Incommensurate modulations are increasingly being recognized as a common phenomenon in solid-state compounds ranging from inorganic materials to molecular crystals. The origins of such modulations are often mysterious, but appear to be as diverse as the compounds in which they arise. In this Article, we describe the crystal structure and bonding of Co3Al4Si2, the δ phase of the Co-Si-Al system, whose modulated structure can be traced to a central concept of inorganic chemistry: the 18 electron rule. The structure is monoclinic, conforming to the 3 + 1D superspace group C/2m(0β0)s0. The basis of the crystal structure is a rod packing of columns of the fluorite (CaF2) type, a theme that is shared by the recently determined structure of Fe8Al(17.4)Si(7.6). The columns are arranged into sheets, within which the fluorite structure's primitive cubic network of Si/Al atoms continues uninterrupted from column to column. Between the sheets, layers of interstitial Si/Al atoms occur, some of which are arranged with a periodicity incommensurate with that of the fluorite-type columns. Strong modulations in the interstitial layers result. Electronic structure calculations, using a DFT-calibrated Hückel model on a commensurate approximate structure, reveal that the complex pattern of atoms within these interstitial layers serves to distribute Si/Al atoms around the Co atoms in order to reach 18 electron counts (filled octadecets). Central to this bonding scheme is the covalent sharing of electron pairs between Co atoms. The shared electron pairs occupy orbitals that are isolobal to classical Co-Co σ and π bonds, but whose stability is tied to multicenter character involving bridging Si/Al atoms. Through these features, Co3Al4Si2 expands the structural and electronic manifestations of the 18 electron rule in solid-state inorganic compounds.

The concept of frustration between competing geometrical or bonding motifs is frequently evoked in explaining complex phenomena in the structures and properties of materials. This idea is of particular importance for metallic systems, where frustration forms the basis for the design of metallic glasses, a source of diverse magnetic phenomena, and a rationale for the existence of intermetallics with giant unit cells containing thousands of atoms. Unlike soft materials, however, where conflicts can be synthetically encoded in the molecular structure, staging frustration in the metallic state is challenging due to the ease of macroscopic segregation of incompatible components. In this Article, we illustrate one approach for inducing the intergrowth of incompatible bonding motifs with the synthesis and characterization of two new intermetallic carbides: Mn16SiC4 (mC42) and Mn17Si2C4 (mP46). Similar to the phases Mn5SiC and Mn8Si2C in the Mn-Si-C system, these compounds appear as intergrowths of Mn3C and tetrahedrally close-packed (TCP) regions reminiscent of Mn-rich Mn-Si phases. The nearly complete spatial segregation of Mn-Si (intermetallic) and Mn-C (carbide) interactions in these structures can be understood from the differing geometrical requirements of C and Si. Rather than macroscopically separating into distinct phases, though, the two bonding types are tightly interwoven, with most Mn atoms being on the interfaces. DFT chemical pressure analysis reveals a driving force stabilizing these interfaces: the major local pressures acting between the Mn atoms in the Mn-Si and Mn-C systems are of opposite signs. Joining the intermetallic and carbide domains together then provides substantial relief to these local pressures, an effect we term epitaxial stabilization.

This Article presents the synthesis, structure determination, and bonding analysis of Fe(8)Al(17.4)Si(7.6). Fe(8)Al(17.4)Si(7.6) crystallizes in a new monoclinic structure type based on columns of the fluorite (CaF(2)) structure type. As such, the compound can be seen as part of a structural series in which the fluorite structure-adopted by several transition metal disilicides (TMSi(2))-is fragmented by the incorporation of Al. Electronic structure analysis using density functional theory (DFT) and DFT-calibrated Hückel calculations indicates that the fluorite-type TMSi(2) phases (TM = Co, Ni) exhibit density of states (DOS) pseudogaps near their Fermi energies. An analogous pseudogap occurs for Fe(8)Al(17.4)Si(7.6), revealing that its complex structure serves to preserve this stabilizing feature of the electronic structure. Pursuing the origins of these pseudogaps leads to a simple picture: the DOS minimum in the TMSi(2) structures arises via a bonding scheme analogous to those of 18 electron transition metal complexes. Replacement of Si with Al leads to the necessity of increasing the (Si/Al):TM ratio to maintain this valence electron concentration. The excess Si/Al atoms are accommodated through the fragmentation of the fluorite type. The resulting picture highlights how the elucidating power of bonding concepts from transition metal complexes can extend into the intermetallic realm.

Interstitials, mixed occupancy, and partial substitution of one geometrical motif for another are frequently encountered in the structure refinements of intermetallic compounds as disorder or the formation of superstructures. In this article, we illustrate how such phenomena can serve as mechanisms for chemical pressure (CP) release in variants of the CaCu5 type. We begin by comparing the density functional theory CP schemes of YCo5, an f-element free analogue of the permanent magnet SmCo5, and its superstructure variant Y2Co17 = [Y2(Co2)1]­Co15 (Th2Zn17-type) in which one-third of the Y atoms are replaced by Co2 dumbbells. The CP scheme of the original YCo5 structure reveals intensely anisotropic pressures acting on the Y atoms (similar to CP schemes of other CaCu5-type phases). The Y atoms experience large negative pressures along the length of the hexagonal channels they occupy while being simultaneously squeezed by the channel walls. Moving to the Y2Co17 structure provides significant relief to this CP scheme: the inserted Co2 pairs densify the atomic packing along the hexagonal channels while providing space for the bulging of the walls to better accommodate the remaining Y atoms. This Y/Co2 substitution pattern thus yields a much smoother CP scheme, but residual pressures remain. The experimental relevance of these remaining stresses is investigated through a structural refinement of a Ru-substituted variant of Y2Co17 using single crystal X-ray diffraction. A comparison of the Y2Co17 CP scheme with the observed Ru/Co ordering reveals that Ru preferentially substitutes for Co atoms whose net CPs are most negative, in accord with the larger size of the Ru atoms. These results hint that a wider variety of elemental site preferences may be understandable from the viewpoint of CP relief.

The structures of complex intermetallic compounds can often be interpreted in terms of assemblies of units from simpler parent phases. For example, dodecagonal quasicrystals appear, when viewed down their high-symmetry axes, as plane-filling arrangements of square and triangular tiles corresponding to the Cr 3 Si and Al 3 Zr 4 structure types, respectively. The atomic arrangements and cell-dimensions at the (100) faces of the cells of these structures provide a close geometrical match, which underlies not only dodecagonal quasicrystals and their approximants but also the much more common σ-phase structure. In this article, we show that such intergrowth of parent structures can arise from more than just geometrical coincidences but can be driven by a complementary matching of atomic packing forces. DFT-chemical pressure (CP) analysis on elemental versions of the Cr 3 Si and Al 3 Zr 4 types reveal that in both cases arrays of positive interatomic pressures inhibit the formation of optimal contacts elsewhere in the structures. When they are lined up at the potential Cr 3 Si/Al 3 Zr 4 interfaces, however, positive pressures from the two structures interdigitate rather than coincide, providing the opportunity for the relaxation of strained interatomic contacts. That such relief is afforded by the interfaces is confirmed by CP analysis of the σ-phase (FeCr-type) structure. Building on this scheme, we introduce the CP interface function to represent how the CP features of atoms within a structure impact planes or other surfaces that could serve as interfaces between different structures. Using this function, we then explore how the favorability of interfaces between Cr 3 Si-and Al 3 Zr 4 -type units is tuned by partial elemental substitution with Si, as well as their potential matches with Laves phase units. The emerging picture provides an account for features of the quasicrystal approximants Mn 7 VSi 2 and Mn 81.5 Si 18.5 , as well as a framework for approaching intermetallic intergrowth structures more broadly.