In this paper, the deviation from eutectic composition in boundary layer for eutectic growth is studied by phase-field method. According to a series of artificial phase diagram, the lamellar eutectic growth of these alloy is simulated during directional solidification. At steady state, average growth velocity of eutectic lamella is equal to the pulling velocity. With the increasing of the liquidus slope of β phase, the average composition in boundary layer would deviate from eutectic composition and the deviation increases. The constitutional undercooling difference between both solid phases caused by the deviation increases with the increasing of the deviation. The β phase would develop a depression under the influence of the deviation.

The entropy production per unit time is calculated for the regular lamellae -, and for the regular rods formation, respectively. The entropy production is a function of some parameters which define the eutectic phase diagram, coefficient of the diffusion in the liquid, and some capillary parameters connected with the mechanical equilibrium located at the triple point of the solid/liquid interface. Minimization of the entropy production allowed to formulate mathematically the so-called Growth Law for both envisaged eutectic morphologies.

In this study, the modification mechanism and growth process of Al3(Sc, Zr) particles in as-cast Al-Si-Mg-Cu based alloy with addition of Sc and Zr were systematically investigated. It was found that 0.57 wt-%Sc addition caused a significant refinement in the average grain size of the investigated alloy, which brought about a remarkable transformation in as-cast microstructure, from thick dendritic shape to fine equiaxed structure. A large amount of primary Al3(Sc, Zr) particles with the dimension of around 5-6 μm were also observed within the equiaxed grain. Due to the identical orientation and similar crystal structure between primary Al3(Sc, Zr) particles and α-Al matrix, the primary particles always served as heterogeneous nucleus for the α-Al matrix. In addition, these cusped cubic primary Al3(Sc, Zr) particles showed triangle, star, rhomboid morphologies are generated from sectioning the particle in (111), (100) and (110) planes, respectively. Particularly, the typical eutectic structure which contained odd number-layer (Al3(Sc, Zr)+α-Al+  +Al3(Sc, Zr)) was observed within the investigated particles.