Features of the Use of Equilibrium State Diagrams for Description of Crystal Growth from Metastable Melts

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The crystallization of metastable metal alloys is characterized by a high rate of the crystallization front, which leads to the effect of "impurity capture" and deviation from the local equilibrium near the surface of the growing crystal. To calculate the growth rate of the crystalline nuclei, a method was developed for prediction of deviation of the components’ concentration near the crystal surface from the equilibrium values. A crystal nucleus was considered to be growing from the initial multicomponent phase, due to interphase transition of the components through its surface. It became possible to distinguish the equilibrium and non-equilibrium effect of the nucleus growth rate by decomposing the molar rate of the product formation near equilibrium, as a function of the molar concentration of the components in the Taylor series and limiting with the linear members. The practical calculations were carried out for the crystallization of the amorphous alloy Fe73,5Cu1Nb3Si13,5B9 of the FINEMET type. The local deviations were investigated for the silicon concentration from the equilibrium values at the surface of the growing crystal.

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Solid State Phenomena (Volume 299)

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622-627

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January 2020

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© 2020 Trans Tech Publications Ltd. All Rights Reserved

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[1] A.D. Drozin, Growth of Microparticles of the Products of Chemical Reactions in a Liquid Solution: Monograph, YuUrGU, Chelyabinsk, (2007).

Google Scholar

[2] P.A. Gamov, A.D. Drozin, M.V. Dudorov, Model for Nanocrystal Growth in an Amorphous Alloy, Russian Metallurgy (Metally), 11 (2012) 101-105.

DOI: 10.1134/s0036029512110055

Google Scholar

[3] I.S. Miroshnichenko, Quenching from Liquid State, Metallurgia, Moscow, (1984).

Google Scholar

[4] D.M. Herlach, P. Galenko, D. Holland-Moritz, Metastable Solids from Undercooled Melts, Elsevier, Amsterdam, (2007).

DOI: 10.1016/s1470-1804(07)80023-x

Google Scholar

[5] J.C. Baker, J.W. Cahn, Solute Trapping by Rapid Solidification, Acta Met. 17 (1969) 575-578.

DOI: 10.1016/0001-6160(69)90116-3

Google Scholar

[6] M.J. Aziz, Model for solute redistribution during rapid solidification, J. Appl. Phys. 53 (2) (1982) 1158-1168.

DOI: 10.1063/1.329867

Google Scholar

[7] H. Garcke, B. Nestler, B. Stinner, A diffuse interface model for alloys with multiple components and phases, SIAM J Appl. Math. 64, 3 (2004) 775-799.

DOI: 10.1137/s0036139902413143

Google Scholar

[8] P.K. Galenko, H. Gomez, N.V. Kropotin, Unconditionally stable method and numerical solution of the hyperbolic phase-field crystal equation, Phys. Rev. E, 88 (2013) 013310.

DOI: 10.1103/physreve.88.013310

Google Scholar

[9] C.V. Thompson, F. Spaepen, Homogeneous crystal nucleation in binary metallic melts, Acta Metallurgica, 31 (1983) 2021-2027.

DOI: 10.1016/0001-6160(83)90019-6

Google Scholar

[10] I. Prigogine, R. Defay,  Chemical Thermodynamics, Longmans Green, London, (1954).

Google Scholar

[11] P. Glansdorff, I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations, Mir, Moscow, (1973).

Google Scholar

[12] S. Kjelstrup, D. Bedeaux, Non-equilibrium Thermodynamics of Heterogeneous Systems, Series on Advances in Statistical MechanicsVol. 16, World Scientific, Singapore, (2008).

DOI: 10.1142/6672

Google Scholar

[13] A.D. Drozin, Theoretical analysis of the nucleation of non-metallic inclusions in the liquid metal, Russian Metallurgy (Metally), 5 (1987) 73-77.

Google Scholar

[14] A.D. Drozin, Mathematical model for the growth of deoxidation products in a liquid metal, Russian Metallurgy (Metally), 6 (1987) 19-22.

Google Scholar

[15] M.V. Dudorov, Decomposition of crystal-growth equations in multicomponent melts, J. Crystal Growth 396 (2014) 45-49.

DOI: 10.1016/j.jcrysgro.2014.03.035

Google Scholar

[16] U. Köster, U. Schünemann, Blank nanocrystalline materials by crystallization of metall - metalloid glasses, Mat.Sci., A133 (1991) 611-615.

DOI: 10.1016/b978-0-444-89107-5.50148-9

Google Scholar

[17] I.B. Kekalo, B.A. Samarin, Physical Metallography of Precision Alloys, Metallurgiya, Moscow, (2007).

Google Scholar

[18] М. Knobel, R. Sato Turtelli, H.R. Reichenberg, Compositional evolution and magnetic properties of nanociystalline Fe73,5Cu1Nb3Si13,5B9, J.Appl. Phys. 71 12 (1992) 6008-6012.

Google Scholar

[19] V.E. Roshchin, A.V. Roshchin, Foundation of the production of nanocrystalline and amorphous metals, YuUrGU, Chelyabinsk, (2009).

Google Scholar

[20] Y. Yoshizawa, S. Oguma, K. Yamauchi, New Fe‐based soft magnetic alloys composed of ultrafine grain structure, J. Appl. Phys. 64 (1988) 6044-6046.

DOI: 10.1063/1.342149

Google Scholar

[21] Y. Yoshizawa, K. Yamauchi, Fe-Based Soft Magnetic Alloys Composed of Ultrafine Grain Structure, Materials Translation, JIM. 5 4 (1990) 307-314.

DOI: 10.2320/matertrans1989.31.307

Google Scholar

[22] G. Herzer, Nanocrystalline soft magnetic materials, Phys. Scr. 49 (1993) 307-314.

DOI: 10.1088/0031-8949/1993/t49a/054

Google Scholar

[23] Yu.N. Goykhenberg, P.A. Gamov, M.V. Dudorov, V.E. Roshchin, The structure of 5BDSr amorphized alloy Used to make the nanocrystalline tape, Bul.SUSU. Metallurgy, 39 (2012) 128-133.

Google Scholar