Frustrated Packing in Simple Structures: Chemical Pressure Hindrance to Isolobal Bonds in the TiAl₃ type and ZrAl_2.6Sn_0.4

Abstract

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.

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

“…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].…”

Selective Chemical Substitution of Cu in the Structure of TiAl3 Type InPd3: Experimental and Theoretical Studies

“…The importance of specific site preference [22–27] in the pseudo‐binary/ ternary system motivates us to reinvestigate InPd 3‐x Cu x (x=0–1). In this report, the InPd 3‐x Cu x (x=0–1) were synthesized by conventional high temperature method, and crystal structures were reinvestigated by single crystal and powder X‐ray diffraction and first‐principles electronic structure calculations.…”

“…[23][24] Another interesting example of selective substitution was recently reported by Osman and Bobev, where Zn selectively substitutes one of the Li-positions in Li 15 Ge 4 and forms Li 14 ZnGe 4 . [25] The importance of specific site preference [22][23][24][25][26][27] in the pseudo-binary/ ternary system motivates us to reinvestigate InPd 3-x Cu x (x = 0-1). In this report, the InPd 3-x Cu x (x = 0-1) were synthesized by conventional high temperature method, and crystal structures were reinvestigated by single crystal and powder X-ray diffraction and first-principles electronic structure calculations.…”

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

“…In its focus on how interatomic interactions would be influenced by expansion or contraction of a structure, the CP method complements other tools, such as the crystal orbital Hamilton population , or electron localization function/localizability indicator, − which offer detailed analyses of the electronic structure for a static geometry. The CP distributions created with this approach can elucidate a variety of phenomena, including the formation of superstructures, , soft phonon modes, incommensurate modulations, ,, substitution patterns, and the forces underlying chemical bonds. − 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 …”