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The precipitation of non‐metallic inclusions in Ti‐deoxidised steels is analysed with the multiphase equilibrium code CEQCSI which is based on the IRSID slag model. For that purpose, the slag model has been extended to systems containing titanium oxides, using data available in the literature, and validated with industrial results obtained on various steel grades. Applications concerning slag‐metal reactions in ladle metallurgy are described. 2 applications concerning inclusions in Ti‐deoxidised steels are also presented: (a) experimental study of the effect of steel contamination by magnesia refractory lining on the composition of oxide inclusions in a Ti‐deoxidised steel: there is a good correlation between analysed oxide compositions and compositions predicted by the model; (b) evaluation of the optimised steel composition to obtain Al2O3‐TiO2 inclusions during solidification for steels pertaining to the so‐called “metallurgy of oxides in steels”.

The equilibration between CaO-SiO 2 -MgO-Al 2 O 3 -CaF 2 (-TiO 2 ) slag and Fe-11 mass pct Cr ferritic stainless steel melts was investigated at 1873 K in order to clarify the effect of Al and Ti addition as well as that of slag composition on the formation of complex oxide inclusions. The activity of oxygen calculated from the classical Wagner formalism changes from about a O = 0.0002 to 0.001 and the values of a O from [Al]/(Al 2 O 3 ) and that from [Si]/(SiO 2 ) equilibria are in relatively good agreement with each other with some scatters. The phase stability diagram of the inclusions and the equilibrium iso- [O] lines in the Fe-11 mass pct Cr-0.5 mass pct Si-0.3 mass pct Mn-0.0005 mass pct Mg steel melts was constructed by using FACTSAGE 5.5 program as a function of Al and Ti contents. The computed iso-[O] lines were slightly larger than the values estimated from the slag-metal equilibria. The composition of the inclusions could be plotted on the computed MgO-Al 2 O 3 -TiO x phase diagram. The inclusions in the steel melts equilibrated with the basic slags are located in the ''spinel + liquid'' region, while those in equilibrium with the less basic slags are mostly in the ''liquid'' single phase. This is in good accordance to the observed morphology of the inclusions. However, in cases of high concentration of Ti and Al, the inclusions were found to be spinel + liquid, even though the less basic slags are equilibrated. When plotted on logarithmic scales, the mole ratio X MgO  X Al 2 O 3 X Ti 2 O 3 À Á of the inclusions (spinel potential) was expressed as a linear function of a Mg  a 2 Al  a O a 2 Ti Ä Å of the steel melts with a slope of unity theoretically expected. Also, the spinel potential is very low and nearly constant when the activity of Al 2 O 3 is less than that of TiO 2 in the slag saturated by MgO, whereas it linearly increases by increasing the log a Al 2 O 3 =a TiO 2 ð Þat X Al 2 O 3 =X TiO 2 ð Þ >1.

In the calculation. the volume element is supposedto contain only one mole of chemical elements. Integration which takes into account Brody-Flemings approximation makes it possible to obtain an equation expressing the numberof moles in the solid (N~(~)) with respect to successive molar concentrations at the interface (X~(A)):

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