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By investigating the effects of the configurational entropy, the vibrational entropy and the bonding strength of solid-liquid atoms on the structure of solid-liquid interface, a model for the interface energy of rough solid-liquid interface has been developed. From present model, the non-dimensional solid-liquid interface energies for metals at melting point are predicted to be 0.66-0.73, which are almost equal to the experimental result (0.66-0.75) obtained from grain boundary method. The solid-liquid interface energy decreases with increasing undercooling. At the maximum undercoolings that metals have reached, the non-dimensional solid-liquid interface energies predicted from present model are equal to 0.52-0.56. They are near to the experimental results (0.49-0.57) obtained from nucleation undercooling method. The predicted results of solid-liquid interface energy for metals from present model are in very good agreement with the experimentally measured results at melting point and undercooled state.

Using an electromagnetic levitation facility with a laser heating unit, silicon droplets were highly undercooled in the containerless state. The crystal morphologies on the surface of the undercooled droplets during the solidification process and after solidification were recorded live by using a highspeed camera and were observed by scanning electron microscopy. The growth behavior of silicon was found to vary not only with the nucleation undercooling, but also with the time after nucleation. In the earlier stage of solidification, the silicon grew in lateral, intermediary, and continuous modes at low, medium, and high undercoolings, respectively. In the later stage of solidification, the growth of highly undercooled silicon can transform to the lateral mode from the nonlateral one. The transition time of the sample with 320 K of undercooling was about 535 ms after recalescence, which was much later than the time where recalescence was completed.

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A criterion for judging the nucleation form in highly undercooled liquid has, respectively, been derived from the nucleation and structure of liquid. It is found that the nucleation form of a highly undercooled liquid can be judged by determining the S v in the liquid (where S v is the surface area of the supposed catalyst in a unit volume of the liquid). When the determined value of S v is equal to 10 10Ϯ1 m Ϫ1 , the liquid has nucleated homogeneously; it has nucleated heterogeneously if the determined value of S v is less than 10 10Ϯ1 m Ϫ1 . By calculating the values of S v in highly undercooled aluminum, copper, and silver, it is found that only silver melted under a slag has been undercooled to its undercooling of homogeneous nucleation.