A theoretical approach for the interpretation of liquid metal surface tension measurements in the presence of oxygen

Abstract

Theoretical models describing the transport of oxygen in metal/atmosphere systems under different fluid-dynamic conditions have been developed by different authors. In the present study, as in previous ones, the molecular diffusion is the process mainly controlling the exchange of matter between the liquid metal and the atmosphere. So, in this paper a diffusional model is proposed accounting for volatile oxides and for gas phase homogeneous reactions by means of two limiting conditions: instantaneous reactions and null reactions. For the boundary conditions, the model assumes a bulk flow composition of the gas layer surrounding the liquid on the upper side and a local equilibrium constraint at the liquid interface. The asymptotic behavior of the system is described, enabling the prediction of the direction of the net oxygen flux. It has been demonstrated that the results obtained are valid for any type of homogeneous gas phase reactivity, provided that no oxide fog is formed in the gas. The model is useful to correctly guide technological processes such as single crystal growth: in the paper the application to the melt silicon/oxygen system is discussed. Finally, the present model can synthesize apparently contradictory experimental measurements of surface tension available in literature into a unique portrait.