Relating single-impact events to macrokinetic features in mechanical alloying processes

It has been shown that structural evolution occurring in powder mixtures subjected to mechanical treatment by milling follow well-defined conversion trends as a function of milling time. Sigmoidal curves were observed in the case of the mechanical alloying of transition metal mixtures, whereas a simpler kinetic course with a progressively decreasing transformation rate was found to characterize the disordering process of intermetallic equilibrium compounds by mechanical milling. Under the stipulation that collisions are the dominant energy transfer events, a kinetic model is developed to relate the observed macrokinetic features to the discrete powder fractions, which transform at each impact. Because of its intrinsic qualities, the milling process was regarded as discrete processing. A statistical approach was followed to work out a set of differential equations, solutions of which provide a sound description of the transformation kinetics in terms of conventional rate expressions. The model allows one to reproduce the different kinetic behaviors by means of a single, unifying mathematical formalism. Furthermore, quantifying the structural evolution rate by suitable kinetic constants permits the exploration of the reactive behavior of a system treated under different milling regimes or to compare, on an absolute basis, different systems processed under similar conditions.