Theoretical Analysis Of The Effect Of Anisotropic Surface Tension On Eutectic Growth

Eutectic growth is one of fundamental subjects in material science,and the interface between the solid and liquid phase plays an important role in the growth of the crystal.In the solidification,the crystal growth will be affected by many factors,such as undercooling,interface kinetics,anisotropic surface tension,melt convection,etc.(1)In the lamellar eutectic growth system,we consider the two-dimensional model with anisotropic surface tension and obtain the global uniformly valid asymptotic solutions.The analytical solution reveals the effect of anisotropic surface tension on the interface shape of lamellar eutectic growth near the triple point.The temperature distribution at the interface shows a noticeable non-uniformity and there is a thin boundary layer for temperature and concentration near the triple point.As the anisotropic surface tension increases,the interface temperature away from the triple point increases,whereas near the triple point the interface temperature decreases.Compared with the lamellar eutectic growth with isotropic surface tension,the anisotropic surface tension changes the position of the triple point and accelerates the growth of the lamellar eutectic.(2)We investigate the global instability mechanisms of lamellar eutectic growth with asymptotic approach.A dispersion relation between the wave number and the perturbation amplification rate is obtained.Similar to the case of isotropic surface tension,the eutectic growth system involves two types of global instability mechanisms:the ’exchange of stability’ invoked by the non-oscillatory,unstable modes and the global wave instabilities invoked by four types of oscillatory unstable modes,namely antisymmetric-antisymmetric(AA-),symmetric-antisymmetric(SA-),antisymmetric-symmetric(AS-)and symmetric-symmetric(SS-)-modes.The anisotropic surface tension,by decreasing the corresponding stability critical number ε*,stabilizes both the’exchange of stability’ mechanism and the global instability mechanism for the AA-,SA-and SS-modes.However,by increasing the corresponding stability critical number ε*,the anisotropic surface tension destabilizes the global instability mechanism for the AS-mode.(3)We deal with solidification of rod eutectic growth and give some research results about the rod eutectics.We study the rod eutectic growth under two special phase diagram conditions.The relation between the interface kinetics,growth velocity,rod spacing and interface undercooling can be derived.By using the principle of minimum undercooling,we obtain the expression of rod spacing.In the end of the thesis,an asymptotic solution of the solute diffusion equation with flow terms for the rod eutectic in the weak convective melt in directional solidification is obtained.