Approximant Crystal Research Articles

Structural and magnetic properties of the 1/1 Sm-Au-Al and Ho-Au-Al quasicrystal approximants

Tsai-type 1/1 RE-Au-Al approximant crystal (AC) phases RE14AuxAl86-x (RE = Gd, Tb) display a large homogeneity range (50 < x < 75) across which distinct changes of magnetic properties – from spin glass to ferromagnetic (FM) to antiferromagnetic (AFM) – and intricate changes in structural properties occur. Here we analyzed selected 1/1 Ho- and Sm-Au-Al AC phases in the range 53 < x < 71 with single crystal X-ray diffraction and magnetometry. We find that the Al/Au ordering behavior and associated structural changes with x are similar in both systems, and match that observed for RE = Gd, suggesting that the structural evolution with x is rather independent from the type of RE. On the other hand, the magnetic properties, and notably the type of long-range order obtained at large x, are strongly depending on the RE. Ho14AuxAl86-x samples with x = 61 – 71 consistently displayed a ferrimagnetic behavior whereas Sm14AuxAl86-x samples with x = 67 and 71 revealed AFM behavior.

Eu Doping in the GdCd7.88 Quasicrystal and Its Approximant Crystal GdCd6.

The effect of Eu doping in the Tsai quasicrystal (QC) GdCd7.88 and its periodic 1/1 approximant crystal (AC) GdCd6 are investigated. This represents the first synthesis of Eu-containing stable QC samples, where three samples with the final composition Gd1-xEuxCd7.6±α at Eu doping concentrations x = 0.06, 0.13, and 0.19 are obtained (α ∼ 0.2). They are compared to two 1/1 ACs with compositions Gd1-xEuxCd6 (x = 0.12, 0.16). In addition, a new type of 1/1 AC, differing only by the inclusion of extra Cd sites unique to the Eu4Cd25 1/1 AC, has been discovered and synthesized for the concentrations Gd1-xEuxCd6+δ (x = 0.25, 0.33, 0.45, 0.69, 0.73, and 0 < δ ≤ 0.085). Due to the preferred cube morphology of its single grains, we refer to them as c-type 1/1 ACs and to the conventional standard ones as s-type. In both QCs and s-type ACs, the Eu content appears to saturate at a concentration of ∼20%. On the other hand, any Gd| Eu ratio is allowed in the c-type ACs, varying continuously between GdCd6 and Eu4Cd25. We describe and contrast the changes in composition, atomic structure, specific heat, and magnetic properties induced by Eu doping in the quasicrystalline phase and the s-type and c-type 1/1 ACs. By comparing our results to the literature data, we propose that the occupancy of the extra Cd sites can be used to predict the stability of Tsai-type quasicrystalline phases.

Catalytic Properties and Their Relation with Adsorption Energies Calculated by Density Functional Theory in Pd-Containing 1/1 Approximant Crystals

Quasicrystals and approximant crystals (ACs) have a unique complex structure with many crystallographically non-equivalent sites. In order to apply this characteristic potential to catalysts, we investigated catalytic properties of Pd-containing Tsai-type 1/1 ACs, i.e., Al-Pd-Sc and Ga-Pd-Sc, in the acetylene hydrogenation reaction and also performed density functional theory calculations of adsorption energies of reactants and products. The catalytic properties are found to significantly depend on the kind of the semimetal element such as Al and Ga, where the Al-Pd-Sc 1/1 AC shows higher catalytic activity and selectivity. The adsorption energy of reactant acetylene is smaller in the Al-Pd-Sc 1/1 AC whereas the amount of product ethylene are comparable for both ACs. Therefore, the adsorption rate of reactants is increased while the desorption rate of products remains almost the same in the Al-Pd-Sc 1/1 AC. Furthermore, the adsorption energies are found to differ significantly from site to site, implying a superior potential of ACs for designation of active sites using many non-equivalent crystallographic sites for high catalytic performance.

Magnetic dynamics and nonreciprocal excitation in uniform hedgehog order in icosahedral 1/1 approximant crystal

The hedgehog state in the icosahedral quasicrystal (QC) has attracted great interest as the theoretical discovery of topological magnetic texture in aperiodic systems. The revealed magnetic dynamics exhibits nonreciprocal excitation in the vast extent of the reciprocal lattice {varvec{q}}-energy omega space, whose emergence mechanism remains unresolved. Here, we analyze the dynamical as well as static structure of the hedgehog order in the 1/1 approximant crystal (AC) composed of the cubic lattice with spatial inversion symmetry. We find that the dispersion of the magnetic excitation energy exhibits nonreciprocal feature along the N-P-Gamma line in the {varvec{q}} space. The dynamical structure factor exhibits highly structured intensities where high intensities appear in the high-energy branches along the Gamma-H line and the P-Gamma-N line in the {varvec{q}} space. The nonreciprocity in the 1/1 AC and also in the QC is understood to be ascribed to inversion symmetry breaking by the hedgehog ordering. The sharp contrast on the emergence regime of nonreciprocal magnetic excitation between the QC and the 1/1 AC indicates that the emergence in the vast {varvec{q}}-omega regime in the QC is attributed to the QC lattice structure.

Thermoelectric properties of Tsai-type Au–(Al, Ga, In)–Gd approximants

In this work, the thermoelectric properties of Tsai-type Au–(Al, Ga, In)–Gd approximant crystals (ACs) are investigated over a temperature range of 300–773 K. The changes in lattice constants and effective speed of sound suggest a weaker chemical bonding caused by a replacement of Al by heavier Ga or In atoms. Based on electrical conductivity measurements, Au–Al–Gd shows the deepest pseudogap in spectrum conductivity at the Fermi level, followed by Au–Ga–Gd and Au–In–Gd ACs. The lattice thermal conductivity at 300 K is as low as 0.71–0.81 W m−1 K−1 and asymptotically approaches a minimum lattice thermal conductivity of 0.52–0.59 W m−1 K−1 as calculated using the Cahill model. As a result, the highest power factor and dimensionless figure of merit reach ∼120 µW m−1 K−2 and ∼0.008 at ∼700 K for the Au–In–Gd system. Our systematic approach of weakening the chemical bonding nature by heavy atom substitution promises a better thermoelectric performance of Tsai-type ACs.

Magnetism and topological property in icosahedral quasicrystal

Quasicrystal (QC) has no periodicity but has a unique rotational symmetry forbidden in periodic crystals. Lack of microscopic theory of the crystalline electric field (CEF) in the QC and approximant crystal (AC) has prevented us from understanding the electric property, especially the magnetism. By developing the general formulation of the CEF in the rare-earth based QC and AC, we have analyzed the CEF in the QC Au-SM-Tb and AC (SM=Si, Ge, and Ga). The magnetic anisotropy arising from the CEF plays an important role in realizing unique magnetic states on the icosahedron (IC). By constructing the minimal model with the magnetic anisotropy, we have analyzed the ground-state properties of the IC, 1/1 AC, and QC. The hedgehog state is characterized by the topological charge of one and the whirling-moment state is characterized by the topological charge of three. The uniform arrangement of the ferrimagnetic state is stabilized in the QC with the ferromagnetic (FM) interaction, which is a candidate for the magnetic structure recently observed FM long-range order in the QC Au-Ga-Tb. The uniform arrangement of the hedgehog state is stabilized in the QC with the antiferromagnetic interaction, which suggests the possibility of the topological magnetic long-range order.

Reinvestigation of the Thermoelectric Properties of Fe‐Substituted Icosahedral Al–Pd–Re Quasicrystals

Icosahedral quasicrystals (QCs) have a glass‐like, low thermal conductivity because of their complex crystal structures, and a moderate power factor because of deep pseudogap formation in their electronic density of states (DOS) at the Fermi level originating from icosahedral symmetry and covalent bonding nature. These features are beneficial for high‐performance thermoelectric materials. Densified bulk samples of icosahedral Al–Pd–Re–Fe QCs are synthesized by arc‐melting, annealing, and spark plasma sintering methods. It is found that a 2/1‐approximant crystal (AC) can be produced by higher Fe substitution [Al71Pd20(Re1–xFex)9 ()]. The thermoelectric properties of Al71Pd20(Re1–xFex)9 (where x = 0, 0.2, 0.4, 0.65, 0.7, and 0.75) are evaluated between 373 and 973 K. Fe substitution enhances the power factor and reduces the phonon thermal conductivity by a concept of “weakly bonded rigid heavy clusters” (WBRHCs) and an increase in the carrier concentration, enhancing the dimensionless figure of merit (zT). The 2/1‐AC phase has a much higher electrical conductivity and a moderate Seebeck coefficient in the mid‐temperature region due to a considerable increase in carrier concentration; this results in the highest power factor of 900 μW m−1 K−2, and zT value for the 2/1‐Al−Pd−Re−Fe AC is 0.26 at 573 K.

Singular magnetic dilution behavior in a quasicrystal approximant

We report the effect of magnetic dilution on the physical properties of $({\mathrm{Gd}}_{1\ensuremath{-}x}{\mathrm{Y}}_{x}){\mathrm{Cd}}_{6}$ approximant crystals (ACs), close siblings of their corresponding quasicrystal (QC). Compared to the pure system ${\mathrm{GdCd}}_{6}$, we observe remarkable changes in the thermodynamic and magnetic bulk properties near and below the static-ordering temperatures from diluting the magnetic Gd atoms with nonmagnetic Y atoms by only 1--3% $(x=0.01--0.03)$. On the other hand, the corresponding QC system exhibits a monotonic change in its spin-glass behavior upon the magnetic dilution. We discuss the origin of the magnetic-dilution behavior in the present AC system in terms of possible magnetic frustration and short-range magnetic correlation that can be linked to its peculiar structure.

Topological magnetic textures and long-range orders in terbium-based quasicrystal and approximant

The quasicrystal (QC) possesses a unique lattice structure with rotational symmetry forbidden in periodic crystals. The electric property is far from complete understanding. It has been a long-standing issue whether magnetic long-range order is realized in the QC. Here, we report our theoretical discovery of the ferromagnetic long-range order in the Tb-based QC. The difficulty in past theoretical studies on the QC was lack of the microscopic theory of the crystalline electric field (CEF), which is crucially important in the rare earth systems. By analyzing the CEF in the Tb-based QC, we clarify that magnetic anisotropy plays a key role in realizing unique magnetic textures in the Tb-based QC and approximant crystal (AC). By constructing the minimal model, we show that various magnetic textures on the icosahedron, at whose vertices Tb atoms are located, are realized. We find that the hedgehog state is characterized by the topological charge of one and the whirling-moment state is characterized by an unusually large topological charge of three. The hedgehog and whirling-moment states are shown to be realized as antiferromagnetic orders transcribed as the emergent monopole and antimonopole in the 1/1 AC. We find that these states exhibit the topological Hall effect under applied magnetic field accompanied by the topological as well as metamagnetic transition. Our model and the determined phase diagram are expected to be relevant to the broad range of the rare earth-based QCs and ACs with strong magnetic anisotropy, which are useful not only to understand magnetism but also, to explore topological properties.

Comparative study of high-temperature specific heat for Al–Pd–Mn icosahedral quasicrystals and crystal approximants

Quasicrystals (QCs) have a peculiar structural order characterized by quasiperiodicity and non-crystallographical point group symmetry. To reveal their characteristic physical property reflecting the peculiar structural order, specific heat measurements were performed for Al–Pd–Mn icosahedral QCs (i-QCs) and a series of crystal approximants (CAs) of 2/1- 1/1- and 1/0-cubic types at 400–1200 K. The measured specific heat per atom at constant pressure was converted to that at constant volume by using data of the thermal expansion coefficient and bulk modulus. Below ∼700 K, the values of all the specimens of i-QCs and CAs were close to ( Boltzman’s constant), i.e., they obeyed Dulong–Petit’s law. With further increase in temperature, the i-QCs showed a dramatic increase in with increasing temperature, and reached at 1100 K. In contrast, the 2/1 CAs showed a similar but slightly smaller increase in whereas the 1/1 and 1/0 CAs showed a negligible increase. The systematic behavior of in the order of CAs and QC demonstrates that a large excessive specific heat is a characteristic feature of QCs, reflecting the peculiarity of their structural order. Its possible physical mechanism was discussed in terms of anharmonic atomic vibrations, electronic excitations, and phasonic excitations.

Elastic softening in quantum critical Yb-Al-Au approximant crystal and quasicrystal

The elastic property of quantum critical quasicrystal (QC) Yb15Al34Au51 is analyzed theoretically on the basis of the approximant crystal (AC) Yb14Al35Au51. By constructing the realistic effective model in the AC, we evaluate the 4f-5d Coulomb repulsion at Yb as Ufd≈1.46eV realizing the quantum critical point (QCP) of the Yb-valence transition. The RPA analysis of the QCP shows that softening in elastic constants occurs remarkably for bulk modulus and longitudinal mode at low temperatures. Possible relevance of these results to the QC as well as the pressure-tuned AC is discussed.

Crystalline Electronic Field in Rare-Earth Based Quasicrystal and Approximant: Analysis of Quantum Critical Au–Al–Yb Quasicrystal and Approximant

On the basis of the point charge model, we formulate the crystalline electronic field (CEF) Hamiltonian $H_{\rm CEF}$ in the rare-earth based quasicrystal (QC) and approximant crystal (AC) with ligand ions located at pseudo 5-fold configurations by using the operator equivalent method. By setting the total angular momentum $J=7/2$, the CEF in the quantum critical QC Au$_{51}$Al$_{34}$Yb$_{15}$ and the 1/1 AC Au$_{51}$Al$_{35}$Yb$_{14}$ is analyzed with consideration for the effect of Al/Au mixed sites. We find that the ratio of the valences of ligand ions $x=Z_{\rm Al}/Z_{\rm Au}$ plays an important role in characterizing the CEF ground state. As $x$ decreases from $x=3$, the 4f wave function of the CEF ground state with the flat shape lying in the mirror plane is deformed around $x\approx 0.8$ to the flat shape perpendicular to the pseudo 5-fold axis at $x=0$. The formulated $H_{\rm CEF}$ by $J$ is generally applicable to rare-earth-based QCs and ACs, which is useful to analyze the CEF.

High-Temperature Specific Heat of Al–Cu–Ru Icosahedral Quasicrystals and 1/1 Crystal Approximants

We report the results of specific heat measurements for Al–Cu–Ru icosahedral quasicrystals (i-QCs) and 1/1 crystal approximants (1/1-CAs) in the temperature range from 350 to 1250 K. The i-QCs and 1/1-CAs showed a marked upward deviation of the specific heat from the value of Dulong-Petit’s law above 600 K, reaching approximately 1.5 times the value at 1100 K. In addition, some i-QCs showed a large broad peak in the specific heat at approximately 1200 K. The origin of these excessive specific heat values above the Dulong-Petit value is discussed considering the high-dimensional nature of the structural order in the QCs and CAs.

Concomitant singularities of Yb-valence and magnetism at a critical lattice parameter of icosahedral quasicrystals and approximants

Non-Fermi-liquid (NFL), a significant deviation from Fermi-liquid theory, usually emerges near an order-disorder phase transition at absolute zero. Recently, a diverging susceptibility toward zero temperature was observed in a quasicrystal (QC). Since an electronic long-range ordering is normally absent in QCs, this anomalous behaviour should be a new type of NFL. Here we study high-resolution partial-fluorescence-yield x-ray absorption spectroscopy on Yb-based intermediate-valence icosahedral QCs and cubic approximant crystals (ACs), some of which are new materials, to unveil the mechanism of the NFL. We find that for both forms of QCs and ACs, there is a critical lattice parameter where Yb-valence and magnetism concomitantly exhibit singularities, suggesting a critical-valence-fluctuation-induced NFL. The present result provides an intriguing structure–property relationship of matter; size of a Tsai-type cluster (that is a common local structure to both forms) tunes the NFL whereas translational symmetry (that is present in ACs but absent in QCs) determines the nature of the NFL against the external/chemical pressure.

Effects of crystalline electronic field and onsite interorbital interaction in Yb-based quasicrystal and approximant crystal

To get an insight into a new type of quantum critical phenomena recently discovered in the quasicrystal Yb15Al34Au51 and approximant crystal (AC) Yb14Al35Au51 under pressure, we discuss the property of the crystalline electronic field (CEF) at Yb in the AC and show that uneven CEF levels at each Yb site can appear because of the Al/Au mixed sites. Then we construct the minimal model for the electronic state on the AC by introducing the onsite Coulomb repulsion between the 4f and 5d orbitals at Yb. Numerical calculations for the ground state shows that the lattice constant dependence of the Yb valence well explains the recent measurement done by systematic substitution of elements of Al and Au in the quasicrystal and AC, where the quasicrystal Yb15Al34Au51 is just located at the point from where the Yb-valence starts to change drastically. Our calculation convincingly demonstrates that this is indeed the evidence that this material is just located at the quantum critical point of the Yb-valence transition.

The toroidal unit cell of a quasicrystal

The problem of finding the toroidal unit cell of a quasicrystal is formulated in terms of a matrix (graph) divisor. Such a unit cell is an analog of the crystal’s unit cell with cyclic boundary conditions, but is not a crystal approximant of the latter. The proposed approach may be used for calculating the energy-band structure of quasicrystals.

Probing of the pseudogap via thermoelectric properties in the Au-Al-Gd quasicrystal approximant

The pseudogap of the recently discovered Au-Al-Gd quasicrystal approximant crystal (AC) is investigated over a wide electron-per-atom $(e/a)$ ratio of $\ensuremath{\sim}0.5$ using thermoelectric properties as an experimental probe. This Au-Al-Gd AC provides an ideal platform for fine probing of the pseudogap among a number of known ACs because the Au-Al-Gd AC possesses an extraordinarily wide single-phase region with respect to the variation in the electron concentration [A. Ishikawa, T. Hiroto, K. Tokiwa, T. Fujii, and R. Tamura, Phys. Rev. B 93, 024416 (2016)], in striking contrast to, for instance, binary stoichiometric $\mathrm{C}{\mathrm{d}}_{6}\mathrm{R}$ ACs. As a result, a salient peak structure is observed in the Seebeck coefficient, $S$, with the composition as well as that of the power factor ${S}^{2}\ensuremath{\sigma}$, in addition to a gradual variation in the conductivity, $\ensuremath{\sigma}$, and $S$. These two features are directly associated with rapid and slow variations, respectively, of spectral conductivity $\ensuremath{\sigma}(E)$, and hence the fine structure inside the pseudogap, in the vicinity of the Fermi level ${E}_{\mathrm{F}}$. Based on the observed continuous variation of the Fermi wave vector reported in the previous experimental work, fine tuning of ${E}_{\mathrm{F}}$ toward an optimal position was attempted, which led to the successful observation of a sharp peak in ${S}^{2}\ensuremath{\sigma}$ with a value of $\ensuremath{\sim}270\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{W}/\mathrm{m}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{K}}^{2}$ at 873 K. This is the highest value ever reported among both Tsai-type and Bergman-type compounds. The dimensionless figure of merit was determined as 0.026 at 873 K, which is also the highest reported among both Tsai-type and Bergman-type compounds.

Thermoelectric properties of Tsai-type Au–Al–RE (RE: Yb, Tm, Gd) quasicrystals and approximants

The thermoelectric properties of Tsai-type Au–Al–RE (RE: Yb, Tm, Gd) icosahedral quasicrystals (QCs) and their approximant crystals (ACs) have been investigated from 373 K to 873 K. Comparison of their thermoelectric properties above room temperature is of great interest since resonant states are likely to be present in the electronic density of states near the Fermi level for the Au–Al–Yb QC, which should influence the thermoelectric properties and, hence, the dimensionless figure of merit. The electrical conductivity of Au–Al–Yb ACs varies significantly, i.e. from 3000 Ω−1 cm−1 to 5200 Ω−1 cm−1, with changing the Au/Al composition whereas the other compounds have conductivities of ∼3000 Ω−1 cm−1. Such an anomalous behavior of the Au–Al–Yb ACs is understood to be due to the existence of a resonant peak originating from hybridization of Yb f-states and Au/Al sp-states. A maximum power factor of 230 μW m−1 K−2 at 873 K is obtained in 1/1-Au48Al37Yb15 AC, which is significantly higher than those of Al-based icosahedral phases at the same temperature. On the other hand, the room-temperature thermal conductivities for Au–Al–RE compounds range from 3 to 4 W m−1 K−1, reflecting their complex crystal structures with a large unit cell and mixed and/or partially occupied sites. Consequently, both 1/1-Au50Al35Yb15 and Au48Al37Yb15 ACs have similar maximum figures of merit of 0.014 at 873 K.

X-ray diffraction study of the icosahedral AlCuFe quasicrystal at megabar pressures

We report in-situ synchrotron X-ray diffraction study of icosahedral (i)-AlCuFe quasicrystal (QC) at high pressure up to 104GPa under ambient temperature using the diamond anvil technique. With compression, there is no obvious change of the diffraction pattern within the measured pressure range. Five characteristic peaks from the i-AlCuFe QC maintain up to 104GPa. The unit cell volume of the i-AlCuFe QC decreases monotonously until 72GPa. The experimental P–V compression curve below 72GPa was fitted to the Birch–Murnaghan equation of state with V0=2023(19)Å3, K0=131(7)GPa, K′=4.0 (fixed). The resulting EoS parameters are approximately consistent with those observed in previous study. A discontinuous volume change is observed between 72 and 75GPa. These observed results indicate a phase transition from i-AlCuFe QC to an approximant crystal (AC) which has a similar local atomic arrangement as the QC. This study suggests that i-AlCuFe QC maintains its structure at least up to 72GPa and then transforms to AC with small displacement of atoms.

Structures, phase stabilities, and electrical potentials of Li-Si battery anode materials

The Li-Si materials system holds promise for use as an anode in Li-ion battery applications. For this system, we determine the charge capacity, voltage profiles, and energy storage density solely by ab initio methods without any experimental input. We determine the energetics of the stable and metastable Li-Si phases likely to form during the charging and discharging of a battery. Ab initio molecular dynamics simulations are used to model the structure of amorphous Li-Si as a function of composition, and a genetic algorithm coupled to density-functional theory searches the Li-Si binary phase diagram for small-cell, metastable crystal structures. Calculations of the phonon densities of states using density-functional perturbation theory for selected structures determine the importance of vibrational, including zero-point, contributions to the free energies. The energetics and local structural motifs of these metastable Li-Si phases closely resemble those of the amorphous phases, making these small unit cell crystal phases good approximants of the amorphous phase for use in further studies. The charge capacity is estimated, and the electrical potential profiles and the energy density of Li-Si anodes are predicted. We find, in good agreement with experimental measurements, that the formation of amorphous Li-Si only slightly increases the anode potential. Additionally, the genetic algorithm identifies a previously unreported member of the Li-Si binary phase diagram with composition Li${}_{5}$Si${}_{2}$ which is stable at 0 K with respect to previously known phases. We discuss its relationship to the partially occupied Li${}_{7}$Si${}_{3}$ phase.