Authors: Xingang Zhao | Oleksandr I. Malyi | Alex Zunger
Source: Physical Review Materials (article, 2024-12-26)
Field: Materials Science — Materials Chemistry

Polymorphous nature of the local structure of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>δ</mml:mi><mml:mtext>−</mml:mtext><mml:mi mathvariant="normal">B</mml:mi><mml:msub><mml:mi mathvariant="normal">i</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math> 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 $\ensuremath{\delta}\text{\ensuremath{-}}\mathrm{B}{\mathrm{i}}_{2}{\mathrm{O}}_{3}$---an important functional material associated with its record oxygen transport. The standard first step in theoretical structure prediction involves calculation of the ``Convex Hull'' diagram C (x, S, $\mathrm{T}=0$) contrasting the zero temperature energies of all currently imaginable competing phases at different compositions x and structures S, retaining the phases that persist with respect to decomposition into other constituents. Proximity of the energy of a structure to the Convex Hull indicates its expected theoretical stability. Surprisingly, the documented nominal fluorite crystal structure of $\ensuremath{\delta}\text{\ensuremath{-}}\mathrm{B}{\mathrm{i}}_{2}{\mathrm{O}}_{3}$---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 $\ensuremath{\delta}$ phase to be a zero-gap metal, in stark contrast with its known insulating properties. Second, phonon calculations indicate that the nominal 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 \ensuremath{\delta} 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 noncubic 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. Algorithm ; Materials science ; Computer science Ferroelectric and Piezoelectric Materials ; Crystal Structures and Properties ; Advanced ceramic materials synthesis