Trivalent lanthanide ions (La3+, EU(3+), and Lu3+) in solid materials can be effectively extracted by methanol-modified carbon dioxide containing a suitable fluorinated beta-diketone (such as HFA, TTA, or FOD) at 60 degrees C and 150 atm. Addition of a small amount of water to the solid samples can significantly increase the extraction efficiency. Tributyl phosphate (TBP) shows a strong positive synergistic effect with the fluorinated beta-diketones for the extraction of the lanthanides in supercritical CO2 without methanol modifier. Quantitative extraction of the lanthanides (92-98%) from sand or a cellulose-based solid material can be achieved using a mixture of TBP and one of the fluorinated beta-diketones in neat CO2 at 60 degrees C and 150 atm. The synergistic effect depends on the structure and fluorine substitution in the beta-diketone. In soil matrix, TBP+HFA are more effective than TBP+TTA or TBP+FOD for lanthanide extraction in supercritical CO2. Without fluorine substitution, as in the case of acetylacetone, the positive synergistic extraction of lanthanides with TBP is negligible. With the mixed-ligand approach, high efficiencies of lanthanide extraction from aqueous solutions by neat CO2 can also be accomplished.