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Efficient Si-melting

In a metallurgical process at Elkem there is a need for efficient melting of silicon.
Some relevant data for Si (Wikipedia):
Melting point: 1414 °C
Heat capacity at 25 °C: 19.8 J/mole K = 0.70 kJ/kg K
Heat of fusion (melting): 50.21 kJ/mole = 1788 kJ/kg
Liquid density (at melting point): 2 570 kg/m3
Solid density (at room T): 2 329 kg/m3
Hence, silicon melting requires a lot of energy. More energy is needed for melting than to heat Si to the melting point. Solid Si is less dense than liquid Si. Hence, solid particles will float.

As a comparison, ice/water has the following properties:
Melting point: 0 °C
Heat capacity at -10 °C: 2.05 kJ/kg K
Heat capacity at 20 °C: 4.18 kJ/kg K
Heat of fusion (melting): 334 kJ/kg
Liquid density (at melting point): 998 kg/m3
Solid density (at melting point): 917 kg/m3

One option for melting Si is to use an induction furnace. A crucible is surrounded by an electric coil. While solid silicon is a semiconductor, molten Si is a metal with high electric conductivity. The liquid Si can therefore be heated by induction currents caused by a high alternating current in the coil. Depending on the conductivity of the crucible material, a small or large fraction of the power can be induced in the crucible.
 

Melting will normally start with a certain amount of molten silicon in the crucible. In the beginning of a melting cycle a high fraction of the power is induced in the crucible above the silicon level. The resulting high maximum temperature in this region is a limiting factor for the power input.

Towards the end of the cycle a higher fraction of the power is induced directly in the metal. The power induced in the crucible is distributed almost evenly along the height, within the region covered by the coil. Hence, more power can be induced now.

To increase the melting rate more power is needed in the melting region at the top of the silicon. One limiting factor seems to be heat transfer to the molten silicon.
If the induction frequency is lowered, a higher fraction of the power will be induced directly in the metal. Then more power can be applied without getting higher temperatures than before in the crucible walls.

As part of an evaluation on how to improve melting capacity, Elkem wants improved insight about other consequences of lower frequency and higher power input. The ESGI discussions should focus on changes in the fluid flow and in the melting at the top of the liquid silicon.

 

Problem presented by:
Svenn Anton Halvorsen (Teknova)

 

Study group contributors:
Andrew Crosby (University of Cambridge)
Neil Deacon (University of East Anglia)
Jeff Dewynne (University of Wollongong)
Andrew Lacey (Heriot-Watt University)
William Lee (University of Limerick)
John Ockendon (University of Oxford)
Robert Whittaker (University of East Anglia)
 

Related resources:

Problem brief

Initial presentation

Final presentation

Final report: Please email david.allwright@industrialmaths.net for a copy.

Other materials projects

Other Study Group projects

 

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