The lanthanides from La through about Er are found in measurable amounts in used nuclear fuel (plus the chemically analogous yttrium), with maximum yields (by mass) of neodymium and cerium. Yttrium behaves chemically very much like a lanthanide and is in fact found in nature in association with lanthanide minerals. These elements exist in solution and in the solid state in the trivalent oxidation state, with the minor exceptions of tetrava — lent cerium (Ce4+) and divalent europium (Eu2+). Because the valence elec­trons are placed in relatively constricted 4f valence orbitals, which shield the increasing nuclear charge across the series poorly, the cations decrease in size (by about 20%) from La3+ to Lu3+. [4] The bonding in coordination complexes appears to involve minimal covalent interactions. As a result, the coordination geometry of the complexes formed by the ions is usually dic­tated more by ligand steric constraints, by packing factors (in the solid state), and by rearrangement of the donor atoms in the ligands. In most situations, comparatively simple electrostatic models can be applied to cor­relate thermodynamic data describing lanthanide interactions with com — plexing agents or solvent molecules. This aspect of lanthanide chemistry has been discussed in detail by Choppin. [5] These cations are strongly hydrated, but comparatively weakly hydrolyzed, in part because of their compara­tively large size (cation radii average about 100 pm). The pKa values for the Ln3+ cations range from about 10 for La3+ to 7.8 for Lu3+, with the corre­sponding pH for precipitation of Ln(OH)3(s) ranging from 7.8 for La3+ to about 6.7 for Lu3+. The average primary hydration numbers for La3+ through Sm3+ are 9, for Gd3+ to Lu3+ the cations are octahydrates. Europium(III) represents the transition from hydration numbers of 9 to 8, exhibiting an average hydration number of 8.6. These metal ions form moderately stable soluble complexes with a wide variety of complexing agents. Complex sta­bility typically increases across the series, but only occasionally in a linear fashion all of the way across the series. Lanthanide ions form insoluble oxides/hydroxides, fluorides, sulfides, carbonates, and phosphates, though most of these are readily dissolved in acidic solutions.