It's called "liquid-liquid extraction" [1] and requires crushing the rock and mixing it with an extractant (see D2EHPA [2] which is also used in uranium extract

It's called "liquid-liquid extraction" [1] and requires crushing the rock and mixing it with an extractant (see D2EHPA [2] which is also used in uranium extraction) into a nasty acidic slurry. It is then separated into a aqueous layer containing the waste and a nonpolar solvent that strips the rare earth elements bound up with the extractant. All the different rare earth elements then have to be separated out of the nonpolar solvent using even more toxic chemicals, each of which leaves behind a different hazardous waste. Fun(?) fact: This process looks a lot like the alkali extraction process used to make cocaine, DMT, and a variety of other drugs. [1] https://en.wikipedia.org/wiki/Liquid%E2%80%93liquid_extraction https://en.wikipedia.org/wiki/Liquid%E2%80%93liquid_extracti... [2] https://en.wikipedia.org/wiki/Di-(2-ethylhexyl)phosphoric_acid https://en.wikipedia.org/wiki/Di-(2-ethylhexyl)phosphoric_ac...