Kinetic transition in the order-disorder transformation at a solid/liquid interface

Phase-field analysis for the kinetic transition in an ordered crystal structure growing from an undercooled liquid is carried out. The results are interpreted on the basis of analytical and numerical solutions of equations describing the dynamics of the phase field, the long-range order parameter as well as the atomic diffusion within the crystal/liquid interface and in the bulk crystal. As an example, the growth of a binary A₅₀B₅₀ crystal is described, and critical undercoolings at characteristic changes of growth velocity and the long-range order parameter are defined. For rapidly growing crystals, analogies and qualitative differences are found in comparison with known non-equilibrium effects, particularly solute trapping and disorder trapping. The results and model predictions are compared qualitatively with results of the theory of kinetic phase transitions (Chernov 1968 Sov. Phys. JETP26, 1182-1190) and with experimental data obtained for rapid dendritic solidification of congruently melting alloy with order-disorder transition (Hartmann et al. 2009 Europhys. Lett.87, 40007 (doi:10.1209/0295-5075/87/40007)).This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.