Formation of an Intermediate Valence Icosahedral Quasicrystal in the

Jun 25, 2019 - We report on the formation of a new icosahedral quasicrystal (iQC) in the Au–Sn–Yb alloy system. This iQC has a primitive icosahedr...
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Article Cite This: Inorg. Chem. 2019, 58, 9181−9186

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Formation of an Intermediate Valence Icosahedral Quasicrystal in the Au−Sn−Yb System Tsunetomo Yamada,*,† Yoko Nakamura,‡ Tetsu Watanuki,§ Akihiko Machida,§ Masaichiro Mizumaki,∥ Kiyofumi Nitta,∥ Akira Sato,⊥ Yoshitaka Matsushita,⊥ and An-Pang Tsai‡,#

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Department of Applied Physics, Faculty of Science, Tokyo University of Science, 6-3-1, Niijuku, Katsushika-ku, Tokyo 125-8585, Japan ‡ Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, Miyagi 980-8577, Japan § Synchrotron Radiation Research Center, National Institutes for Quantum and Radiological Science and Technology, 1-1-1 Kouto, Sayo, Hyogo 679-5148, Japan ∥ Japan Synchrotron Radiation Research Institute (JASRI), 1-1-1 Kouto, Sayo, Hyogo 679-5198, Japan ⊥ Research Network and Facility Services Division, National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan ABSTRACT: We report on the formation of a new icosahedral quasicrystal (iQC) in the Au−Sn−Yb alloy system. This iQC has a primitive icosahedral lattice with a lattice constant aico of 0.5447(7) nm and a composition that was determined to be Au60.0Sn26.7Yb13.3. X-ray absorption spectroscopy measurement of the near Yb L 3 edge demonstrates that the Yb valence in the iQC is an intermediate valence between divalent (4f14) and trivalent (4f13) at ambient pressure and was determined to be 2.18+. The results are compared to those for a corresponding 2/1 cubic approximant crystal. The formation of this new iQC is discussed in terms of the atomic size factor (δ) and the valence electron-to-atom ratio (e/a).

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INTRODUCTION Quasicrystals (QCs) are long-range ordered solids in which the diffraction pattern exhibits symmetries that are incompatible with translational symmetry.1,2 A realistic structural model has been developed for a binary icosahedral (i) QC, Cd5.7Yb, and consists of two building units: Tsai-type rhombic triacontahedron (RTH) clusters and double Friauf polyhedra (DFP),3−5 as depicted in panels a and b of Figure 1, respectively. Each RTH cluster is comprised of five successive shells: moving from the center to the outside, a Cd4 tetrahedron, a Cd20 dodecahedron, an Yb12 icosahedron, a Cd32 icosidodecahedron, and a Cd92 RTH. Each DFP has two Yb atoms located on its longer body diagonal. In addition, there are 1/1 and 2/1 cubic approximant crystals (cACs) formed with these compositions, very close to that of the iQC, which are given by the formulas Cd6Yb and Cd5.8Yb, respectively.6,7 Panels c and e of Figure 1 show atomic arrangements of Yb atoms in the structure models of 1/1-cAC, 2/1-cAC, and iQC. The atomic structure of the 1/1-cAC can be described as solely RTH clusters, while those of 2/1-cAC and iQC are composed of both RTH clusters and DFPs.3,6,7 In these structures, the RTH cluster networks consist of two types linkages, i.e., b- and c-linkages, as shown in panels f and g of Figure 1. In the b© 2019 American Chemical Society

linkage, the RTH clusters are touching each other and sharing a rhombic surface, and in the c-linkage, the RTH clusters are interpenetrated.3,5,7 In addition, the local cluster configuration is expressed by a notation (CN, Nb, Nc), where CN is the coordination number of the RTH clusters and Nb and Nc stand for the number of RTH clusters connected by b- and clinkages, respectively.8 In the iQC, there are 18 different local cluster configurations and the most frequent ones are (12, 7, 5) and (12, 6, 6).9,10 The local cluster configurations of 1/1- and 2/1-cAC are (14, 6, 8) and (13, 6, 7), respectively, and neither configuration is present in the iQC. To date, iQCs with a structure identical to that of Cd5.7Yb have been found in many alloy systems. Most of these iQCs contain rare-earth (R) elements, e.g., binary Cd88R12 (R = Y and Gd−Tm)11 and ternary Cd−Mg−R,12,13 Ag42In42Yb16,14 and Au−Al−(Yb, Tm) iQCs.15,16 The most important characteristic is that these iQCs are all composed of the same RTH, where R atoms occupy the icosahedral shell, as shown in Figure 1, which enables a study of the physical properties in terms of the type of R elements. Special attention Received: March 20, 2019 Published: June 25, 2019 9181

DOI: 10.1021/acs.inorgchem.9b00801 Inorg. Chem. 2019, 58, 9181−9186

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Figure 1. Two building units of the Cd5.7Yb iQC: (a) rhombic triacontahedron cluster and (b) double Friauf polyhedron. White and red spheres represent Cd and Yb, respectively. Atomic arrangements of Yb atoms in the structure models of (c) 1/1-cAC, (d) 2/1-cAC, and (e) iQC. Red and green spheres represent Yb atoms located on the icosahedron shell and on the two sites inside the double Friauf polyhedron, respectively. Two different RTH cluster connections: (f) b-linkage and (g) c-linkage.

second example of an IV iQC that is realized at ambient pressure after the Au−Al−Yb iQC. The results were compared with those of the corresponding Au−Sn−Yb 2/1-cAC.22

has recently been drawn to Ce-, Eu-, and Yb-containing compounds because these R elements possess charge (valence) degrees of freedom. These studies have evolved to realize intermediate valence (IV) states in iQCs because IV compounds have the potential to exhibit various phenomena, including valence fluctuation, charge ordering, heavy Fermion behavior, and complex magnetic ordering. In pioneering research, the first IV iQC was realized by the application of pressure to the Cd5.7Yb iQC; the Yb valence increases and reaches 2.33 at 31.7 GPa from the divalent (4f;14 J = 0) at ambient pressure.17 Similarly, an IV was also observed in the Cd−Mg−Yb iQC. In this case, the Yb valence reached 2.71 at 57.6 GPa, which is very close to the trivalent state (4f13; J = 7 /2).18 Recently, the IV state (IVS) was first observed at ambient pressure in the Au−Al−Yb iQC and the Yb valence was estimated to be 2.61 under those conditions. In addition, non-Fermi liquid behavior was observed in this compound at temperatures below 10 K.19 This has more recently been brought to light by the observation of a quantum critical state.20 However, the Au−Al−Yb iQC is the only iQC in which the IVS was observed at ambient pressure. Therefore, there has been increasing interest in the search for new IV iQCs under ambient conditions. Herein, we report the formation of a new iQC in the Au− Sn−Yb alloy system. A self-flux technique was used as an exploratory synthetic tool, similar to the technique applied for binary Zn88Sc12 and Cd88R12 (R = Y and Gd−Tm) iQCs by Canfield et al.21 in 2010 and Goldman et al.11 in 2013. Dendritic crystal agglomerates of the Au−Sn−Yb iQC were obtained, and the composition and structure were characterized. In addition, the IVS of the Yb ion was observed at ambient pressure in the iQC by X-ray absorption spectroscopy measurement of the near Yb L3 edge. This new iQC is the

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EXPERIMENTAL DETAILS

In the binary Au−Sn phase diagram, there is a eutectic point at 553 K with a composition of Au71Sn29. The eutectic composition is close to that of the 2/1-cAC (Au60.3Sn24.6Yb15.1);22 therefore, a eutectic composition with a relatively low melting temperature is beneficial for use as a flux to grow a single crystal. Ten Au−Sn−Yb alloys were prepared with nominal compositions of (Au7Sn3)100−xYbx (x = 1−10) from pure elements of Yb (99.9 wt %), Au (99.995 wt %), and Sn (99.99 wt %). Herein, we abbreviate these as ASY(x). The elements were placed inside an alumina crucible, and then the crucible was sealed inside silica tubes under a reduced-pressure Ar atmosphere. A stainless steel mesh was placed in the middle of the crucible to separate the solvent flux from the crystals. The elements were melted in an electrical furnace at 1273 K for 2 h, cooled to 853 K, and held at that temperature for 3 h. The melt was then slowly cooled to 595 K at a rate of 5 K/h, after which the single-grain crystals were separated from the flux using a centrifuge. Single-crystal X-ray diffraction (XRD) measurements at 295 K were conducted using a laboratory single-crystal XRD system equipped with a charge-coupled device (CCD) (Saturn 724 HG, Rigaku) and a partial χ-type goniometer. Single-crystal samples of approximately 50 μm were picked up from the crushed alloys and mounted on thin glass needles. Data collection was performed using Mo Kα radiation (λ = 0.071073 nm) generated by a rotating anode-type X-ray generator (MicroMax007HF, Rigaku). The collected images were analyzed using the CrysAlisPRO computer program (Rigaku Oxford Diffraction, 2015). Chemical compositions for the obtained singlegrain crystals were determined using inductively coupled plasma atomic emission spectroscopy (ICP-AES) using a CCD optic system (ARCOS, SPECTRO). X-ray absorption near edge structure (XANES) spectroscopy at the Yb L3 edge was conducted at room temperature using beamline 9182

DOI: 10.1021/acs.inorgchem.9b00801 Inorg. Chem. 2019, 58, 9181−9186

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Figure 2. Scanning electron microscopy and optical microscope images of single-grain crystals of (a) the Au−Sn−Yb iQC and (b) 2/1-cAC obtained in the ASY(3) and ASY(10) samples, respectively.

Figure 3. Reconstructed reciprocal layers perpendicular to the (a) 2-fold, (b) 3-fold, and (c) 5-fold directions for the Au−Sn−Yb iQC and those perpendicular to the (d) 2-fold, (e) 3-fold, and (f) pseudo-5-fold directions for the Au−Sn−Yb 2/1-cAC, reconstructed from laboratory singlecrystal XRD data. The strong reflections indicated by A and B in panel a are indexed as 20/32 and 18/29, respectively, after the index scheme of Cahn et al.29

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BL22XU at SPring-8 for an iQC sample in ASY(3). A cracked piece of the alloy was crushed to make its form with a thickness of

RESULTS

Faceted grains were obtained for ASY(3−10) and separated from the Au−Sn solvent by centrifugation at 595 K. No grains remained in the crucible after centrifugation of ASY(1) and ASY(2), which indicates that Yb was completely dissolved in the eutectic phase at 595 K. For AGY(3−10), two different crystal morphologies were observed, as shown in Figure 2. Dendritic crystal agglomerates were found in ASY(3−6), and the size of each single crystal was approximately 100 μm. The morphology with a pentagonal dodecahedron shape was clearly observed, which suggests that the obtained single crystals could be iQC. On the other hand, for the single-grain crystals in ASY(8−10), triangular surfaces were clearly observed. For

approximately 10 μm and a diameter of 100 μm. The monochromatic X-ray beam collimated with a diameter of 40 μm was directed at the center of the sample. Transmission XANES spectra were acquired by scanning the incident X-ray energy between 8.77 and 9.11 keV using two ionization chambers filled with N2 gas to monitor the incident and transmitted X-ray intensities. A 2/1-cAC sample in ASY(10) was also measured in a similar manner using powdered specimens on beamlines BL22XU and BL01B1 at SPring-8, and low-temperature experiments down to 3 K were additionally performed at BL01B1 using a cryostat. 9183

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analyzed by the same procedure described in ref 19. From the fitting procedure, the Yb valences were determined to be 2.18+ and 2.27+ for iQC and 2/1-cAC, respectively, both of which are close to divalent. This is the second example of an IV iQC realized under ambient conditions, subsequent to Au−Al−Yb iQC. In addition, the Au−Sn−Yb 2/1-cAC is the first example of IV 2/1-cAC.

ASY(7), the mixture of single-grain crystals exhibited both morphologies. Figure 3 shows reciprocal layers reconstructed from XRD data, perpendicular to the (a) 2-fold, (b) 3-fold, and (c) 5-fold directions for a single crystal in ASY(3) and those perpendicular to the (d) 2-fold, (e) 3-fold, and (f) pseudo-5fold directions for a single crystal in ASY(10). The diffraction from the crystal in ASY(3) could be indexed as a primitive icosahedral lattice with an icosahedral lattice parameter (aico) of 0.5447(7) nm. On the other hand, that for the crystal in ASY(10) could be indexed as a primitive cubic lattice with a lattice parameter of 2.43305(1) nm. This is close to the lattice parameter for the 2/1-cAC (2.426 nm), which was estimated from the relation between the icosahedral lattice parameter of the iQC and the lattice constant (aq/p) of its corresponding q/ p-cAC: aq / p =

2(p + qτ ) (2 + τ )

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DISCUSSION The formation condition of iQCs has been discussed in terms of the Hume−Rothery rule, i.e., valence electron concentration and atomic size factor.24 The former is the valence electron concentration or valence electron-to-atom ratio (e/a), and the latter is defined as δ = rL/rS, where rL and rS are radii of the large (L) and small (S) atoms, respectively. The stable quasicrystals commonly have the corresponding e/a ratio, and a high stability is observed when the δ factor is favored. For Tsai-type iQCs, the e/a value ranges between 2.0 and 2.15 and the ideal δ value is equal to 1.288.25 Because both e/a and δ factors are affected by a change in the Yb valence, it is natural to consider that the IVS is closely related to the formation of the Au−Sn−Yb iQC. In considering the formation condition, we find that the e/a and δ factors are competing as follows. (1) When we assume trivalent Yb, the e/a and δ values are estimated to be 2.07 and 1.18, respectively. The e/a is closer to the typical value, while the δ is significantly lower than the ideal value. (2) When we assume divalent Yb, the e/a value is estimated to be 1.93, which deviates from the typical value, while δ is 1.32, which is closer to the ideal value. Here, the δ factors were calculated using radii listed in ref 26. In both cases, either e/a or δ factors do not meet the formation conditions; thus, the formation of IVS of Yb ions is reasonable in terms of the Hume−Rothery rule. In the Au−Sn−Yb iQC with IV of Yb ions (2.18+), the e/a and δ values of the iQC are estimated to be 1.96 and 1.29, respectively. Here, a radius of the Yb ion with a valence of 2.18+ was estimated to be 0.190 nm assuming that the radius of the Yb ion changes linearly with its valence. The resulting e/a and δ values are similar to that of the IV Au−Al−Yb iQC, where e/a and δ values are estimated to be 1.92 and 1.26, respectively. In both IV iQCs, the δ values are close to the ideal one (1.288) while the e/a values are slightly lower than that of other isostructural iQCs ranging from 2.0 to 2.15. Therefore, it can be said that the IVS of the Yb ions in these IV iQCs is realized so that the δ factor is favored. In terms of the concentration of large atoms (Yb), two characteristic features can be raised for the Au−Sn−Yb iQC. (i) The Yb concentration is lower than that of the other known Yb-containing iQCs (e.g., Cd 5.7 Yb, Ag 42 In 42 Yb 16 , and Au51Al34Yb15 iQCs). (ii) The Yb concentration is similar to that of large atoms (R or Sc) in Cd88R12 and Zn88Sc12 iQCs. The former feature indicates that the R sites in the Cd5.7Yb model (i.e., the Yb12 icosahedron site and two Yb sites inside DFP) are not fully occupied by Yb in the Au−Sn−Yb iQC. Recent structural analysis of the Cd88R12 and Zn88Sc12 iQCs revealed that occupational disorder of mixed R/Cd and Sc/Zn exists at the Yb sites in the Cd5.7Yb iQC model.27,28 Although structural determination is currently underway in our group, point (ii) means that such occupational disorder is also present in the Au−Sn−Yb iQC. In the Au−Sn−Yb iQC and 2/1-cAC, the Yb valence was found to be close to divalent. Taking into account the trend in Yb-based IV compounds,18 that is, Yb 4f electron character

aico

where τ is the golden mean of (1 + 5 )/2 and q/p is any rational approximant of τ, such as 1/1, 2/1, and 3/2.23 The cubic phase obtained in ASY(10) was thus identified as the 2/ 1-cAC to the iQC. The compositions were determined to be Au60.0Sn26.7Yb13.3 and Au59.4Sn26.3Yb14.3 for iQC and 2/1-cAC, respectively. The composition of 2/1-cAC was in agreement with that reported for Au60.3Sn24.6Yb15.1 within 1% error, although independent methods were applied.22 Figure 4 shows Yb L3 edge XANES spectra for the Au−Sn− Yb iQC and 2/1-cAC. The absorption edge had clear double peaks that correspond to the energies of Yb3+ and Yb2+, which demonstrates that the valence of Yb ions is between divalent and trivalent in both iQC and 2/1-cAC. The spectra were

Figure 4. Normalized Yb L3 XANES spectra of the Au−Sn−Yb iQC (top) and 2/1-cAC (bottom) at room temperature (○). Each spectrum is fitted by the sum (solid red line) of the divalent (dotted line) and trivalent (dashed line) components. Normalization was applied so that the higher-energy data up to 9.11 keV asymptotically approach a value of unity. 9184

DOI: 10.1021/acs.inorgchem.9b00801 Inorg. Chem. 2019, 58, 9181−9186

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changes from itinerant to localized as the Yb valence increases from divalent to trivalent, we consider the Yb 4f electrons in Au−Sn−Yb iQCs and 2/1-cAC to exhibit an itinerant character, namely a valence fluctuation state. In fact, the XANES spectra for 2/1-cAP were observed to remain unchanged down to 3 K within experimental resolution, which indicates that the Yb valence is practically temperatureindependent. This is consistent with the interpretation that Yb 4f electrons in these compounds exhibit an itinerant character. When a 4f electron system has an itinerant character, it generally exhibits a higher Kondo temperature, which results in the temperature independence of the Yb valence below room temperature. On the other hand, the Yb 4f electrons in the Au−Al−Yb iQC exhibit a localized character in the highertemperature range above several kelvin, as shown by the magnetic moment.19 Additionally, quantum critical phenomena emerge at low temperatures typically below several kelvin.20 The Yb valence in the Au−Al−Yb iQC is 2.61,19 which is in the medium range between divalent and trivalent, and the quantum critical state between itinerant and localized character develops as the temperature decreases to 0 K. Therefore, the Au−Sn−Yb iQC can be characterized as a different type of IV iQC from Au−Al−Yb iQC in terms of the itinerant and localized character of 4f electrons.

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(1) Shechtman, D.; Blech, I.; Gratias, D.; Cahn, J. W. Metallic Phase with Long-Range Orientational Order and No Translational Symmetry. Phys. Rev. Lett. 1984, 53, 1951−1953. (2) Levine, D.; Steinhardt, P. J. Quasicrystals: A New Class of Ordered Structures. Phys. Rev. Lett. 1984, 53, 2477−2480. (3) Takakura, H.; Gómez, C. P.; Yamamoto, A.; de Boissieu, M.; Tsai, A. P. Atomic structure of the binary icosahedral Yb-Cd quasicrystal. Nat. Mater. 2007, 6, 58−63. (4) Tsai, A. P.; Guo, J. Q.; Abe, E.; Takakura, H.; Sato, T. J. A stable binary quasicrystal. Nature 2000, 408, 537−538. (5) Guo, J. Q.; Abe, E.; Tsai, A. P. Stable icosahedral quasicrystals in binary Cd-Ca and Cd-Yb systems. Phys. Rev. B: Condens. Matter Mater. Phys. 2000, 62, R14605−R14608. (6) Gómez, C. P.; Lidin, S. Structure of Ca13Cd76: A novel approximant to the MCd5.7 quasicrystals (M = Ca, Yb). Angew. Chem., Int. Ed. 2001, 40, 4037−4039. (7) Gómez, C. P.; Lidin, S. Comparative structural study of the disordered MCd6 quasicrystal approximants. Phys. Rev. B: Condens. Matter Mater. Phys. 2003, 68, 024203. (8) Henley, C. L. Sphere packings and local environments in Penrose tilings. Phys. Rev. B: Condens. Matter Mater. Phys. 1986, 34 (2), 797. (9) Takakura, H. Geometrical property of the cluster model of the Yb−Cd icosahedral quasicrystal. Philos. Mag. 2008, 88 (13−15), 1905−1912. (10) Takakura, H.; Strzałka, R. Cluster environments in a twelve-fold packing model of icosahedral quasicrystals. J. Phys.: Conf. Ser. 2017, 809 (1), 012002. (11) Goldman, A. I.; Kong, T.; Kreyssig, A.; Jesche, A.; Ramazanoglu, M.; Dennis, K. W.; Bud’ko, S. L.; Canfield, P. C. A family of binary magnetic icosahedral quasicrystals based on rare earths and cadmium. Nat. Mater. 2013, 12, 714−718. (12) Guo, J. Q.; Abe, E.; Tsai, A. P. Stable Cd-Mg-Yb and Cd-MgCa icosahedral quasicrystals with wide composition ranges. Philos. Mag. Lett. 2002, 82, 27−35. (13) Guo, J.; Abe, E.; Tsai, A. P. Stable icosahedral quasicrystals in the Cd−Mg−RE (RE= rare earth element) systems. Jpn. J. Appl. Phys. 2000, 39, L770. (14) Guo, J. Q.; Tsai, A. P. Stable icosahedral quasicrystals in the AgIn-Ca, Ag-In-Yb, Ag-In-Ca-Mg and Ag-In-Yb-Mg systems. Philos. Mag. Lett. 2002, 82, 349−352. (15) Ishimasa, T.; Tanaka, Y.; Kashimoto, S. Icosahedral quasicrystal and 1/1 cubic approximant in Au−Al−Yb alloys. Philos. Mag. 2011, 91, 4218−4229. (16) Tanaka, K.; Tanaka, Y.; Ishimasa, T.; Nakayama, N.; Matsukawa, S.; Deguchi, K.; Sato, N. K. Tsai-type quasicrystal and its approximant in Au-Al-Tm alloys. Acta Phys. Pol., A 2014, 126, 603. (17) Kawana, D.; Watanuki, T.; Machida, A.; Shobu, T.; Aoki, K.; Tsai, A. P. Intermediate-valence quasicrystal of a Cd-Yb alloy under pressure. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81, 220202. (18) Watanuki, T.; Kawana, D.; Machida, A.; Tsai, A. P. Pressureinduced formation of intermediate-valence quasicrystalline system in a Cd-Mg-Yb alloy. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 054207. (19) Watanuki, T.; Kashimoto, S.; Kawana, D.; Yamazaki, T.; Machida, A.; Tanaka, Y.; Sato, T. J. Intermediate-valence icosahedral Au-Al-Yb quasicrystal. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 86, 094201. (20) Deguchi, K.; Matsukawa, S.; Sato, N. K.; Hattori, T.; Ishida, K.; Takakura, H.; Ishimasa, T. Quantum critical state in a magnetic quasicrystal. Nat. Mater. 2012, 11, 1013−1016. (21) Canfield, P. C.; Caudle, M. L.; Ho, C. S.; Kreyssig, A.; Nandi, S.; Kim, M. G.; Lin, X.; Kracher, A.; Dennis, K. W.; McCallum, R. W.; Goldman, A. I. Solution growth of a binary icosahedral quasicrystal of Sc12Zn88. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81, 020201.

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CONCLUSIONS We reported the formation of a new iQC in the Au−Sn−Yb system. Dendritic single-crystal agglomerates of the iQC were synthesized by the self-flux technique. Single-crystal XRD revealed this new phase to be a primitive iQC with an icosahedral lattice constant of 0.5447(7) nm. In addition, the Yb L3 edge XANES indicated that the Yb ions in the iQC and corresponding 2/1-cAC are in IVSs of 2.18+ and 2.27+, respectively. The Au−Sn−Yb iQC is the second example of an IV iQC that has been realized at ambient pressure, after Au− Al−Yb iQC. Yb 4f electrons in the Au−Sn−Yb iQC are thought to exhibit an itinerant character, while those in the Au−Al−Yb iQC exhibit a localized character. Finally, the stability of the iQC was discussed in terms of the atomic size factor (δ) and valence electron-to-atom ratio (e/a), whereby the IVS of the Yb ions is realized so that the δ factor is favored.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Tsunetomo Yamada: 0000-0003-0138-9778 Yoshitaka Matsushita: 0000-0002-4968-8905 An-Pang Tsai: 0000-0002-7905-9915 Notes

The authors declare no competing financial interest. # Deceased May 25, 2019.

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ACKNOWLEDGMENTS This research was partially supported by JSPS KAKENHI Grants JP15K05193 and JP18K13987. Y.N. thanks M. de Boissieu for stimulating discussions during her stay in SIMaP. The XANES experiments at SPring-8 were performed with approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposals 2013A3701, 2013B1183, and 2014A3701). A.-P.T. acknowledge support from the “Dynamic 9185

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Inorganic Chemistry (22) Morita, Y.; Tsai, A. P. Approximants in the Ag−In−M and Au− Sn−M (M = Ca or Rare Earth Metals) Systems. Jpn. J. Appl. Phys. 2008, 47, 7975. (23) Goldman, A. I.; Kelton, R. F. Quasicrystals and crystalline approximants. Rev. Mod. Phys. 1993, 65, 213. (24) Tsai, A. P. A test of Hume-Rothery rules for stable quasicrystals. J. Non-Cryst. Solids 2004, 334, 317−322. (25) Mitani, T.; Ishimasa, T. A metastable icosahedral quasicrystal in the Zn−Mg−Yb alloy system. Philos. Mag. 2006, 86, 361−366. (26) Pearson, W. B. The Crystal Chemistry and Physics of Metals and Alloys; Wiley: New York, 1972. (27) Yamada, T.; Takakura, H.; Euchner, H.; Pay Gómez, C.; Bosak, A.; Fertey, P.; de Boissieu, M. Atomic structure and phason modes of the Sc−Zn icosahedral quasicrystal. IUCrJ 2016, 3, 247−258. (28) Yamada, T.; Takakura, H.; Kong, T.; Das, P.; Jayasekara, W. T.; Kreyssig, A.; Beutier, G.; Canfield, P. C.; de Boissieu, M.; Goldman, A. I. Atomic structure of the i-R-Cd quasicrystals and consequences for magnetism. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 94, 060103. (29) Cahn, J. W.; Shechtman, D.; Gratias, D. Indexing of icosahedral quasiperiodic crystals. J. Mater. Res. 1986, 1, 13−26.

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DOI: 10.1021/acs.inorgchem.9b00801 Inorg. Chem. 2019, 58, 9181−9186