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Characterization microwave absorption from active carbon/BaSmxFe12−xO19/polypyrrole composites analyzed with a more rigorous method

  • Ying Liu
  • Michael G. B. Drew
  • Yue Liu
Article
  • 11 Downloads

Abstract

There are problems with the conventional method of determining reflection loss for microwave absorption material. In particular, it is concluded that the ability of a material to absorb microwaves is related with sample thickness of the material. Based on this wrong conclusion, a model is then proposed on the quarter-wavelength’s sample thickness. However, it is shown in the present work that the conclusion together with the model is incorrect and that the associated experimental work needs therefore to be re-evaluated. In this work we evaluate our own experimental work on microwave absorption of a composite correctly and demonstrate the errors in the previous method. C/BaSmxFe12−xO19 has been prepared by the hydrothermal method and C/BaSmxFe12−xO19/PPY by in situ polymerization. The microwave absorption of the composites has then been characterized with an appropriate method. The maximum reflection loss was achieved at x = 0.2 consistently for both C/BaSmxFe12−xO19 and C/BaSmxFe12−xO19/PPY. The result shows that the components of active carbon, polypyrrole, and ferrite in the composites have a positive cooperating effect on microwave absorption. It is also clearly demonstrated that the result is independent of sample thickness.

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    A. Mukherjee, S. Basu, P.K. Manna, S.M. Yusuf, M. Pal, Giant magnetodielectric and enhanced multiferroic properties of Sm doped bismuth ferrite nanoparticles. J. Mater. Chem. C 2, 5885–5891 (2014)CrossRefGoogle Scholar
  2. 2.
    Y. Liu, J. Wei, Y. Guo, T. Yang, Z. Xu, Phase transition, interband electronic transitions and enhanced ferroelectric properties in Mn and Sm co-doped bismuth ferrite films. RSC Adv. 6, 96563–96572 (2016)CrossRefGoogle Scholar
  3. 3.
    K. Yang, Y. Liu, M.G.B. Drew, Y. Liu, Preparation and characterization of BaSmxFe12–xO19/polypyrrole composites. J. Mater. Sci.: Mater. Electron. 29(15), 13148–13160 (2018)Google Scholar
  4. 4.
    C. Li, Y. Zhang, S. Ji, X. Jiang, Z. Zhang, L. Yu, Microwave absorption properties of γ-Fe2O3/(SiO2)x–SO3H/polypyrrole core/shell/shell microspheres. J. Mater. Sci. 53, 5270–5286 (2018)CrossRefGoogle Scholar
  5. 5.
    J. Jin, Y. Liu, M.G.B. Drew, Y. Liu, Preparation and characterizations of Ba1-xPbxFe12O19/polypyrrole composites. J. Mater. Sci.: Mater. Electron. 28, 11325–11331 (2017)Google Scholar
  6. 6.
    F. Meng, H. Wang, F. Huang, Y. Guo, Z. Wang, D. Hui, Z. Zhou, Graphene-based microwave absorbing composites: a review and prospective. Composites B 137, 260–277 (2018)CrossRefGoogle Scholar
  7. 7.
    Y. Liu, R. Tai, M.G.B. Drew, Y. Liu, Preparation and characterizations of active carbon/barium ferrite/polypyrrole composites. J. Mater. Sci.: Mater. Electron. 28, 6448–6455 (2017)Google Scholar
  8. 8.
    S. Stankovich, D.A. Dikin, G.H.B. Dommett, K.M. Kohlhaas, E.J. Zimney, E.A. Stach, R.D. Piner, S.T. Nguyen, R.S. Ruoff, Graphene-based composite materials. Nature 442, 282–286 (2006)CrossRefGoogle Scholar
  9. 9.
    T. Zheng, J. Wu, Enhanced piezoelectric activity in high-temperature Bi1 – x–ySmxLayFeO3 lead-free ceramics. J. Mater. Chem. C 3, 3684–3693 (2015)CrossRefGoogle Scholar
  10. 10.
    C.-J. Cheng, A.Y. Borisevich, D. Kan, I. Takeuchi, V. Nagarajan, Nanoscale structural and chemical properties of antipolar clusters in Sm-doped BiFeO3 ferroelectric epitaxial thin films. Chem. Mater. 22, 2588–2596 (2010)CrossRefGoogle Scholar
  11. 11.
    R. Che, Y. Jiang, L. Wei, X. He, Preparation and thermal analysis kinetics of the core–nanoshell composite materials doped with Sm. J. Therm. Anal. Calorim. 116, 905–913 (2014)CrossRefGoogle Scholar
  12. 12.
    Y. Liu, X. Li, M.G.B. Drew, Y. Liu, Increasing microwave absorption efficiency in ferrite based materials by doping with lead and forming composites. Mater. Chem. Phys. 162(15), 677–685 (2015)CrossRefGoogle Scholar
  13. 13.
    Y. Liu, H. Yu, M.G.B. Drew, Y. Liu, A systemized parameter set applicable to microwave absorption for ferrite based materials. J. Mater. Sci.: Mater. Electron. 29(2), 1562–1575 (2018)Google Scholar
  14. 14.
    Y. Yin, X. Liu, X. Wei, R. Yu, J. Shui, Porous CNTs/Co composite derived from zeolitic imidazolate framework: a lightweight, ultrathin, and highly efficient electromagnetic wave absorber. ACS Appl. Mater. Interfaces 8, 34686–34698 (2016)CrossRefGoogle Scholar
  15. 15.
    P. Liu, V. Ming, H. Ng, Z. Yao, J. Zhou, Y. Lei, Z. Yang, H. Lv, L.B. Kong, Facile synthesis and hierarchical assembly of flowerlike NiO structures with enhanced dielectric and microwave absorption properties. ACS Appl. Mater. Interfaces 9, 16404–16416 (2017)CrossRefGoogle Scholar
  16. 16.
    C. Li, S. Ji, X. Jiang, G.I.N. Waterhouse, Z. Zhang, L. Yu, Microwave absorption by watermelon-like microspheres composed of c-Fe2O3, microporous silica and polypyrrole. J. Mater. Sci. 53, 9635–9649 (2018)CrossRefGoogle Scholar
  17. 17.
    P. Liu, Z. Yao, J. Zhou, Z. Yang, L.B. Kong, Small magnetic Co-doped NiZn ferrite/grapheme nanocomposites and their dual-region microwave absorption performance. Small magnetic Co-doped NiZn ferrite/grapheme nanocomposites and their dual-region microwave absorption performance. J. Mater. Chem. C 4, 9738–9749 (2016)CrossRefGoogle Scholar
  18. 18.
    B. Zhao, L. Liang, J. Deng, Z. Bai, J. Liu, X. Guo, K. Gao, W. Guo, R. Zhang, 1D Cu@Ni nanorods anchored on 2D reduced graphene oxide with interfacial engineering to enhance microwave absorption properties. CrystEngComm 19, 6579–6587 (2017)CrossRefGoogle Scholar
  19. 19.
    B. Zhao, J. Liu, X. Guo, W. Zhao, L. Liang, C. Ma, R. Zhang, Hierarchical porous Ni@boehmite/nickel aluminum oxide flakes with enhanced microwave absorption ability. Phys. Chem. Chem. Phys. 19, 9128–9136 (2017)CrossRefGoogle Scholar
  20. 20.
    W. Xu, Y.-F. Pan, W. Wei, G.-S. Wang, Nanocomposites of oriented nickel chains with tunable magnetic properties for high-performance broadband microwave absorption. ACS Appl. Nano Mater. 1, 1116–1123 (2018)CrossRefGoogle Scholar
  21. 21.
    H. Liu, Y. Li, M. Yuan, G. Sun, H. Li, S. Ma, Q. Liao, Y. Zhang, In situ preparation of cobalt nanoparticles decorated in N–doped carbon nanofibers as excellent electromagnetic wave absorbers. ACS Appl. Mater. Interfaces 10(26), 22591–22601 (2018)CrossRefGoogle Scholar
  22. 22.
    Y. He, S. Pan, L. Cheng, J. Luo, Y. Xu, J. Yu, J. Chang, Effect of Dy, Pr on microwave absorption properties of Ce2Co17 alloy. J. Mater. Sci.: Mater. Electron. 29, 12624–12631 (2018)Google Scholar
  23. 23.
    J. Xi, Y. Liu, Y. Wu, J. Hu, W. Gao, E. Zhou, H. Chen, Z. Chen, Y. Chen, C. Gao, Multifunctional bicontinuous composite foams with ultralow percolation thresholds. ACS Appl. Mater. Interfaces 10, 20806–20815 (2018)CrossRefGoogle Scholar
  24. 24.
    P. He, Z.-L. Hou, K.-L. Zhang, J. Li, K. Yin, S. Feng, S. Bi, Lightweight ferroferric oxide nanotubes with natural resonance property and design for broadband microwave absorption. J. Mater. Sci. 52, 8258–8267 (2017)CrossRefGoogle Scholar
  25. 25.
    J. Feng, Z. Li, Y. Jia, B. Yang, S. Liu, X. Zhao, L. Li, L. Zuo, Significant high-frequency electromagnetic wave absorption performance of Ni2 + xMn1–xGa alloys. J. Mater. Sci. 53, 11779–11790 (2018)CrossRefGoogle Scholar
  26. 26.
    Y. Liu, K. Zhao, M. Drew, Y. Liu, A theoretical and practical clarification on the calculation of reflection loss for microwave absorbing materials. AIP Adv. 8, 015223 (2018)CrossRefGoogle Scholar
  27. 27.
    L. Zhang, Y. Zong, Z. Li, K. Huang, Y. Sun, Y. Lan, H. Wu, X. Li, X. Zheng, Design of spinous Ni/N-GN nanocomposites as novel magnetic/dielectric microwave absorbents with highefficiency absorption performance and thin thickness. J. Mater. Sci. 53, 9034–9045 (2018)CrossRefGoogle Scholar
  28. 28.
    X. Liu, C. Hao, H. Jiang, M. Zeng, R. Yu, Hierarchical NiCo2O4/Co3O4/NiO porous composite: a lightweight electromagnetic wave absorber with tunable absorbing performance. J. Mater. Chem. C 5, 3770–3778 (2017)CrossRefGoogle Scholar
  29. 29.
    N. Li, G.-W. Huang, Y.-Q. Li, H.-M. Xiao, Q.-P. Feng, N. Hu, S.-Y. Fu, Enhanced microwave absorption performance of coated carbon nanotubes by optimizing the Fe3O4 nanocoating structure. ACS Appl. Mater. Interfaces 9, 2973–2983 (2017)CrossRefGoogle Scholar
  30. 30.
    C. Zhang, B. Wang, J. Xiang, C. Su, C. Mu, F. Wen, Z. Liu, Microwave absorption properties of CoS2 nanocrystals embedded into reduced graphene oxide. ACS Appl. Mater. Interfaces 9, 28868–28875 (2017)CrossRefGoogle Scholar
  31. 31.
    W. Liu, L. Liu, Z. Yang, J. Xu, Y. Hou, G. Ji, A versatile route toward the electromagnetic functionalization of metal–organic framework-derived three-dimensional nanoporous carbon composites. ACS Appl. Mater. Interfaces 10, 8965–8975 (2018)CrossRefGoogle Scholar
  32. 32.
    K. Wang, Y. Chen, R. Tian, H. Li, Y. Zhou, H. Duan, H. Liu, Porous Co–C core–shell nanocomposites derived from Co-MOF-74 with enhanced electromagnetic wave absorption performance. ACS Appl. Mater. Interfaces 10, 11333–11342 (2018)CrossRefGoogle Scholar
  33. 33.
    Y. Liu, Z. Chen, Y. Zhang, R. Feng, X. Chen, C. Xiong,. L. Dong, Broadband and lightweight microwave absorber constructed by in situ growth of hierarchical CoFe2O4/reduced graphene oxide porous nanocomposites. ACS Appl. Mater. Interfaces 10, 13860–13868 (2018)CrossRefGoogle Scholar
  34. 34.
    S. Zhou, Y. Huang, X. Liu, J. Yan, X. Feng, Synthesis and microwave absorption enhancement of CoNi@SiO2@C hierarchical structures. Ind. Eng. Chem. Res. 57, 5507–5516 (2018)CrossRefGoogle Scholar
  35. 35.
    P. Liu, Y. Huang, J. Yan, Y. Zhao, Magnetic graphene@PANI@porous TiO2 ternary composites for high-performance electromagnetic wave absorption. J. Mater. Chem. C 4, 6362–6370 (2016)CrossRefGoogle Scholar
  36. 36.
    F. Wen, F. Zhang, Z. Liu, Investigation on microwave absorption properties for multiwalled carbon nanotubes/Fe/Co/Ni nanopowders as lightweight absorbers. J. Phys. Chem. C 115, 14025–14030 (2011)CrossRefGoogle Scholar
  37. 37.
    D. Chen, F. Luo, W. Zhou, D. Zhu, Effect of Ti3SiC2 addition on microwave absorption property of plasma sprayed Ti3SiC2/NASICON coatings. J. Mater. Sci.: Mater. Electron. 29(16), 13534–13540 (2018)Google Scholar
  38. 38.
    Y. Liu, Y. Fu, L. Liu, W. Li, J. Guan, G. Tong, Low-cost carbothermal reduction preparation of monodisperse Fe3O4/C core–shell nanosheets for improved microwave absorption. ACS Appl. Mater. Interfaces 10, 16511–16520 (2018)CrossRefGoogle Scholar
  39. 39.
    C. Zhang, C. Mu, J. Xiang, B. Wang, F. Wen, J. Song, C. Wang, Z. Liu, Microwave absorption characteristics of CH3NH3PbI3 perovskite/carbon nanotube composites. J. Mater. Sci. 52, 13023–13032 (2017)CrossRefGoogle Scholar
  40. 40.
    W. Chu, Y. Wang, Y. Du, R. Qiang, C. Tian, X. Han, FeCo alloy nanoparticles supported on ordered mesoporous carbon for enhanced microwave absorption. J. Mater. Sci. 52, 13636–13649 (2017)CrossRefGoogle Scholar
  41. 41.
    J. Zhou, Y. Chen, H. Li, R. Dugnani, Q. Du, H. UrRehman, H. Kang, H. Liu, Facile synthesis of three-dimensional lightweight nitrogen-doped graphene aerogel with excellent electromagnetic wave absorption properties. J. Mater. Sci. 53, 4067–4077 (2018)CrossRefGoogle Scholar
  42. 42.
    J. Deng, S. Li, Y. Zhou, L. Liang, B. Zhao, X. Zhang, R. Zhang, Enhancing the microwave absorption properties of amorphous CoO nanosheet-coated Co (hexagonal and cubic phases) through interfacial polarizations. J. Colloid Interface Sci. 509, 406–413 (2018)CrossRefGoogle Scholar
  43. 43.
    S. Gao, Q. An, Z. Xiao, S. Zhai, Z. Shi, Significant promotion of porous architecture and magnetic Fe3O4 NPs inside honeycomb-like carbonaceous composites for enhanced microwave absorption. RSC Adv. 8, 19011–19023 (2018)CrossRefGoogle Scholar
  44. 44.
    Y. Liu, M.G.B. Drew, Y. Liu, Optimizing the methods of synthesis for barium hexagonal ferrite—an experimental and theoretical study. Mater. Chem. Phys. 134, 266–272 (2012)CrossRefGoogle Scholar
  45. 45.
    Y. Liu, M.G.B. Drew, Y. Liu, Y. Liu., F.L. Cao, A comparative study of Fe3O4/polyaniline composites with octahedral and microspherical inorganic kernels. J. Mater. Sci. 49(10), 3694–3704 (2014)CrossRefGoogle Scholar
  46. 46.
    Y. Wu, Y. Liu, W. Wang, J. Wang, C. Zhang, Z. Wu, P. Yan, K. Li, Microwave absorption enhancement and loss mechanism of lamellar MnO2 nanosheets decorated reduced graphene oxide hybrid. J. Mater. Sci.: Mater. Electron. (2018).  https://doi.org/10.1007/s10854-018-0354-9 CrossRefGoogle Scholar
  47. 47.
    G.M. Shi, L. Sun, X. Wang, X. Bao, Excellent electromagnetic wave absorption properties of LaOCl/C/MnO composites. J. Mater. Sci.: Mater. Electron. 29(3), 2236–2243 (2018)Google Scholar
  48. 48.
    Y. Liu, R. Tai, M.G.B. Drew, Y. Liu, Several theoretical perspectives of ferrite based materials—part 1: transmission-line theory and microwave absorption. J. Supercond. Nov. Magn. 30(9), 2489–2504 (2017)CrossRefGoogle Scholar
  49. 49.
    J. Deng, X. Zhang, B. Zhao, Z. Bai, S. Wen, S. Li, S. Li, J. Yang, R. Zhang, Fluffy microrods to heighten the microwave absorption properties through tuning the electronic state of Co/CoO. J. Mater. Chem. C 6, 7128–7140 (2018)CrossRefGoogle Scholar
  50. 50.
    Laird Tech Notes: Theory and Application of RF/Microwave Absorbers. https://www.lairdtech.com/sites/default/files/public/ABS-CS-RF%20Microwave%20Absorbers-Laird_081214.pdf
  51. 51.
    Y. Zuo, Z. Yao, H. Lin, J. Zhou, P. Liu, W. Chen, C. Shen, Coralliform Li0.35Zn0.3Fe2.35O4/polyaniline nanocomposites: facile synthesis and enhanced microwave absorption properties. J. Alloys Compd. 746, 496–502 (2018)CrossRefGoogle Scholar
  52. 52.
    S. Li, Y. Huang, N. Zhang, M. Zong, P. Liu, Synthesis of polypyrrole decorated FeCo@SiO2 as a high-performance electromagnetic absorption material. J. Alloys Compd. 774, 532–539 (2019)CrossRefGoogle Scholar
  53. 53.
    A.N. Hapishah, M.M. Syazwan, M.N. Hamidon, Synthesis and characterization of magnetic and microwave absorbing properties in polycrystalline cobalt zinc ferrite (Co0.5Zn0.5Fe2O4) composite, J. Mater. Sci.: Mater. Electron. 29, 20573–20579 (2018)Google Scholar
  54. 54.
    J. Gu, Y. Xie, W. Chen, C. Hu, F. Qiao, Z. Xu, X. Liu, X. Zhao, G. Zhang, Inter-diffusion of Cu2+ ions into CuS nanocrystals confines the microwave absorption properties. CrystEngComm 20, 6565–6572 (2018)CrossRefGoogle Scholar
  55. 55.
    Z. Lou, Y. Li, H. Han, H. Ma, L. Wang, J. Cai, L. Yang, C. Yuan, J. Zou, Synthesis of porous 3D Fe/C composites from waste wood with tunable and excellent electromagnetic wave absorption performance. ACS Sustain. Chem. Eng. 6, 15598–15607 (2018)CrossRefGoogle Scholar
  56. 56.
    C. Zhou, C. Wu, M. Yan, Hierarchical FeCo@MoS2 nanoflowers with strong electromagnetic wave absorption and broad bandwidth. ACS Appl. Nano Mater. 1, 5179–5187 (2018)CrossRefGoogle Scholar
  57. 57.
    S. Gao, Q. An, Z. Xiao, S. Zhai, D. Yang, Controllable N–doped carbonaceous composites with highly dispersed Ni nanoparticles for excellent microwave absorption. ACS Appl. Nano Mater. 1, 5895–5906 (2018)CrossRefGoogle Scholar
  58. 58.
    J. Qiao, D. Xu, L. Lv, X. Zhang, F. Wang, W. Liu, J. Liu, Self-assembled ZnO/Co hybrid nanotubes prepared by electrospinning for lightweight and high-performance electromagnetic wave absorption. ACS Appl. Nano Mater. 1, 5297–5306 (2018)CrossRefGoogle Scholar
  59. 59.
    Y. Wang, C. Li, X. Han, D. Liu, H. Zhao, Z. Li, P. Xu, Y. Du, Ultrasmall Mo2C nanoparticle-decorated carbon polyhedrons for enhanced microwave absorption. ACS Appl. Nano Mater. 1, 5366–5376 (2018)CrossRefGoogle Scholar
  60. 60.
    X. Liang, B. Quan, J. Chen, W. Gu, B. Zhang, G. Ji, Nano bimetallic@carbon layer on porous carbon nanofibers with multiple interfaces for microwave absorption applications. ACS Appl. Nano Mater. 1, 5712–5721 (2018)CrossRefGoogle Scholar
  61. 61.
    H. Li, S. Bao, Y. Li, Y. Huang, J. Chen, H. Zhao, Z. Jiang, Q. Kuang, Z. Xie, Optimizing the electromagnetic wave absorption performances of designed Co3Fe7@C yolk–shell structures. ACS Appl. Mater. Interfaces 10, 28839–28849 (2018)CrossRefGoogle Scholar
  62. 62.
    D. Kuang, L. Hou, S. Wang, B. Yu, D. Lianwen, L. Lin, H. Huang, J. He, M. Song, Enhanced electromagnetic wave absorption of Ni–C core-shell nanoparticles by HCP-Ni phase. Mater. Res. Express 5, 095013 (2018)CrossRefGoogle Scholar
  63. 63.
    I. Oransky, A. Marcus, Harvard and the Brigham call for more than 30 retractions of cardiac stem cell research. STAT. https://www.statnews.com/2018/10/14/harvard-brigham-retractions-stem-cell/. Accessed 14 Oct 2018
  64. 64.
    Harvard calls for retraction of dozens of studies by noted cardiologist, New York Times. http://www.staradvertiser.com/2018/10/16/news/harvard-calls-for-retraction-of-dozens-of-studies-by-noted-cardiologist/. Accessed 16 Oct 2018
  65. 65.
    Y. Liu, M.G.B. Drew, Y. Liu, Similarity between chemistry and mathematics in reasoning. Chem. Educ. 23, 231–236 (2018)Google Scholar
  66. 66.
    V.I. Chizhik, Y.S. Chemyshev, A.V. Donects, V.V. Frolov, A.V. Komolkin, M.G. Shelyapina, Magnetic Resonance and Its Applications (Springer, New York, 2014)CrossRefGoogle Scholar
  67. 67.
    Z.-P. Liang, P.C. Lauterbur, Principles of Magnetic Resonance Imaging, A Signal Processing Perspective (IEEE Press, New York, 2000)Google Scholar
  68. 68.
    C.K. Mann, T.J. Vickers, W.M. Gulick, Instrumental Analysis (Harper & Row, New York, 1974)Google Scholar
  69. 69.
    Y. Liu, R. Tai, Y. Liu, Crystal field and magnetic properties. Huaxue Jiaoyu (Chin. J. Chem. Educ.) 36(6), 1–10 (2015). (in Chinese)Google Scholar
  70. 70.
    Y. Liu, Y. Liu, M.G.B. Drew, The use of three simple related procedures in determining the Russell-Saunders terms of equivalent electrons. Chem. Educ. 17, 118–124 (2012)Google Scholar
  71. 71.
    Y. Liu, B. Liu, Y. Liu, M.G.B. Drew, Observations on calculations of configuration interaction and basis set superposition error. Chem. Educ. 16, 202–205 (2011)Google Scholar
  72. 72.
    B. Lambet, E.P. Mazzola, Nuclear Magnetic Resonance Spectroscopy, An Introduction to Principles, Applications, and Experimental Methods (Prentice-Hall, Upper Saddle River, 2003)Google Scholar
  73. 73.
    Y. Liu, Y. Liu, M.G.B. Drew, Correlation between Fourier series expansion and Hückel orbital theory. J. Math. Chem. 51(2), 503–531 (2013)CrossRefGoogle Scholar
  74. 74.
    Y. Liu, J. Jin, M.G.B. Drew, Y. Liu, Several theoretical perspectives of ferrite based materials—parts 2: close packing model for crystal structure. J. Supercond. Nov. Magn. 30(10), 2777–2789 (2017)CrossRefGoogle Scholar
  75. 75.
    M. Nespolo, Comments on the article ‘comparison of calculations for interplanar distances in a crystal lattice’. Crystallogr. Rev. 23(4), 302–303 (2017)CrossRefGoogle Scholar
  76. 76.
    B.K. Vainshtein, V.M. Fridkin, V.L. Indenbom, Structure of Crystals (Modern Crystallography vol. 2). Second, Enlarged Edition (Springer, Berlin, 1995), pp. 139, 349, 359, 362–363Google Scholar
  77. 77.
  78. 78.
    C. Hammond, The Basics of Crystallography and Diffraction. Third Edition. International Union of Crystallography (Oxford University Press, Oxford, 2009), pp. 63–76Google Scholar
  79. 79.
    R. Desiraju, Perspectives in Supramolecular Chemistry (Crystal Design: Structure and Function. Volume 7), (Wiley, Chichester, 2003), pp. 82 84, 90Google Scholar
  80. 80.
    M.S. Dresselhaus, G. Dresselhaus, A. Jorio, Group Theory, Application to the Physics of Condensed Matter (Springer, Berlin, 2008), pp. 196, 210, 230–233 250Google Scholar
  81. 81.
    A. Authier, Physical Properties of Crystals (International Tables for Crystallography, Volume D) (Kluwer Academic Publishers, London, 2003), p. 446Google Scholar
  82. 82.
    W. Fischer, H. Burzlaff, E. Hellner, J.D.H. Donnay, Space Groups and Lattice Complexes (U.S. Department of Commerce, National Bureau of Standards, Washington, DC, 1973)CrossRefGoogle Scholar
  83. 83.
    M. Nespolo, The ash heap of crystallography: restoring forgotten basic knowledge. J. Appl. Cryst. 48, 1290–1298 (2015)CrossRefGoogle Scholar
  84. 84.
    Q. Fan, A new method of calculating interplanar spacing: the position-factor method. J. Appl. Cryst. 45, 1303–1308 (2012)CrossRefGoogle Scholar
  85. 85.
    Q. Fan, A new method of calculating planar density: the position-duplication-number method. J. Appl. Cryst. 49, 1454–1458 (2016)CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.College of Chemistry and Chemical EngineeringShenyang Normal UniversityShenyangPeople’s Republic of China
  2. 2.School of ChemistryThe University of ReadingReadingUK

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