A model of convection-induced oscillatory structure formation in peritectic alloys

In the two-phase region of a peritectic system, experimental studies have s hown that the primary phase (alpha) often forms a large treelike structure that is surrounded by the peritectic phase (beta). The formation of this no vel structure has been attributed to the presence of convection in the liqu id. Here, specific physical mechanisms of convection-induced treelike struc ture formation are proposed. A mathematical model based on advection-diffus ion of solute, with prototype flows for advection, is presented and solved numerically to show that an oscillating fluid motion can give rise to a com plex oscillatory, treelike structure. Three different regimes are establish ed: diffusive, steady convective, and unsteady convective regimes. In the d iffusive regime, a banded structure is predicted within a narrow compositio n range, and the spacing of the bands is dictated by the nucleation underco olings of the two phases. Under steady convection, the primary phase transf orms into the peritectic phase with a curved alpha:beta interface. Finally, in the presence of oscillating convection, a treelike shape of the primary phase is predicted, as observed experimentally.