 Solution

The host is zirconolite, with ideal end-member composition $\mathrm{CaZrT}{\mathrm{i}}_2{\mathrm{O}}_7$. In the proposed formula, the substitution is formallyIt is an isovalent substitution: the mean charge of the mixed zirconium/plutonium site remains $+4$, soNo compensating oxygen vacancy or aliovalent co-substituent is required by this particular charge account. Suitable oxidation state is essential; the same formula interpreted with only trivalent plutonium would not be charge balanced.

In zirconolite-2M the zirconium site has an oxygen coordination number of seven. The ionic radius of plutonium(IV) is larger than that of zirconium(IV), so increasing its occupancy changes local strain and the preferred arrangement of the cation layers. The observed progression in the investigated substitution series was zirconolite-2M → zirconolite-4M → pyrochlore structure, rather than unlimited substitution in one unchanged monoclinic lattice. The primary study found a 2M solid-solution limit near $x=0.15$, a narrow 4M range near $x=0.41$, and a pyrochlore composition at $x=0.60$ in ${\mathrm{CaZr}}_{1-x}{\mathrm{Pu}}_x\mathrm{T}{\mathrm{i}}_2{\mathrm{O}}_7$. These are experimental observations for that series, not universal boundaries independent of preparation and oxidation state.^[ref]

Consequently the nominal $x=0.20$ composition identifies a zirconolite-based waste-form design, but does not by itself prove a pure 2M product. Diffraction and phase-composition measurements are needed. At larger substitution, the fluorite-related pyrochlore arrangement accommodates a different cation distribution and coordination environment.