Quasicrystal Approximant Research Articles

Classical spin models and basic magnetic interactions on 1/1-approximant crystals

We study classical spin models on the 1/1 Tsai-type approximant lattice using Monte Carlo and mean-field methods. Our aim is to understand whether the phase diagram differences between Gd- and Tb-based approximants can be attributed to anisotropy induced by the crystal-electric field. To address this question, we treat Gd ions as Heisenberg spins and Tb ions as Ising spins. Additionally, we consider the presence of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction to replicate the experimentally observed correlation between magnetic properties and electron concentration. Surprisingly, our findings show that the transition between ferromagnetic and antiferromagnetic order remains unaltered by the anisotropy, even when accounting for the dipole interaction. We conclude that a more comprehensive model, extending beyond the free-electron gas RKKY interaction, is likely required to fully understand the distinctions between Gd- and Tb-based approximants. Our work represents a systematic exploration of the impact of anisotropy on the ground-state properties of classical spin models in quasicrystal approximants. Published by the American Physical Society 2024

High- and Low-Energy Photoemission Study of Strongly Correlated Au–Ga–Ce Quasicrystal Approximants: Localized 4f Nature and Disorder Effects

High- and Low-Energy Photoemission Study of Strongly Correlated Au–Ga–Ce Quasicrystal Approximants: Localized 4<i>f</i> Nature and Disorder Effects

Aperiodic approximants bridging quasicrystals and modulated structures

Aperiodic crystals constitute a class of materials that includes incommensurate (IC) modulated structures and quasicrystals (QCs). Although these two categories share a common foundation in the concept of superspace, the relationship between them has remained enigmatic and largely unexplored. Here, we show “any metallic-mean” QCs, surpassing the confines of Penrose-like structures, and explore their connection with IC modulated structures. In contrast to periodic approximants of QCs, our work introduces the pivotal role of “aperiodic approximants”, articulated through a series of k-th metallic-mean tilings serving as aperiodic approximants for the honeycomb crystal, while simultaneously redefining this tiling as a metallic-mean IC modulated structure, highlighting the intricate interplay between these crystallographic phenomena. We extend our findings to real-world applications, discovering these tiles in a terpolymer/homopolymer blend and applying our QC theory to a colloidal simulation displaying planar IC structures. In these structures, domain walls are viewed as essential components of a quasicrystal, introducing additional dimensions in superspace. Our research provides a fresh perspective on the intricate world of aperiodic crystals, shedding light on their broader implications for domain wall structures across various fields.

Single-crystal neutron diffraction study on the Ho13.6Au61.1Al25.3 quasicrystal approximant

A single-crystal neutron diffraction study was conducted on a Ho13.6Au61.1Al25.3 Tsai-type quasicrystal approximant synthesised by the self-flux method. The magnetisation measurements reveal a ferrimagnetic behaviour with a transition below 6 K. In agreement with the magnetometry data, a non-coplanar whirling spin order in the icosahedral clusters around the crystallographic [1 1 1] direction with a ferrimagnetic arrangement was observed from single-crystal neutron diffraction measurements below 5.5 K. The magnetic structure of Ho13.6Au61.1Al25.3 is compared to the previously published magnetic structures of related RE-Au-SM (RE = Tb and Ho; SM = Al, Si and Ga) systems.

Comparative study of ferromagnetism in non-Heisenberg 1/1 and 2/1 quasicrystal approximants

Comparative study of ferromagnetism in non-Heisenberg 1/1 and 2/1 quasicrystal approximants

Magnetic frustration and glassiness in an icosahedral i−Tb−Cd quasicrystal

The dynamical magnetic properties of the icosahedral i−Tb−Cd quasicrystal (QC) were investigated by means of squid magnetometry. At low temperatures, below T∼4.5 K, we observe conventional spin glass features including aging, memory, and rejuvenation. Interestingly, from T∼4.5 to 10 K, the spin configuration is also found to evolve with time (i.e., age as in spin glass), yet without memory. This suggests a reentrantlike behavior for the i−Tb−Cd QC, where upon cooling from high temperatures, the system first displays a magnetically frustrated phase before turning into a spin glasslike one at the lowest temperatures. We discuss the nature and possible origin of this magnetic behavior, in the light of the results obtained in the i−Gd−Cd QC, and ternary Tb-based quasicrystal approximants. Published by the American Physical Society 2024

Tuning the stability of a model quasicrystal and its approximants with a periodic substrate.

Quasicrystals and their periodic approximants are complex crystalline phases. They have now been observed in many metallic alloys, soft matter systems, and particle simulations. In recent experiments of thin-film perovskites on solid substrates, the type of complex phase was found to change depending on thermodynamic conditions and the type of substrate used. Here, we investigate the effect of a substrate on the relative thermodynamic stability of a two-dimensional model quasicrystal and its approximants. Our simulation model is particles interacting via the Lennard-Jones-Gauss potential. Our numerical methods are molecular dynamics simulations and free energy calculations that take into account phason flips explicitly. For substrates interacting weakly with the particles, we observe an incommensurate-commensurate transition, in which a continuous series of quasicrystal approximants locks into a small number of approximants. Interestingly, we observe that the 3/2 approximant exhibits phason mode fluctuations in thermodynamic equilibrium. Such fluctuations are reminiscent of random tiling and a phenomenon usually associated only with quasiperiodic order. For stronger substrates, we find an enhancement of the stability of the dodecagonal quasicrystal and variants of square lattices. We explain all observed phenomena by the interplay of the model system with the substrate. Our results demonstrate that designing novel complex periodic and quasiperiodic structures by choice of suitable substrates is a promising strategy.

Structural Analysis of the Gd-Au-Al 1/1 Quasicrystal Approximant Phase across Its Composition-Driven Magnetic Property Changes.

Gd14AuxAl86-x Tsai-type 1/1 quasicrystal approximants (ACs) exhibit three magnetic orders that can be finely tuned by the valence electron concentration (e/a ratio). This parameter has been considered to be crucial for controlling the long-range magnetic order in quasicrystals (QCs) and ACs. However, the nonlinear trend of the lattice parameter as a function of Au concentration suggests that Gd14AuxAl86-x 1/1 ACs are not following a conventional solid solution behavior. We investigated Gd14AuxAl86-x samples with x values of 52, 53, 56, 61, 66, and 73 by single-crystal X-ray diffraction. Our analysis reveals that increasing Au/Al ordering with increasing x leads to distortions in the icosahedral shell built of the Gd atoms and that trends observed in the interatomic Gd-Gd distances closely correlate with the magnetic property changes across different x values. Our results demonstrate that the e/a ratio alone may be an oversimplified concept for investigating the long-range magnetic order in 1/1 ACs and QCs and that the mixing behavior of the nonmagnetic elements Au and Al plays a significant role in influencing the magnetic behavior of the Gd14AuxAl86-x 1/1 AC system. These findings will contribute to improved understanding towards tailoring magnetic properties in emerging materials.

Search for new Eu-based magnetic quasicrystal approximants

Search for new Eu-based magnetic quasicrystal approximants

Synthesis, structure, and physical properties of a Y–Au-Ge 1/1 Tsai-type quasicrystal approximant and Y14(Au,Ge)51 with the Gd14Ag51 structure type

Exploration of the Au–Ge rich part of the pseudo-binary section Yx(Au0.70Ge0.30)100-x (3 < x < 18) in the Y–Au-Ge system afforded the intermetallic compounds Y3(Au0.7054Ge0.2946)19-x (x ≈ 0.38) and Y14(Au0.8313Ge0.1687)51, which are new representatives of the cubic 1/1 Tsai-type approximant crystal (YbCd6 parent type, space group Im3‾.) and the hexagonal Gd14Ag51 structure type (space group P6/m), respectively. Y3(Au0.7054Ge0.2946)19-x decomposes peritectically into Y14(Au,Ge)51 phase and melt at around 700 °C. In this respect the Y–Au-Ge system deviates from the Y–Au–Si system which firstly contains a second type of 1/1 approximant crystal phase with higher Y content, Y3.25(Au,Si)18-x (x ≈ 0.11) and, secondly, adjacent at higher Y composition there is a stoichiometric and ordered tetragonal phase YAu3Si. Y3(Au,Ge)19-x and Y14(Au,Ge)51 exhibit bulk superconductivity of conventional type-II BCS type albeit with very low transition temperatures (below 1 K), which is very similar to the corresponding compounds in the Y–Au–Si system.

Highly oriented microtube arrays of decagonal quasicrystal approximants in Al20Si20Mn20Fe20Ga20 high-entropy alloy

The unique structures of micro/nanotubular materials have received extensive attention, while the micro/nanotubular structures of quasicrystals or quasicrystal-related phases, especially oriented arrays, are rarely found. Here, oriented microtube arrays of high-entropy decagonal quasicrystal approximants are prepared in Al20Si20Mn20Fe20Ga20 alloy by simple melt spinning. Transmission electron microscopy revealed microtubes are mostly composed of alternating arrangements of (1/0, 2/1) quasicrystal approximant domains (lattice constants: a = 0.73 nm, b = 1.23 nm, and c = 2.24 nm) and defective (1/0, 2/1) domains. However, heat treatment leads to the change of the structure and morphology of microtubes. At 873 K, a primitive cubic phase existed, and at 973 K, microtube morphology disintegrated and the (1/0, 2/1)-related domain transformed into complex domains, showing instability. By nanoindentation testing, microtubes show the hardness of 10.9 GPa and the elastic modulus of 189.3 GPa. However, after heat treatment at 873 K, these values decreased to 5.3 GPa and 128.4 GPa, and to 3.2 GPa and 107.9 GPa at 973 K. We demonstrate that the formation of microtubes is mainly related to the temperature gradient, twinning growth of approximant domains, and also the insufficient supply of raw materials in the later stages of solidification.

New Al-alloys with dispersed stable quasicrystal approximant phases: Overcoming the barrier of conventional casting processing and microstructure design

Multi-stage manufacturing processes, high production costs and narrow two-phase field of Al-alloys containing Al-FCC and quasicrystals or approximants phases have been barriers to the widespread use of these alloys in technological applications. In the present work, we demonstrated that new Al-alloys with dispersed stable quasicrystal approximant phases can be produced by conventional metallurgical fabrication methods. Six alloys containing different volume fractions (5% up to 40%) of the approximant α-phase were designed and produced by conventional solidification in a graphite mold. The hardness and tribological properties of Al-FCC matrix with different volume fractions of the quasicrystal approximant phase were evaluated. A wide range of wear rates, from 2.1 × 10−3 mm3/Nm to 6.3 × 10−4 mm3/Nm, could be achieved by tuning the volume fraction of the α-phase ranging from 5% up to 40%, respectively. Low coefficient of friction values around 0.3 were observed after the running-in periods, regardless of the α-phase content, indicating that the quasicrystal approximant phase played a critical role. The alloy containing 25% of α-phase was chosen to be processed by different manufacturing processes to show that the morphology of the stable approximant α-phase can also be controlled. This finding opens new perspectives for the commercial application of products derived from such light- and wear-resistant materials.

Quasicrystal approximants in the two-dimensional Ba-Ti-O system on Pd(111): A LEED, XPS, and STM study

Long-range aperiodically ordered dodecagonal oxide quasicrystals (OQCs) have been observed on Pt(111), together with a variety of related approximants. All structures contain barium, titanium, and oxygen atoms in ${\mathrm{Ti}}_{n}{\mathrm{O}}_{n}$ ring structures with rings of $n$ = 4, 7, and 10. Barium decorates the larger rings and forms a dodecagonal square-triangle-rhombus tiling. In contrast to these studies on Pt(111), we report here on Ba-Ti-O layers on Pd(111), which has a 1% smaller lattice constant than Pt(111). We find a series of quasicrystal approximants with unit cells consisting of up to 60 triangles, 22 squares, and eight rhombuses. The latter resembles the largest quasicrystal approximant reported to date. The basis for these structures are local patches of the $\ensuremath{\sigma}$-phase square-triangle approximant, into which rhombuses are incorporated due to the formation of ordered antiphase domain boundaries in two orthogonal directions. A structural phase diagram of all quasicrystal approximants on Pd(111) system is presented.

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

The exploratory synthesis of gold-based polar intermetallic phases has revealed many new compounds with unprecedented crystal structures, unique bonding arrangements, and interesting electronic features. Here, we further understand the complexity of gold's crystal chemistry by studying the Na-Au-Cd ternary composition space. A nearly continuous structure transformation is observed between the seemingly simple binary NaAu2-NaCd2 phases, yielding three new intermetallic compounds with the compositions Na(Au0.89(5)Cd0.11(5))2, Na(Au0.51(4)Cd0.49(4))2, and Na8Au3.53(1)Cd13.47(1). Two compounds adopt different Laves phases, while the third crystallizes in a complex decagonal quasicrystal approximant. All three compounds are related through Friauf-Laves polyhedral building units with the gold/cadmium ratio found to control the transition among the unique crystal structures. Electronic structure calculations subsequently revealed the metallic nature of all three compounds with a combination of polar covalent Na-(Au/Cd) interactions and covalent (Au/Cd)-(Au/Cd) bonding interactions stabilizing each structure. These results highlight the crystal and electronic structure relationship among Laves phases and quasicrystal approximants enabled by the unique chemistry of gold.

Giant magnetoresistance in the crystalline YCd6 intermetallic compound

Giant magnetoresistance (GMR) in bulk nonmagnetic compounds has received considerable attention since this phenomenon challenged the classical understanding of electron transport under a magnetic field. Here, we report magnetotransport properties of the diamagnetic intermetallic compound ${\mathrm{YCd}}_{6}$ for applied magnetic fields up to 35 T and temperatures down to 0.4 K that reveal GMR. We argue that the large MR value can be explained in terms of field-induced pseudogaps on a Fermi surface. These results are relevant to the understanding of the Fermi-surface topology of quasicrystal approximants.

Competition between spin-glass and antiferromagnetic states in Tsai-type 1/1 and 2/1 quasicrystal approximants

Systematic research was performed to investigate magnetic properties of the Tsai-type $\mathrm{Ga}\text{\ensuremath{-}}\mathrm{Pd}\text{\ensuremath{-}}RE$ ($RE=\mathrm{Gd}$, Tb, Dy, and Ho) systems, where both 1/1 and 2/1 quasicrystal approximants (ACs) are attainable at the same compositions as thermodynamical stable phases. Most of the samples exhibited spin-glass (SG)-like freezing behavior at low temperatures except Ga-Pd-Tb 2/1 AC and Ga-Pd-Ho 1/1 AC. The former showcased antiferromagnetic order at 5.78 K while the latter did not show any anomaly down to 1.8 K. Furthermore, 2/1 ACs were noticed to be less frustrated than their corresponding 1/1 ACs (based on the empirical rule of $|{\ensuremath{\theta}}_{\mathrm{w}}/{T}_{\mathrm{f}}|$ ) presumably due to the disorder-free environment in the nearest neighbor of the rare-earth sites that form a network of distorted octahedron in the 2/1 ACs. The spin dynamic in SG samples was also characterized by means of ac magnetic susceptibility measurements. The results evidenced a weak response of the freezing temperatures to the measurement frequency in the Heisenberg systems, i.e., Gd-contained ACs, in contrast to the non-Heisenberg systems, i.e., Tb-, Dy-, and Ho-contained ACs, where significant dependency is noticed for the latter. The spin-glass samples were further examined by fitting their freezing temperatures to the Vogel-Fulcher law.

Emergence of long-range magnetic order from spin-glass state by tuning electron density in a stoichiometric Ga-based quasicrystal approximant

This study reports the observation of ferromagnetic (FM) order in the non--Au-based approximant crystals (ACs) using an approach whereby a total electron-per-atom ($e/a$) ratio of the spin-glass ${\mathrm{Ga}}_{50}{\mathrm{Pd}}_{36}{\mathrm{Gd}}_{14}$ 1/1 AC is lowered by simultaneously substituting certain ratios of a trivalent Ga and a zero-valent Pd by a monovalent Au. The emergence of FM order by this method was confirmed via magnetic susceptibility, magnetization, and specific-heat measurements. The findings of this study open up opportunities in developing long-range magnetic orders from stoichiometric ACs, quasicrystals, and even other (Ruderman--Kittel--Kasuya--Yosida) RKKY compounds with spin-glass ground state.

Examination of the critical behavior and magnetocaloric effect of the ferromagnetic Gd-Au-Si quasicrystal approximants

We investigate the critical behavior and magnetocaloric effects of the Gd-Au-Si (GAS) ferromagnetic quasicrystal approximants, ${\mathrm{Gd}}_{13.7}{\mathrm{Au}}_{72.7}{\mathrm{Si}}_{13.6}$ [referred to as GAS(0)] and ${\mathrm{Gd}}_{15.4}{\mathrm{Au}}_{68.6}{\mathrm{Si}}_{16.0}$ [GAS(100)]. The former is a conventional Tsai-type 1/1 approximant crystal, while the latter has a slightly different atomic decoration from the Tsai type (thus referred to as ``pseudo-Tsai'' type). Their critical exponents at the ferromagnetic transitions are close to those of the mean-field theory. Both GAS systems exhibit an interesting magnetic-field dependence of the specific heat, which is reflected in the behavior of their magnetocaloric effect (MCE). The MCE is characterized by an adiabatic cooling (heating) effect over a relatively broad temperature range below $\ensuremath{\sim}30$ K, which stems from a broad feature in the specific heat.

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 Cr3Si and Al3Zr4 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 Cr3Si and Al3Zr4 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 Cr3Si/Al3Zr4 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 CPinterface 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 Cr3Si- and Al3Zr4-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 Mn7VSi2 and Mn81.5Si18.5, as well as a framework for approaching intermetallic intergrowth structures more broadly.

A tale of two closely related 1/1 Tsai-type quasicrystal approximants in the RE–Au–M (RE = rare-earth elements, M = p-block elements) systems

A tale of two closely related 1/1 Tsai-type quasicrystal approximants in the RE–Au–<i>M</i> (RE = rare-earth elements, <i>M</i> = <i>p</i>-block elements) systems