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

Abstract

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. 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.

The Intermetallic Reactivity Database: Compiling Chemical Pressure and Electronic Metrics toward Materials Design and Discovery

“…Let’s compare the CP features associated with these squares in the parent structures. To do this, we plot in Figure b,c the CP interface function for these planes, which sums the distant-weighted projections of the nearby atoms’ CP features onto the desired surface (and can be generated from the CP data deposited in the IRD). Here, the projected net pressures are represented with a color map, with strong positive pressures appearing in red, negative in blue, and near zero in pale green.…”

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

“…To illustrate this concept, we begin with a model system whose CP origins are well understood, the σ-phase (FeCr) structure type, a member of the Frank−Kasper tetrahedrally close-packed structures (Figure 1). 70−74 In an earlier examination of this structure, 57 we saw that its classic construction from two parent structures, the Cr 3 Si and Al 3 Zr 4 structure types, 75 can be viewed as a CP-driven intergrowth. Unit-cell-sized fragments of the two parents meet at shared layers of atoms in such a way that interatomic contacts with intense CPs in one structure coincide with contacts experiencing weaker CPs, creating the impression of complementary building blocks docking with each other.…”

“…57 The surface color goes from dark red where the CP interface function is most positive to light green where it is near zero to deep blue at points where it is highly negative. 57 Comparing the CP interface function for the interface nucleus to the CP lobe magnitudes and orientations (Figure 2b), the positive CPs of the kagome nets directed through the convex hull are registered on the surface as vivid red spots. The remainder of the surface shows relatively mild pressures (green), with some soft negative CP (light blue) being evident along the sides of the interface nucleus, where it is bounded by chains of atoms running along c (black).…”

“…Representations of the CPs acting between the surface of an interface nucleus and its surrounding environment were constructed using the CP interface function. 57 Using the atomic coordinates for a chosen interface nucleus within a given structure, we first determine the convex hull of the interface nucleus, and then build a surface of points lying on the convex hull, along which the CP interface surface is calculated as…”

From Laves Phases to Quasicrystal Approximants in the Na–Au–Cd System

“…For instance, polar intermetallics are known to form quasicrystalline phases that display forbidden rotational symmetries (5-, 8-, 12-fold, etc. ). − Similarly, quasicrystal approximants (ACs) are conventional crystalline polar intermetallic phases that exhibit local structural motifs with similar forbidden rotational symmetries, analogous chemical compositions, and comparable e/a values. , The challenge with using e/a to understand polar intermetallics is that calculating the e/a ratio is not often straightforward for metallic systems. , …”