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How does the Betterton-Kroll process separate bismuth from lead?

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A labeled periodic table element box for bismuth shows atomic number 83, symbol Bi, atomic weight 208.9804, electron configuration, and properties including solid state, rhombohedral crystal structure, and weakly acidic oxides. — bismuth Properties of bismuth.

The Betterton-Kroll process, also known as the Asarco process, is a pyrometallurgical method used to remove bismuth from lead bullion.12

The process functions through the following steps:

Addition of Reagents: Calcium and magnesium are added to a molten lead-bismuth bath.1
Compound Formation: The bismuth reacts with these metals to form compounds that possess higher melting points and lower densities than the surrounding molten lead.12
Separation: Because these compounds are lighter than lead, they rise to the surface of the melt, where they are removed as a solid dross.12
Recovery: The bismuth can subsequently be recovered from the skimmed calcium-magnesium compounds by treatment with chlorine.1

This method is typically employed after the lead has undergone softening, desilvering, and dezincing, and it is capable of producing refined lead with bismuth levels between 0.005 and 0.01 percent.2