Atomic-Scale Tuning of Tsai-Type Clusters in RE–Au–Si Systems (RE = Gd, Tb, Ho)

Tsai-type quasicrystals and approximants are distinguished by a cluster unit made up of four concentric polyhedral shells that surround a tetrahedron at the center. Here we show that for Tsai-type 1/1 approximants in the RE–Au–Si systems (RE = Gd, Tb, Ho) the central tetrahedron of the Tsai clusters can be systematically replaced by a single RE atom. The modified cluster is herein termed a “pseudo-Tsai cluster” and represents, in contrast to the conventional Tsai cluster, a structural motif without internal symmetry breaking. For each system, single-phase samples of both pseudo-Tsai and Tsai-type 1/1 approximants were independently prepared as millimeter-sized, faceted, single crystals using the self-flux synthesis method. The full replacement of tetrahedral moieties by RE atoms in the pseudo-Tsai 1/1 approximants was ascertained by a combination of single-crystal and powder diffraction studies, as well as energy dispersive X-ray spectroscopy (EDX) analyses with a scanning electron microscope (SEM). Differential scanning calorimetry (DSC) studies revealed distinctly higher decomposition temperatures, by 5–35 K, for the pseudo-Tsai phases. Furthermore, the magnetic properties of pseudo-Tsai phases are profoundly and consistently different from the Tsai counterparts. The onset temperatures of magnetic ordering (Tmag) are lowered in the pseudo-Tsai phases by ∼30% from 24 to 17 K, 11.5 to 8 K, and 5 to 3.5 K in the Gd–Au–Si, Tb–Au–Si, and Ho–Au–Si systems, respectively. In addition, the Tb–Au–Si and Ho–Au–Si systems exhibit some qualitative changes in their magnetic ordering, indicating decisive changes in the magnetic state/structure by a moment-bearing atom at the cluster center.


I. INTRODUCTION
The discovery of quasicrystals (QCs) in the early 1980s has provided a new perspective for realizing long-range positional order without imposing periodicity in three dimensions. 1 The atomic arrangement of a QC can be described as a projection of a periodic lattice in higher dimensions (hyperspace). 2 According to this description, the nonperiodic structures of QCs in 3D are irrational projections from their periodic structures in hyperspace. The method benefits from a prior knowledge of local atomic arrangements (atomic clusters) in the QCs to fully model their structures. 3 Approximants of quasicrystals (ACs) are conventional crystals (3D periodic) with atomic clusters and chemical compositions similar to those of their related QCs. 4 ACs play a pivotal role by providing local structural information needed to determine the structures of QCs. Unlike the case for QCs, AC structures can be determined using standard crystallographic techniques.
The largest and most investigated group of QCs and ACs is the Tsai-type group. It is distinguished by its specific constituent atomic cluster type. 5 A conventional Tsai cluster is made up of four concentric polyhedral shells around a central tetrahedron which usually exhibits positional disorder under ambient conditions. The first shell is a dodecahedron, which is followed by a RE icosahedron. The third and fourth shells are an icosidodecahedron and a rhombic triacontahedron, respectively. 3 Figure 1 shows the Tsai cluster of the 1/1 AC in the Gd−Au−Si system (space group Im3). There are subtle but important structural variations between the parent Tsai-type 1/1 AC, YbCd 6 , and corresponding ACs in ternary systems. The prototype compound is binary, and Yb and Cd atoms reside unambiguously on their preferred atomic shells: Yb is only found in the icosahedral shell, whereas Cd forms the remaining shells as well as the central tetrahedron. Under ambient conditions this tetrahedron is orientationally disordered: crystallographically the four vertices distribute over 12 symmetry-equivalent sites (each occupied to 1/3) resulting in a 12-vertex cuboctahedron as shown in Figure 1 (far left). 6,7 The disordered tetrahedron has been the focus of numerous studies, through which it was established that under ambient conditions the disorder in the binary systems is dynamic in nature 8 and that the lowering temperature and/or increasing the pressure induces intricate transitions to ordered superstructures. 9,10 In ternary Tsai-type 1/1 ACs, such as RE−Au−M (RE = rare-earth elements, M = p-block elements), the tetrahedron is decorated by a Au/M mixed atomic position. Hence, the tetrahedron unit is both orientationally and chemically disordered. Dynamic disorder, as observed for binary RECd 6 ACs, is not known for ternary systems.
There are very few reports where the disordered tetrahedron in Tsai-type phases is partially or even fully replaced by a single atom. The replacing atom is typically the largest in that specific system and is located at the cluster center: i.e., the Wyckoff position 2a. The phenomenon was first reported by Fornasini et al., who investigated the Yb(Zn,Al) ∼6 and YbZn ∼6 1/1 ACs and showed that Yb partially, up to 70%, replaces the disordered Zn/Al tetrahedron. 11 Later, similar findings of single atoms replacing the disordered tetrahedron were reported for (Ca,Yb)−Au−Sn 12 and (Yb,Gd)−Au−Ge ACs. 13,14 Recently, we studied the Tsai-type 1/1 AC in the Tb−Au−Si system and could show that a successive replacement of the tetrahedron by a single Tb atom may be achieved by diligent control of the starting compositions and elaborate heat treatments of samples. 15 Yet, several synthesis steps were necessary for achieving a complete substitution of the tetrahedron, and although samples large enough for singlecrystal X-ray diffraction could be obtained, they were not large enough or had insufficient quality to perform more elaborate physical property measurements, surface studies, or singlecrystal neutron diffraction measurements. An important finding of this study, however, was that tuning the chemistry of the cluster center leads to altered magnetic properties for the Tb− Au−Si AC. It has been speculated that Tsai-type QCs containing RE elements may display unique magnetic structures on the basis of the ordering of spins in a quasiperiodic structure. 16,17 While long-range magnetic order has not yet been observed in Tsai-type QCs, several kinds of magnetic order have recently been reported for RE-containing Tsai-type ACs. 18−23 Tuning the chemistry of the Tsai cluster center may hold the key to unveiling a new family of magnetic quasicrystals and approximants and an increased understanding of magnetic order in Tsai type ACs and QCs.
This study, by taking three different 1/1 approximant systems as an example, identifies the synthesis conditions for obtaining phase-pure, single-crystalline samples of ACs where the cluster center is 100% occupied by a single RE atom. We report crystal structures and bulk magnetic properties and suggest that these compounds should be acknowledged as phases distinctly different from those of Tsai-type ACs.

II. EXPERIMENTAL SECTION
II.a. Synthesis. The starting chemicals were commercially obtained as elemental granules from Chempur (Gd, Tb, Ho, and Au, all with purity 99.99 atom %) and Highways International (Si Figure 1. A Tsai-type cluster unit: arranged from left to right we see a disordered tetrahedron, dodecahedron, RE-icosahedron, icosidodecahedron, and rhombic-triacontahedron, respectively. The polyhedra were plotted using the refined structure model of a Gd−Au−Si standard Tsai-type 1/1 AC (space group Im3). The cluster units are centered at the lattice points (Wyckoff position 2a), forming a bcc packing of interpenetrating triacontahedral clusters. Atomic positions have been displayed by thermal ellipsoids at the 70% probability level. The polyhedra have been proportionally scaled with respect to each other.  24 The CCS consists of two 2 mL flat-bottom cylindrical crucibles and an alumina fritted disk with holes of ∼0.7−1 mm in diameter designed to separate the grains from the melt. The binary alloy Au 79 Si 21 was employed as the starting material. Thus, during reactions with RE the Au:Si ratio was invariant and the ternary system was considered as pseudobinary: i.e., RE−(Au 79 Si 21 ). The alloy was prepared by arc melting. The arc furnace was connected to high-purity Ar gas, and 5−7 g batches of the Au−Si mixture were melted on a water-cooled copper hearth. The arc furnace was flushed three times with Ar, and a titanium getter was continuously melted for ∼5 min to remove any residual oxygen before melting the samples. The samples were fully melted five times to ensure homogeneity. The total mass loss during melting was negligible (<0.4 wt %).
Six reactions, one for each sample, with the nominal compositions and weights shown in Table 1 were carried out. Samples are abbreviated as follows: Gd−Au−Si, GAS; Tb−Au−Si, TAS; Ho−Au− Si, HAS; and XXX(IT) and XXX(CC) when a Tsai phase (tetrahedron at the cluster center) and pseudo-Tsai phase (RE at the cluster center) was targeted, or represented, respectively. For each synthesis, the reactants were carefully weighed and sealed inside a glovebox (Ar atmosphere, <0.1 ppm of O 2 ). All reactions were carried out in CCS which were encapsulated inside stainless-steel ampules under an inert Ar atmosphere. Silica wool was inserted between the outer wall of the CCS and the inner wall of the stainless-steel tubes for thermal insulation during subsequent centrifugation after the reactions. A commercial multistep programmable muffle furnace was employed to set the temperatures for the actual reactions. Typically, ampules were first heated to 1000°C during 10 h and kept for 10 h to ensure homogeneous melts. Then the temperature was slowly lowered (see Table 1) to allow sufficient time for crystal growth during crossing of the solidus line of the pseudobinary system. Reactions were terminated by isothermally centrifuging off excess melt.
II.b. Characterization. The samples were studied with powder Xray diffraction (PXRD), single crystal X-ray diffraction (SCXRD), differential scanning calorimetry (DSC), scanning electron microscopy (SEM) coupled with energy dispersive X-ray spectroscopy (EDX), and magnetic property measurements. A Bruker D8 powder diffractometer with θ−2θ diffraction geometry and a Cu Kα radiation (Kα 1 = 1.540598 Å and Kα 2 = 1.544390 Å) was used for collecting PXRD intensities at room temperature. PXRD data were analyzed with the HighScore Plus 3.0 software from PANalytical. Powdered samples were applied to a zero-diffraction plate, and diffraction patterns were measured in a 2θ range of 5−90°. In all PXRD experiments silicon powder was added as an internal standard. A Bruker D8 single-crystal X-ray diffractometer with Mo Kα radiation (Kα = 0.71073 Å) upgraded with an Incoatec Microfocus Source (IμS, beam size ∼100 μm at the sample position) and an APEX II CCD area detector (6 cm × 6 cm) was utilized to collect SCXRD intensities at room temperature. SCXRD data reduction and numerical absorption corrections were performed using the APEX III software from Bruker. 25 Both structure solution (by charge flipping) and refinements were performed using the software package JANA2006. 26 The charge-flipping algorithm incorporated in the program Superflip was used to obtain structure solutions. 27 The crystal structures were visualized using Diamond 3.2K4. 28 Electron densities were calculated from observed SCXRD intensities by Fourier methods in JANA2006 and visualized in VESTA 3.4.7. 29 DSC measurements were performed with a NETZSCH STA 449 F1 Jupiter instrument. Sample specimens (total mass 10−15 mg) were placed in a polycrystalline sapphire crucible (OD 5 mm, ID 4 mm) and a heating/cooling cycle to 1150°C was performed at a rate of 5°C/ min under an Ar flow of ∼150 mL/min. An empty crucible served as a reference. Samples were recovered after the measurement and analyzed by PXRD. Scanning electron microscopy (SEM) investigations employed a JEOL JSM-7000F instrument equipped with a backscatter detector. Compositional analysis was performed by energy dispersive X-ray (EDX) spectroscopy, and compositional homogeneity was examined through backscatter imaging. Prior to the SEM/ EDX experiments selected grains were cross section polished using an Ar + ion beam in a SM-09011 Cross Section Polisher instrument from JEOL. Backscattered electron images were recorded with an acceleration voltage of 20 kV and high beam current. EDX was mapped over larger areas (∼50 × ∼50 μm) for 600 s. The dc magnetization and ac susceptibility of the samples were measured as a function of temperature on an MPMS XL SQUID magnetometer from Quantum Design Inc. A magnetic field of H = 10 Oe was employed in the dc experiments, while an ac excitation with an amplitude of 4 Oe was used in the ac ones. Note that the remnant magnetic field in the magnetometer was minimized (∼−1 Oe) before collecting the magnetic data. The dc magnetization was recorded as a function of magnetic field up to ±50 kOe at T = 2 K in the same instrument.  Inorganic Chemistry pubs.acs.org/IC Article clusteris typically RE ∼13.6 (Au−Si) ∼86.4 ; 13,30 these ACs are herein referred to as IT phases (inner tetrahedron). The proportion of Au:Si in the IT phases is close to 4:1, and coincidentally, this ratio corresponds closely to the eutectic composition in the binary Au−Si system (Au 79 Si 21 ). 31 The melting point of the eutectic is extraordinarily low, ∼364°C, and thusconsidering the systems as pseudobinary, i.e. RE-(Au 79 Si 21 )ideal conditions are provided for the flux growth of IT phase crystals from Au 79 Si 21 -rich melts. In this work pure samples of millimeter-sized IT phase crystals were synthesized from melts containing between 5 and 11% RE. The common existence of AC phases with altered Tsai clusters in RE−Au−Si systems, i.e. with the central tetrahedron replaced by a single RE atom (herein denoted CC or pseudo-Tsai phases), was first suspected from DSC investigations of IT phases. Experiments would show one pronounced thermal event upon heating but two distinct events upon cooling. The DSC traces of these heating−cooling cycles are sketched in Figure 2a. The behavior was interpreted as such that, upon heating, the melting of the IT phase is observed. Upon cooling, melts with composition RE ∼13.6 (Au−Si) ∼86.4 form a CC phase (with composition RE ∼15.4 (Au−Si) ∼84.6 , see discussion below) and a Au−Si-richer melt when the solidus line was crossed. The second thermal event corresponds to the peritectic formation of the IT phase from the melt and CC phase. PXRD patterns of samples after a DSC heating−cooling cycle showed significantly broadened and/or split peaks, indicating the presence of two AC phases with different cell parameters (such PXRD patterns are shown in Figure S1 in the the Supporting Information). This interpretation implies that the peritectic decomposition of the IT phase into melt and CC phase is comparatively slow, or even kinetically hindered, in comparison to its peritectic formation upon cooling. A sketch of a pseudobinary phase diagram containing both IT phase and CC phase and indicating the thermal events of the DSC experiment is shown in Figure 2b.
The phase diagram sketch has been subsequently used as a guide for synthesis. Pure samples of millimeter-sized CC phase crystals were synthesized from melts containing ∼14% RE which were slowly cooled to T > 800°C and subsequently centrifuged (red arrow in Figure 2b). The corresponding synthesis procedure for the IT phases is indicated as blue arrows in Figure 2b. Figure 2c depicts examples of crystals obtained after melt centrifugation.
The compositional difference between the IT and CC phases is clearly revealed in EDX analysis on a cross section polished crystal specimen. Further, CC phases have a smaller cubic lattice parameter (by 0.6−0.8%) in comparison to their corresponding IT phases. Figure 3 shows examples of the PXRD patterns and backscattered SEM images of the IT and CC phases in the GAS system. Similar plots for the TAS and HAS systems are given in Figure S2 in the Supporting Information. EDX gives the compositions Gd 15.4(4) Au 68.6(3) -Si 16.0(3) and Gd 13.7(3) Au 72.7(3) Si 13.6(3) for GAS(CC) and GAS-(IT), respectively, which are very close to the expected values from the structure refinement (see section III.b). The compositional difference of GAS(CC) and GAS(IT) is manifested as a contrast difference in the backscattered electron image. The lattice parameters for GAS(CC) and GAS(IT) are 14.5781(18) and 14.7014(13) Å, respectively. EDX compositions and lattice parameters for all compounds are given in Table 1. Although we explicitly show the existence of a CC phase only for RE−Au−Si (RE = Gd, Tb, Ho), it is inferred that this phase is generally present in RE−Au−M (M = p element) systems.
III.b. Atomic Structures of the IT and CC Phases. Both IT and CC phases crystallize in the space group Im3 and contain two clusters in the unit cell. Figure 1 shows the Tsai cluster of the conventional Tsai-type 1/1 AC GAS(IT). The cluster midpoints coincide with the corners and the body center of the cubic unit cell (Wyckoff position 2a), and clusters interpenetrate through their fourth (rhombic-triacontahedron) shell. The structures of TAS(IT) and HAS(IT) are virtually identical with that of GAS(IT). All have orientationally disordered (Au/Si) 4 tetrahedral units at the cluster center defined by a 12-vertex cuboctahedron through a position 24g that has a total occupancy of 1/3, which is constrained as such during refinement. The Au:Si ratio for this position (Au7/Si7)   14.5781 (18) 14.549 (3) 14.4599 (12) 14.7014 (13) 14.6525 (17) 14.6525 (17 Inorganic Chemistry pubs.acs.org/IC Article is ∼3:2. In GAS(CC), TAS(CC), and HAS(CC) the central tetrahedron is fully replaced by a single fully occupied RE atom. This is clearly revealed in the SCXRD data, where the electron density maps at low isolevels (13 e/Å 3 ) show no trace of tetrahedral residues while the central RE density is clearly visible. The residual electron densities around the cluster center are comparably low for such a complex structure with heavy elements, which indicates that the CC phases are well and fully described by the presence of a single RE atom inside the dodecahedral cavity. The structure refinement results for the investigated IT and CC phases are compiled in Table 2 and  Figure 4 shows electron density isosurface plots around the cluster centers and the dodecahedron shell for GAS(IT) and GAS(CC). Similar plots for TAS and HAS systems are shown in Figure S3 in the Supporting Information, . The electron densities were obtained from observed SCXRD intensities and calculated from standard Fourier synthesis after the final structure refinement. The generated ".PGRID" file for each structure is provided as Supporting Information. For GAS(IT) the observed electron density around the cluster center corresponds to the disordered (Au/Si) 4 tetrahedron and there is no electron density at the exact cluster center 2a position. Vice versa, for GAS(CC) the electron density is concentrated at the exact cluster center (position correspond-ing to Gd2), whereas the area where the (Au/Si) 4

tetrahedron located in GAS(IT) is void of electron density.
Replacing the relatively larger (Au/Si) 4 tetrahedron with a single RE atom introduces positional disorder on other atomic sites in the CC phase. Interatomic distances on the dodecahedral shell appear reduced from ∼2.74 Å (Au3− Au5/Si5) and ∼2.34 Å (Au5/Si5−Au5/Si5) to ∼2.62 Å and ∼2.23 Å, respectively, when GAS(IT) is compared with GAS(CC). A significant atomic displacement is particularly observed on a Au atom (Au3 in Table S1 in the Supporting Information) at the dodecahedral shell (first shell in Figure 1). Large atomic displacement parameters and elongated electron densities in the ⟨111⟩ crystallographic directions were observed. Figure 4 shows the observed electron density isosurface near the dodecahedron shell for the GAS phases. A better structure refinement (lower R1, wR2 and GOF values in Table 2) was obtained when the Au3 atom was modeled as the two split positions Au3 and Au3′, with the sum of occupancies for these two positions restricted to unity in the CC phase. The new Au3′ position is very close to the Si8 site located at 1/4,1/4,1/4, resulting in unphysically short interatomic distances between Au3′ and Si8 sites (∼1.42 Å for GAS(CC)). We therefore conclude that these two sites are mutually exclusive, meaning that one cannot exist in the presence of the other. Therefore, the occupancy of the position Si8 in the CC phase was refined with the condition that the site must be vacant when the Au3′ site is occupied. For the IT phase compounds the Si8 site is fully occupied and there is no Au3′ site (only a fully occupied Au3 position). Our physical interpretation of the Au3−Au3′ splitting is based on the fact that we can only directly observe an electron density distribution which is a weighted average of two distinctly different local environments in the crystal: occupied and vacant sites of the Si8 atom. Whenever the Si8 atom is present, the adjacent Au atoms move to the more distant Au3 positions to achieve physically sound Au−Si distances (∼2.714, ∼2.792, and ∼2.709 Å for the Au3−Si8 pairs in the GAS(CC), TAS(CC), and HAS(CC) structures, respectively), while the same Au atoms relax to the Au3′ positions only around vacant Si8 sites. Another question is why vacant Si8 sites are only encountered in the CC phases and not in the IT phases. We can at present only speculate about the driving force behind the Si8 vacancy formation at the 1/4,1/4,1/4 position. However, it is known from the prototypic binary RE−Cd approximants that this position (also known as a Cd 8 cube interstitial site) can host additional atoms only in ACs with RE atoms equal in size or larger than Pr, 32 while these positions are vacant for the ACs with smaller RE atoms. This indicates that the relative atomic size of the RE which affects the size of the unit cell (and therefore interatomic distances) will have an effect on this occupancy. The unit cell of the CC phases is consistently smaller than that of the IT phases, and a similar shrinkage of the unit cell is also observed for RE−Cd approximants as the radius of the RE atom diminishes. We therefore believe that the replacement of tetrahedral moieties by single RE atoms at the cluster centers causes a shrinkage of the structure that favors vacancy formation.
The disordered-tetrahedral unit is the only icosahedral symmetry breaking unit among the atomic shells of the Tsai cluster. It has internally restricted Tsai-type QCs and ACs from possessing full local icosahedral symmetry. Replacing the tetrahedral unit with a single atom lifts this restriction, which in III.c. Thermal Analysis of IT and CC Phases. As initially mentioned, the existence of the CC phase in ternary RE−Au−   Si phase systems was first recognized from DSC measurements. Figure 5 compiles DSC thermograms for the IT and CC phases of the investigated RE−Au−Si systems (GAS(IT), GAS(CC), TAS(IT), TAS(CC), HAS(IT), HAS(CC)) during a heating−cooling cycle. In all cases a complete melt was achieved at the highest temperature, 1150°C. Generally, heating traces of the IT phases show one prominent endothermic event between 860 and 880°C, which is assigned to melting (cf. the phase diagram sketch, Figure 2b). Smaller endothermic peaks prior may be related to peritectic decomposition into CC phase and melt and/or order−disorder transitions arising from the central tetrahedron unit. Notably, such smaller peaks prior to the prominent endothermic event are absent in the heating traces of the CC phases. The thermal behavior of GAS and TAS is in qualitative agreement with the phase diagram sketch shown in Figure 2b, when it is assumed that peritectic decompositions upon heating generally are too slow to be resolved in DSC experiments: GAS(IT) melts at 870−880°C and forms peritectically at 810°C. GAS(CC) melts at ∼890−900°C and forms peritectically at 845°C. TAS(IT) melts at 875−880°C and forms peritectically at 800°C. TAS(CC) melts at 875− 910°C and forms peritectically at 805°C. Also, HAS(IT) follows this simplified picture, with melting at 860−865°C and peritectic formation at 820°C. The thermal behavior of HAS(CC), however, is clearly more complicated, showing two events upon heating and three upon cooling. The temperature difference between the melting point (solids) of the IT phase composition and the peritectic formation of the IT phase has been exploited for the synthesis of the CC phase. It is not yet clear whether the CC phases are thermodynamically stable at low temperatures or represent high-temperature phases. Annealing experiments at 600°C for 1 month did not indicate decomposition for GAS(CC) and TAS(CC), whereas slight changes in the PXRD pattern of HAS(CC) could be observed, as shown in Figure S4 in the Supporting Information.
It is important to point out that our strategy does not provide any information whether the region 13.6 < atom % RE < 15.4 in the RE−Au−Si phase diagram is a two-phase region or rather represents a solid solution. Our previous study of the Tb−Au−Si system indicates a solid solution behavior, at least for RE = Tb. 15 III.d. Magnetic Property Measurements. ACs play an important role in elucidating the atomic structures of QCs. Similarly, the study of their magnetic properties is expected to help in understanding the magnetic order in aperiodic QCs. 23,33 In this respect, the study of TAS has been especially fruitful. Recently, Hiroto et al. presented a complete magnetic structure solution from single-crystal neutron diffraction data for TAS(IT) showing intricate noncollinear and noncoplanar ferrimagnetic-like ordering on the icosahedral Tb shell of the Tsai cluster. 21 Further, Gebresenbut et al. showed that a successive replacement of the central tetrahedron unit in the Tsai cluster by a single Tb atom leads to a lowering of the magnetic ordering temperature. 15 However, millimeter-sized single crystals of TAS(CC) synthesized from excess flux as in the present case were not available at the time.
The dc magnetic properties of IT and CC phases are compared in Figure 6 (top row). In all three systems studied here, the magnetization is found to rise sharply as the temperature decreases. For TAS and HAS, the shape of the magnetization curves is reminiscent of those of ferrimagnets. 34,35 The onset of magnetic ordering is somehow less sharp for TAS(CC) than for TAS(IT). On the other hand, the ZFC-FC curves of GAS seem to be significantly different from those of TAS and HAS; the GAS systems exhibit sharper, ferromagnetic-like onsets of magnetic ordering, and the difference between ZFC and FC curves is not as significant as that between TAS and HAS. The flat susceptibility curves of the GAS systems at low temperatures suggest that the measured susceptibility is limited by demagnetizing effects (e.g., for GAS(CC), the susceptibility is about 0.03 emu/g Oe, which corresponds to the SI value of 5.65 or 1/N with N ≈ 0.18). We define T mag as the temperature for the maximum slope of the susceptibility for all samples except for TAS(CC), for which we define T mag as the temperature of the maximum in the ZFC magnetization. The experimental values of T mag are given in Table 3. The magnetic-ordering temperatures T mag of the IT phases are systematically higher than those of the corresponding CC phases. The IT phases have been investigated previously, and our results are in good agreement with the previous studies. 13,23,33 In particular, GAS(IT) was compared with Gd−Au−Ge 1/1 AC, and the latter exhibits a frequency-dependent ac susceptibility. 33 As revealed in this study, GAS(IT) and GAS(CC) do not exhibit clear frequency dependence in the ac magnetic susceptibility, suggesting that the type of magnetic transition of GAS may be different from that of the Gd−Au−Ge 1/1 AC.
The in-and out-of-phase components of the ac susceptibility data for TAS(IT), HAS(IT), and HAS(CC) are compatible with that of ferro-/ferrimagnets, with a sharp peak around T mag in both components. However, it can be seen in Figure 6, e.g. in the out-of-phase component data, that the sharp peak is accompanied by some frequency dependence below T mag , which may reflect slow relaxation inherent to the complex magnetic order determined by recent neutron-scattering experiments for such systems. 21 TAS(CC) exhibits, however, a strikingly different behavior, as the temperature onset of magnetic ordering is found to significantly depend on the frequency, in a spin-glass-like way, 36 suggesting a short-range and glassy magnetic order for this system. The temperature onset of ordering seems sharper (long-range) in an earlier crystal of TAS(CC), 15 however. We have checked that the ac susceptibility of that crystal is qualitatively similar to that of our present TAS(CC): i.e., it reflects a glassy behavior.
In spite of ferrimagnetic-like ordering, we observe a linear Curie−Weiss law temperature dependence of the inverse susceptibility surprisingly down to low temperature, as low as just above T mag for both systems (see Figure S5 in the Supporting Information); this feature indicates that the present magnetic systems are distinguished from the ordinary ferrimagnets. 34 That feature indicates that the 4f electrons are well localized in a wide temperature range and the present Inorganic Chemistry pubs.acs.org/IC Article systems would be classified into the group of localized-electron magnetic systems. For information, the extracted Curie−Weiss temperatures Θ P (estimated in the temperature interval of 50 ≲ T ≲ 300 K) are given in Table 3. The values of effective magnetic moments (p eff ) extracted from the experimental data are given in Table 3, and the values are in good agreement with the theoretical g J J J + values, where g J is the Lande g factor. TAS and HAS show similar magnetic behavior in their IT phases. In both cases, the temperature onset of magnetic ordering and Θ P were found to decrease in the CC phases. However, TAS(CC) and HAS(CC) exhibit significant differences in their ac magnetic response. This suggests that the rare-earth magnetic state/order on icosahedral sites is more or less similar but the cluster-center rare-earth contributions to the magnetic states are significantly different between TAS and HAS; the cluster-center Tb 3+ moments yield magnetic frustration/disorder and glassiness in the TAS(CC) system. Figure 7 shows the magnetic-field dependence of magnetization M measured at T = 2 K. The M−H curves of GAS systems are soft-ferromagnetic-like. Note that the magnetization values at H = 50 kOe are given in Table 3. The difference in the slope of M−H curves at the low-field region for the IT and CC systems should be ascribed to the demagnetization effect. In GAS(IT), we observe an almost complete saturation of M with a value close to the theoretical value of g J J = 7 μ B /Gd 3+ at H = 50 kOe, where μ B is the Bohr magneton. In the case of TAS and HAS, the M−H curves of both materials are ferrimagnetic-like for the IT and CC phases, with no saturation up to 50 kOe. The magnetization M (H = 50 kOe) amounts to ∼5.2−5.3 μ B /Tb for TAS and 6.3−7.0 μ B /Ho for HAS, respectively. These high-field magnetization values are smaller than the theoretical values of g J J = 9 μ B /Tb 3+ and g J J = 10 μ B /Ho 3+ ; this can be ascribed to the crystalelectric-field effect. Also, the M−H curves may reflect the complex magnetic structure of the material, with a resulting moment of about ∼4 μ B /RE (estimated near H = 0). As mentioned above, the coercivity of the TAS(IT) at low temperatures is relatively large (∼250 Oe at 2 K), as observed earlier 15 and as suggested by the negative ZFC magnetization observed at low temperatures for this sample (see Figure 6b). The coercivity at the same temperature is much lower for HAS systems; however, the measurement temperature is closer to T mag in that case.

IV. CONCLUSIONS
The atomic structures, formation conditions, compositions, and temperatures for Tsai and pseudo-Tsai type 1/1 ACs in the RE−Au−Si (RE = Gd, Tb, Ho) systems have been determined. Tsai (IT phase) refers to the more prevalent compounds where a tetrahedral moiety is at the center of the atomic cluster, whereas pseudo-Tsai (CC phase) refers to the case where a RE atom fully replaces the tetrahedron. In both cluster types concentric atomic shells of a dodecahedron, an icosahedron, an icosi-dodecahedron, and a triacontahedron surround the central units. A schematic partial pseudobinary phase diagram between RE and Au 79 Si 21 was proposed and used as a guide to prepare large (several millimeters) single crystals of both Tsai and pseudo-Tsai phases. We speculate that the existence of pseudo-Tsai phases is a more general phenomenon that occurs in more systems than those presented here, and hence they should be acknowledged as an independent group of compounds that is structurally similar yet physically different from Tsai phases.
All the compounds investigated herein have shown ferro-or ferrimagnetic-like ordering at low temperatures, except TAS-(CC), which exhibits a spin-glass-like behavior. However, the temperature onsets of ordering were found to shift to lower temperatures for the CC phases in comparison to their ITcounterparts; for GAS, TAS, and HAS systems T mag shifts from ∼22 to 17 K, ∼11 to 7 K, and ∼5 to 3.5 K, respectively. Now that firm procedures for the upscaled synthesis of phase-pure pseudo-Tsai phases have been established, the door stands open for the exploration of physical properties, atomic surfaces, magnetic structures, and non-Fermi liquid properties of these compounds that exist alongside their Tsai counterparts with crucially different physical properties. Furthermore, the possibility emerges of the parallel existence of pseudo-Tsai type quasicrystals with properties yet unknown.
Atomic coordinates and temperature parameters, PXRD results of DCS run specimen for each sample, PXRD and SEM results for TAS and HAS systems, electron density isosurface plots for TAS and HAS systems, PXRD patterns of samples before and after annealing, and temperature dependence of the inverse magnetic susceptibility for all compounds (PDF)  The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.