Founder: Northern (Arctic) Federal University named after M.V. Lomonosov

Editorial office address: Russian Federation, 163002, Arkhangelsk, Naberezhnaya Severnoy Dviny 17, office 1410a

Phone: (818-2) 21-61-00(15-33)



Choice of Approximation Function Based on the Structural Data of 8 % Co–92 % Wc Alloy. Pp. 77–83.

Версия для печати

Section: Physics. Mathematics. Informatics




Astapova Elena Stepanovna, Amur State University (Blagoveshchensk, Russia)

Borilko Anton Sergeevich, Postgraduate Student, Amur State University (Blagoveshchensk, Russia)

Astapov Ivan Aleksandrovich, Institute for Material Studies, Far Eastern Branch of the Russian Academy of Sciences (Khabarovsk, Russia)


The paper is devoted to the choice of approximation function to calculate the coherent-scattering region, exemplified by the hard alloy with 8 % Co–92 % WC. The constants of approximation functions Cauchy 1, Cauchy 2, Laue and Gaussian function were fitted by means of numerical methods. Function availability estimation was gained with the mean-square residual.


Gaussian function, Cauchy function, Laue function, approximation, mean-square residual, block, thin crystal structure.

The full-text version of the article can be requested through the university’s library.


  1. Astapov I.A., Verkhoturov A.D. Modelirovanie protsessa modifitsirovaniya poverkhnosti tverdykh splavov metodom EIL [Simulation of the Surface Modification of Solid Alloys by Electrospark Doping]. Informatika i sistemy upravleniya, 2007, no. 2 (14), pp. 20–30.
  2. Verzhbitskiy V.M. Chislennye metody. Matematicheskiy analiz i obyknovennye differentsial’nye uravneniya [Numerical Methods. Mathematical Analysis and Ordinary Differential Equations]. Moscow, 2001.
  3. Gorelik S.S, Skakov Yu.A., Rastorguev L.N. Rentgenograficheskiy i elektronnoop-ticheskiy analiz [X-Ray and Electron-Optical Analysis]. Moscow, 2001.
  4. Ivanov A.N. Difraktsionnye metody issledovaniya materialov: konspekt lektsiy [Diffraction Methods of Material Analysis. A Summary of Lectures]. Moscow, 2008.
  5. Krivoglaz M.A. Difraktsiya rentgenovskikh luchey i neytronov v neideal’nykh kristallakh [X-Ray and Neutron Diffraction in Real Crystals]. Kiev, 1983.