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

The 18-n electron-counting rule provides structural guidelines for electronically feasible transition metal (T)-main group (E) phases, contributing toward the goal of material design. However, the availability of numerous potential structure types at any electron count creates a challenge for the prediction of the preferred structures of specific compounds, as is illustrated by the concept of 18-n+m isomerism. In this Article, we explore the driving forces stabilizing one 18-n+m isomer over another with an analysis of the structure of PdSn2, a layered intergrowth of the fluorite and CuAl2 structure types. The DFT-reversed approximation Molecular Orbital (DFT-raMO) method reveals that PdSn2 and its hypothetical parent structures all adhere to bonding schemes approximating the electronic configurations expected from the 18-n rule, with various degrees of isolobal Pd-Pd bonding and Sn clustering. However, partial electron transfer between the Pd 5p orbitals to the Sn 5s orbitals contributes to the absence of convincing electronic pseudogaps near their Fermi energies. As such, there is no clear electronically driven preference among the structure types. This situation allows for atomic packing effects to prevail: DFT-Chemical Pressure (DFT-CP) analysis illustrates that in the fluorite-type parent structure, positive Pd-Sn CPs lead to overcompression of the Pd atoms and a stretching of the relatively open Sn sublattice. In contrast, in the CuAl2-type parent structure, Sn atoms cluster into tetrahedra, opening space for an expanded Pd environment and the formation of Pd-Pd interactions. However, the tetrahedral packing of the Sn atoms here leads to frustration between negative and positive Sn-Sn CPs. Through the development of the angular CP correlation function (CPcor+) as a tool to quantify frustration among interatomic interactions, we demonstrate how the observed PdSn2 structure balances these effects by tuning the degree of Sn-Sn clustering and expansion of the Pd environment. These observations point to generalizations for most 18-n+m isomers, where increased main group ligand clustering (+m) and isolobal bonds (+n) can accommodate compositions with different T and E atomic sizes.

Interface Nuclei in the Y-Ag-Zn System: Three Chemical Pressure-Templated Phases with Lamellar Mg2Zn11- and CaPd5+x-Type Domains.

The interface nucleus approach was recently presented as a framework for understanding and predicting the emergence of modular intermetallic phases, i.e., complex structures derived from the assembly of units from simpler parent structures. Here, we present the synthesis and crystal structures of three new modular intermetallics in the Y-Ag-Zn system that support this strategy: YAg2.79Zn2.80 (I), YAg2.44Zn3.17 (II), and YAg2.71Zn2.71 (III). Each of these structures is derived from an intergrowth of slabs of the Mg2Zn11 and CaPd5+x types, with the chief differences being in the thickness and degree of disorder within the CaPd5+x-type domains. The merging of the parent structure domains is facilitated by their sharing a common geometrical unit, a double hexagonal antiprism. The use of this motif as an interface nucleus mirrors its role in another family of structures: an intergrowth series combining the CaCu5 and Laves phase structure types, as in the PuNi3-type phase YNi3. However, there is a key difference between the two series. While in the CaCu5/Laves intergrowths, the interface between the parent structures arises perpendicular to the interface nucleus's unique (hexagonal) axis, in the Mg2Zn11/CaPd5+x-type intergrowths revealed here, the interfaces run parallel to this axis. Using CP analysis of the Mg2Zn11/CaPd5+x-type parent structures, we trace this behavior to the different directions of high-CP compatibility of the interface nuclei in the Mg2Zn11/CaPd5+x and CaCu5/Laves structure type pairs. In this way, the Y(Ag/Zn)5+x phases highlight the role that interface nuclei play in directing the domain morphologies of modular intermetallic phases.

Toward Predicting the Assembly of Modular Intermetallics from Chemical Pressure Analysis: The Interface Nucleus Approach.

Complex intermetallic phases are often constructed from domains derived from simpler structures arranged into hierarchical assemblies. These modular arrangements offer intriguing prospects, such as the integration of the properties of distinct compounds into a single material or for the emergence of new properties from the interactions among different domains. In this article, we develop a strategy for the design of such complex structures, which we term the interface nucleus approach. Within this framework, the assembly of complex structures is facilitated by interface nuclei: geometrical motifs shared by two parent structures that serve as a region of overlap to nucleate or seed the formation of a combined structure. Our central hypothesis is that the formation of an interface between structures at these motifs creates opportunities for the relief of atomic packing stresses, as revealed by Density Functional Theory-Chemical Pressure (DFT-CP) analysis: when corresponding interatomic contacts in two structures exhibit complementarity─negative CP with positive CP or intense CP with mild CP─the intergrowth allows for a more balanced packing arrangement. To illustrate the application of the interface nucleus concept, we analyze three modular intermetallic structures, the σ-phase (FeCr), PuNi3, and Ca6Cu6Al5 types. In each case, the assembly of the structure can be connected to complementary CP features in an interface nucleus shared by its parent structures, while the distribution of the interface nuclei in the parents serves to template the geometry of the overall framework. In this way, the interface nucleus approach points toward avenues for the design of modular intermetallics from the CP schemes of potential partner structures.

As predicted and more: modulated channel occupation in YZn5+x.

Like many complex intermetallic phases, the crystal structures of REZn5+x compounds (RE = lanthanide or Group 3 element) based on the EuMg5 type have gradually unfolded. The original reports described a complex hexagonal structure with an unusual combination of tetrahedrally close-packed regions and open spaces, as well as observations of superstructure reflections. More recently, we reinvestigated the structure of YZn5, reclassifying it as the EuMg5+x-type compound YZn5+x (x ≃ 0.2), in which disordered channels run along c through the spaces formerly considered open. In addition, DFT-chemical pressure (DFT-CP) analysis of ordered models of YZn5+x highlighted paths for communication between neighboring channels setting the stage for superstructure formation. Herein, the experimental elucidation of this effect is presented with the synthesis and structure determination of a modulated form of YZn5+x. By slow-cooling samples of YZn5+x from the annealing temperature, crystals were obtained that exhibit satellite reflections with the modulation wavevector q = {1\over 3}a* + {1\over 3}b* + 0.3041c*. Structure solution and refinement using a (3+1)D model in superspace group P31c({1\over 3}\,\!{1\over 3}σ3)00s reveals incommensurate order in the structure's channels. Here, two Zn sites associated with the channels are present, each with discontinuous atomic domains that are slanted in the x3x4 plane. Their slanting corresponds to adjustments along the c axis for the presence or absence of close neighbors along that axis, while the occupation patterns of neighboring channels are shifted by {1\over 3} of the modulation period. These features follow earlier predictions from CP analysis, highlighting how this approach can be used predictively in search of new phenomena.

Self-Consistent Chemical Pressure Analysis: Resolving Atomic Packing Effects through the Iterative Partitioning of Space and Energy.

While planewave DFT methods offer capabilities to calculate the relative stabilities and many physical properties exhibited by solid state structures, their detailed numerical output does not easily map onto the often empirical concepts and parameters used by synthetic chemists or materials scientists. The DFT-chemical pressure (CP) method is an approach to bridging this divide by explaining or anticipating a variety of structural phenomena in terms of atomic size and packing effects, but its reliance on adjustable parameters has limited the method's predictive potential. In this article, we present the self-consistent (sc)-DFT-CP analysis, in which the criterion of self-consistency is used to automatically solve these parameterization issues. We begin by illustrating the need for this improved method with the results for a series of CaCu5-type/MgCu2-type intergrowth structures, where unphysical trends emerge that have no clear structural origin. To address these challenges, we derive iterative treatments for assigning ionicity and for the partitioning of the EEwald + Eα terms in the DFT total energy into homogeneous and localized terms. In this method, self-consistency is achieved between the input and output charges from a variation of the Hirshfeld charge scheme, while the partitioning of the EEwald + Eα terms is adjusted to create equilibrium between the net atomic pressures calculated within atomic regions and from the interatomic interactions. The behavior of the sc-DFT-CP method is then tested using electronic structure data for several hundred compounds from the Intermetallic Reactivity Database. Finally, we return to the CaCu5-type/MgCu2-type intergrowth series with the sc-DFT-CP approach, showing that trends in the series are now easily traced to changes in the thicknesses of the CaCu5-type domains and lattice mismatch at the interface. Through this analysis and the complete update to the CP schemes in the IRD, the sc-DFT-CP method is demonstrated as a theoretical tool for the investigation of atomic packing issues across intermetallic chemistry.

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

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.

Emergent Transitions: Discord between Electronic and Chemical Pressure Effects in the REAl3 (RE = Sc, Y, Lanthanides) Series.

Atomic packing and electronic structure are key factors underlying the crystal structures adopted by solid-state compounds. In cases where these factors conflict, structural complexity often arises. Such is born in the series of REAl3 (RE = Sc, Y, lanthanides), which adopt structures with varied stacking patterns of face-centered cubic close packed (FCC, AuCu3 type) and hexagonal close packed (HCP, Ni3Sn type) layers. The percentage of the hexagonal stacking in the structures is correlated with the size of the rare earth atom, but the mechanism by which changes in atomic size drive these large-scale shifts is unclear. In this Article, we reveal this mechanism through DFT-Chemical Pressure (CP) and reversed approximation Molecular Orbital (raMO) analyses. CP analysis illustrates that the Ni3Sn structure type is preferable from the viewpoint of atomic packing as it offers relief to packing issues in the AuCu3 type by consolidating Al octahedra into columns, which shortens Al-Al contacts while simultaneously expanding the RE atom's coordination environment. On the other hand, the AuCu3 type offers more electronic stability with an 18-n closed-shell configuration that is not available in the Ni3Sn type (due to electron transfer from the RE dz2 atomic orbitals into Al-based states). Based on these results, we then turn to a schematic analysis of how the energetic contributions from atomic packing and the electronic structure vary as a function of the ratio of FCC and HCP stacking configurations within the structure and the RE atomic radius. The minima on the atomic packing and electronic surfaces are non-overlapping, creating frustration. However, when their contributions are added, new minima can emerge from their combination for specific RE radii representing intergrowth structures in the REAl3 series. Based on this picture, we propose the concept of emergent transitions, within the framework of the Frustrated and Allowed Structural Transitions principle, for tracing the connection between competing energetic factors and complexity in intermetallic structures.

Temporary Cohabitation: The Metastable Phase Au4Si.

The prediction, identification, and characterization of phases away from equilibrium conditions remain difficult challenges for material science. Herein, we demonstrate how systems whose phase diagrams contain deeply incising eutectics can offer opportunities to address these challenges. We report the synthesis of a new compound in the Au-Si system, a textbook example of a system with a deep eutectic. Au4Si crystallizes in a complex √18×√2×1 superstructure of the PtHg4 type, based on the distortion of vertex-sharing Si@Au8 cubes into bisdisphenoids. Au4Si decomposes upon heating and at room temperature even in high vacuum, highlighting its metastability. Electronic structure analysis reveals a pseudogap at the Fermi energy, which is enhanced by the superstructure through the relief of Au-Au antibonding interactions. The pseudogap is associated with a Zintl-type bonding scheme, which can be extended to the locally ordered liquid. These results highlight the potential for metastable phases to form in deep eutectics that preserve the local structures of the liquid.

Chemical Pressure-Derived Assembly Principles for Dodecagonal Quasicrystal Approximants and Other Complex Frank-Kasper Phases.

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 Cr3Si and Al3Zr4 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 Cr3Si and Al3Zr4 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 Cr3Si/Al3Zr4 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 CPinterface 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 Cr3Si- and Al3Zr4-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 Mn7VSi2 and Mn81.5Si18.5, as well as a framework for approaching intermetallic intergrowth structures more broadly.

Buffering Octahedra in Mo4Zr9P: Intergrowth as a Solution to the Frustrated Packing of Tricapped Trigonal Prisms and Icosahedra.

Atomic packings based on icosahedra and tricapped trigonal prisms are prone to frustration─indeed, these polyhedra represent common configurations in metallic glasses. In this Article, we illustrate how these packing issues can serve as a driving force for the formation of modular intermetallic structures. Using Density Functional Theory-Chemical Pressure (DFT-CP) analysis, we relate the Hf9Mo4B-type structure of Mo4Zr9P to interatomic pressures experienced by the atoms in two parent structures: Zr3P, whose structure is built from tricapped trigonal prisms, and ZrMo2, a Laves phase containing icosahedra. CP analysis of Zr3P reveals that it has particularly frustrated packing because of the entangling of its tricapped trigonal prisms. In the ternary phase, the frustration is significantly relieved as the units become isolated from each other. Further analysis points to the stabilizing effect of a face-sharing network of octahedra in Mo4Zr9P that largely separates the structure into Zr-Mo and Zr-P domains and serves as a buffering region for the relaxation of interatomic distances. These conclusions are generalized to the broader members of this structure type with the examination of the CP schemes for the isostructural Mo4Zr9B, Al5Co2, and Mg5Pd2 phases. Finally, we screen the structural literature using the ToposPro software to identify three additional structure types that have similar intergrowth patterns: the Dy4CoCd, La23Ni7Mg4, and Gd14Co3In3 types. An analysis of the interatomic distances within the octahedral networks of these structures suggests that these networks commonly facilitate the reconciliation of packing incompatibilities in intermetallic chemistry.

Frustrated Packing in Simple Structures: Chemical Pressure Hindrance to Isolobal Bonds in the TiAl3 type and ZrAl2.6Sn0.4.

While simple close-packed arrangements convey a sense of optimization, they can, in fact, host competition between different types of interactions. The TiAl3 structure type, for example, represents one of a series of ordered TE3 variants (T = transition metal, E = main group element) of the face-centered cubic structure, alongside the AuCu3 and ZrAl3 types. These structures differ in their T-T connectivity corresponding to the 18-n rule: electronic pseudogaps occur at electron concentrations of 18-n/T atom, where n is the number of electron pairs each T atom shares with other T atoms in T-T isolobal bonds. Facile stacking variations interrelate these structures, presumably setting the stage for an electronically precise series. However, the prototype of the TiAl3 type itself violates the 18-n rule, with its count of 13 electrons/Ti atom calling for n = 5 rather than the 4 isolobal T-T bonds/T atom available in this type. Here, we investigate the factors underlying this deviation from the 18-n rule and their relation to the new TiAl3-type compound ZrAl3-xSnx (x ∼ 0.4). First, the relative stabilities of the TiAl3 and ZrAl3 types are compared for TAl3 compounds (T = Zr and Ti). While for T = Zr, the structure adhering to the 18-n rule is highly preferred, for T = Ti, the energy difference essentially vanishes. This trend is connected through DFT-Chemical Pressure (CP) analysis to a tension that emerges in TiAl3 between the optimization of the T-T isolobal bonds and the space requirements of Al-Al contacts elsewhere. This picture elucidates the transition of ZrAl3 from its own type to the TiAl3-type upon partial Sn substitution in ZrAl2.6Sn0.4: the incorporation of Sn brings the electron count closer to that predicted for the TiAl3 type, while electronegativity and CP direct the larger Sn atoms to the site that resists isolobal bond formation in TiAl3.

At the Limits of Isolobal Bonding: π-Based Covalent Magnetism in Mn2Hg5.

Magnetic ordering in inorganic materials is generally considered to be a mechanism for structures to stabilize open shells of electrons. The intermetallic phase Mn2Hg5 represents a remarkable exception: its crystal structure is in accordance with the 18-n bonding scheme and non-spin-polarized density functional theory (DFT) calculations show a corresponding pseudogap near its Fermi energy. Nevertheless, it exhibits strong antiferromagnetic ordering virtually all the way up to its decomposition temperature. In this Article, we examine how these two features of Mn2Hg5 coexist through the development of a DFT implementation of the reversed approximation Molecular Orbital (raMO) analysis. In the non-spin-polarized electronic structure, the DFT-raMO approach confirms that Mn2Hg5 adheres to the 18-n rule: its chains of Mn atoms are linked through isolobal triple bonds, with three electron pairs being shared at each Mn-Mn contact in one σ-type and two π-type functions. Because each Mn atom has 6 isolobal Mn-Mn bonds, it achieves a filled 18-electron count at the compound's electron concentration of 18 - 6 = 12 electrons/Mn. A pseudogap thus occurs at the Fermi energy. Upon the introduction of antiferromagnetic order, the original pseudogap widens and deepens, suggesting enhancement of a stabilizing effect already present in the nonmagnetic state. A raMO analysis reveals that antiferromagnetism enlarges the gap by allowing diradical character to enter into the Mn-Mn isolobal π bonds, reminiscent of the dissociation of a classic covalent bond. Antiferromagnetism is accompanied by residual bonding in the π system, making Mn2Hg5 a vivid realization of the concept of covalent magnetism.

Frustrated and Allowed Structural Transitions at the Limits of the BaAl4 Type: The (3 + 2)D Modulated Structure of Dy(Cu0.18Ga0.82)3.71.

While elemental substitution is the most common way of tuning properties in solid state compounds, this approach can break down in fantastic ways when the stability range of a structure type is exceeded. In this article, we apply the Frustrated and Allowed Structural Transitions (FAST) principle to understand how structural complexity, in this case incommensurate modulations, can emerge at the composition limits of one common intermetallic framework, the BaAl4 type. While the Dy-Ga binary intermetallic system contains no phases related to the BaAl4 archetype, adding Cu to form a ternary system creates a composition region that is rich in such phases, including some whose structures remain unknown. We begin with an analysis of electronic and atomic packing issues faced by the hypothetical BaAl4-type phase DyGa4 and a La3Al11-type variant (in which a fraction of Ga2 pairs are substituted by single Ga atoms). Through an inspection of its electronic density of states (DOS) distribution and DFT-Chemical Pressure (CP) scheme, we see that the stability of BaAl4-type DyGa4 is limited by an excess of electrons and overly large coordination environments around the Dy atoms, with the latter factor being particularly limiting. The inclusion of Cu into the system is anticipated to soothe both issues through the lowering of the valence electron count and the release of positive CPs between atoms surrounding the Dy atoms. With this picture in mind, we then move to an experimental investigation of the Dy-Cu-Ga system, elucidating the structure of Dy(Cu0.18Ga0.82)3.71(1). In this compound, the BaAl4 type is subject to a 2D incommensurate modulation (q1 = 0.31a* + 0.2b*, q2 = 0.31a* - 0.2b*), which can be modeled in the (3+2)D superspace group Pmmm(αß0)000(α-ß0)000. The resulting structure solution contains blocks of the La3Al11 type, with the corners of these domains serving to shrink the Dy coordination environments. These results highlight how the addition of a well-chosen third element to a binary system with a missing-but plausible-compound (BaAl4-type DyGa4) can bring it to the cusp of stability with intriguing structural consequences.

Mn39Si9Nx: Epitaxial Stabilization as a Pathway to the Formation of Intermetallic Nitrides.

The realization of the full potential of nitrogen-containing solid-state materials is limited by the inert and gaseous nature of N2. In this Communication, we describe the simple synthesis yet complex structure of the new phase Mn39Si9Nx (x = 0.84). The formation of this intermetallic subnitride appears to be facilitated by the high solubility of nitrogen in manganese metal, while its structural features are guided by the complementary internal packing strains of Mn-Si and Mn-N domains, an effect known as epitaxial stabilization. These domains intergrow into a composite structure based on the interpenetration of tetrahedrally close-packed (TCP) and Mackay cluster-like modules. We anticipate that other systems combining nitrogen with the TCP packing of metals will be similarly driven toward intergrowth, opening a path to a broader family of intermetallic nitrides.

Entropy-Driven Incommensurability: Chemical Pressure-Guided Polymorphism in PdBi and the Origins of Lock-In Phenomena in Modulated Systems.

Incommensurate order, in which two or more mismatched periodic patterns combine to make a long-range ordered yet aperiodic structure, is emerging as a general phenomenon impacting the crystal structures of compounds ranging from alloys and nominally simple salts to organic molecules and proteins. The origins of incommensurability in these systems are often unclear, but it is commonly associated with relatively weak interactions that become apparent only at low temperatures. In this article, we elucidate an incommensurate modulation in the intermetallic compound PdBi that arises from a different mechanism: the controlled increase of entropy at higher temperatures. Following the synthesis of PdBi, we structurally characterize two low-temperature polymorphs of the TlI-type structure with single crystal synchrotron X-ray diffraction. At room temperature, we find a simple commensurate superstructure of the TlI-type structure (comm-PdBi), in which the Pd sublattice distorts to form a 2D pattern of short and long Pd-Pd contacts. Upon heating, the structure converts to an incommensurate variant (incomm-PdBi) corresponding to the insertion of thin slabs of the original TlI type into the superstructure. Theoretical bonding analysis suggests that comm-PdBi is driven by the formation of isolobal Pd-Pd bonds along shortened contacts in the distorted Pd network, which is qualitatively in accord with the 18-n rule but partially frustrated by the population of competing Bi-Bi bonding states. The emergence of incomm-PdBi upon heating is rationalized with the DFT-Cemical Pressure (CP) method: the insertion of TlI-type slabs result in regions of higher vibrational freedom that are entropically favored at higher temperatures. High-temperature incommensurability may be encountered in other materials when bond formation is weakened by competing electronic states, and there is a path for accommodating defects in the CP scheme.

Intermetallic Reactivity: Ca3Cu7.8Al26.2 and the Role of Electronegativity in the Stabilization of Modular Structures.

The structural chemistry of intermetallic phases is generally viewed in terms of what crystal structure will be most stable for a given combination of metallic atoms. Yet, individual atoms do not always make the best reference points. As the number of elements involved in compounds increases, their structures can often appear to be assembled from structural motifs derived from simpler compounds nearby in the phase diagram rather than fundamentally new arrangements of atoms. In this Article, we explore the notion that complex multinary phases can be viewed productively in terms of motif-preserving reactions between binary compounds, as opposed to direct reactions of the component elements. We present the targeted synthesis and structure solution of Ca3Cu7.8Al26.2, an intermetallic phase whose placement in the phase diagram is suggestive of a reaction between CaAl4 and CuAl2. Single-crystal X-ray diffraction analysis reveals that this compound crystallizes in the Y3TaNi6+xAl26 (or stuffed BaHg11) structure type and is constructed from three modules: Ca@(Cu/Al)16 polyhedra derived from the BaAl4 type, Cu@Al8 cubes, and Al13 cuboctahedra. To help understand this arrangement, we identify forces driving the reactivity of one of the supposed starting materials, CaAl4, through visualization of its atomic charge distribution and chemical pressure (CP) scheme, which suggest that the Al sites closest to the Ca atoms should show a high affinity for substitution by Cu atoms. Such a process on its own, however, would lead to overly long Ca-Cu distances and electron deficiency. When Cu is made available to CaAl4 in the Ca-Cu-Al ternary system, its incorporation in the Ca coordination environments instead nucleates domains of a fluorite-like CuAl2 phase, which act as nodes in the primitive cubic framework of CaAl4- and fluorite-like units. The cubic holes created by this framework are occupied by Al13 face-centered-cubic fragments that donate electrons while also resolving negative CPs in the Ca environments. This structural chemistry illustrates how new elements added to a binary compound at sites with conflicting electronic and atomic size preferences can serve as anchor points for the growth of domains of different bonding types, a notion that can be applied as a more general design strategy for new intermetallic intergrowth structures.

Frustrated and Allowed Structural Transitions: The Theory-Guided Discovery of the Modulated Structure of IrSi.

To the experienced molecular chemist, predicting the geometries and reactivities of a system is an exercise in balancing simple concepts such as sterics and electronics. In this Article, we illustrate how recent theoretical developments can give this combination of concepts a similar predictive power in intermetallic chemistry through the anticipation and discovery of structural complexity in the nominally MnP-type compound IrSi. Analysis of the bonding scheme and DFT-Chemical Pressure (CP) distribution of the reported MnP-type structure exposes issues pointing toward new structural behavior. The placement of the Fermi energy below an electronic pseudogap indicates that this structure is electron-poor, an observation that can be traced via the 18-n rule to the structure's Ir-Ir connectivity. In parallel with this, the structure's CP scheme highlights facile paths of atomic motion that could enable a structural response to this electronic deficiency. Combined, these analyses suggest that IrSi may adopt a more complex structure than previously recognized. Through synthesis and detailed structural investigation of this phase, we confirm this prediction: single-crystal X-ray diffraction reveals an incommensurately modulated structure with the (3+1)D superspace group P21/n(0ßγ)00 and q ≈ -0.22b* + 0.29c*. The structural modulations increase the average number of Ir-Ir bonds to nearly match the 18-n expectations of the phase through Ir-Ir trimerization along negative CPs with the incommensurability arising from the difficulty of contracting and stretching the Ir-Ir contacts in a regular pattern without expanding the structure along directions of negative Si-Si CP. Integrating these results with prior analyses of related systems points to a simple guideline for materials design, the Frustrated and Allowed Structural Transitions (FAST) principle: the ease with which competing structural phenomena can be experimentally realized is governed by the degree to which they are supported by the coordination of the atomic packing and electronic factors.

Cation Clustering in Intermetallics: The Modular Bonding Schemes of CaCu and Ca2Cu.

Electropositive metals such as the alkaline earths or lanthanides are generally assumed to act largely as spectator cations in solid state compounds. In polar intermetallic phases, atoms of such elements are indeed often placed at the peripheries of anions or polyanionic fragments. However, they also show a pronounced tendency to cluster with each other in these peripheral regions in a manner suggestive of multicenter bonding. In this Article, we theoretically investigate the bonding schemes that underlie these cationic cluster arrangements, focusing on CaCu (whose two polymorphs are based on the intergrowth of the FeB- and CrB-types) and Ca2Cu (a Ca-intercalated derivative of CaCu). The structures of these phases are based on Cu zigzag chains embedded in matrices of Ca atoms arranged into increasingly well-developed fragments of closest-packed arrangements. Using reversed approximation Molecular Orbital (raMO) analysis, the Cu chains of both structures are revealed to be connected via nearly fully occupied Cu-Cu isolobal σ-bonds, such that the Cu atoms control 11.67 of the 13 and 15 electrons/formula unit of CaCu and Ca2Cu, respectively. Most of the remaining electrons are drawn to multicenter bonding functions in the Ca sublattices despite the availability of additional Cu 4p orbitals, indicating that the electronegativity difference between Ca and Cu is insufficient to achieve formal Cu oxidation states far beyond -1. The metallic nature of the Ca-based bonding subsystem is reflected in the raMO analysis by a plurality of resonance structures that can be generated from the occupied crystal orbitals. Across these bonding schemes, a separation of the electronic structure into largely self-contained Ca-Ca and Ca-Cu states is a consistent theme. This modularity in the bonding can be correlated to the ease with which this and related systems rearrange FeB- and CrB-type features, which may provide clues to identifying other intermetallic families with similar degrees of structural versatility.

Templating Structural Progessions in Intermetallics: How Chemical Pressure Directs Helix Formation in the Nowotny Chimney Ladders.

In the structural diversity of intermetallic phases, hierarchies can be perceived relating complex structures to relatively simple parent structures. One example is the Nowotny Chimney Ladder (NCL) series, a family of transition metal-main group (T-E) compounds in which the T sublattices trace out helical channels populated by E-atom helices. A sequence of structures emerges from this arrangement because the spacing along the channels of the E atoms smoothly varies relative to that of the T framework, dictated largely by optimization of the valence-electron concentration. In this Communication, we show how this behavior is anticipated and explained by the Density Functional Theory-Chemical Pressure (DFT-CP) schemes of the NCLs. A CP analysis of the RuGa2 parent structure reveals CP quadrupoles on the Ga atoms (telltale signs of soft atomic motion) that arise from overly short Ru-Ga contacts along one axis and underutilized spaces in the perpendicular directions. In their placement and orientation, the CP quadrupoles highlight a helical path of facile movement for the Ga atoms that avoids further compression of the already strained Ru-Ga contacts. The E atoms of a series of NCLs (in their DFT-optimized geometries) are all found to lie along this helix, with the CP quadrupole character being a persistent feature. In this way, the T sublattice common to the NCLs encodes helical paths by which the E-atom spacing can be varied, creating a mechanism to accommodate electronically driven compositional changes. These results illustrate how CP schemes can be combined with electron-counting rules to create well-defined structural sequences, potentially guiding the discovery of new intermetallic phases.

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

Many complex intermetallic structures feature a curious juxtaposition of domains with strict 3D periodicity and regions of much weaker order or incommensurability. This article explores the basic principles leading to such arrangements through an investigation of the weakly ordered channels of Fe2Al5. It starts by experimentally confirming the earlier crystallographic model of the high-temperature form, in which nearly continuous columns of electron density corresponding to disordered Al atoms emerge. Then electronic structure calculations on ordered models are used to determine the factors leading to the formation of these columns. These calculations reveal electronic pseudogaps near 16 electrons/Fe atom, an electron concentration close to the Al-rich side of the phase's homogeneity range. Through a reversed approximation Molecular Orbital (raMO) analysis, these pseudogaps are correlated with the filling of 18-electron configurations on the Fe atoms with the support of isolobal σ Fe-Fe bonds. The resulting preference for 16 electrons/Fe requires a fractional number of Al atoms in the Fe2Al5 unit cell. Density functional theory-chemical pressure (DFT-CP) analysis is then applied to investigate how this nonstoichiometry is accommodated. The CP schemes reveal strong quadrupolar distributions on the Al atoms of the channels, suggestive of soft atomic motions along the undulating electron density observed in the Fourier map that allow the Al positions to shift easily in response to compositional changes. Such a combination of preferred electron counts tied to stoichiometry and continuous paths of CP quadrupoles could provide predictive indicators for the emergence of channels of disordered or incommensurately spaced atoms in intermetallic structures.