Orbital Origins of Helices and Magic Electron Counts in the Nowotny Chimney Ladders: the 18 – n Rule and a Path to Incommensurability

Abstract

Valence electron count is one of the key factors influencing the stability and structure of metals and alloys. However, unlike in molecular compounds, the origins of the preferred electron counts of many metallic phases remain largely mysterious. Perhaps the clearest-cut of such electron counting rules is exhibited by the Nowotny chimney ladder (NCL) phases, compounds remarkable for their helical structural motifs in which transition metal (T) helices serve as channels for a second set of helices formed from main group (E) elements. These phases exhibit density of states pseudogaps or band gaps, and thus special stability and useful physical properties, when their valence electron count corresponds to 14 electrons per T atom. In this Article, we illustrate, using DFT-calibrated Hückel calculations and the reversed approximation Molecular Orbital analysis, that the 14-electron rule of the NCLs is, in fact, a specific instance of an 18 - n rule emerging for T-E intermetallics, where n is the number of E-supported T-T bonds per T atom. The structural flexibility of the NCL series arises from the role of the E atoms as supports for these T-T bonds, which simply requires the E atoms to be as uniformly distributed within the T sublattice as possible. This picture offers a strategy for identifying other intermetallic structures that may be amenable to incommensurability between T and E sublattices.

Phase stability and thermoelectric properties of semiconductor-like tetragonal FeAl2

“…This t-FeAl 2 was theoretically predicted to be stable (or at least metastable) [5,6], but could not be synthesized at ambient pressure [7]. Theoretical studies also predicted that t-FeAl 2 exhibits a band-gap near the Fermi level, which was explained by the 14 electrons rule or 18 − n (n = 4) electrons rule, where n is the average number of Fe-Fe bonds [5,6,[8][9][10][11][12]. Indeed, analog compounds RuAl 2 and RuGa 2 have been reported as narrow bandgap semiconductors with a high power factor, S 2 σ [7, [13][14][15][16].…”

Ferromagnetic Order, Strong Magnetocrystalline Anisotropy, and Magnetocaloric Effect in the Layered Telluride Fe3−δGeTe2

“…2 Only recently, such empirical rules started receiving explanations, for which the knowledge of the experimental electronic structure is of great significance. 3 In particular, this is true for numerous compounds formed by a combination of a transition metal and a p-block metal or semimetal. In such compounds, a strong hybridization between d and p states gives rise to unexpected features of the electronic structure and, hence, peculiarities in transport and magnetic properties.…”

“…The (Ge1) 3 edges of the octahedra are condensed on the 6 3 net in the middle of the [Fe 2.9 GeTe 2 ] layer. Thus, each layer is composed by two slabs of edge-shared Fe1(Ge1) 3 (Te1) 3 octahedra with the (Ge1) 3 edges consolidated in the middle of the layer and (Te1) 3 edges forming a plain net, which confines the layer. The [Fe 2.9 GeTe 2 ] layers are separated by Te atoms, and a van der Waals gap exists between them in Fe 2.9 GeTe 2 , since no Fe atoms occupy the Fe3 interstitial site.…”

Hf3Fe4Sn4 and Hf9Fe4−Sn10+: Two stannide intermetallics with low-dimensional iron sublattices

“…This is especially true for intermetallic compounds, where comprehensive electron counting rules that predict material stability are lacking in many, though not all, cases. [1][2][3][4] Our approach to the discovery of new intermetallic compounds focuses on the flux technique in order to promote reactant diffusion to overcome kinetic barriers, allowing discovery and single crystal growth of new phases. 5,6 A few compounds have been reported in the Hf -Fe -Sn ternary system.…”