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I recently read the following statements related to Manufacture of steel via Bessemer Process:

When no more $\ce{CO}$ is produced (i.e. blue flame disappears) a calculated amount of Spiegeleisen (an alloy of $\ce{Fe, Mn, C}$) is added and distributed throughout the mass by blowing air for some time.

Why do we need to add Spiegeleisen at the end? Is it to reduce the oxides of iron (that might have been formed)? Or due to some other reasons, like, say $\ce{Mn}$ to make steel harder and increase its tensile strength? But latter doesn't convince me, since we could have added $\ce{Mn}$ directly on order to get the same results. Also what's the meaning of calculated amount, how do we calculate the amount to be added, and why?

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I didn't think Bessemer was used anymore. Spiegeleisen is more likely to be called ferro-manganese today. I expect it is added at the end to minimize losses of Mn to the slag. Mn does contribute to hardenability but the primary reason for its use is to combine with residual sulfur to make MnS . MnS stringers can be harmful but are an improvement because otherwise the S will mostly be in grain boundaries reducing ductility and toughness. ( Bessemer process adds nitrogen to the steel reducing the toughness). Calculated amount would be based on the total weight of Mn that must be added to get the desired content in the steel , such as 0.5 weight %.The added amount would need to allow for expected loss to slag, etc.

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