Hidden Structural Order in Orthorhombic Tantalum Pentoxide (Ta$_2$O$_5$)

We investigate using first-principles calculations the atomic structure of the orthorhombic phase of Ta$_2$O$_5$. Although this structure has been studied for decades, the correct structural model is controversial owing to the complication of structural disorder. We identify a new low-energy high-symmetry structural model where all Ta and O atoms have correct formal oxidation states of +5 and -2, respectively, and the experimentally reported triangular lattice symmetry of the Ta sublattice appears dynamically at finite temperatures. To understand the complex atomic structure of the Ta$_2$O$_3$ plane, a triangular graph-paper representation is devised and used alongside oxidation state analysis to reveal infinite variations of the low-energy structural model. The structural disorder of Ta$_2$O$_5$ observed in experiments is attributed to the intrinsic structural variations, and oxygen vacancies that drive collective relaxation of the O sublattice.