Generality of the 18-n Rule: Intermetallic Structural Chemistry Explained through Isolobal Analogies to Transition Metal Complexes

Abstract

Intermetallic phases exhibit a vast structural diversity in which electron count is known to be one controlling factor. However, chemical bonding theory has yet to establish how electron counts and structure are interrelated for the majority of these compounds. Recently, a simple bonding picture for transition metal (T)-main group (E) intermetallics has begun to take shape based on isolobal analogies to molecular T complexes. This bonding picture is summarized in the 18-n rule: each T atom in a T-E intermetallic phase will need 18-n electrons to achieve a closed-shell 18-electron configuration, where n is the number of electron pairs it shares with other T atoms in multicenter interactions isolobal to T-T bonds. In this Article, we illustrate the generality of this rule with a survey over a wide range of T-E phases. First, we illustrate how three structural progressions with changing electron counts can be accounted for, both geometrically and electronically, with the 18-n rule: (1) the transition between the fluorite and complex β-FeSi2 types for TSi2 phases; (2) the sequence from the marcasite type to the arsenopyrite type and back to the marcasite type for TSb2 compounds; and (3) the evolution from the AuCu3 type to the ZrAl3 and TiAl3 types for TAl3 phases. We then turn to a broader survey of the applicability of the 18-n rule through a study of the following 34 binary structure types: PtHg4, CaF2 (fluorite), Fe3C, CoGa3, Co2Al5, Ru2B3, β-FeSi2, NiAs, Ni2Al3, Rh4Si5, CrSi2, Ir3Ga5, Mo3Al8, MnP, TiSi2, Ru2Sn3, TiAl3, MoSi2, CoSn, ZrAl3, CsCl, FeSi, AuCu3, ZrSi2, Mn2Hg5, FeS2 (oP6, marcasite), CoAs3 (skutterudite), PdSn2, CoSb2, Ir3Ge7, CuAl2, Re3Ge7, CrP2, and Mg2Ni. Through these analyses, the 18-n rule is established as a framework for interpreting the stability of 341 intermetallic phases and anticipating their properties.

Principles of weakly ordered domains in intermetallics: the cooperative effects of atomic packing and electronics in Fe2Al5

“…The phase appears to be more flexible with lower electron counts, with electron counts as low as 15.0 in Al-poor compositions apparently being accessible. This greater flexibility towards electron-poor configurations over electron-rich ones is commonly observed in structures governed by the 18 À n bonding scheme (Yannello & Fredrickson, 2015), as the lower electron counts can open opportunities for isolobal interactions.…”

Electronic structure, magnetic properties, and mixed valence character of Ce2Ni3Si5 from first principles calculations

“…Other U eff values around 5.4 eV were applied to check the influence on the splitting of the 4f band and on the magnetic properties. For all DFT + U calculations, the U eff value of 5.1 eV was applied for Ni . In the present work, including the spin‐orbit coupling is not yet feasible.…”

“…WWW.C-CHEM.ORG theory has not been established yet how electron counts and structure are interrelated for the majority of these compounds. [30] In the present study, different U eff values (0 to 9.4 eV) are applied to check their influence on the splitting of the Ce 4f band (Fig. 4).…”

Inducing Complexity in Intermetallics through Electron–Hole Matching: The Structure of Fe14Pd17Al69

“…Thed esire for closed-shell electron counts can provide one such attractive force.I ntermetallic structures are becoming increasingly understandable in terms of bonding schemes, such as the Zintl concept, [9] Mott-Jones model, [10] or the 18Àn rule. [11] Many compounds,h owever, show deviations from these schemes,i ndicative of non-optimized bonding that could drive new structural chemistry.F igure 1s hows two examples:T iAl 3 [12] and NiAl, [13] whose Fermi energies (E F ) narrowly miss minima in their electronic density of states Figure 1. The electron-holem atching strategy for creating complex intermetallicsfrom the intergrowtho fdistinct domains, illustrated with the Ti-Ni-Al system.T iAl 3 and NiAl are electron-poor and -rich relative to their ideal electron counts.…”

“…These mismatches can be readily understood from the 18Àn bonding scheme,anelectron counting rule that governs transition metal-main group (T-E) intermetallic phases with Econtent greater than 50 %. [11] Here,the electronic structure of the compound is envisioned as being based on filled 18 electron configurations on the Ta toms,w ith each Ta tom requiring 18Àn valence electrons for ac losed-shell electron configuration, where n is the number of T À Tb onds it participates in. TheEa toms primarily participate through bonding contributions to T-centered orbitals,though separate EÀEb onding orbitals may appear, requiring additional electrons.…”