The polymorphous nature of the local structure of δ-Bi₂O₃

It is well established that theoretical prediction of the stable crystal structure of a compound is essential to calculating its electronic properties. When the theoretically predicted structure conflicts with the experimentally assessed structure, it is natural to assume that theory is wrong. An example is δ-Bi₂O₃ —an important functional material associated with its record oxygen transport. The documented nominal fluorite crystal structure of δ-Bi₂O₃ with Pn-3m space group—refined from X-ray diffraction (XRD) —is nowhere near the bottom of the convex hull calculated with state-of-the-art Density Functional Theory (DFT). This apparent failure of theory comes with additional puzzles. First, using the measured nominal structure as input to DFT band theory predicts the delta phase to be a zero-gap metal, in stark contrast with its known insulating properties, Second, phonon calculations indicate that the nominal XRD fluorite structure is not even dynamically stable, exhibiting imaginary phonons. Third, extending the Convex Hull concept to finite temperatures C(x,S,T) via “Compressive Sensing” machine learning reveals that the documented nominal crystal structure has high free energy above the convex hull. Here, we study theoretically the possibility that the refined structure for the δ phase was, in fact, an effective average ‘virtual structure’, not to be taken literally. To test this, we retain the global macroscopic crystallographic cell symmetry but increase the unit cell to a supercell, allowing local atomic positions to deviate from the artificially imposed average, seeking minimum calculated total energy. This reveals a macroscopically cubic but locally non-cubic distribution of low symmetry local motifs. Importantly, this ‘polymorphous network’ distribution has a lower total energy, it correctly predicts an insulating phase and agrees with the measured Pair Distribution Function much better than the literature average structure. It appears that experimentally determined high symmetry virtual average structure is not realistic.