I am looking for a way to separate metal oxides on the Moon. Please bear with me - it's for an ultra-hard science fiction project. Processes typical on Earth are not effective there. Heat is cheap on the Moon, there is strong constant sun that is easily concentrated. Heat also dissipates slowly thanks to the vacuum, and reflective insulation can be used to slow heat loss much more.
So, I wondered if a form of controlled fractional crystallization could be used to get pure olivine from a molten melt of rock, and then the olivine could be split into forsterite and fayalite the same way. The forsterite might make decent clear glass, or if not, the fayalite can be processed with hydrogen to get iron, water, and silica, and the silica can be used to make glass. It might be necessary to apply centrifugal force to get the crystals to separate in the Moon's low gravity. If the technique works, it would seem the same process could be used to isolate other metal oxides through other paths.
Hydrogen and carbon atoms are present on the level of around 100 ppm. Am I correct in thinking that mineral separation would occur this way and could be controlled to get good purity? I know there are engineering issues, but in terms of the geochemistry, is it correct that crystallization and settling would occur in this way?
(Note: I heavily edited this after my continued searching on the topic finally got me to 'fractional crystallization', and then I came across a few things that made me rethink the whole thing.)