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Analysis of thermal diffuse scattering intensity of scandium oxide (Sc2O3)

Wang Rui-Gang ,  Liu Ze-Peng ,  Xiang-Lian ,  Sun Yong

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Analysis of thermal diffuse scattering intensity of scandium oxide (Sc2O3)

Wang Rui-Gang, Liu Ze-Peng, Xiang-Lian, Sun Yong
Acta Phys. Sin., 2024, 73(6): 063401.
doi: 10.7498/aps.73.20231241
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  • Abstract

    Atoms in crystals will generate thermal diffuse scattering during thermal vibration. Thermal diffuse scattering analysis has great potential applications in condensed matter physics and material science research. Scandium oxide (Sc2O3) has unique physical and chemical properties, which make it have high research and application value. In this work, X-ray diffraction experiment is performed on Sc2O3 at room temperature of 26 ℃. The thermal diffuse scattering intensity exhibits a clear vibrational shape. The full diffraction back-based intensity equation of Sc2O3 is expanded, and the theoretical value of the thermal diffuse scattering intensity is calculated until the full diffraction back-based intensity spectrum of the 14th nearest atom (r = 0.3816 nm) is calculated. By fitting the theoretical value to the experimental value, we can see the inter-atomic thermal vibration correlation effect μ values corresponding to the nearest neighbor atom to the 7th nearest neighbor atom, the values of distance r from the nearest neighbor atom to the 7th nearest neighbor atom are 0.2067, 0.2148, 0.2161, 0.2671, 0.2945, 0.3229 and 0.3265nm, respectively, corresponding to their inter-atomic thermal vibration correlation effect μ values of 0.64, 0.63, 0.62, 0.61, 0.60, 0.58 and 0.57. Research result shows that the intensity of thermal diffuse scattering in Sc2O3 is closely related to the atomic thermal vibration, the most significant influence on the vibration shape of thermal diffuse scattering intensity is the thermal vibration correlation effect between the 7th nearest atom Sc1-Sc2. Inter-atomic thermal vibration correlation effect μ values will provide important parameters for studying the mechanical and thermal properties of materials, laying the foundation for the next-step calculating specific heat and interatomic force constant, and thus playing a crucial role in the use and development of materials.

    Authors and contacts

    • College of Physics and Electronic Information, Inner Mongolia Minzu University, Tongliao 028043, China

      • Corresponding author: Xiang-Lian, nmmdxl@163.com
    • Funds: Project supported by the Natural Science Foundation of Inner Mongolia, China (Grant Nos. 2018MS01007, 2022MS01014, 2023LHMS01011), the Doctor Research Start-up Fund of Inner Mongolia Minzu University, China (Grant No. BS625), and the Basic Scientific Research Projects in Colleges and Universities directly under Inner Mongolia Autonomous Region.

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    Kulikov B P, Baranov V N, Bezrukikh A I, Deev V B, Motkov M M 2018 Metallurgist 61 1115Google Scholar

    [2]

    唐冲冲, 常化强, 包晓刚, 刘贵清, 刘奎仁 2012 中国稀土学报 30 680

    Tang C C, Chang H Q, Bao X G, Liu G Q, Liu K R 2012 CJCR 30 680
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    Masanori H, Kouji Y, Hiromasa Y, Toru H O 2008 J. Alloys Compd. 474 124Google Scholar

    [4]

    Zhigachev A O, Rodaev V V, Zhigacheva D V, Lyskov N V, Shchukina M A 2021 Ceram. Int. 47 32490Google Scholar

    [5]

    Pu Y C, Li S R, Yan S, Huang X, Wang D, Ye Y Y, Liu Y Q 2019 Fuel 241 607Google Scholar

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    Nakazono K, Takahashi R, Yamada Y, Sato S 2021 Mol. Catal. 516 111996Google Scholar

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    Sha H Y, He Z Z, Li C, Wang X Y, Jiang Q, Zeng F M, Su Z M 2019 Opt. Mater. 93 39Google Scholar

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    Xue J M, Li F, Liu Y Q, Yang F, Hou Z X 2023 Appl. Surf. Sci. 613 155984Google Scholar

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    Zhang C, Zhou Z X, Tang Z M, Ballo D, Wang C, Jian G 2022 J. Alloys Compd. 889 161622Google Scholar

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    Poirot N, Bregiroux D, Boy P, Autret-Lambert C, Belleville P, Bianchi L 2015 Ceram. Int. 41 3879Google Scholar

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    Toshiyuki M T I J L 2005 J. Am. Ceram. Soc. 88 817Google Scholar

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    Jiang B X, Hu C, Li J, Kou H, Shi Y, Liu W B, Pan Y B 2011 J. Rare Earths 29 951Google Scholar

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    Lu S Z, Yang Q H 2012 Chin. Phys. B 21 047801Google Scholar

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    Lu X, Jiang B X, Li J, Liu W B, Wang L, Ba X B, Hu C, Liu B L, Pan Y B 2013 Ceram. Int. 39 4695Google Scholar

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    Ma M Z, Dong L L, Jing W, Xu T, Kang B, Hou F 2019 Proceedings of the 11th International Conference on High-Performance Ceramics Kunming, China, May 25–29, 2019 p012080
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    Dai Z F, Liu Q, Hrenia D, Dai J W, Wang W, Li J 2018 Opt. Mater. 75 673Google Scholar

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    Wang Y, Sun X D, Qiu G M 2007 J. Rare Earths 25 68Google Scholar

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    Jacobsohn L G, Serivalsatit K, Quarles C A, Ballato J 2015 J. Mater. Sci. 50 3183Google Scholar

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    杨丛松, 陈博, 王芳, 郑剑平, 赵建翔 2017 稀有金属 41 163Google Scholar

    Yang C S, Chen B, Wang F, Zheng J P, Zhao J X 2017 Chin. Rare Metals 41 163Google Scholar

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    Kong P F, Pu Y T, Ma P, Zhu J L 2020 Thin Solid Films 714 138357Google Scholar

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    Sakuma T, Shimoyama T, Basar K, Xianglian, Takahashi H, Arai M, Ishii Y 2005 Solid State Ion 176 2689Google Scholar

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    Arai M, Sakuma T 2001 J. Phys. Soc. Jpn. 70 144Google Scholar

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    Beni G, Platzman P M 1976 Phys. Rev. B 14 1514
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    Basar K, Xianglian, Sakuma T, Takahashi H, Igawa N 2009 ITB J. Sci. (Bdg.) 41 50Google Scholar

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    Sakuma T, Makhsun, Sakai R, Xianglian, Takahashi H, Basar K, Igawa N, Sergey A D 2015 AIP Conf. Proc. 1656 020002Google Scholar

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    Wada T, Sakuma T, Sakai R, Uehara H, Xianglian, Takahashi H, Kamishima O, Igawa N, Sergey A D 2012 Solid State Ion 225 18Google Scholar

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    Sakuma T, Mohapatra S R, Uehara H, Sakai R, Xianglian, Takahashi H, Igawa N, Basar K 2011 Atom Indonesia 36 121Google Scholar

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    Sakuma T, Xianglian, Shimizu N, Mohapatra S R, Isozaki N, Uehara H, Takahashi H, Basar K, Igawa N, Kamishima O 2010 Solid State Ion 192 54Google Scholar

    [29]

    Sakuma T, Xianglian, Siagian S, Basar K, Takahashi H, Igawa N, Kamishima O 2010 J. Therm. Anal. Calorim. 99 173Google Scholar

    [30]

    Basar K, Siagian S, Xianglian, Sakuma T, Takahashi H, Igawa N 2008 Nucl. Instrum. Methods Phys. Res. A 600 237Google Scholar

    [31]

    香莲, 赵敏兰, 佐久间隆, 井川直樹 2015 原子与分子物理学报 32 499Google Scholar

    Xianglian, Zhao M L, Sakuma T, Igawa N 2015 J. at. Mol. Sci. 32 499Google Scholar

    [32]

    Xianglian, Sakuma T, Mohapatra S R, Uehara H, Takahashi H, Kamishima O, Igawa N 2012 Mol. Simul. 38 448Google Scholar

    [33]

    Xianglian, Basar K, Honda H, Siagian S, Ohara K, Sakuma T, Takahashi H, Igawa N, Ishii Y 2007 Solid State Ion 179 776Google Scholar

    [34]

    郭田田, 香莲, 包文秀, 包桂芝 2018 光散射学报 30 182Google Scholar

    Guo T T, Xianglian, Bao W X, Bao G Z 2018 J. Light Scatter. 30 182Google Scholar

    [35]

    Sakuma T 1992 J. Phys. Soc. Jpn. 61 4041Google Scholar

    [36]

    刘泽朋, 王瑞刚, 香莲, 包桂芝 2023 内蒙古民族大学学报(自然科学版) 38 199Google Scholar

    Liu Z P, Wang R G, Xianglian, Bao G Z 2023 J. Inner Mongolia Minzu Univ. (Nat. Sci.) 38 199Google Scholar

    [37]

    Rietveld H M 1967 Acta Cryst. 22 151Google Scholar

    [38]

    Izumi F, Ikeda T 2000 Mater. Sci. Forum 399 198Google Scholar

    [39]

    Lonsdale K 1962 International Tables for X-Ray Crystallography (Vol. III) (United Kingdo: Published by International Union of Crystallography) pp72–103

  • 图 1  (a) Sc2O3的X射线衍射实验图谱; (b) Sc2O3的热漫散射强度图谱

    Figure 1.  (a) X-ray diffraction experimental pattern of Sc2O3; (b) thermal diffuse scattering intensity spectrum of Sc2O3.

    DownLoad: Full-Size Img PowerPoint

    图 2  (a)原子独立振动产生的热漫散射强度; (b) Sc2O3的Compton散射强度; (c) Sc2O3全衍射背底强度

    Figure 2.  (a) Thermal diffuse scattering intensity generated by independent vibration each atom; (b) Compton scattering intensity of Sc2O3; (c) Sc2O3 full diffraction back-base intensity.

    DownLoad: Full-Size Img PowerPoint

    图 3  Sc2O3的全衍射背底强度的计算结果和实验结果的对比　(a)最近邻原子; (b)第1—3近邻原子; (c)第1—5近邻原子; (d) 第1—7近邻原子; (e)第1—9近邻原子; (f)第1—11近邻原子

    Figure 3.  Comparison between calculated and experimental results of the total diffraction back-base intensity of Sc2O3: (a) The nearest neighbor atom; (b) the 1–3 nearest neighbor atomic; (c) the 1–5 nearest neighbor atomic; (d) the 1–7 nearest neighbor atomic; (e) the 1–9 nearest neighbor atom; (f) the 1–11 nearest neighbor atom.

    DownLoad: Full-Size Img PowerPoint

    图 4  Sc2O3晶体结构模型和原子间距离

    Figure 4.  Sc2O3 crystal structure model and interatomic distance.

    DownLoad: Full-Size Img PowerPoint

    图 5  Sc2O3粉末晶体的各原子间相关效应产生的热漫散射强度

    Figure 5.  Thermal diffuse scattering intensity generated by the inter atomic correlation effect of Sc2O3 powder crystal.

    DownLoad: Full-Size Img PowerPoint

    图 6  Sc2O3在室温26 ℃下原子间热振动相关效应值μ与原子间距离r的图谱, 以及与其他几种材料的的对比

    Figure 6.  Spectrum of the inter-atomic thermal vibration correlation effect values μ and the inter-atomic distance r of Sc2O3 at room temperature of 26 ℃. The corresponding spectra of other materials are also given.

    DownLoad: Full-Size Img PowerPoint

    表 1  (2)式中各参数物理意义

    Table 1.  Physical meaning of each parameter in Eq. (2).

    参数物理意义参数物理意义
    $k$仪器参数$ {N_0} $晶体内晶胞数
    ${u_i}$单位晶胞内i原子数${Z_{{r_{s\left( i \right)s'\left( j \right)}}}}$配位数
    ${f_i}$i原子散射因子${r_{s\left( i \right)s'\left( j \right)}}$晶胞内i原子与j原子间距
    ${B_i}$i原子各向同性温度因子${\sigma _{{\text{incoh}}}}$非干涉性的原子散射截面
    Ie单个电子散射强度θ散射角
    λ入射光线波长
    DownLoad: CSV

    表 2  Sc2O3的晶体结构参数

    Table 2.  Crystal structure parameters of Sc2O3.

    x y z B/nm2
    Sc1 0.2500 0.2500 0.2500 0.003329
    Sc2 0.4649 0 0.2500 0.011085
    O 0.3928 0.1528 0.3802 0.009657
    DownLoad: CSV

    表 3  Sc2O3的原子间热振动相关效应值μ

    Table 3.  Interatomic thermal vibration related effect values of Sc2O3.

    原子间距离r/nm 配位数Z 原子间相关效应值$ \mu $
    O-Sc2 0.2067 2 0.64
    O-Sc2 0.2148 1 0.63
    O-Sc1 0.2161 1 0.62
    O-O 0.2671 4 0.61
    O-O 0.2945 1 0.60
    O-O 0.3229 2 0.58
    Sc1-Sc2 0.3265 6 0.57
    DownLoad: CSV
  • [1]

    Kulikov B P, Baranov V N, Bezrukikh A I, Deev V B, Motkov M M 2018 Metallurgist 61 1115Google Scholar

    [2]

    唐冲冲, 常化强, 包晓刚, 刘贵清, 刘奎仁 2012 中国稀土学报 30 680

    Tang C C, Chang H Q, Bao X G, Liu G Q, Liu K R 2012 CJCR 30 680
    [3]

    Masanori H, Kouji Y, Hiromasa Y, Toru H O 2008 J. Alloys Compd. 474 124Google Scholar

    [4]

    Zhigachev A O, Rodaev V V, Zhigacheva D V, Lyskov N V, Shchukina M A 2021 Ceram. Int. 47 32490Google Scholar

    [5]

    Pu Y C, Li S R, Yan S, Huang X, Wang D, Ye Y Y, Liu Y Q 2019 Fuel 241 607Google Scholar

    [6]

    Nakazono K, Takahashi R, Yamada Y, Sato S 2021 Mol. Catal. 516 111996Google Scholar

    [7]

    Sha H Y, He Z Z, Li C, Wang X Y, Jiang Q, Zeng F M, Su Z M 2019 Opt. Mater. 93 39Google Scholar

    [8]

    Xue J M, Li F, Liu Y Q, Yang F, Hou Z X 2023 Appl. Surf. Sci. 613 155984Google Scholar

    [9]

    Zhang C, Zhou Z X, Tang Z M, Ballo D, Wang C, Jian G 2022 J. Alloys Compd. 889 161622Google Scholar

    [10]

    Poirot N, Bregiroux D, Boy P, Autret-Lambert C, Belleville P, Bianchi L 2015 Ceram. Int. 41 3879Google Scholar

    [11]

    Toshiyuki M T I J L 2005 J. Am. Ceram. Soc. 88 817Google Scholar

    [12]

    Jiang B X, Hu C, Li J, Kou H, Shi Y, Liu W B, Pan Y B 2011 J. Rare Earths 29 951Google Scholar

    [13]

    Lu S Z, Yang Q H 2012 Chin. Phys. B 21 047801Google Scholar

    [14]

    Lu X, Jiang B X, Li J, Liu W B, Wang L, Ba X B, Hu C, Liu B L, Pan Y B 2013 Ceram. Int. 39 4695Google Scholar

    [15]

    Ma M Z, Dong L L, Jing W, Xu T, Kang B, Hou F 2019 Proceedings of the 11th International Conference on High-Performance Ceramics Kunming, China, May 25–29, 2019 p012080
    [16]

    Dai Z F, Liu Q, Hrenia D, Dai J W, Wang W, Li J 2018 Opt. Mater. 75 673Google Scholar

    [17]

    Wang Y, Sun X D, Qiu G M 2007 J. Rare Earths 25 68Google Scholar

    [18]

    Jacobsohn L G, Serivalsatit K, Quarles C A, Ballato J 2015 J. Mater. Sci. 50 3183Google Scholar

    [19]

    杨丛松, 陈博, 王芳, 郑剑平, 赵建翔 2017 稀有金属 41 163Google Scholar

    Yang C S, Chen B, Wang F, Zheng J P, Zhao J X 2017 Chin. Rare Metals 41 163Google Scholar

    [20]

    Kong P F, Pu Y T, Ma P, Zhu J L 2020 Thin Solid Films 714 138357Google Scholar

    [21]

    Sakuma T, Shimoyama T, Basar K, Xianglian, Takahashi H, Arai M, Ishii Y 2005 Solid State Ion 176 2689Google Scholar

    [22]

    Arai M, Sakuma T 2001 J. Phys. Soc. Jpn. 70 144Google Scholar

    [23]

    Beni G, Platzman P M 1976 Phys. Rev. B 14 1514
    [24]

    Basar K, Xianglian, Sakuma T, Takahashi H, Igawa N 2009 ITB J. Sci. (Bdg.) 41 50Google Scholar

    [25]

    Sakuma T, Makhsun, Sakai R, Xianglian, Takahashi H, Basar K, Igawa N, Sergey A D 2015 AIP Conf. Proc. 1656 020002Google Scholar

    [26]

    Wada T, Sakuma T, Sakai R, Uehara H, Xianglian, Takahashi H, Kamishima O, Igawa N, Sergey A D 2012 Solid State Ion 225 18Google Scholar

    [27]

    Sakuma T, Mohapatra S R, Uehara H, Sakai R, Xianglian, Takahashi H, Igawa N, Basar K 2011 Atom Indonesia 36 121Google Scholar

    [28]

    Sakuma T, Xianglian, Shimizu N, Mohapatra S R, Isozaki N, Uehara H, Takahashi H, Basar K, Igawa N, Kamishima O 2010 Solid State Ion 192 54Google Scholar

    [29]

    Sakuma T, Xianglian, Siagian S, Basar K, Takahashi H, Igawa N, Kamishima O 2010 J. Therm. Anal. Calorim. 99 173Google Scholar

    [30]

    Basar K, Siagian S, Xianglian, Sakuma T, Takahashi H, Igawa N 2008 Nucl. Instrum. Methods Phys. Res. A 600 237Google Scholar

    [31]

    香莲, 赵敏兰, 佐久间隆, 井川直樹 2015 原子与分子物理学报 32 499Google Scholar

    Xianglian, Zhao M L, Sakuma T, Igawa N 2015 J. at. Mol. Sci. 32 499Google Scholar

    [32]

    Xianglian, Sakuma T, Mohapatra S R, Uehara H, Takahashi H, Kamishima O, Igawa N 2012 Mol. Simul. 38 448Google Scholar

    [33]

    Xianglian, Basar K, Honda H, Siagian S, Ohara K, Sakuma T, Takahashi H, Igawa N, Ishii Y 2007 Solid State Ion 179 776Google Scholar

    [34]

    郭田田, 香莲, 包文秀, 包桂芝 2018 光散射学报 30 182Google Scholar

    Guo T T, Xianglian, Bao W X, Bao G Z 2018 J. Light Scatter. 30 182Google Scholar

    [35]

    Sakuma T 1992 J. Phys. Soc. Jpn. 61 4041Google Scholar

    [36]

    刘泽朋, 王瑞刚, 香莲, 包桂芝 2023 内蒙古民族大学学报(自然科学版) 38 199Google Scholar

    Liu Z P, Wang R G, Xianglian, Bao G Z 2023 J. Inner Mongolia Minzu Univ. (Nat. Sci.) 38 199Google Scholar

    [37]

    Rietveld H M 1967 Acta Cryst. 22 151Google Scholar

    [38]

    Izumi F, Ikeda T 2000 Mater. Sci. Forum 399 198Google Scholar

    [39]

    Lonsdale K 1962 International Tables for X-Ray Crystallography (Vol. III) (United Kingdo: Published by International Union of Crystallography) pp72–103
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  • Received Date:  31 July 2023
  • Accepted Date:  19 December 2023
  • Available Online:  26 December 2023
  • Published Online:  20 March 2024

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