How are scandium and yttrium related to the rare-earth elements?

Scandium and yttrium are classified as rare-earth elements because they belong to Group 3 of the periodic table, alongside lanthanum. While the term "rare-earth element" is often used to refer specifically to the lanthanides (cerium through lutetium), scandium and yttrium are included in the broader chemical grouping due to their shared characteristics and periodic placement.12

Their relationship to the other rare earths is defined by several factors:

• Chemical Similarity: Like the lanthanides, scandium and yttrium are generally trivalent (forming $R^{3+}$ ions) and exhibit chemical behaviors that are often similar to the other rare-earth elements.314
• Geochemical Association: Yttrium has an ionic radius (0.9 Å) nearly identical to that of holmium, which causes it to occur naturally alongside the heavy lanthanides in minerals.45
• Distinct Geochemistry: Scandium’s geochemistry differs significantly from the other rare earths. Because its ionic radius (0.745 Å) is much smaller than that of the smallest lanthanide, it is essentially absent from typical rare-earth minerals and is instead recovered as a by-product of other mining operations.534