Source: http://dopovidi-nanu.org.ua/en/archive/2019/1/7
Timestamp: 2019-04-21 08:06:45+00:00

Document:
Generalizations of the method of moments and the Hall—Williamson one are presented without a priori assumptions about the distribution law for microstrains with regard for the nature of a dispersion function due to the presence of coherent scattering. The developed approach is based on the analysis of the shape of the complete physical profile restored using the Tikhonov regularization method and allows one to determine the distribution function of microstrains.
1. Čerňanský, M. (1999). Restoration and preprocessing of physical profiles from measured data. Snyder, R.L., Bunge, H.J. and Fiala, J. (Eds.) Microstructure analysis from diffraction (pp. 613-651). Oxford: Oxford Univ. Press.
2. Jones, F. W. (1938). The Measurement of Particle Size by the X-ray Method. Proc. Roy. Soc. Ser. A., 166, No. 924. pp. 16-48.
3. Warren, B. E. (1963). X-ray study of deformed metals. Uspekhi fiziki metallov, No. 5, pp.171-237 (in Russian).
4. Tikhonov, A. N., Goncharskiy, A. V., Stepanov, V. V. & Yagola, A. G. (1990). Numerical methods for solving ill-posed problems. Moscow: Nauka (in Russian).
8. Vasil’ev, D. M. (1977). Diffraction methods of research structures. Moscow: Metallurgiya (in Russian).
9. Grigor’ev, O. N. (2012). Ceramics and cermets based on oxygen-free refractory compounds. Poroshkovaya metallurgiya, No.11/12, pp. 100-116 (in Russian).
10. Reshetnyak, M. V. & Sobol’, O. V. (2008). Nhancement of structure and substructure analysis of W2B5-TiB2 quasi-binary nano-crystalline condensed and bulk materials with application of “New_profile” soft-ware for X-ray diffraction data treatment. Fizicheskaya inzheneriya poverhnosti, 6, No. 3-4, pp. 180-188 (in Russian).
11. Grigor’ev, O. N., Kryachko, L. A., Bega, N. D., Laptev, A. V., Golovkova, M. E., Rozhenko, N. N. & Bersudskiy, E. I. (2013). Effect of ball milling on structural characteristics of tungsten powder. Elektronnaya mikroskopiya i prochnost’ materialov, No. 19, pp. 114-122 (in Russian).
12. Grigor’ev, O. M., Kartuzov, V. V. & Rozhenko, N. M. (2017). Increase of exactness of quantitative estimates of the Hall—Williamson graphic method due to digital processing of X-ray patterns. Elektronna mіkrosko pіya і mіtsnіst’ materіalіv, No. 23, pp. 16-35 (in Ukrainian).
13. Korolyuk, V. S., Portenko, N. I., Skorokhod, A. V. & Turbin, A. F. (1985). A Handbook on Probability Theory and Mathematical Statistics. Moscow: Nauka (in Russian).
14. Rozhenko, N. M., Kartuzov, V. V. & Gusachuk, D. A. (2017). Determination of density function of microstrains into mechanically activated tungsten powders by method of X-ray diffraction. Naukovі notatki, No. 57, pp. 161-167 (in Ukrainian).
15. Bega, M. D., Vinokurov, V. B., Galanov, B. O., Grigor’ev, O. M., Kartuzov, V. V., Mazur, P. V., Rozhenko, N. M. & Stepanenko, A. V. (2016). Study of the substructure of the tungsten carbide powder during milling by radiography methods. Elektronna mіkroskopіya і mіtsnіst’ materіalіv, No. 22, pp. 58-72 (in Ukrainian).

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