Atomic Modulation Functions, Periodic Nodal Surfaces and the three-dimensional incommensurately modulated (1 − x)Bi2O3 · xNb2O5, 0.06 < x < 0.23, solid solution

Superspace group symmetry is used to parameterize the compositional and displacive degrees of freedom associated with the complex, three-dimensional incommensurately modulated (1 - x)Bi₂O₃ · xNb₂O₅, 0.06 < x < 0.23, type II solid solution. The metal and oxygen ion Atomic Modulation Functions are shown to be closely related to the so-called D Periodic Nodal Surface. The structural consequences of this shape for real three-dimensional physical space are spelt out and used to test the structural plausibility of previously proposed structural models.