Application of effective potential formalism to mechanical alloying in Ag–Cu and Cu–Fe systems

We have used the competing dynamics model and the effective potential formalism for studying phase stability during mechanical milling of Ag–Cu and Cu–Fe systems. We first present a method for extracting an effective potential for systems in which the atomic mobility may depend on alloy composition. Using an estimate for the typical ballistic diffusivity, we apply this formalism to calculate the dynamical phase diagram for the Ag–Cu and Cu–Fe binary systems under mechanical milling. For the Ag–Cu system, the dynamical phase diagram exhibits a miscibility gap that closes in on itself at low temperatures, due to the exponentially decreasing thermal diffusivity (and hence, increasing influence of ballistic diffusivity) with decreasing temperature. In the Cu–Fe system, in which the effective potential for both the bcc and fcc phases need to be taken into account, the fcc phase is shown to be stabilized at low temperatures for all the alloys, except the almost pure iron (which is stabilized in its bcc form). These results are critically compared with available experimental results.