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 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. Furthermore, 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.