Search for high-pressure phases of yttrium via a data assimilation approach

We investigate the distorted face-centered-cubic (dfcc) phase of yttrium (Y) using a data-assimilation-based structure search that combines high-resolution powder x-ray diffraction (XRD) data with machine-learning interatomic potentials. By exploring supercells containing up to 128 atoms, we identify three low-enthalpy phases: the previously reported $I4_1/a$ structure and two additional structures, $Ibam$ and $R\overline{3}$. No data-assimilation-derived structure relaxes to the previously proposed $R\overline{3}m$ phase. Phonon calculations show that $I4_1/a$, $Ibam$, and $R\overline{3}$ are dynamically stable, whereas $R\overline{3}m$ exhibits imaginary modes near the $\Gamma$ point, indicating dynamical instability. Enthalpy calculations using both PBE and r$^{2}$SCAN place the four candidate structures within about 10 meV/atom, indicating a complex energy landscape with multiple competing minima, although $R\overline{3}m$ is consistently highest in enthalpy and r$^{2}$SCAN favors $I4_1/a$ throughout the dfcc pressure range. Rietveld refinements of the powder XRD profile at 60 GPa further narrow the viable structural models to $I4_1/a$ and $Ibam$, both of which reproduce the experimental data better than $R\overline{3}m$ and $R\overline{3}$. Taken together with the energetic ordering and dynamical stability, these results identify $I4_1/a$ as the most plausible structure of the dfcc phase of Y, with $Ibam$ remaining a close competing candidate, particularly toward the high-pressure side of the dfcc region.