Na_3.16(2)U^V,VI _0.84(2)O₄ is obtained from the reaction of sodium with uranium dioxide under oxygen potential conditions typical of a sodium-cooled fast nuclear reactor. In the event of a breach of the steel cladding, it would be the dominant reaction product forming at the rim of the mixed (U,Pu)O₂ fuel pellets. High-temperature X-ray diffraction measurements show that a distortion of the uranium environment in Na_3.16(2)U^V,VI _0.84(2)O₄ results in a strongly anisotropic thermal expansion. A comparison with several related sodium metallates Na_n-2Mⁿ⁺O_n-1 - including Na₃SbO₄ and Na₃TaO₄, whose crystal structures are reported for the first time - has allowed us to assess the role played in the lattice expansion by the Mⁿ⁺ cation radius and the Na/M ratio. On this basis, the thermomechanical behavior of the title compound is discussed, along with those of several related double oxides of sodium and actinide elements, surrogate elements, or fission products.