Emergent Transitions: Discord between Electronic and Chemical Pressure Effects in the REAl₃ (RE = Sc, Y, Lanthanides) Series

Abstract

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 REAl 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 REAl 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.

Entropic Control of Bonding, Guided by Chemical Pressure: Phase Transitions and 18-n+m Isomerism of IrIn3

“…The IrIn 3 -type compound is not the first case where the DOS pseudogaps expected from the 18- n rule and structural connectivity are absent or misplaced. In a series of RE Al 3 (RE = Sc, Y, lanthanides), the connectivity of the Ni 3 Sn-type members appears to follow the 18- n rule, but the DOS distribution for this structure shows it is electron-deficient with respect to the nearest pseudogap . DFT-raMO analysis revealed that Al–Al bonding states withdraw electrons from the RE atoms, raising the number of electrons needed for the 18- n electron configurations.…”

“…The quality and degree of localization of the raMOs across the series were monitored with the P sphere metric, the fraction of the raMO’s electron density within a sphere of a defined radius ( r sphere ) centered on the target function . raMOs with relatively high P sphere values were considered occupied by electron pairs.…”

“…The quality and degree of localization of the raMOs across the series were monitored with the P sphere metric, the fraction of the raMO's electron density within a sphere of a defined radius (r sphere ) centered on the target function. 40 raMOs with relatively high P sphere values were considered occupied by electron pairs. When P sphere values are inconsistent across a series or relatively low, the raMOs are manually inspected for their resemblance to the target function.…”

“…In a series of REAl 3 (RE = Sc, Y, lanthanides), the connectivity of the Ni 3 Sn-type members appears to follow the 18-n rule, but the DOS distribution for this structure shows it is electron-deficient with respect to the nearest pseudogap. 40 DFT-raMO analysis revealed that Al−Al bonding states withdraw electrons from the RE atoms, raising the number of electrons needed for the 18-n electron configurations. Could a similar mechanism be at work here?…”

“…This phenomenon of main group-based crystal orbitals crossing below other bands has been observed in other T−E intermetallics. 40 The depopulation of the 6p x orbitals does, however, come with an advantage. Recall that the tri-capped trigonal prism units form chains along the a-axis.…”