Magnetically stabilized Fe8(µ4-S)6S8 clusters in Ba6Fe25S27.

We have prepared Ba6Fe25S27, and studied its magnetic properties and electronic structure. Single crystal diffraction revealed a cubic phase (Pm3[combining macron]m) with a = 10.2057(9) Å and Z = 1. Within the large cubic cell, tetrahedrally coordinated Fe atoms arrange into octonuclear Fe8(µ4-S)6(S8) clusters, which can be described as a cube of Fe atoms with six face-capping and eight terminal S atoms. SQUID magnetometry measurements reveal an antiferromagnetic transition at 25 K and anomalous high-temperature dependence of magnetic susceptibility that is non-Curie like-two magnetic signatures which mimic behavior seen in the parent phases of Fe-based superconductors. Using a combined DFT and molecular orbital based approach, we provide an interpretation of the bonding and stability within Ba6M25S27 (M = Fe, Co, Ni) and related M9S8 phases. Through a σ-bonding molecular orbital model of the transition metal coordination environments, we illustrate how the local stability can be enhanced through addition of Ba. In addition, we perform spin-polarized DFT calculations on Ba6Fe25S27 to determine the effect of adopting an antiferromagnetic spin state on its electronic structure. By studying the magnetic properties from an empirical and computational perspective, we hope to elucidate what aspects of the magnetic structure are significant to bonding.

Acid-base chemistry in the formation of Mackay-type icosahedral clusters: µ3-acidity analysis of Sc-rich phases of the Sc-Ir system.

The crystal structures of intermetallic phases offer a wealth of geometrical features (helices, multishelled clusters, and host-guest motifs) whose formation has yet to be explained or predicted by chemical theory. A recently developed extension of the acid-base concept to metallic systems, the µ3-acidity model, provides an avenue for developing this understanding for intermetallics formed from transition metals. In this Article, we illustrate how this approach can be used to understand one of the most striking geometrical entities to emerge in intermetallic chemistry, the Mackay cluster of icosahedral quasicrystals. We present µ3-acidity analyses, based on DFT-calibrated Hückel calculations, for a series of Sc-Ir intermetallics: ScIr (CsCl-type), Sc2Ir (Ti2Ni-type), Sc11Ir4, and the Mackay cluster containing phases Sc57Ir13 and Sc44Ir7. We begin by illustrating that a µ3-acidity model correctly predicts that each of these phases is stable relative to disproportionation into their neighboring compounds when a common set of Hückel parameters and d-orbital occupancies is used. Next, we explain these results by developing a relationship between the distance distribution of homoatomic contacts within an atom's coordination sphere and the µ3-neutralization it experiences. For a given average homoatomic distance, the role of heteroatomic contacts is higher when the distribution of homoatomic contacts is narrower. This effect is key to the strength of the acid-base neutralization of the Sc-rich phases, where the Sc atoms find a scarcity of Ir atoms from which to obtain neutralization. Under these circumstances, Sc-Ir contacts should be maximized, whereas the number and distance variations of the Sc-Sc contacts should be minimized. These expectations are borne out by the observed crystal structures. In particular, the Mackay clusters of Sc57Ir13 and Sc44Ir7, in which a central Ir atom is icosahedrally coordinated by a pentagonal dodecahedral array of face-sharing Sc octahedra, represent a natural way of merging the competing needs for enhancing Sc-Ir interactions while diminishing those between the Sc atoms.

Structural acid-base chemistry in the metallic state: how µ3-neutralization drives interfaces and helices in Ti21Mn25.

Intermetallic phases remain a large class of compounds whose vast structural diversity is unaccounted for by chemical theory. A recent resurgence of interest in intermetallics, due to their potential in such applications as catalysis and thermoelectricity, has intensified the need for models connecting their compositions to their structures and stability. In this Article, we illustrate how the µ3-acidity model, an extension of the acid/base concept based on the Method of Moments, offers intuitive explanations for puzzling structural progressions occurring in intermetallics formed between transition metals. Simple CsCl-type structures are frequently observed for phases with near 1:1 ratios of transition metals. However, in two compounds, TiCu and Ti21Mn25, structures are adopted which deviate from this norm. µ3-Acidity analysis shows that the formation of CsCl-type phases in these exceptional systems would yield an imbalance in the acid/base strength pairing, resulting in overneutralization of the weaker partner and thus instability. Intriguing geometrical features emerge in response, which serve to improve the neutralization of the constituent elements. In both TiCu and Ti21Mn25, part of the structure shields weaker acids or bases from their stronger partners by enhancing homoatomic bonding in the sublattice of the weaker acid or base. In TiCu, this protection is accomplished by developing doubled layers of Ti atoms to reduce their heteroatomic contacts. In Ti21Mn25 the structural response is more extreme: Ti-poor TiMn2 domains are formed to guard Mn from the Ti atoms, while the remaining Ti segregates to regions between the TiMn2 domains. The geometrical details of this arrangement fine-tune the acid/base interactions for an even greater level of stability. The most striking of these occurs in the Ti-rich region, where a paucity of Mn neighbors leads to difficulty in achieving strong neutralization. The Ti atoms arrange themselves in helical tubes, maximizing the surface area for Ti-Mn interactions. Through these examples, we show how the µ3-acidity model provides simple explanations for some of the beautiful structural motifs observed in intermetallic crystals. The foundation of the model in the Method of Moments makes it applicable to a variety of other contexts, including glasses, defects, and nanostructured surfaces.

Perceiving molecular themes in the structures and bonding of intermetallic phases: the role of Hückel theory in an ab initio era.

Qualitative molecular orbital theory is central to our understanding of the bonding and reactivity of molecules and materials across chemistry. Advances in computational technology and methodology, however, have made ab initio or density functional theory calculations a simpler alternative, offering reliable results on increasingly large systems in a reasonable time-scale without the need for concerns about the approximations and parameterization of semi-empirical one-electron based methods. In this perspective, we illustrate how the availability of higher-level computational results can augment, rather than supplant, the insights provided by approaches such as the simple and extended Hückel methods. We begin by describing a way to parameterize Hückel-type Hamiltonians against DFT results for intermetallic systems. The potential for chemical understanding embodied by such orbital-based models is then demonstrated with two schemes of bonding analysis that originated in them (but can be extended to DFT results): the µ(3)-acid/base model and the µ(2)-Hückel chemical pressure analysis, which translate the molecular concepts of acidity and electronic/steric competition, respectively, into the context of intermetallic chemistry.

The µ3 model of acids and bases: extending the Lewis theory to intermetallics.

A central challenge in the design of new metallic materials is the elucidation of the chemical factors underlying the structures of intermetallic compounds. Analogies to molecular bonding phenomena, such as the Zintl concept, have proven very productive in approaching this goal. In this Article, we extend a foundational concept of molecular chemistry to intermetallics: the Lewis theory of acids and bases. The connection is developed through the method of moments, as applied to DFT-calibrated Hückel calculations. We begin by illustrating that the third and fourth moments (µ(3) and µ(4)) of the electronic density of states (DOS) distribution tune the properties of a pseudogap. µ(3) controls the balance of states above and below the DOS minimum, with µ(4) then determining the minimum's depth. In this way, µ(3) predicts an ideal occupancy for the DOS distribution. The µ(3)-ideal electron count is used to forge a link between the reactivity of transition metals toward intermetallic phase formation, and that of Lewis acids and bases toward adduct formation. This is accomplished through a moments-based definition of acidity which classifies systems that are electron-poor relative to the µ(3)-ideal as µ(3)-acidic, and those that are electron-rich as µ(3)-basic. The reaction of µ(3) acids and bases, whether in the formation of a Lewis acid/base adduct or an intermetallic phase, tends to neutralize the µ(3) acidity or basicity of the reactants. This µ(3)-neutralization is traced to the influence of electronegativity differences at heteroatomic contacts on the projected DOS curves of the atoms involved. The role of µ(3)-acid/base interactions in intermetallic phases is demonstrated through the examination of 23 binary phases forming between 3d metals, the stability range of the CsCl type, and structural trends within the Ti-Ni system.