Mathematical Model of Nanostructure Formation in Binary Alloys at Electron Beam Treatment

Abstract:

The paper presents a thermoconcentration and capillary mathematical model, describing the formation of 10 to 100 nm structures in the surface layers of binary alloys irradiated by low-energy, high-current electron beams of submillisecond duration. The model is studied by the example of “ferrum - carbon” and “titanium – carbon” systems. It comprises Navier-Stokes equation, thermoconductivity and diffusion equations, as well as surface kinematic and dynamic boundary conditions. The effect of electron beam on material is specified as various temperature and concentration gradients. A dispersion equation for thermocapillary waves in nanowavelength range is developed and analyzed with thin layer approximation. The critical wavelength, leading to this instability, is revealed. It is found out that its values are 17.39 nm for Fe-С and 69.7 nm for Ti-C at the depth of penetration ~ 10^-5 m. Wavelengths are compared to the dimensions of crystallization cells and structures, which are formed in them. The paper shows that the model provides a rational explanation of registered regularities.

• Periodical: Materials Science Forum (Volume 870)
• Pages: 34-39
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.870.34
• Online since: September 2016
• Authors: Sergey A. Nevskii*, Vladimir Sarychev, Sergey V. Konovalov, D. Kosinov, Irina Panchenko
• Keywords: Binary Alloys, Electron Beam Treatment, Nanostructure, Thermoconcentration Capillary Instability

References

[1] Y.F. Ivanov, Y.A. Kolubaeva, D.A. Bessonov, S. V Vorobev., V.E. Gromov, V.Y. Tsellermaer, K.V. Ivanov, On the fatigue strength of grade 20CR13 hardened steel modified by an electron beam, J. Surf. Investig. X-ray, Synchrotron Neutron Tech. 7 (2013).

DOI: 10.1134/s1027451013010126

[2] V.E. Gromov, V.V. Sizov, S.V. Vorob'ev, S.V. Konovalov, Y.F. Ivanov, Increase in the fatigue durability of stainless steel by electron-beam surface treatment, J. Surf. Investig. X-ray, Synchrotron Neutron Tech. 7 (2013) 94–98.

DOI: 10.1134/s1027451013010114

[3] V.A. Grishunin, V.E. Gromov, S.V. Konovalov, Y.F. Ivanov, A.D. Teresov, Evolution of the phase composition and defect substructure of rail steel subjected to high-intensity electron-beam treatment, J. Surf. Investig. X-ray, Synchrotron Neutron Tech. 7 (2013).

DOI: 10.1134/s1027451013050091

[4] V.D. Sarychev, S.A. Nevskii, V.E. Gromov, The theoretical analysis of stress-strain state of materials with gradient structure, Mater. Phys. Mech. 22 (2015) 157 – 169.

[5] Yu.F. Ivanov, E.A. Petrikova, N.N. Cherenda, A.D. Teresov, Hardening of the surface layer of silumin by electron beam, Adv. Mater. Res. 872 (2014) 162-166.

DOI: 10.4028/www.scientific.net/amr.872.162

[6] B. Gao, Y. Hao, W.F. Zhuang, G.F. Tu, W.X. Shi, S.W. Li, S.Z. Hao, C. Dong, M.C. Li, Study on continuous solid solution of Al and Si elements of a high current pulsed electron beam treated hypereutectic Al17. 5Si alloy, Phys. Procedia. 18 (2011).

DOI: 10.1016/j.phpro.2011.06.079

[7] E.A. Lukashov, E.V. Radkevich, N.N. Yakovlev, Structurization of the instability zone and crystallization, J. Math. Sci. 179 (2011), 491–514.

DOI: 10.1007/s10958-011-0606-1

[8] S.M. Zen'kovskaya, Long-wave oscillatory Marangoni instability in a horizontal liquid layer, J. Appl. Math. and Mech. 71 (2007) 755– 61.

[9] A.A. Golovin, S.H. Davis., A.A. Nepomnyashchy, A convective Cahn—Hillard model for the formation of facets and carners in crystal growth, Phys. D. 118 (1998) 202−230.

DOI: 10.1016/s0167-2789(98)00181-x

[10] N.B. Volkov, A. Ya Leyvi., A.E. Mayer, K.A. Talala, A.P. Yalovets, The dynamics of under surface condensed substance irradiated by intense energy stream, AIP Conf. Proceed. 849 (2006) 268-272.

DOI: 10.1063/1.2337211

[11] N.B. Volkov , A.Y. Leivi , K.A. Talala, A.P. Yalovets, Thermocapillary convection in a target irradiated by an intense charged particle beam, Tech. Phys. 55 (2010) 484-490.

DOI: 10.1134/s1063784210040080

[12] ASM Metals HandBook - Materials Characterization Vol. 10. ASM International, 2002. 1310.

[13] W.E. Forsythe, Smithsonian physical tables, Norwich, New York, (2003).

[14] S.V. Raikov, K.V. Sosnin, Yu.F. Ivanov, E.A. Budovskikh, V.E. Gromov, Structurally-Phase States of Surface Titanium VT1-0 Layers After Electroexplosive Carbonization with a Weighed Zirconium Oxide Powder Sample and Electron Beam Treatment, Russ. Phys. J. 57 (2014).

DOI: 10.1007/s11182-014-0232-8