Why are rare-earth elements difficult to separate from one another?

Rare-earth elements are difficult to separate primarily because of their extreme chemical similarity, which stems from their electron configuration.1

In these elements, the 4f electrons are "localized" within the ion core and lie inside the outer valence electrons. Because these 4f electrons do not directly participate in chemical bonding, the elements generally exhibit the same +3 oxidation state and share very similar chemical properties.12

Furthermore, this similarity is reinforced by the lanthanide contraction—a steady, systematic decrease in atomic and ionic radii as the atomic number increases. Because the ions remain similar in size and charge, they are difficult to distinguish using standard chemical processes. While they can be separated using techniques like ion exchange by introducing complexing agents to exploit slight variations in stability, their inherent chemical likeness remains a fundamental challenge in their isolation.213