gadolinium is primarily a strong neutron absorber. The supplied thermal cross section for gadolinium-157 is very large, so capture removes neutrons that could otherwise sustain nuclear fission. This is a criticality-control role rather than a requirement to complete the host formula. The isotope-specific number must not be assigned unchanged to natural gadolinium.
hafnium supplies an additional neutron poison with favourable retention chemistry. Its supplied natural-abundance thermal cross section is much smaller than that of gadolinium-157 but still appreciable. Chemically, tetravalent hafnium resembles zirconium and can remain associated with a durable titanate host. Keeping the absorber with the fissile inventory during alteration is as important as its initial neutron capture strength: a highly absorbing constituent offers poor long-term protection if it is preferentially lost. These considerations explain using complementary absorbers rather than ranking them solely by their initial thermal cross sections.
uranium addition chiefly addresses isotopic dilution, including the long-term daughter inventory. plutonium-239 alpha decay produces uranium-235. Added uranium-238 lowers the uranium-235 fraction of that future uranium inventory; depleted uranium adds less uranium-235 initially than natural uranium. uranium-238 also absorbs some neutrons, but its small listed cross section does not make it a substitute for the strong absorbers. The long-term daughter issue and the retention of gadolinium and hafnium are explicit concerns in ceramic waste-form development.[ref]
These are complementary physical purposes, not proof of criticality control in radioactive waste from three cross-section values. neutron energy, isotopic composition, geometry, moderation, absorber distribution and their coupled evolution matter. Incorporation in the same durable waste form helps maintain association, but neither uranium addition nor chemical immobilisation makes deliberate element separation physically impossible.