Getting more out of an incommensurately modulated structure: the example of K_5Yb(MoO_4)_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 $\beta$ coefficient of the modulation vector q = $\beta b*$ 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 can be represented as a polytypic modification with 1/2b*\le q\le 2/3b*; phases $\gamma$ (q = 1/2b*) and \alpha (q = 1b*) are the lowest and the highest temperature members of the K5Yb(MoO4)4 family, respectively.