Theoretical and numerical investigations of rod growth of an Ni–Zr eutectic alloy

In this work, the directional solidification of NiZr–NiZr\(_2\) eutectics under isothermal conditions is investigated through numerical and theoretical means. Multiple three-dimensional phase-field simulations, including a large-scale simulation, are performed to study the free pattern selection and the velocity–spacing relation of the evolving solidification microstructures. The computed velocities for different spacings of the stoichiometric NiZr rods in the as-well stoichiometric NiZr\(_2\) matrix are compared with the predictions of the classical Jackson–Hunt analysis. Due to certain simplifying assumptions invoked in the original theory which are not entirely representative of the numerically realized microstructures, significant deviations are observed between the two. In view of this, an extended theory is formulated accounting for the global hexagonal arrangement of the evolving rods as well as the solidification front curvatures. Owing to that, a superior compliance is achieved between the analytical and simulated growth kinetics. The key elements of symmetry incorporation are of particular importance, especially in applications to ternary systems.