Structure relations in the family of the solid solution Hf x Zr1-x O2

Hafnium Zirconium Oxide Hf x Zr1-x O2 is a potentially ferroelectric material with great perspectives in semiconductor applications, due to its compatibility with silicon technologies and its low toxicity. Despite its chemical simplicity, the solid solution Hf x Zr1-x O2 comprises a large variety of different phases. We compiled a complete list of experimentally and theoretically reported Hf x Zr1-x O2 structures. All of them are symmetrically related to the common aristotype with Fluorite type structure. The symmetry relationships between those structures have been determined and are presented in a Barnighausen-like tree. Interestingly, not all symmetry reductions follow the conventional group-subgroup relations and involve severe atomic shifts. 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 Barnighausen-like tree was used to transform the indices of a reflection before and after a phase transition. This conversion allows the study of (dis)appearing reflections during phase transitions.

Automated summary

Hafnium Zirconium Oxide (Hf x Zr1-x O2) is a promising ferroelectric material for semiconductor applications due to its compatibility with silicon technologies and low toxicity. The material exhibits various phases, and studying their symmetry relationships provides insights into structural changes and phase transitions.