Polytype family representations of octahedrally coordinated adaptive structures in Ta₂O₅: energetic and dynamic stability from first principles

This study broadens the understanding of the crystalline structures of Ta₂O₅, renowned for its inherent adaptive characteristics, by a unified and systematic approach to reconstruct crystalline structures as polytypes. This approach is applied to the layered adaptive structure and the Wadsley-Roth crystallographic shear (CS) adaptive structure, which were conventionally considered separately. The λ phase and the γ phase are investigated as representative phases of each type of adaptive structure, respectively, and the newly proposed <i>Pmma</i> phase is also examined. Using glide or screw symmetry operations, the individual phase is decomposed into smaller structural units, enabling the construction of an infinite number of polytypic variants. These variants are categorized into distinct polytype families and integrated into a single schematic encompassing both layered and CS adaptive structures. First principles calculations reveal that energy differences between the polytypic variants are generally smaller than the thermal energy at ambient temperature, suggesting that various stacking sequences can appear experimentally. Dynamically, on the other hand, polytypic variants with regular and frequent alternations of the structural units are favorable. These theoretical predictions are supported by previous experimental observations of the orthorhombic low-temperature phase (L-Ta₂O₅) with various periodicities. The high-symmetry λ and γ phases are corroborated as benchmark phases within their respective polytype families.