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

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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.