1 Quasicrystal

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Synthesis and Atomic Structure of the Yb−Ga−Au 1/1 Quasicrystal Approximant Tsunetomo Yamada,*,† Takuya Kurihara,‡ Yurii Prots,§ Akira Sato,∥ Yoshitaka Matsushita,∥ Yuri Grin,§ and An Pang Tsai‡ †

Department of Applied Physics, Faculty of Science, Tokyo University of Science, Katsushika-ku, Tokyo 125-8585, Japan Institute of Multidisciplinary Research for Advanced Materials (IMRAM), Tohoku University, Sendai-shi 980-8577, Miyagi, Japan § Max-Planck-Institut für Chemische Physik fester Stoffe, 01187 Dresden, Germany ∥ Research Network and Facility Services Division, National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan

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‡

ABSTRACT: The Yb−Ga−Au 1/1 quasicrystal approximant (AP) composition ranges from Yb14.0Ga20.6Au65.4 to Yb14.8Ga46.3Au38.9, and single crystals of the 1/1 AP having the composition Yb13.8Ga26.1Au60.1 were obtained by the self-flux technique. X-ray structural analysis demonstrated that the atomic structure [space group Im3; a = 14.6889(9) Å] can be described by the bodycentered packing of Tsai-type rhombic triacontahedron (RTH) clusters. The positional disorder in these clusters, interpreted as the average of an orientationally disordered tetrahedron and triangle, results in positional disorder in the outer shells. The elemental distributions and positions of mixtures of Au and Ga atoms in the RTH clusters correspond to those in the isostructural Yb15Al36Au49 1/1 AP.

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INTRODUCTION Icosahedral quasicrystals (iQCs) are long-range ordered materials that exhibit 5-fold rotational symmetry in their diffraction patterns that are incompatible with translational symmetry in three-dimensional space.1,2 The atomic structures of iQCs can be described using superspace formalism,3 and a higher-dimensional structural model has been developed for the binary iQC YbCd5.7.4−6 This atomic structure consists of two building units, Tsai-type rhombic triacontahedron (RTH) clusters and double Friauf polyhedra (DFP), with ordering of the constituent elements. Each RTH cluster comprises five successive shells. As one moves outward from the center, these are a Cd 4 tetrahedron, a Cd 20 dodecahedron, a Yb 12 icosahedron, a Cd32 icosidodecahedron, and a Cd92 rhombic triacontahedron. Two Yb atoms are located on the longer body diagonal of each DFP.4 In addition, two periodic crystals related to YbCd5.7, known as approximants (APs), form near the iQC in the phase diagram. These are the YbCd6 1/1 and YbCd5.8 2/1 APs.7,8 Both the Yb−Cd APs and the iQC are composed of the same building units; thus, it is important to examine the APs to understand the formation, stability, and atomic structure of the iQC. The stability of iQCs has been discussed in terms of the Hume−Rothery rules [i.e., the valence electron concentration (e/a) and atomic size factor (δ)].9 The former is the number of valence electrons per atom, while the latter is defined as δ = rL/rS, where rL and rS are the atomic radii of the larger (L) and smaller (S) atoms, respectively. The substitution of various © XXXX American Chemical Society

other elements for Yb and/or Cd has shown that the isostructural phases of the YbCd5.7 iQC form in various ternary systems, including Sc−M−Zn (M = Mg, Mn, Fe, Co, Ni, Cu, Ag, Au, Pd, or Pt),10−13 R−Mg−Zn (R = Y, Ga, Tb, Dy, Ho, Er, Tm, Yb, or Lu),14,15 Sc−Ga−Cu,16 Yb−In−Ag,17 and Yb−Al−Au.18 For these iQCs, the value of e/a falls between 1.95 and 2.15, while δ is between 1.17 and 1.26 (and therefore close to the ideal value of 1.288).19 Such substitutions also result in structural disorder and thus contribute to structural stability, based on the entropy stabilization mechanism. Thus, assessing crystallographic randomness in the atomic structures is also a crucial aspect of obtaining insights into the stability of iQCs. Crystallographic randomness, such as positional and occupational disorder, is termed “site splitting” and “chemical mixing” in the spatially averaged structures obtained by standard X-ray structural analysis. In the Tsai-type RTH clusters, positional and occupational disorders are found at the cluster center and at other specific sites, respectively. The former is attributed to the orientational disorder of tetrahedra.7,8 As an example, it has been shown that the Zn4 tetrahedra are dynamically disordered above 160 K in the ScZn6 1/1 AP,20,21 which results in 12 atomic positions at the cluster center having an occupancy of 1/3.22 Below 160 K, a monoclinic superstructure forms as a result of orientational Received: February 21, 2019

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DOI: 10.1021/acs.inorgchem.9b00513 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry

Figure 1. Powder X-ray diffraction patterns for the polycrystalline alloys Yb14GaxAu84−x with Ga contents from x = 15 to 50 and calculated intensities determined using the refined structure for the Yb13.65Ga22.96Au63.39 1/1 AP. Peaks of secondary phases are indicated by the arrow or arrowheads.

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ordering of the Zn4 tetrahedra in an antiparallel fashion along the [110] direction of the high-temperature cubic phase.23−25 The latter is frequently seen in ternary compounds. However, the selective occupation of various constituent elements has been observed in RTH clusters. As an example, the vertices of the triacontahedron shell are preferentially occupied by Mg atoms when the Cd sites in both the Yb−Mg−Cd 1/1 AP and the iQCs are occupied by Mg.26,27 The presence of ordered and mixed sites thus indicates that both the electronic structure and the extent of partial chemical disorder are important factors in the stabilization mechanism. Recently, the discovery of quantum criticality in the Yb−Al− Au iQC28 has produced significant interest in Au-based iQCs and the corresponding APs. A Rietveld analysis of the Yb−Al− Au 1/1 AP has demonstrated positional disorder at the cluster centers and the presence of atomic mixing of Au and Al at specific sites in RTH clusters.18 Because these characteristics were also found in the isostructural Yb−Ge−Au 1/1 AP,29−31 they appear to be peculiar to Au-based APs and iQCs. To verify this hypothesis, structural analysis of other Au-based APs is required, particularly the Yb−Ga−Au 1/1 AP32 and Yb− Sn−Au 2/1 AP,33 which correspond to the recently discovered Yb−(Ga, Sn)−Au iQCs.34,35 In this study, we performed a structural analysis of the Yb− Ga−Au 1/1 AP. We initially surveyed the composition region of the 1/1 AP and found that this compound has a wide composition range, from Yb14.0Ga20.6Au65.4 to Yb14.8Ga46.3Au38.9. Second, an X-ray structural analysis was performed, using a single crystal obtained by a self-flux technique. The resulting atomic structure of the 1/1 AP is discussed in terms of positional and occupational disorder and compared with that of the isostructural Yb−Al−Au 1/1 AP.

EXPERIMENTAL DETAILS

Polycrystalline alloys were synthesized from high-purity Yb(3N), Ga(6N), and Au(4N). These metals were combined according to the desired composition Yb14GaxAu86−x (x = 15, 20, 25, 30, 35, 40, 45, or 50) and subsequently melted under Ar in an arc furnace. The resulting ingots were wrapped with Mo foil, sealed inside quartz tubes under Ar, and annealed at 913 K for 672 h in an electric furnace. Herein, we abbreviate these alloys as YGA(x). Single crystals of the Yb−Ga−Au 1/1 AP were obtained using the self-flux technique. High-purity Yb(3N), Ga(4N), and Au(4N) were combined according to the composition Yb5(Ga1/3Au2/3)95, transferred to an alumina crucible, and sealed in a silica tube under Ar. A stainless-steel mesh was placed in the middle of the crucible to separate the solvent flux from the crystals. The metals were melted at 1273 K for 2 h and then cooled to 1023 K and held at that temperature for 3 h in an electrical furnace. Following this, the melt was slowly cooled to 643 K at a rate of 3 K/h, after which the single crystals were separated from the flux using a centrifuge. Powder X-ray diffraction (XRD) and scanning electron microscopy (SEM) were used to characterize the obtained phases. The powder XRD experiments employed Cu Kα1 radiation (λ = 1.54056 Å), and indexing of the diffraction patterns and lattice parameter determination were performed using the WinCSD software package.36 The compositions of the various specimens were analyzed using SEM together with wavelength dispersive X-ray spectroscopy (WDX). Intensity data for crystal structure analysis were collected using a RIGAKU Saturn CCD single-crystal diffractometer equipped with VariMax confocal optics for Mo Kα radiation (λ = 0.71073 Å). Prior to the diffraction experiment, the crystals were flash-cooled to 113 K (at the sample position) in a stream of cold N2 gas. Prior to these analyses, single crystals, each 16 μm × 20 μm × 21 μm, were selected from crushed alloys and mounted on thin glass needles. The distance between the sample and the detector was set at 45 mm, and systematic scans with omega rotations were conducted with an oscillation width of 0.3°. Indexing of reflections, integration, and B


Article

Inorganic Chemistry Table 1. Compositions of the 1/1 AP Samples in the Yb−Ga−Au System

YGA(15) YGA(20) YGA(25) YGA(30) YGA(35) YGA(40) YGA(45) YGA(50) single crystal

1/1 approximant

secondary phase

analyzed composition (atom %)

analyzed composition (atom %)

Au

Ga

Yb

Au

Ga

Yb

65.4(6) 64.8(6) 59.88(3) 54.1(3) 50.19(7) 45.24(6) 40.5(1) 38.9(1) 60.1(1)

20.6(4) 21.1(4) 25.74(6) 31.99(3) 35.07(7) 40.21(7) 44.6(2) 46.3(1) 26.1(1)

14.0(2) 14.1(3) 14.39(5) 14.60(5) 14.7(1) 14.54(3) 14.9(3) 14.8(2) 13.8(1)

− 69.3(2) 63.4(1) 57.63(7) − − − 24.81(9) −

− 9.5(2) 15.0(3) 20.49(4) − − − 54.89(9) −

− 21.2(2) 21.6(2) 21.88(4) − − − 20.30(4) −

absorption corrections for intensities were performed using the CrysAlisPro software package (Rigaku Oxford Diffraction).

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RESULTS AND DISCUSSION Material Synthesis and Composition Analysis. Figure 1 shows the powder XRD patterns obtained from the polycrystalline YGA(x) alloys having various Ga concentrations from x = 15 to 50. All of the peaks can be indexed to a body-centered cubic lattice, except for some small peaks, as indicated by the arrow and arrowheads in the figure. The overall intensity distributions are quite similar to those calculated from the refined structure for the Yb13.65Ga22.96Au63.39 1/1 AP, as discussed in the next subsection. Single-phase samples of the 1/1 AP were obtained for YGA(35), YGA(40), and YGA(45), and no secondary phases were evident in SEM images of these materials. However, three types of unidentified phases were observed in other samples, as follows. The diffraction peak indicated by the arrow in the YGA(15) pattern may be assigned to a solid solution of Ga in Au. The peaks indicated by open arrowheads in the YGA(20), YGA(25), and YGA(30) patterns can be assigned to an unknown Yb−Au−Ga compound. The peaks indicated by closed arrowheads in the YGA(50) pattern can most likely be assigned to YbGaxAu4−x.37 The SEM−WDX data showed Yb concentrations of approximately 20 atom % in the unidentified phases within YGA(20), YGA(25), YGA(30), and YGA(50). The results of the composition analysis based on SEM−WDX for the 1/1 AP are summarized in Table 1, from which the composition for this material is believed to range from Yb14.0Au65.4Ga20.6 to Yb14.8Ga44.6Au38.9. Figure 2 plots the cubic lattice parameter against the nominal Ga concentration for the Yb−Ga−Au 1/1 AP. The lattice parameter is seen to continually decrease, from 14.7524(3) to 14.5335(5) Å, with an increase in Ga concentration. Interestingly, this decrease in the lattice parameter follows Vegard’s law between 25% and 40% Ga. This result is consistent with the fact that Ga (1.411 Å) has an atomic radius that is smaller than that of Au (1.442 Å). However, the decrease in the lattice parameter may not be explained simply by the increase in Ga concentration, for two reasons. First, the change in the lattice parameter [Δa = 0.2189(5) Å] is much larger than the value predicted (Δa = 0.13 Å) on the basis of the atomic radii of Ga and Au. Second, the Yb concentration also changes along with the Ga concentration (see Table 1), which should also affect the lattice parameter. Therefore, structural determinations of the Ga-poor and Ga-rich Yb−Ga−Au 1/1 AP phases are necessary to explain in detail the changes in the lattice parameter.

Figure 2. Plot of the lattice parameter vs the nominal Ga concentration for the Yb−Ga−Au 1/1 AP. The linear relationship is indicated by the dashed line.

Recently, the formation of two types of 1/1 APs in the Yb− Ge−Au system was reported. In both cases, the atomic structures consist up of Tsai-type RTH clusters but with different central shells. In the Ge-poor phase, four atoms (a mixture of Au and Ga) are situated at the cluster center, while in the Ge-rich phase, a single Yb atom occupies the center.29−31 This results in different compositions and lattice parameters {i.e., Yb14.0Ge22.0Au64.0 [a = 14.724(2) Å] and Yb16.0Ge20.5Au63.5 [a = 14.605(4) Å]}. These two 1/1 APs may also form in the Yb−Ga−Au system, and the increase in the lattice parameter with a decrease in Ga concentration may be explained by the occupation of four atoms (a mixture of Au and Ga) at the cluster center. Structural Determination. The atomic structure of the Yb−Ga−Au 1/1 AP was investigated by preparing single crystals using the self-flux technique. Millimeter-sized single crystals of the Yb−Ga−Au 1/1 AP were obtained from a sample with a starting composition of Yb5(Ga1/3Au2/3)95, and no secondary phase was observed in the backscattering SEM image of these crystals. The composition of the crystals was determined to be Yb13.8(1)Ga26.1(1)Au60.1(1) by SEM−WDX analysis. In the single-crystal XRD experiments, 55154 reflections were acquired and then merged into 2225 independent reflections, assuming space group Im3. The intensities of equivalent reflections were averaged with an internal residual Rint of 0.0789. C


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Inorganic Chemistry The initial structure was obtained by ab initio phasing of the diffraction intensities based on a charge flipping algorithm,38,39 utilizing the program SUPERFLIP.40 The structure was found to be isostructural to a Ru3Be17-type structure,41 consisting of eight sites: M1−M6, M8, and Yb1. This structure can be described by the body-centered packing of Tsai-type RTH clusters consisting of four successive shells. As one moves from the center outward, these are an M20 dodecahedron shell comprising M2(24g) and M4(16f), an Yb12 icosahedron shell made of Yb (24g), an M32 icosidodecahedron shell made of M1(48h) and M6(12d), and an M92 rhombic triacontahedron shell composed of M1(48h), M3(24g), M4(16f), and M5(12e). An additional M8(8c) site at the 1/4 1/4 1/4 location in the middle of the line connecting the origin and the body-center positions (a c-linkage or [111] linkage) was also observed. The structural parameters and secondary extinction parameter were refined against 2094 unique reflections larger than 2σ(F2), utilizing SHELIXL.42 After iterations of the refinement, different Fourier syntheses yielded a residual peak at 0 0.094 0.084 (24g). This site is herein termed M7 and was included in the refinement (refinement 1), assuming a mixture of Au and Ga at the M7 site. The resulting structure is isostructural to an YbCd6-type structure,43 in which four Cd atoms are situated inside the dodecahedron shell. Therefore, we fixed the site occupation factor (SOF) for the M7 site at 1/ 3, so that a total of four atoms were located at the cluster center. The fitting converged with reliability indices of R1 = 0.0866 and wR2 = 0.2150, and the difference Fourier syntheses yielded high positive residual peaks near the dodecahedron and icosidodecahedron shells. These included a residual peak with a value of 40.88 e−/Å3 at 0 0.44 0 (0.58 Å from M6), a residual peak with a value of 29.72 e−/Å3 at 0 0.27 0.07 (0.46 Å from M2), a residual peak with a value of 25.67 e−/Å3 at 0 0.23 0.9 (0.33 Å from M2), and a residual peak with a value of 18.46 e−/Å3 at 0.04 0.08 0 (0.32 Å from M7). These results indicate additional atomic occupations at these peak positions. Because the distances between these atomic sites and the residual peak positions were much smaller than realistic interatomic distances, these additional positions cannot be occupied at the same time. Therefore, these positions can be taken into account by splitting the M2, M6, and M7 sites during the refinement. In addition, the difference Fourier syntheses yielded a negative residual peak with a value of −26.69 e−/ Å3 at 0 0.25 0.08 (0.09 Å from M2). This is clear evidence of splitting of the M2 site, because this peak position is between the M2 site and the position of the positive residual peak. In a further refinement (refinement 2), we split M2 into M2a and M2b, M6 into M6a and M6b, and M7 into M7a and M7b. The sum of the SOFs for each M2 and M6 was set to unity, while that for M7 was set to 1/3. In addition, mixtures of Au and Ga were assigned to M2, M6, and M7 with the same ratios that were obtained during refinement 1 [i.e., Au/Ga = 0.463/0.537 (for M2a; M2b), 0.550/0.450 (for M6a; M6b), and 0.219/0.114 (for M7a; M7b)]. The refinement converged at R1 = 0.0331 and wR2 = 0.0935. Good agreement was found between the refined composition (Yb13.65Ga22.96Au63.39) and the composition obtained from the SEM−EDX data [Yb13.8(1)Ga26.1(1)Au60.1(1)]. The crystallographic information and parameters for data collection and structural refinement are provided in Table 2. The atomic coordinates, SOFs, and equivalent isotropic atomic displacement parameters (ADPs) are given in Table 3, and the anisotropic displacement parameters are summarized in Table 4. The introduction of

Table 2. Crystallographic Information and Parameters for the Data collection and Structural Refinement of the Yb13.65Ga22.96Au63.39 1/1 AP Crystal Data nominal composition molar mass (g/mol) temperature (K) space group a (Å) cell volume (Å3) crystal form crystal size (μm) Z F(000) calculated density (g/cm3)

Yb24Ga40.4Au111.6 29002.01 113 Im3 (No. 204) 14.6889(9) 3169.3(6) irregular 16 × 20 × 21 1 11768 15.195 Data Collection radiation type Mo Kα detector CCD, Saturn 724 HG, Rigaku data collection method ω scans θmin, θmax (deg) 1.961, 43.917 no. of measured reflections 55154 no. of independent reflections 2225 no. of observed reflections [F2 ≥ 2σ(F2)] 2094 absorption correction method spherical absorption coefficient (mm−1) 154.809 Refinement refined composition Yb13.65Ga22.96(25)Au63.39(29) Rint 0.0789 no. of parameters 66 R1 [F2 ≥ 2σ(F2)] 0.0331 wR2 (all data) 0.0935 S 1.095 ρmax, ρmin (e−/Å3) 4.043, −6.474

splitting at the M2, M6, and M7 sites resulted in an R index lower than that obtained from refinement 1. Thus, the positional disorder at these sites is essential to describing the atomic structure. Here, we note that no residual peak was observed at the cluster center, demonstrating the absence of Yb at this position. Because the present sample is Ga-poor (having 26.1 atom % Ga), the lack of Yb at the cluster center is consistent with the speculation that the larger lattice constant in Figure 2 is explained by the occupation of four atoms (a mixture of Au and Ga) at the cluster center. However, the possibility of Yb occupation at the cluster center should be examined on the basis of a different sample with Ga-rich compositions, and the synthesis of Ga-rich single crystals of the Yb−Ga−Au 1/1 AP is currently underway in our laboratory. Figure 3 shows the shell structures of the Yb13.65Ga22.96Au63.39 1/1 AP, as generated using the VESTA-3 software program.44 The first shell consists of M7a and M7b sites, which form a cuboctahedron and a distorted icosahedron, respectively. The second dodecahedron shell consists of M2 (24g) and M4 (16f) sites, and the former is occupied by a mixture of Au and Ga and composed of two split positions that have a distance of 0.6 Å. The latter is exclusively occupied by Au. The third icosahedron shell consists of Yb1 (24g) and is exclusively occupied by Yb, while the fourth icosidodecahedron shell consists of M1 (48h) and M6 (12d) sites. The former is exclusively occupied by Au, while the latter is occupied by a mixture of Au and Ga and composed of two split positions that have a distance of 0.5 Å along a direction parallel D


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Inorganic Chemistry

Table 3. Atomic Coordinates, Site Occupation Factors (SOFs), and Equivalent Isotropic Displacement Parameters (Ueq) for the Yb13.65Ga22.96Au63.39 1/1 AP site

atom

Wyckoff position

SOF

x

y

z

Ueq (Å2)

Yb1 M1 M2a M2b M3 M4 M5 M6a M6b M7a M7b M8

Yb Au Au/Ga Au/Ga Au Au Ga Au/Ga Au/Ga Au/Ga Au/Ga Ga

24g 48h 24g 24g 24g 16f 12e 12d 12d 24g 24g 8c

1 1 0.189(3)/0.176(3) 0.329(3)/0.306(3) 1 1 1 0.339(9)/0.394(10) 0.124(9)/0.141(10) 0.114(3)/0.0486(11) 0.114(3)/0.0509(11) 1

0.18723(3) 0.34092(2) 0 0.23077(16) 1/2 0.14975(2) 1/2 0.3933(3) 0.4253(9) 0.0852(4) 0.0421(3) 1/4

0.30606(3) 0.20185(2) 0.26576(16) 0.08840(13) 0.09654(2) =x 0.20267(11) 0 0 0 0.0861(3) 1/4

0 0.10287(2) 0.06850(13) 0 0.14131(2) =x 0 0 0 0.0920(4) 0 1/4

0.01417(7) 0.01540(6) 0.0151(4) 0.0309(4) 0.01385(7) 0.01784(9) 0.0136(2) 0.0167(4) 0.0173(15) 0.0399(14) 0.0265(9) 0.0172(3)

Table 4. Anisotropic Atomic Displacement Parameters (Uij) for the Yb13.65Ga22.96Au63.39 1/1 APa site

U11

U22

U33

U23

U13

U12

Yb1 M1 M2a M2b M3 M4 M5 M6a M6b M7a M7b

0.01253(13) 0.01417(10) 0.0152(5) 0.0342(10) 0.01442(12) 0.01784(9) 0.0147(5) 0.0126(12) 0.017(4) 0.038(2) 0.0225(17)

0.01602(15) 0.01671(10) 0.0150(9) 0.0388(7) 0.01345(12) =U11 0.0133(5) 0.0259(5) 0.0206(13) 0.047(3) 0.0358(18)

0.01397(14) 0.01532(10) 0.0152(6) 0.0197(4) 0.01370(12) =U11 0.0129(5) 0.0116(4) 0.0137911) 0.035(3) 0.0213(14)

0 0.00151(7) 0.0009(5) 0 0.00070(9) −0.00152(7) 0 0 0 0 0

0 0.00017(7) 0 0 0 =U23 0 0 0 −0.0061(19) 0

0.00004(11) 0.00052(7) 0 0.0031(7) 0 =U23 0 0 0 0 −0.0026(13)

a

An isotropic parameter was used for M8.

2.9 Å in Au as well as the distance in the third neighboring M7a−M7b, the first neighboring M7a−M7a and M7b−M7b distances are found to be shorter than expected (see Table 5). Hence, these sites cannot be occupied by two atoms simultaneously. For this reason, the positional disorder at the center of the RTH cluster can be understood as the average of three types of shells oriented along six or 12 directions. The associated atom occupations are (i) occupation at M7a, (ii) occupation at M7b, and (iii) occupation at both M7a and M7b (Figure 4b−d). In the first case, M7a forms a cuboctahedron, which is often seen in isostructural RCd6 and ScZn6 1/1 APs. The positional disorder at M7a is interpreted as the average of tetrahedra in six orientations, as depicted in Figure 4e, which corresponds to “type II disorder” as described in ref 8. In this case, each tetrahedron shell is significantly distorted, resulting in an edge length of 2.5−3.2 Å. In the second case, M7b forms a distorted icosahedron, which has never before been observed in other isostructural 1/1 APs. Thus, the positional disorder at M7b is different from either “type I disorder” or “type II disorder” in ref 8. The neighboring positions on the distorted icosahedron cannot be occupied by any atoms at the same time because the realistic interatomic distance (1.2−1.5 Å) is too short (see Table 5). Instead, atoms can occupy the second neighboring position, which results in an interatomic distance of 2.5−2.7 Å. Therefore, the fact that the positional disorder at M7b can be interpreted as an average of triangles in 12 orientations is not unexpected, as depicted in Figure 4f. In the third case, the fourth neighboring site (where d is approximately 2.6 Å) can be occupied simultaneously. This leads to six different combinations for the atomic occupation,

Figure 3. Shell structures of the Yb13.65Ga22.96Au63.39 1/1 AP with a unit cell. Labels M1−K8 are the same as those used in Table 2.

to the 2-fold axis. The fifth RTH shell comprises the two inequivalent sites M3 (24g) and M5 (12e), which are exclusively occupied by Au and Ga, respectively, and the additional M8 (8c) site is fully occupied by Ga. Figure 4a presents the total electron density isosurfaces around the M7 position, as obtained via a maximum entropy method and utilizing the DYSNOMIA software package45 with R = 0.0179 and wRa = 0.0192. The peanut-shaped electron density isosurface confirms the splitting of the M7 site into M7a and M7b. This characteristic isosurface shape is not observed for the isostructural RCd6 (R = rare-earth elements) and ScZn6 1/1 APs. Compared to the interatomic distance of E


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Inorganic Chemistry

Figure 4. Positional disorder at the center of the Tsai-type RTH cluster in the Yb13.65Ga22.96Au63.39 1/1 AP. (a) Electron density distribution at M7 with an isosurface level = 20 e−/Å3. Atomic positions of (b) M7a, (c) M7b and (d) M7a and M7b. (e) An interpretation of the positional disorder at M7a by a superposition of six tetrahedra. (f) An interpretation of the positional disorder at M7b by a superposition of twelve triangles. (g) An interpretation of the positional disorder at M7a and M7b by a superposition of six tetrahedra. (h) Electron density distributions at M2 and M6 with an isosurface level = 20 e−/Å3. (i) Atomic positions of M2a, M2b, M6a and M6b.

occupations is evident. Specifically, M1, M3, and M4 are occupied by Au and M5 and M8 are occupied by Ga/Al. The atomic ordering follows an empirical rule for isostructural approximants. This rule states that the middle edge positions of the RTH shell (M3) are occupied by pure p-block elements (i.e., Al, Ga, In, Sn, Ge, or Si), while the vertex positions of the shell (M5) are predominantly occupied by d-block elements (i.e., Zn, Cd, Ag, or Au).26 In addition, positions M2, M6, and M7 are commonly occupied by mixtures of Au and Ga/Al in both Yb−Ga−Au and Yb−Al−Au 1/1 APs. Recently, we have observed superlattice reflections in the X-ray diffraction patterns of the isostructural Au−Si−Yb 1/1 AP. The superstructure of this compound may be composed of two different Tsai-type RTH clusters having different elemental distributions as a result of the atomic ordering at the M2 and M6 sites. Thus, the superstructure of the Au−Si−Yb 1/1 AP may provide some insights into the atomic ordering and disorder in such structures, and a structural analysis of this superstructure is now in progress.

as shown in Figure 4g, where two atoms occupy M7a and two others occupy M7b. The edge length of the tetrahedron shell ranges from 2.5 to 2.7 Å, and the shell is closer to the ideal tetrahedron than in the first case. Figure 4h) shows the electron density isosurfaces at the M2 and M6 sites as obtained using the maximum entropy method. The peanut shape of the electron density isosurfaces confirms the site splitting of M2 to M2a and M2b and of M6 to M6a and M6b (Figure 4i). The interatomic distances between M2a and M6a [d2 = 2.127(5) Å] and between M2a and M2a [d4 = 2.012(4) Å] are too short; thus, these sites cannot be occupied by two atoms at the same time. Therefore, the site splitting at M2 and M6 results from the orientational disorder of the central shell. At present, it is uncertain whether the orientational disorder at the central shell is dynamical. Further study is necessary to answer this question. Via comparison of the atomic structures of the Yb−Ga−Au 1/1 AP and the isostructural Yb−Al−Au 1/1 AP,18 a strong correspondence between those two in terms of selective atomic F


Inorganic Chemistry

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CONCLUSIONS The composition of the Yb−Ga−Au 1/1 quasicrystal AP was found to vary from Yb14.0Ga20.6Au65.4 to Yb14.8Ga46.3Au38.9. Structural determination was carried out using single-crystal Xray diffraction data, and the atomic structure was found to be composed of Tsai-type rhombic triacontahedron clusters. The positional disorder at the cluster center was interpreted as the average of orientationally disordered tetrahedra and triangles. Au and Ga atoms in the dodecahedron and icosidodecahedron shells and at the cluster centers were found to be disordered, while atomic ordering of the constituent elements was observed at the remaining sites. The selective occupations and the positions of the mixed sites in the Yb−Ga−Au 1/1 AP were found to be similar to those in the isostructural Yb−Al− Au 1/1 AP.

Table 5. Interatomic Distances for the M7a and M7b Sites atom 1

atom 2

interatomic distance (Å)

Au7a|Ga7a

Au7a|Ga7a Au7a|Ga7a Au7a|Ga7a Au7a|Ga7a Au7a|Ga7a Au7a|Ga7a Au7a|Ga7a Au7a|Ga7a Au7a|Ga7a Au7a|Ga7a Au7a|Ga7a Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b Au7b|Ga7b

1.8446(61) 1.8446(57) 1.8446(57) 1.8446(61) 2.5030(83) 2.7028(83) 3.1886(76) 3.1886(75) 3.1886(75) 3.1886(76) 3.6837(83) 1.2368(62) 1.5491(36) 1.5491(57) 1.5491(36) 1.5491(57) 2.3512(53) 2.3512(53) 2.3512(60) 2.3512(60) 2.5294(62) 2.8156(62) 0.7331(59) 1.3986(69) 1.3986(69) 1.9562(55) 1.9562(55) 1.9698(59) 2.6208(72) 2.6310(64) 2.6310(64) 2.9652(61) 2.9652(61) 3.1955(68)

Au7b|Ga7b

Au7a|Ga7a

Article

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ASSOCIATED CONTENT

Accession Codes

CCDC 1878462 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Tsunetomo Yamada: 0000-0003-0138-9778 Yurii Prots: 0000-0002-7418-9892 Yoshitaka Matsushita: 0000-0002-4968-8905 Yuri Grin: 0000-0003-3891-9584 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS T.Y. acknowledges financial support from JSPS KAKENHI Grant JP18K13987. A.P.T. acknowledges support from the “Dynamic Alliance for Open Innovation Bridging Human, Environment and Materials”.

The stability of iQCs and APs has been discussed in terms of Hume−Rothery rules.9 The contributions of the e/a and δ parameters to the stability of the Yb−Ga−Au 1/1 APs are currently uncertain, as a result of the wide composition range of the Yb−Ga−Au 1/1 AP, from Yb14.0Ga20.6Au65.4 to Yb14.8Ga46.3Au38.9. Assuming that Yb, Ga, and Au have two valence electrons, three valence electrons, and one valence electron, respectively, this wide composition range results in e/ a values between 1.55 and 2.07. Note that, on the basis of the magnetic susceptibility values of other compounds in this composition range,46,47 assuming a valence of two for Yb is reasonable. The lower value of e/a in the range mentioned above is unexpected and deviates significantly from the empirical values (2.00−2.05) reported for Tsai-type QCs and APs. It is therefore evident that the ordering/disorder kinetics or atomic dynamics (i.e., the contribution of entropy) should be taken into consideration. The effect of e/a does not completely explain the stability of the APs in this family. Second, the ratio of the atomic size factor, δ = rL/rS (where rL is the size of an Yb atom and rS is the average size of a Ga−Au mixture weighted by the concentrations), ranges from 1.35 to 1.36. This value is slightly larger than the ideal value (1.288) for a Tsai-type cluster.19 Thus, further investigations are necessary to elucidate the contributions of these factors to phase stability.

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REFERENCES

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1 Quasicrystal

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