Structure relations in the family of Hf$_x$Zr$_{1-x}$O$_2$ solid solution

Hafnium Zirconium Oxide Hfx Hf$_x$Zr$_{1-x}$O$_2$ is a potentially ferroelectric material with high perspectives in semiconductor applications, due to their compatibility with silicon technologies and their low toxicity. Despite their chemical simplicity, the Hfx Hf$_x$Zr$_{1-x}$O$_2$ family comprises a large variety of different phases. We compiled a complete list of experimentally and theoretically reported Hfx Hf$_x$Zr$_{1-x}$O$_2$ structure types. All of them are symmetrically related to the common aristotype with Fluorite structure. The transition paths between those strucutre types have been determined and are presented in a Bärnighausen diagram. Interestingly, not all transitions follow the conventional group-subgroup relations and involve severe atomic shifts indicating martensitic type transitions. Further, the structures were compared to each other in detail regarding the dimensionality of atomic shifts and the accompanied lattice distortions. Finally, the information provided by the Bärnighausen diagram was used to convert the indices of a reflection before and after a phase transition. This conversion allows the study of (dis)appearing reflections during phase transitions