The extraction and processing of rare earths is extraordinarily complex. At a high level, it involves three steps.
Concentration. Scientists experiment to find a unique acid solution capable of dissolving the target rare earth. Because every ore is different, each requires its own cocktail. Once the right blend is found, the target mineral dissolves into the acid like salt in water.
Separation. At this stage, the mixture is a dark, sludgy, radioactive slurry. Centrifuges and filters are used to remove everything except the target mineral.
Extraction. The acid is evaporated away, leaving behind a greyish powder of the target material.
This three-step process may need to be repeated hundreds of times to achieve a pure concentration.
Connections
Rare Earth Element Processing Cannot Be Standardized
Rare Earth Refining Cannot Target High Priced Materials
Reference
� The Elements of Power