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

Abstract

As with other electron counting rules, the 18-n rule of transition metal–main group (T–E) intermetallics offers a variety of potential interatomic connectivity patterns for any given electron count. What leads a compound to prefer one structure over others that satisfy this rule? Herein, we investigate this question as it relates to the two polymorphs of IrIn3: the high-temperature CoGa3-type and the low-temperature IrIn3-type forms. DFT-reversed approximation Molecular Orbital analysis reveals that both structures can be interpreted in terms of the 18-n rule but with different electron configurations. In the IrIn3 type, the Ir atoms obtain largely independent 18-electron configurations, while in the CoGa3 type, Ir–Ir isolobal bonds form as 1 electron/Ir atom is transferred to In–In interactions. The presence of a deep pseudogap for the CoGa3 type, but not for the IrIn3 type, suggests that it is electronically preferred. DFT-Chemical Pressure (CP) analysis shows that atomic packing provides another distinction between the structures. While both involve tensions between positive Ir–In CPs and negative In–In CPs, which call for the expansion and contraction of the structures, respectively, their distinct spatial arrangements create very different situations. In the CoGa3 type, the positive CPs create a framework that holds open large void spaces for In-based electrons (a scenario suitable for relatively small T atoms), while in the IrIn3 type the pressures are more homogenously distributed (a better solution for relatively large T atoms). The open spaces in the CoGa3 type result in quadrupolar CP features, a hallmark of low-frequency phonon modes and suggestive of higher vibrational entropy. Indeed, phonon band structure calculations for the two IrIn3 polymorphs indicate that the phase transition between them can largely be attributed to the entropic stabilization of the CoGa3-type phase due to soft motions associated with its CP quadrupoles. These CP-driven effects illustrate how the competition between global and local packing can shape how a structure realizes the 18-n rule and how the temperature can influence this balance.

Navigating the 18-n+m Isomers of PdSn2: Chemical Pressure Relief through Isolobal Bonds and Main Group Clustering

“…Such a situation, however, does not mean that 18- n + m picture is inapplicable, just as some Zintl phases also lack pseudogaps but exhibit structures perfectly in-line with the Zintl scheme. ,, We note that the absence of striking pseudogaps at the Fermi energy in the DOS distributions also has precedence in some 18- n + m compounds, which nonetheless have bonding interpretable in terms of 18- n + m configurations. An obscured pseudogap can arise from the presence of unanticipated isolobal bonds, as in Ni 3 Sn-type YAl 3 , T–T π-bonding in TiAl 3 , or the unexpected population of main group-based cages, as seen in IrIn 3 -type IrIn 3 and IrAl 4 . In these cases, the Fermi energies were misaligned with respect to the nearest pseudogap.…”

“…We term this diversity of structural possibilities 18-n+m isomerism. 23 With so many electronically viable options, other factors such as atomic size ratios can become decisive in determining the observed structure for any given compound. In this Article, we explore how such interactions underlie the observed structure of PdSn 2 , with broader lessons for 18-n compounds.…”

“…However, for any given electron count, there are numerous structures that can fulfill this requirement, especially when we consider changes in n being coupled to the transfer of electrons between the T and E sublattices. We term this diversity of structural possibilities 18- n + m isomerism . With so many electronically viable options, other factors such as atomic size ratios can become decisive in determining the observed structure for any given compound.…”

“…How do systems navigate all the possible 18- n + m isomers to find the most stable structure? In our recent investigations of 18- n + m isomerism in REAl 3 phases (RE = lanthanide or group 3 metal) and IrIn 3 , we observed that competition between electronic and atomic packing effects strongly influences which isomer is favored. ,, While explanations for these cases of 18- n + m isomerism have been offered, predictive guiding principles for the design in these materials are still limited. Achieving these goals requires broader consideration of the driving forces and structural mechanisms for increasing or decreasing the n and m values for a compound.…”