Thermodynamic Modeling of Mechanical Alloying in the Fe–Sn System

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.