Abstract
X-ray diffraction analysis and thermodynamic calculations in the Miedema model are used to study the sequence of solid-state reactions during mechanical alloying in the Fe–Sn system. The results indicate that the formation of FeSn2 in the initial stages of the process is a quasi-equilibrium process reducing the volume contribution to the free energy. A simple model, considering a random distribution of particles, is used to obtain an expression for the total free energy, comprising the volume and interface contributions, as a function of particle size. It is shown that the formation of a supersaturated solid solution is thermodynamically possible over a wide composition range if the particle size is reduced to a few nanometers and surface Sn segregation occurs. The limit of the supersaturated solid solution obtained by mechanical alloying is determined by the relationship between the limit of size reduction and the particle size which ensures stabilization of the solid solution. In the Fe–Sn system, the limit of the supersaturated fcc solid solution is found to be 20 at. % Sn.
Similar content being viewed by others
REFERENCES
Cabañas-Moreno, J.G. and López-Hirata, V.M., Copperand Cobalt-Alloys Made by Mechanical Alloying (Overview), Mater. Trans., JIM, 1995, vol. 36, no. 2, pp. 218-227.
Grigor'eva, T.F., Barinova, A.P., Ivanov, E.Yu., and Boldyrev, V.V., X-ray Diffraction Study of the Initial Stages in the Mechanical Alloying of Supersaturated Solid Solutions, Dokl. Akad. Nauk, 1995, vol. 345, no. 3, pp. 343–347.
Grigor'eva, T.F., Barinova, A.P., and Boldyrev, V.V., Effect of Structural Matching on the Stoichiometry Range of Solid Solutions Prepared by Mechanical Alloying, Neorg. Mater., 1995, vol. 31, no. 12, pp. 1551-1556 [Inorg. Mater. (Engl. Transl.), vol. 31, no. 12, pp. 1410-1415].
Yelsukov, E.P., Voronina, E.V., Konygin, G.N., et al., Structure and Magnetic Properties of Fe100 - x Snx (3.2 < x < 62) Alloys Obtained by Mechanical Milling, J. Magn. Magn. Mater., 1996, vol. 166, no. 5, pp. 334–348.
Cabrera, A.F., Sánchez, F.H., and Mendoza-Zélis, L., Mechanical Alloying of Iron and Tin Powders: A Mössbauer Study, Mater. Sci. Forum, 1995, vols. 179-181, pp. 231–236.
Yelsukov, E.P., Dorofeev, G.A., Barinov, V.A., et al., Solid State Reactions in the Fe-Sn System under Mechanical Alloying and Grinding, Mater. Sci. Forum, 1998, vols. 269-272, pp. 151–156.
Sánchez, F.H., Socolovsky, L., Cabrera, A.F., and Mendoza-Zélis, L., Magnetic Relaxations in Mechanically Ground FeSn2, Mater. Sci. Forum, 1996, vols. 225-227, pp. 712–718.
Fecht, H.-J., Nanostructure Formation by Mechanical Attrition, Nanostruct. Mater., 1995, vol. 6, pp. 33–42.
Boer, F.R., Boom, R., et al., Cohesion in Metals, vol. 1: Transition Metal Alloys, Amsterdam: Elsevier, 1988.
Bakker, H., Miedema's Semi-Empirical Model for Estimating Enthalpies in Alloys, Mater. Sci. Brief., 1998, vol. 1, pp. 1–80.
Kuznetsov, V.A., Lipson, A.G., and Sakov, D.M., On the Limit of Crystal Comminution, Zh. Fiz. Khim., 1993, vol. 67, no. 4, pp. 782–786.
Zhang, Z.J., Jin, O., and Liu, B.X., Anomalous Alloying Behavior Induced by Ion Irradiation in a System with a Large Positive Heat of Mixing, Phys. Rev. B: Condens. Matter, 1995, vol. 51, pp. 8076–8085.
Chelikowsky, J.R., Predictions for Surface Segregation in Intermetallic Alloys, Surf. Sci., 1984, vol. 139, pp. 197–203.
Kanunnikova, O.M., Gil'mutdinov, F.Z., and Elsukov, E.P., Photoelectronic Study of Powder Fe1 - x Snx, Perspekt. Mater., 1996, no. 6, pp. 71–74.
Physical Metallurgy, Cahn, R.W. and Haasen, P., Eds., Amsterdam: North-Holland, 1983, vol. 1. Translated under the title Fizicheskoe metallovedenie, Moscow: Metallurgiya, 1987.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dorofeev, G.A., Elsukov, E.P. Thermodynamic Modeling of Mechanical Alloying in the Fe–Sn System. Inorganic Materials 36, 1228–1234 (2000). https://doi.org/10.1023/A:1026629630902
Issue Date:
DOI: https://doi.org/10.1023/A:1026629630902