernaya, B. A. Maksimov, and A. V. Arekcheeva, in Proceedings of the 2nd National Conference on Application of X-rays, Synchroton Radiation, Neutrons and Electrons for Study of Materials (RSNE), Moscow, 1999, p. 126.
A. P. Dudka, A. A. Loshmanov, and B. P. Sobolev, Kristallografiya 43, 605 (1998) [Crystallogr. Rep. 43, 557 (1998)].
P. L. Sanger, Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr. 25, 694 (1969).
V. G. Tsirelson, A. S. Avilov, G. G. Lepeshov, et al., submitted to J. Phys. Chem.
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Translated from Kristallografiya, Vol. 47, No. 1, 2002, pp. 163–171.
Original Russian Text Copyright © 2002 by Dudka.
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Dudka, A.P. Structure analysis by reduced data. IV. IEM—A new program for refinement of structure models of crystals. Crystallogr. Rep. 47, 152–159 (2002). https://doi.org/10.1134/1.1446925
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DOI: https://doi.org/10.1134/1.1446925