【公開日：2025.06.16】【最終更新日：2025.04.17】
課題データ / Project Data
課題番号 / Project Issue Number
22UT0344
利用課題名 / Title
Structural transition in the Cd-Mg-Ce quasicrystalline approximants
利用した実施機関 / Support Institute
東京大学 / Tokyo Univ.
機関外・機関内の利用 / External or Internal Use
外部利用/External Use
技術領域 / Technology Area
【横断技術領域 / Cross-Technology Area】（主 / Main）計測・分析/Advanced Characterization（副 / Sub）-
【重要技術領域 / Important Technology Area】（主 / Main）その他/Others（副 / Sub）-
キーワード / Keywords
金属間化合物, 透過型電子顕微鏡, Quasicrystals, Approximant crystals, Atomic structure,電子顕微鏡/Electron microscopy,電子回折/Electron diffraction
利用者と利用形態 / User and Support Type
利用者名（課題申請者）/ User Name (Project Applicant)
Labib Farid
所属名 / Affiliation
東京理科大学
共同利用者氏名 / Names of Collaborators in Other Institutes Than Hub and Spoke Institutes
ARIM実施機関支援担当者 / Names of Collaborators in The Hub and Spoke Institutes
利用形態 / Support Type
（主 / Main）機器利用/Equipment Utilization（副 / Sub）,機器利用/Equipment Utilization
利用した主な設備 / Equipment Used in This Project
報告書データ / Report
概要（目的・用途・実施内容）/ Abstract (Aim, Use Applications and Contents)
Quasicrystals (QCs) are aperiodically ordered intermetallic compounds that generate non-periodic array of sharp Bragg reflections with 5-fold rotational symmetry in their electron diffraction patterns [1,2]. The approximant crystals (AC), on the other hand, are closely related phases to QCs whose atomic structure comprise the same building units of QCs being arranged periodically (rather than aperiodically). The ACs have a cubic lattice, the size of which increases with their order (on the basis of the cut and projection approach from hyperspace [ 3]) in a way that the higher their order is (following the rational approximation of golden meanτ = 1.61803), the more their atomic structure resembles to that of QC and the larger their lattice parameter become. The lowest order AC (i.e., 1/1 AC), typically, crystalizes in the space group Im -3, in which a multi-shell polyhedron, displayed in Fig. 1a (as a main building unit in their atomic structure), are arranged in a form of body-centred-cubic, as shown in Fig. 1b. Notice that the outer-most shell of the polyhedron is a rhombic triacontahedron (RTH) unit and the inners shells are an icosidodecahedron, an icosahedron, a dodecahedron, and a central tetrahedron, respectively (see Fig. 1a) [4]. In Fig. 1c, the arrangement of the same main building units in the 2/1 AC (space group: Pa-3) is provided. These space groups, however, are sometimes subject to changes depending on subtle parameters within the atomic structure. For example, a tetrahedron unit, which accommodates a very central site of the RTH cluster is commonly disordered orientationally. However, under some circumstances, they become orientationally ordered at low enough temperatures or under a chemical pressure posed by surrounding atoms resulting in different space groups. In the present work, the effect of substitution of Cd by Mg in the binary Cd37Ce6 1/1 AC, which has a cubic lattice with a space group Pn-3, is investigated. For that purpose, Cd 86 -x Mg x Ce 14 ( x = 0-29) 1/1 ACs were successfully synthesized and some of them with high Mg content are selected for the electron diffraction experiments. [1]D. Shechtman, I. Blech, D. Gratias, and JW Cahn, Phys. Rev. Lett. 53 , 1951 (1984). [2]M. Duneau and A. Katz, Phys. Rev. Lett. 54 , 2688 (1985). [3]C. Janot, Quasicrystals: A Primer. Ed. , Vol. 31 (1994). [4]H. Takakura, CP Gómez, A. Yamamoto, M. De Boissieu, and AP Tsai, Nat. Mater. 6 , 58 (2007).
実験 / Experimental
In this research, more than 15 1/1 AC samples within a range of Cd 86-xMgxCe14 (x = 0-29) were successfully synthesized. A sample containing 22 at.% Mg is selected for the selected area electron diffraction (SAED) experiments using TEM, JEM-2010F in Advanced Research Infrastructure for Materials and Nanotechnology (ARIM), at room temperature. For the experiment, the selected samples were crushed in ethanol and transferred to a Cu grid. The analyzed samples by TEM were further analyzed by single crystal X-ray diffraction for attaining more details about their atomic structure.
結果と考察 / Results and Discussion
Based on the diffraction data (both X-ray and electron), two variations of 1/1 ACs were identified within their stability region in the phase diagram of Cd-Mg-Ce. The prototype Cd37Ce6 structure (space group Pn-3) which dominates near the Cd-rich end was found to partly taken over by Cd25Eu4-type structure (space group Fd-3) with a doubled unit cell in the higher-Mg part of the compositional range. Figures 2a and 2b display obtained SAED patterns along the main incidence axes of [100] and [110], respectively, in the Cd64Mg22Ce14 1/1 AC (the corresponding direct space image of which is also shown at the bottom-right corner). In Fig. 2a, the absence of reflections indexed 0kl with k+l being an odd integer is noticed, which is consistent with the space group Pn-3. The reflection conditions of the space group Pn-3 is 0kl with k+l = even and h00 with h = even, in which the three indices can be cyclically permuted. The SAED pattern in Fig. 2b exhibits weak reflections at 00h with h = odd (marked by yellow arrowheads) which contradicts the reflection conditions of the space group Pn-3. The reason for such controversy may be attributed to the dynamic scattering theory, rather than the kinematic one, possibly due to a large thickness of the sample (larger than 1‒10 nm [1]) giving rise to intensity of multiple reflections, so-called multiple scattering phenomenon [2,3]. In the SAED pattern of the 1/1 AC variant with space group Fd-3 along zone axis of [110] (as shown in Fig. 3), weak superlattice reflections (marked by red arrowheads) at (h + ½, −h − ½, 2l +½ or 2l −½) appeared indicating the formation of a doubled unit cell, with which the Miller indices of these extra reflections read (2h + 1, − (2h + 1), 4l +1 or 4l−1) (the corresponding direct space image is shown at the bottom-right corner of Fig. 3). The atomic structures of both 1/1 AC variants with Pn-3 and Fd-3 symmetries were determined by means of single-crystal XRD measurement. In the latter case, two types of RTH clusters are distinguished differing in orientational order/disorder of their central tetrahedral units. Furthermore, preferred sites for Mg substitution are determined to be the vertices of the RTH shell, vertices of an icosidodecahedron located on the two-fold axes and vertices of the innermost tetrahedra with 93%, 87% and 76% occupational fraction of Mg, respectively.[1] I. González Vallejo, G. Gallé, B. Arnaud, S. A. Scott, M. G. Lagally, D. Boschetto, P. E. Coulon, G. Rizza, F. Houdellier, D. Le Bolloc’H, and J. Faure, Phys. Rev. B 97, 054302 (2018).[2]J. Ciston, B. Deng, L. D. Marks, C. S. Own, and W. Sinkler, Ultramicroscopy 108, 514 (2008). [3] J. Gjønnes and A. F. Moodie, Acta Crystallogr. 19, 65 (1965).
図・表・数式 / Figures, Tables and Equations
Fig. 1. (a) Shell structure of a rhombic triacontahedron (RTH) cluster encompassing several inner shells; from the outer most one: an icosidodecahedron, an icosahedron, a dodecahedron, and a central tetrahedron. Arrangement of the RTH clusters within a unit cell of (a) 1/1 approximant crystal (AC), and (b) 2/1 AC.
Fig. 2. Selected area electron diffraction (SAED) patterns taken from Cd64Mg22Ce14 1/1 AC along the main incidence axes of (a) [100] and (b) [110] at room temperature. The overall reflections satisfy the space group of Pn-3 except the 00h with h=odd reflections presumably due to the multiple scattering phenomenon.
Fig. 3. The SAED pattern taken along the incidence axis of [110] from another spot in Cd64Mg22Ce14 1/1 AC at room temperature. The spots satisfy the reflection conditions of the space group Fd-3.
その他・特記事項（参考文献・謝辞等） / Remarks(References and Acknowledgements)
This work was supported in part by Japan Science and Technology Agency through PRESTO (Grant No. JPMJPR1519) and Japan Society for the Promotion of Science through Grants-in-Aid for Scientific Research (Grants No. JP18K04677, JP19H05817, JP19H05818, JP19H05819, JP21H01044 , JP15H02111 and JP19K21847) and JST, CREST Grant No. JPMJCR22O3, Japan.
成果発表・成果利用 / Publication and Patents
論文・プロシーディング（DOIのあるもの） / DOI (Publication and Proceedings)
口頭発表、ポスター発表および、その他の論文 / Oral Presentations etc.
- Farid Labib (東京理科大学), 藤田伸尚, 大橋諭(東北大学), 高倉洋礼(北海道大学), Takayuki Shiino(Uppsala University), 蔡安邦(東北大学), 田村隆治(東京理科大学), Structure transitions of the quasicrystalline 1/1 approximant in the Cd-Mg-Ce system, 日本金属学会2022年秋期第171回講演大会 2022年9月6日から9月8日
- 良質な強磁性準結晶の探索, 竹内 涼, Farid Labib, 石川 明日香, 鈴木 慎太郎(東京理科大学), 藤井 武則 (東京大学), 田村 隆治(東京理科大学), ハイパーマテリアル第27回準結晶研究会 2023年2月27日(月)～3月1日(水)
- 田村 隆治(東京理科大学)Synthesis and magnetic properties of Au-Ga-Dy quasicrystals, ハイパーマテリアル第27回準結晶研究会 2023年2月27日(月)～3月1日(水)
特許 / Patents
特許出願件数 / Number of Patent Applications：0件
特許登録件数 / Number of Registered Patents：0件