Bismuth sodium molybdate, Na0.5Bi0.5-MoO4 (I), M(r) = 275.92, tetragonal, I4(1)/a, a= 5.2717 (1), c = 11.5801 (2) angstrom, V = 321.824 (5) angstrom3, Z = 4, D(n) = 5.69 g cm-3, R(p) = 4.06% (263 reflections, neutron data). Bismuth sodium molybdate, Na0.32-Bi0.56MoO4 (II), M(r) = 284.33, tetragonal, I4(1)/a, a = 5.2785 (1), c = 11.6410 (2) angstrom, V = 324.342 (5) angstrom3, Z = 4, D(n) = 5.82 g cm-3, R(p) = 4.82% (293 reflections, neutron data). Cerium sodium molybdate, Na0.5-Ce0.5MoO4 (III), M(r) = 241.64, tetragonal, I4(1)/a, a = 5.3167 (4), c = 11.6600 (11) angstrom, V = 329.58 (3) angstrom3, Z = 4, D(x) = 4.87 g cm-3, R(p) = 12.34% [105 reflections, X-ray data, Cu Kalpha (1.5415 angstrom) radiation]. Lanthanum sodium molybdate, Na0.5La0.5MoO4 (IV), M(r) = 241.03, tetragonal, I4(1)/a, a = 5.3424 (4), c = 11.7376 (11) angstrom, V = 335.01 (3) angstrom3, Z = 4, D(x)= 4.78 g cm-3, R(p) = 10.82% [107 reflections, X-ray data, Cu Kalpha (1.5415 angstrom) radiation]. The structures have been refined with room-temperature time-of-flight powder neutron diffraction data or X-ray diffraction data as indicated. Results of Rietveld refinements indicate that all of the materials adopt the scheelite (CaWO4) structure, with Na, vacancies and Bi, La or Ce cations randomly distributed on the Ca site, and Mo occupying the W site.