Intermetallic phases have been known to exhibit a wide diversity since Pauling's seminal investigations into NaCd2 in the 1920s that, along with Cd3Cu4 and Mg2Al3, was shown by Samson to crystallize with a giant cubic cell containing >1000 atoms. The concept of structural plasticity – the notion that complex structures emerge from the release of internal stresses that would arise in simpler structures – has recently been used to account for one family of intermetallics, tracing the structures of Ca2Ag7, Ca14Cd51, CaPd5, and CaCd6 to chemical pressure (CP) issues in the CaCu5 type. Here, we extend the ideal of structural plasticity closer to the giant cells elucidated by Pauling and Samson through its application to a series of Mo−Fe−Cr Frank‐Kasper phases. We begin with a DFT‐CP analysis of the MgZn2‐type phase MoFe2, which serves as a parent structure to μ‐Mo6Fe7 and χ‐Mo5Cr6Fe18. The analysis reveals negative CPs around the Mo atoms arising from collisions between the Fe atoms. Tighter Mo coordination is provided in the μ‐ or χ‐phases by substituting some of the Friauf polyhedra of MoFe2 with either μ‐ and χ‐phase units, resulting in layers or blocks of Laves‐like connectivity. Sites preferences in the μ‐phase and the role of Cr substitution in the χ‐phase are explained through the dual lenses of CP and electronegativity. Parallels to the features of NaCd2 hint that such giant‐unit‐celled intermetallics can represent striking manifestations of structural plasticity.

The rational design of materials requires an understanding of the relationships between structure and properties. In some fields, advances in computational tools and modeling have mapped out many of these connections. In the realm of intermetallics, however, principles for such relationships are still needed. Recently, we illustrated how the DFT–Chemical Pressure (CP) analysis can link geometrical motifs within crystalline arrangements to the phonon band structures of intermetallics and thus the physical properties related to vibrations and atomic motion. The key indicators here are quadrupolar CP featuresdistributions in which positive and negative interatomic pressures are oriented perpendicular to one another. These quadrupoles then create low energy paths of motion for the atoms that can be linked to various structural phenomena, such as anisotropic vibrations and incommensurate modulations. In this article, we survey the presence of CP quadrupoles in a collection of TE2 structures (T = transition metal and E = main group element) and the roles they play in the behavior observed for these compounds. We begin by developing a metric for CP quadrupolar character, which can be calculated from the output of CP analysis. After compiling these metrics for 17 TE2 structure types, we delve deeper into four systems detected as exhibiting atomic sites with quadrupolar character: (1) the Co–Sn binary system, where the quadrupoles on the Co atoms in CuAl2-type CoSn2 direct the features of its superstructure in CoSn3; (2) arsenopyrite-type CoSb2, in which the highly quadrupolar CP distributions on the Sb atoms correlate with the motions followed during the phase transition to its high-temperature marcasite-type form; (3) the CrSi2 structure, in which the expansion of the lattice is predicted to open a helical path of potential soft motion analogous to that underlying the Nowotny Chimney Ladder series; and (4) the CdAs2 type, whose CP features anticipate the ability to incorporate Li atoms as guests. Together, these case studies highlight the potential for CP quadrupoles to link local atomic arrangements with a variety of emergent properties in intermetallic phases.

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–x Sn x (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.

A central theme in the structural chemistry of intermetallic phases is that complex structures can be derived from variations on simpler ones. This is vividly demonstrated by the variety of structure types that can be connected to chemical pressure (CP)‐driven transformations of the simple CaCu5 type. In this Article, we investigate an intriguing addition to this family: the EuMg5‐type intermetallics, as exemplified by YZn5. As expected from the large negative CPs around the cations in CaCu5‐type structures, YZn5 exhibits tightened coordination environments around the cations. However, it also contains an unusually inhomogeneous atomic packing, particularly in channels running between the Y atoms along c. Our structural reinvestigation of YZn5 reveals a disordered occupation pattern of Zn atoms within these channels, consistent with the EuMg5+x type, a disordered variant of the EuMg5 type. DFT‐CP analysis indicates that the transition from the CaCu5 type to the YZn5+x structure indeed creates more compact Y environments, but strong tensions remain within the Zn sublattice. These include CP features on the channel walls that provide a mechanism for the communication of structural information between the channels and favorable cooperation in their occupation patterns. Based on these results, a structural model is proposed that explains an earlier observation of superstructure reflections in the diffraction patterns of ErZn5 corresponding to a √3×√3×3 supercell.

The design of noncentrosymmetric (NCS) solid state materials, specifically how to break inversion symmetry between enantiomers, has intrigued chemists, physicists, and materials scientists for many years. Because the chemical complexity of molecular racemic building units is so varied, targeting these materials is poorly understood. Previously, three isostructural racemic compounds with a formula of [Cu(H2O)(bpy)2]2[MF6]2·2H2O (bpy = 2,2’=bipyridine; M = Ti, Zr, Hf) were shown to crystallize in the NCS space group Pna21, of polar, achiral crystal class mm2. In this work, we synthesized five new racemic compounds with the formula [Cu(H2O)(dmbpy)2]2[MF6]2·xH2O (dmbpy = 4,4′/5,5′-dimethyl-2,2′-bipyridine; M = Ti, Zr, Hf). Single crystal X-ray diffraction reveals that the five newly synthesized compounds feature equimolar combinations of Δ- and Λ-Cu(dmbpy)2(H2O)2+ complexes that are assembled into packing motifs similar to those found in the reported NCS structure but all crystallize in centrosymmetric (CS) space groups. Seven structural descriptors were created to analyze the intermolecular interactions on the assembly of Cu racemates in the CS and NCS structures. The structural analysis reveals that in the CS structures, the inversion center results from parallel heterochiral π–π stacking interactions between adjacent Cu racemates regardless of cation geometries, hydrogen bonding networks, or interlayer architectures, whereas in the NCS structure, nonparallel heterochiral π–π interactions between the adjacent Cu racemates preclude an inversion center. The parallel heterochiral π–π interactions in the CS structures can be rationalized by the restrained geometries of the methyl-substituted ligands. This work demonstrates that the introduction of nonparallel stacking can suppress the formation of an inversion center for an NCS racemate. A conceptual framework and practical approach linking the absence of inversion symmetry in racemates is presented for all NCS crystal classes.