Structurally Complex Frank–Kasper Phases and Quasicrystal Approximants: Electronic Origin of Stability

Degtyareva, V.F.; Afonikova, N. S.

doi:10.3390/cryst7120359

Cited by 3 publications

(3 citation statements)

References 43 publications

(75 reference statements)

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“…However, the authors could not calculate the DOS by density functional theory (DFT) because of its large unit cell. Degtyareva et al also suggested Brillouin zone-Fermi sphere interaction as the cause of its stability [21]. An x-ray emission spectroscopy study reported a decrease in the intensity at E F of the Mg 3p and Al 3p spectra of β-Al 3 Mg 2 compared to that of pure Mg or Al, and this was presented as possible evidence of a pseudogap [22].…”

Section: Introductionmentioning

confidence: 97%

“…So attention has focused on the possible role of a pseudogap in stabilizing the structure of the CMAs [20]. Based on detailed first principle calculations, Mizutani et al [20,21] predicted that the stability of β-Al 3 Mg 2 arises from the Hume-Rothery mechanism (its valence electron to atom (e/a) ratio being 2.6), implying the existence of a pseudogap at E F . However, the authors could not calculate the DOS by density functional theory (DFT) because of its large unit cell.…”

Section: Introductionmentioning

confidence: 99%

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Electronic structure of β−Al3Mg2 and Al13Fe4<

et al. 2022

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Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Electronic structure of β−Al3Mg2 and Al13Fe4<

et al. 2022

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“…The inability of ideal tetrahedra to fill 3D space leads to geometric distortions, , and the resulting susceptibility to packing strain likely plays a profound role in the structural preferences of these compounds. Indeed, the atomic size factor is commonly invoked in discussing the stability ranges of the FK structure types (in parallel with electronic effects − ), − particularly the Laves phases for which optimal radius ratios have been derived from hard-sphere models . In this regard, the near-neighbor diagrams of Pearson have elegantly illustrated how the conflicts and compromises in the interatomic distances vary for these structures as functions of the atomic radii. , …”

Section: Introductionmentioning

confidence: 99%

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

Fredrickson

2022

Inorg. Chem.

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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.

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The Mott-Jones Hamilton Population: Energetics of Fermi Sphere–Jones Zone Interactions in Intermetallic Structures

Garman,

Fredrickson

2024

J. Phys. Chem. C

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The Mott–Jones (MJ) model is a classic approach to understanding the electronic stability of metals, alloys, and intermetallic phases with nearly-free electron bands. Here, pseudogaps at specific electron concentrations are attributed to interactions between one-electron states on the free-electron Fermi sphere induced by the presence of a periodic array of atoms. A remarkable feature of this scheme is that the strength of these interactions is deduced from the intensities of peaks in a crystal’s diffraction pattern. However, the reliance on necessary conditions for the MJ effect, such as the matching of strongly diffracting reciprocal lattice vectors with a hypothetical Fermi sphere, means that the evidence for MJ effects is usually based on the presence of a pseudogap rather than a causal connection to it. In this article, we introduce the Mott–Jones Hamilton Population (MJHP) as a method to assess the energetic signatures of these effects. The MJHP represents a planewave analogy to the atomic-orbital based Crystal Orbital Hamilton Population, with extracting contributions to the energy of each band from planewave pairs meeting the MJ conditions. We present two ways of analyzing the MJHPs for a band structure: First, a comprehensive view of the potential MJ effects is created by resolving the MJHPs by band energy and diffraction angle, such that MJ interactions can be detected and correlated to features in the density of states (DOS) distribution and diffraction pattern. The second approach is a weighted DOS distribution, in which the stabilizing and destabilizing character for a subset of planewave pairs is plotted as a function of band energy. To illustrate the MJHP’s use in identifying the MJ coupling vectors and the extent of MJ stabilization in various systems, we explore eight representative examples: β-brass CuZn, δ-brass CuZn3 (ZrTiP0.68-type), γ-brass Cu5Zn8, Al4Cu9, Cu41Sn11-type Li21Si5, AlCu3 (adopting a binary variant of the full Heusler type), the quasicrystal approximant Zn11Au15Cd23, and α-Mn-type Mg17Al12. These applications confirm the importance of the MJ effects in intermetallic systems and highlight how their role can be assessed without assumptions regarding the effective nearly-free electron concentration.

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Structurally Complex Frank–Kasper Phases and Quasicrystal Approximants: Electronic Origin of Stability

Cited by 3 publications

References 43 publications

Electronic structure of β−Al3Mg2 and Al13Fe4<

Electronic structure of β−Al3Mg2 and Al13Fe4<

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

The Mott-Jones Hamilton Population: Energetics of Fermi Sphere–Jones Zone Interactions in Intermetallic Structures

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