I am a materials science (and metallurgy) student and geology enthusiast. Comparing these two subjects side by side, I have found out some interesting pattern.

Ironmaking slag has 40-45% CaO, 30-40% SiO2 , 10-15% Al2O3 , about 5% MgO and 1-2% FeO. Steelmaking slag can have 40-60% CaO, 10-25% SiO2, 2-10% MgO, 5-35% FeO and 0-25% P2O5.

Ironmaking slag can have, among many other minerals, Akermanite, Monticellite, Gehlenite ,Anorthite, Pyroxene etc, along with some spinels. In my opinion , it matches with some feldspathoids with slightly mafic character. Steelmaking slag is more close to alkaline earth mafic rocks and peridotites. It has a good amount of spinels, monticellite, merwinite, silicocarnite, periclase etc.

Answers from metallurgists and Geologists are welcome

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