Phase field model for strong interfacial energy anisotropy of HCP materials

Based on the Karma model and the Eggleston regularization technique of the strong interfacial energy anisotropy, a phase-field model was established for HCP materials. An explicit finite difference numerical method was used to solve phase field model and simulate the dendrite growth behaviors of HCP materials. Results indicate that the dendrite morphology presents obvious six-fold symmetry, and discontinuity in the variation of interface orientation occurs, resulting in a fact that the corners were formed at the tips of the main stem and side branches. When the interfacial energy anisotropy strength is lower than the critical value（1/35）, the steady-state tip velocity of dendrite increases with anisotropy as expected. As the anisotropy strength crosses the critical value, the steady-state tip velocity drops down by about 0.89%. With further increase in anisotropy strength, the steady-state tip velocity increases and reaches the maximum value at anisotropy strength of 0.04, then decreases.

Free dendritic growth model incorporating interfacial nonisosolutal nature due to normal velocity variation

Considering both the effects of the interfacial normal velocity dependence of solute segregation and the local nonequilibrium solute diffusion,an extended free dendritic growth model was analyzed.Compared with the predictions from the dendritic model with isosolutal interface assumption,the transition from solutal dendrite to thermal dendrite moves to higher undercoolings,i.e.,the region of undercoolings with solute controlled growth is extended.At high undercoolings,the transition from the mainly thermal-controlled growth to the purely thermal-controlled growth is not sharp as predicted by the isosolute model,but occurs in a range of undercooling,due to both the effects of the interfacial normal velocity dependence of solute segregation and the local nonequilibrium solute diffusion.Model test indicates that the present model can give a satisfactory agreement with the available experimental data for the Ni-0.7% B（mole fraction） alloy.

Simulation of facet dendrite growth with strong interfacial energy anisotropy by phase field method

Numerical simulations based on a new regularized phase-field model were presented, to simulate the solidification of hexagonal close-packed materials with strong interfacial energy anisotropies. Results show that the crystal grows into facet dendrites,displaying six-fold symmetry. The size of initial crystals has an effect on the branching-off of the principal branch tip along the<100> direction, which is eliminated by setting the b/a(a and b are the semi-major and semi-minor sizes in the initial elliptical crystals, respectively) value to be less than or equal to 1. With an increase in the undercooling value, the equilibrium morphology of the crystal changes from a star-like shape to facet dendrites without side branches. The steady-state tip velocity increases exponentially when the dimensionless undercooling is below the critical value. With a further increase in the undercooling value, the equilibrium morphology of the crystal grows into a developed side-branch structure, and the steady-state tip velocity of the facet dendrites increases linearly. The facet dendrite growth has controlled diffusion and kinetics.

合金凝固列状晶/等轴晶转变

在考虑合金组元局部线性叠加的基础上,结合计算相图,对多元合金凝固枝晶列状/等轴生长特性进行了系统的研究,通过考虑枝晶生长界面前沿的形核生长及竞争,发展了一个适用于多元合金凝固列状晶/等轴晶转变的理论模型,其与实验结果能很好的吻合。

Solidification researches using transparent model materials——A review

A review is given in the paper for solidification researches with transparent model materials. The effective experimental me- thod was first proposed by Jackson and Hunt in 1965. The transparent model materials for solidification researches are a kind of non-faceted crystals known as ＂plastic crystals＂ or ＂globular molecules＂, which have very low entropy of melting as that of metals. According to Jackson＇s theory proposed in 1958, entropy of phase transformation will determine whether the phase interface morphology is smooth or rough in atomic scale, which will lead to faceted or nonfacted phase interface in mi- croscopic and macroscopic scales. Succinonitrile （SCN） and its alloys with water, ethanol, acetone, and NH4C1-H：O solution are most commonly used as transparent model materials for solidification researches of dendritic growth, anisotropy of solid-liquid interfacial energy, crystal nucleation, crystal grain formation, directional solidification, eutectic and peritectic so- lidification, solidification defects formation such as bubble, hot tearing, etc. Among these researches, the most impressive work was the critical test of dendritic growth theories with high purity succinonitrile by Glicksman et al., which gave positive answer to the Ivantsov＇s analysis and negative answer to the ad hoc condition of the maximum velocity hypothesis. The future researches with transparent model materials could be suggested in three aspects： 1） accurate measurement of material proper- ties and alloy phase diagrams in more plastic crystals, especially to find more transparent eutectic and peritectic alloys; 2） accurate measurement of the grain boundary groove shape to obtain precise data of the anisotropy parameters of the interfacial free energy in transparent model materials; 3） to get clear pictures of solidification processes with morphology details in a rela- tively large area, with continuous movement of liquid and particles, in order to give experimental support to numerical simula- tions aimming at accurate description of microstructure formation during solidification of multicomponent alloys under complex conditions of real casting and welding processes.