Modulated structure of potassium sodium strontium barium niobates (KNSBN): harmonic solution

The structures of two specimens of the (K(1 - y)Na(y))(2F - 2)(Sr(x)Ba(1 - x))(2 - F)Nb2O6 family (KNSBN) have been solved and refined (x(I) = 0.6, y(I) = 0.45, F(I) = 1.07 and x(II) = 0.72, y(II) = 0.45, F(II) = 1.08). The KNSBN compounds appear to be incommensurately modulated, as described in a five-dimensional superspace approach with the tetragonal P4bm (pp1/2, p - p1/2) superspace group. Their modulation wavevectors are almost independent of the composition. The description of the modulation is restricted to first-order harmonics in order to limit the number of refined parameters. The modulation mainly affects the positions of the O atoms and their displacements depend on the Sr/Ba ratio. The structural models for the two compounds are not only almost identical, but also analogous to the structural model of the Sr(x)Ba(1 - x)Nb2O6 parent compound: doping with K+ and Na+ cations has no significant influence on the incommensurate modulation, contrary to the strong dependence observed for the physical properties.