Emergent Transitions: Discord between Electronic and Chemical Pressure Effects in the RE Al 3 ( RE = Sc, Y, Lanthanides) Series.

Atomic packing and electronic structure are key factors underlying the crystal structures adopted by solid-state compounds. In cases where these factors conflict, structural complexity often arises. Such is born in the series of RE Al 3 ( RE = Sc, Y, lanthanides), which adopt structures with varied stacking patterns of face-centered cubic close packed (FCC, AuCu 3 type) and hexagonal close packed (HCP, Ni 3 Sn type) layers. The percentage of the hexagonal stacking in the structures is correlated with the size of the rare earth atom, but the mechanism by which changes in atomic size drive these large-scale shifts is unclear. In this Article, we reveal this mechanism through DFT-Chemical Pressure (CP) and reversed approximation Molecular Orbital (raMO) analyses. CP analysis illustrates that the Ni 3 Sn structure type is preferable from the viewpoint of atomic packing as it offers relief to packing issues in the AuCu 3 type by consolidating Al octahedra into columns, which shortens Al-Al contacts while simultaneously expanding the RE atom's coordination environment. On the other hand, the AuCu 3 type offers more electronic stability with an 18- n closed-shell configuration that is not available in the Ni 3 Sn type (due to electron transfer from the RE d z 2 atomic orbitals into Al-based states). Based on these results, we then turn to a schematic analysis of how the energetic contributions from atomic packing and the electronic structure vary as a function of the ratio of FCC and HCP stacking configurations within the structure and the RE atomic radius. The minima on the atomic packing and electronic surfaces are non-overlapping, creating frustration. However, when their contributions are added, new minima can emerge from their combination for specific RE radii representing intergrowth structures in the RE Al 3 series. Based on this picture, we propose the concept of emergent transitions, within the framework of the Frustrated and Allowed Structural Transitions principle, for tracing the connection between competing energetic factors and complexity in intermetallic structures.