本 論文為三元錫化物 R5Co6Sn18(R = Y, Dy, Tm)的單晶製程及物理特性 研究 單晶樣品 以 錫 助熔長晶法 製備， 使用 XRD確認樣品R5Co6Sn18(R = Y, Dy, Tm)晶體結構 皆為 Dy5Co6Sn18-type tetragonal phase。 並且 藉由 量測電阻率 (ρ)、 磁化率 (χ)、 熱電系數 (S)、 熱導率(κ)、 比熱 和計算熱電優質 (ZT)來探討其傳輸 及熱電 性質 。 由磁化率
結果發現樣品 皆為包利順磁性，經過 Curie-Weiss law擬和後得知樣品 的磁矩貢獻主要 來自結構中心的三價稀土元素，並且發現Dy5Co6Sn18有自旋玻璃現象 ，其 凍結溫度 ??會隨著頻率變化而發生偏移 。 由電阻率 結果得知，此系列樣品電阻率隨溫度改變沒有太大的變化，推測 此系列樣品 電阻率 可能 具有半金屬特性。 熱電系數量測結果發現此系列樣品皆為負值，表示其主要傳輸載子為電子。 熱導率結果藉由 Wiedemann Franz law得到電子 (κ?)和聲子 (κ?)的熱傳導率 ，並顯示此系列樣品熱傳導率主要貢獻 來自聲子 (κ? 在 300 K時 κ?值 約為 2~4 W/m–K，此較小的聲子熱傳導率是由於籠狀結構內部原子震動與擾動，增強聲子散射效應使晶格貢獻降低 。 最後藉由計算後發現熱電優質 (ZT)會隨著溫度上升而增加 。

Single crystal of R5Co6Sn18(R = Y, Dy, Tm) have been successfully grown by Sn self-flux method and their structures have been identified by x-ray diffraction as Dy5Co6Sn18 type tetragonal structure. The physical properties of single crystals are measured by electrical resistivity(ρ), magnetic susceptibility(χ), Seebeck coefficient(S), thermal conductivity(κ) and specific heat. From the experimental results, R5Co6Sn18(R = Y, Dy, Tm) were observed paramagnetic behavior in magnetic susceptibility and indicated that the magnetism is mainly a result of the trivalent rare-earth atoms by fitting the Curie-Weiss law. Dy5Co6Sn18 have been performed in the vicinity of its freezing temperature at ?? = 6 K exhibits a cusp-like peak and a strong frequency dependence of the susceptibility that indicates a spin glass behavior. For all studied materials exhibit semi-metallic behavior with weak temperature dependence in electrical resistivity result and indicate that electrons are dominant carriers for the transport via the sign of the Seebeck coefficients is all negative. The result shows that most of contribution of thermal conductivity is from lattice thermal conductivity by using Wiedemann-Franz law and the values are 2~4 W/m–K . Low lattice thermal conductivity can be ascribed to strong rattling vibrations of central atoms lead to phonon scattering and reducing the thermal conductivity. Specific heat results show that R5Co6Sn18(R = Y, Dy, Tm) don’t have any change form 85 K to 300 K. ZT (Thermoelectirc figure of merit) increases with temperature rising.

1 Epp, J. in Materials characterization using nondestructive evaluation (NDE) methods 81-124 (Elsevier, 2016).
2 劉奐甫 . 介金屬 R3Co4Sn13 (R= La Ce Pr Yb) 之單晶製成及核磁共振之
研究 博士 thesis, 國立成功大學 , (2016).
3 Kase, N. et al. Coexistence of Superconductivity and Magnetism in the Tm-Based Reentrant Superconductor Tm5Rh6Sn18. journal of the physical society of japan 78, 073708-073708 (2009).
4 Kuo, C. et al. Characteristics of the phase transition near 147 K in Sr 3 Ir 4 Sn 13. Physical Review B 89, 094520 (2014).
5 Kuo, C. et al. Lattice distortion associated with Fermi-surface reconstruction in Sr 3 Rh 4 Sn 13. Physical Review B 91, 165141 (2015).
6 Wang, L., Wang, C.-Y., Chen, G.-M., Kuo, C. & Lue, C. Weakly-correlated nodeless superconductivity in single crystals of Ca3Ir4Sn13 and Sr3Ir4Sn13 revealed by critical fields, Hall effect, and magnetoresistance measurements. New Journal of Physics 17, 033005 (2015).
7 Hayamizu, H., Kase, N. & Akimitsu, J. Superconducting properties of R3T4Sn13 (R= La, Sr, Ca, T= Rh, Ir) with a quasi-skutterudite structure. Physica C: Superconductivity and its applications 470, S541-S542 (2010).
8 Hayamizu, H., Kase, N. & Akimitsu, J. Superconducting properties of Ca3T4Sn13 (T= Co, Rh, and Ir). journal of the physical society of japan 80, SA114 (2011).
9 Chen, S. & Lue, C. A 27 l NMR study of the mixed valence compound CeFe 2 Al 10. Physical Review B 81, 075113 (2010).
10 Lue, C., Yang, S., Su, T. & Young, B.-L. NMR evidence for the partially gapped state in CeOs 2 Al 10. Physical Review B 82, 195129 (2010).
11 Lue, C.-S., Liu, H., Ingale, B., Li, J. & Kuo, Y. Transport, thermoelectric, and thermal expansion investigations of the cage structure compound CeOs 2 Al 10. Physical Review B 85, 245116 (2012).
12 Lue, C.-S. et al. Transport, thermal, and NMR characteristics of CeRu 2 Al 10. Physical Review B 82, 045111 (2010).
13 Avila, M., Huo, D., Sakata, T., Suekuni, K. & Takabatake, T. Tunable charge carriers and thermoelectricity of single-crystal Ba8Ga16Sn30. Journal of Physics: Condensed Matter 18, 1585 (2006).
14 Von Schnering, H. et al. Crystal structure of the clathrate β-Ba8Ga16Sn30. Zeitschrift für Kristallographie-New Crystal Structures 213, 719-719 (1998).
15 Chen, Y.-X., Du, B.-L., Saiga, Y., Kajisa, K. & Takabatake, T. Crystal growth and thermoelectric properties of type-VIII clathrate Ba8Ga15. 9Sn30. 1− xGex with p-type charge carriers. Journal of Physics D: Applied Physics 46, 205302 (2013).
16 Remeika, J. et al. A new family of ternary intermetallic superconducting/magnetic stannides. Solid State Communications 34, 923-926 (1980).
17 Espinosa, G. Crystal growth and crystal-chemical investigation of systems containing new superconducting and/or magnetic ternary stannides. Materials Research Bulletin 15, 791-798 (1980).
18 Espinosa, G., Cooper, A. & Barz, H. Isomorphs of the superconducting/magnetic ternary stannides. Materials Research Bulletin 17, 963-969 (1982).
19 游子賢游子賢. 介金屬介金屬M5Rh6Sn18 (M = Sc, Y, Lu)之單晶製程及物理特性之研究之單晶製程及物理特性之研究 碩士碩士 thesis, 國立成功大學國立成功大學, (2016).
20 Ali, N. & Datars, W. Superconductivity and magnetism in LuRh1. 2Sn4. 0. Journal of the Less Common Metals 127, 49-54 (1987).
21 Bhattacharyya, A. et al. Unconventional superconductivity in Y 5 Rh 6 Sn 18 probed by muon spin relaxation. Scientific reports 5, 1-8 (2015).
22 Bhattacharyya, A. et al. Broken time-reversal symmetry probed by muon spin relaxation in the caged type superconductor Lu 5 Rh 6 Sn 18. Physical Review B 91, 060503 (2015).
23 Kase, N., Inoue, K., Hayamizu, H. & Akimitsu, J. Highly anisotropic gap function in a nonmagnetic superconductor Y5Rh6Sn18. journal of the physical society of japan 80, SA112 (2011).
24 Kase, N., Kittaka, S., Sakakibara, T. & Akimitsu, J. Superconducting gap structure of the cage compound Sc5Rh6Sn18. journal of the physical society of japan 81, SB016 (2012).
25 黃祥育黃祥育. Lu5M6Sn18 (M = Co, Rh, Ir) 籠狀超導體之物理性質研究籠狀超導體之物理性質研究 碩士碩士 thesis, 國立成功大學國立成功大學, (2018).
26 Feig, M. et al. Crystal structure, chemical bonding, and electrical and thermal transport in Sc 5 Rh 6 Sn 18. Dalton Transactions 49, 6832-6841 (2020).
27 Miraglia, S., Hodeau, J., Marezio, M., Ott, H. & Remeika, J. Relationship between the crystal structure and the reentrant superconducting properties of (Sn1-xErx) Er4Rh6Sn18. Solid state communications 52, 135-137 (1984).
28 Levytskyi, V. et al. Crystal structure and superconducting properties of Sc5Ir6Sn18. Journal of Physics: Condensed Matter 31, 445603 (2019).
29 Chen, Y. et al. Crystal structure, properties, and diffraction data of a new compound Dy5Co6Sn18. Powder Diffraction 23, 26-30 (2008).
30 Kase, N., Anada, T., Terui, Y., Nakano, T. & Takeda, N. Superconductivity of the ternary stannide Y5Co6Sn18. Physica B: Condensed Matter 587, 412149 (2020).
31 Lazaro, F., Van de Pasch, A. & Flokstra, J. Spin glass behaviour in the rare earth ternary stannide HoRh1. 2Sn3. 9. Journal of magnetism and magnetic materials 71, 10-16 (1987).
32 Okudzeto, E. K., Thomas, E. L., Moldovan, M., Young, D. P. & Chan, J. Y. Magnetic properties of the single crystal stannides Ln7Co6Sn23 (Ln= Dy, Ho) and Ln5Co6Sn18 (Ln= Er, Tm). Physica B: Condensed Matter 403, 1628-1629 (2008).
33 Smith, D. Physical Electronics. Vol. 42 (1972).
34 李雅明李雅明. 固態電子學固態電子學. (五南圖書出版股份有限公司五南圖書出版股份有限公司, 2016).
35 Kittel, C. Introduction to solid state physics. (1976).
36 Pollock, D. D. Thermoelectricity: theory, thermometry, tool. (ASTM International, 1985).
37 Jiles, D. Introduction to magnetism and magnetic materials. (CRC press, 2015).
38 Cullity, B. D. & Graham, C. D. Introduction to magnetic materials. (John Wiley & Sons, 2011).
39 Blundell, S. Magnetism in condensed matter. (American Association of Physics Teachers, 2003).
40 Wiener, T. A. Characterization of the dilute Ising antiferromagnet Y1-xTbxNi2Ge2 and the search for a potential Ising spin glass, Citeseer, (2000).
41 Lue, C.-S., Lai, W., Huang, C.-L. & Lee, Y. Spin glass behavior in the CoSi1–xAlx alloys. Journal of magnetism and magnetic materials 282, 334-337 (2004).
42 Lue, C.-S., Öner, Y., Naugle, D. G. & Ross Jr, J. H. Spin glass behavior in FeAl 2. Physical Review B 63, 184405 (2001).
43 Li, D., Nimori, S., Yamamura, T. & Shiokawa, Y. ac susceptibility studies of the spin freezing behavior in U 2 Cu Si 3. Journal of Applied Physics 103, 07B715 (2008).
44 Byrappa, K. & Ohachi, T. Crystal growth technology. (Elsevier, 2003).
45 Cullity, B. D. & Weymouth, J. W. ’Elements of X-ray Diffraction. American Journal of Physics. (1957).
46 Kleiner, R., Koelle, D., Ludwig, F. & Clarke, J. Superconducting quantum interference devices: State of the art and applications. Proceedings of the IEEE 92, 1534-1548 (2004).
47 Fagaly, R. Superconducting quantum interference device instruments and applications. Review of scientific instruments 77, 101101 (2006).
48 Slack, G. A. & Rowe, D. CRC handbook of thermoelectrics. (CRC press Boca Raton, FL, 1995).
49 Mulder, C., Van Duyneveldt, A. & Mydosh, J. Frequency and field dependence of the ac susceptibility of the Au Mn spin-glass. Physical Review B 25, 515 (1982).
50 Mulder, C. & Van Duyneveldt, A. The frequency and field dependence of the ac susceptibility of the AgMn spin glass. Physica B+ C 113, 123-126 (1982).
51 Avila, M. et al. Glasslike versus crystalline thermal conductivity in carrier-tuned Ba 8 Ga 16 X 30 clathrates (X= Ge, Sn). Physical Review B 74, 125109 (2006).
52 Lee, C. et al. Effect of rattling motion without cage structure on lattice thermal conductivity in LaOBiS2− x Se x. Applied Physics Letters 112, 023903 (2018).
53 Ohtaki, M. & Miyaishi, S. Extremely low thermal conductivity in oxides with cage-like crystal structure. Journal of electronic materials 42, 1299-1302 (2013).
54 Hong, A. & Ma, L. Ultralow thermal conductivity in quaternary compound Ag2BaSnSe4 due to square-cylinder cage-like structure with rattling vibration. Applied Physics Letters 118, 143903 (2021).
55 Okamoto, N. L., Kim, J.-H., Tanaka, K. & Inui, H. Splitting of guest atom sites and lattice thermal conductivity of type-I and type-III clathrate compounds in the Ba–Ga–Ge system. Acta materialia 54, 5519-5528 (2006).