On Cyclical Phase Transformations in Driven Alloy Systems: A Mass-Action Kinetics Approach

Cyclical phase transformations occurring under externally driven conditions, such as mechanical alloying, are treated in terms of coupled chemical reactions between participant phases. As a conceptual case, microstructural evolution of a driven system is expressed in terms of simplified chemical reaction. By utilizing law of mass action, two independent differential equations are derived for time-dependent phase concentrations. A stability analysis for the rate equations shows that temporal oscillations in phase concentrations result from an interplay of a non-linear autocatalytic reaction. A limit cycle representing sustained, undamped oscillations is also possible with the model.