phase-field mode for facet crystal growth and measurement of its interface kinetics

利用去年导出的相场模型，建立了硅镍合金过冷熔体中硅的多面枝晶生长相场模型。以及二维枝晶生长实验。在薄界面极限下导出了相场参数，并用于仿真。为了提高计算效率，采用了一种自适应网格算法，并证明了界面佩莱特数必须足够小，以获得正确的生长速度。结果表明，多面枝晶的生长速度与过冷程度呈幂律关系，且枝晶尖端尺寸与生长速度之间存在标度规律。相场模拟应用于Si-6wt%Ni合金过冷熔体中二维面晶硅枝晶生长的后续实验中，其中合金熔膜过冷至115K时，通过高速摄像机现场观察到合金熔膜中枝晶的生长。原位观察和EBSP结晶学分析表明，在过冷50 ~ 110K范围内，均生长出< 21>的孪晶和<100>的无孪晶。当过冷度小于60K时，棒状晶体以< 21>的生长方向生长。测定了不同过冷度下枝晶的生长速度。<211>的枝晶生长速度略大于<100>的枝晶，但数据分布较分散。认为数据的上包络线给出了正确的枝晶生长速度，并与相场模拟进行了比较。两者的生长速度都遵循过冷的幂函数关系，线性动力学系数的值估计为0.01 m/sK。

A phase-field model for faceted dendrite growth of silicon from the undercooled melts of silicon-nickel alloys has been developed by using the phase-field model which is derived last year. and two-dimensional dendrite growth experiments. Phase-field parameters are derived at a thin interface limit and used in the simulations. For increasing computational efficiency an adaptive mesh algorism is used and it is shown that the interfacial Peclet number should be sufficiently small so as to obtain the correct growth velocity. The results show that faceted dendrite growth velocity follows a power law relationship to undercooling and there is a scaling law between the tip size of a dendrite and the growth velocity as sown for silicon. Phase-field simulations have been applied to the subsequent experiments on two-dimensional faceted silicon dendrite growth from the undercooled melt of Si-6wt%Ni alloy, in which the molten alloy film was undercooled up to 115K and dendrites growing in a thin film of the molten alloy were in-situ observed using a high-speed video camera. Both the in-situ observation of dendrite growth morphology and the EBSP crystallographic analysis for solidified samples show that both a <211> twin dendrite and a <100> twin-free dendrite grow in the range of the undercooling from 50 to 110K. At small undercooling less than 60K rod-like crystals grow with <211> growth direction. Growth velocity of dendrites was also measured at different undercooling. Growth velocity of <211> dendrites is slightly larger than that of <100> dendrites though the data are widely scattered. The upper envelope of the data is regarded to give the correct dendrite growth velocity and it is compared with phase-field simulations. Growth velocity in both follows power relationships to undercooling and the value of linear kinetic coefficient is estimated to be 0.01 m/sK.