Getting more out of an incommensurately modulated structure: the example of K₅Yb(MoO₄)₄

A method based on the superspace approach is presented with the aim of generating a family of modular structures from a single incommensurately modulated structure. This approach based on the variation of the modulation vector q is applied to the generation of the K₅Yb(MoO₄)₄, potassium ytterbium tetramolybdate, family of modular structures. The β coefficient of the modulation vector q = βb* is a temperature-dependent variable which determines the modification. Our method gives a unified frame to describe and explain the three temperature-dependent phases of K₅Yb(MoO₄)₄. Phase β can be represented as a polytypic modification with 1/2b* ≤ q ≤ 2/3b*; phases γ (q = 1/2b*) and α (q = 1b*) are the lowest and the highest temperature members of the K₅Yb(MoO₄)₄ family, respectively.