Phase transformations under ball milling: Theory versus experiment

Phases transformations under ball milling can be addressed, from the theoretical point of view, as transitions between stationary states of a "driven" alloy : shear induces some sort of disorder which is annealed by thermal diffusion, between two shearing events. This type of problem has been modelled in great details in the context of irradiation effects on phase stability in alloys. This approach is here applied to phase transformations under ball milling and critically compared to experiments. First we present a detailed study of the order-disorder transition in FeAl under ball milling in an calibrated mill : we find a decoupling of the time evolution of the microstructure and of the degree of long range order. The latter is found to reach a stationary value which depends (in a reversible manner) on the milling conditions. In a well defined range of the latter, hysteresis effects are identified. Kinetics of the transition are well fitted by the simplest model of A2-B2 transition under forcing that we introduced few years ago; the connection between the experimental control parameters (milling intensity and temperature) and the reduced parameters of the model (respectively the thermally activated and the ballistic atomic jump frequencies) can be given a simple physical interpretation. The model also reproduces transient quasi-steady states which are experimentally observed. Moreover, depending on milling conditions, the order-disorder transition is found to be either of first or second order, as predicted by the model. The same approach is shown to rationalise experiments proving the stabilisation by ball milling of immiscible elements into a solid solution at low enough temperature. For this purpose, Monte-Carlo simulations are performed where the atomic disorder introduced by shear events is modelled by shifts of atomic planes. A striking prediction of these simulations is that mesoscopic stationary microstructures can be obtained for appropriate shearing conditions; and that the characteristic length of these microstructures could be tuned by adjusting the milling conditions.