Structural Plasticity in the Frank‐Kasper Realm: Chemical Pressure Roles of the μ‐ and χ‐Phase Units in the Mo−Fe−Cr System

Abstract

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.

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

“…As we saw from the σ-phase, the fusion of D 3 h 15 and D 6 d 14 polyhedra offers substantial CP relief, while our examination of the ν-Mn 81.5 Si 18.5 structure points to a similar complementary match for T d 16 and D 6 d 14 polyhedra. The latter is confirmed by our earlier investigation of the origins of the μ-phase structure …”

“…46−49 In terms of the FK phases, CP analysis has previously accounted for the formation and elemental site preferences of the FK phases μ-Mo 6 Fe 7 and χ-Mo 5 Cr 6 Fe 18 . 50 Despite this progress, the mechanisms by which such packing effects shape the diversity of structures in this family of phases (and broader intermetallic chemistry) remain largely open. An important clue can be derived from their structures.…”

Tutorial on Chemical Pressure Analysis: How Atomic Packing Drives Laves/Zintl Intergrowth in K3Au5Tl

“…The Tl atoms are displaced away from the interface with the K-Au domains toward their remaining Tl neighbors, which were too distant in the KTl parent structure. This Tl-Au positive pressure also induces a twisting of the networks of Au 4 tetrahedra (corresponding to a soft phonon mode correlated with quadrupolar CP features in the Laves phases we previously investigated) [22,23,25]. This motion pushes the Au atoms away from the Tl-rich regions of the structure and toward K atoms with fewer short contacts to the Tl.…”

“…For the expanded unit cell, the localized electron count for each site is tuned so that all the atoms experience equal negative atomic CPs, while for the contracted unit cell, these localized counts are adjusted so that all atoms bear the same amount of positive CP. We have found that using an average of the localized electron counts for each atom in the expanded and contracted auxiliary CP calculations leads consistently to physically meaningful CP schemes for the equilibrium structure [25,36].…”

“…This method is based on the recognition that non-optimal interatomic distances are detectable in the local pressures that surround the atoms of a solid-state lattice, as constructed from the output of DFT calculations. In the study of a variety of intermetallic phases, CP analysis has provided explanations for diverse structural phenomena, such as the insertion of interfaces into simple structures [19,20,24,25], the adoption of local icosahedral symmetry in quasicrystal approximants [26][27][28], the emergence in incommensurability [29][30][31][32][33][34], the stabilizing effects of various kinds of single point substitutions [23][24][25]35,36], and the formation of intergrowth structures [27,35,[37][38][39]. The CP maps generated in the process can also be used to analyze the forces involved in chemical bonding and molecular structure [40][41][42][43].…”