Applied Physics A

, Volume 115, Issue 3, pp 781–790 | Cite as

Three-dimensional structure of polystyrene colloidal crystal by synchrotron radiation X-ray phase-contrast computed tomography

  • Yanan Fu
  • Honglan Xie
  • Biao Deng
  • Guohao Du
  • Rongchang Chen
  • Tiqiao Xiao
Article

Abstract

Colloidal crystal with long-range ordered structure has attracted great attention for their applications in various fields. Although perfect colloidal crystals have been achieved by some fabrications for utilization, little is known about their exact structures and internal defects. In this study, we use synchrotron radiation (SR) phase-contrast computed tomography (CT) to noninvasively access the internal structure of polystyrene (PS) colloidal crystals in three dimensions (3D). The phase-attenuation duality Paganin algorithm phase retrieval was employed to achieve a satisfactory contrast and outline of the spheres. After CT reconstruction, the positions of individual PS particles and structural defects are identified in three dimensions, and the local crystal structure is revealed. Further quantitative analysis of the void system in colloidal crystal illustrates that single voids can be mostly attributed to tetrahedron void of sphere close packing, but the interconnected voids with large volume induce a sphere volume fraction of 59.39 % that reflects a metastable glass behavior of colloidal crystal arrangement. The void orientation result reveals that the 3D close-packing difficulty mainly lies in the stacking of interlayer.

References

  1. 1.
    Y.N. Xia, B. Gates, Y.D. Yin, Y. Lu, Monodispersed colloidal spheres: old materials with new applications. Adv. Mater. 12, 693 (2000)CrossRefGoogle Scholar
  2. 2.
    C. López, Materials aspects of photonic crystals. Adv. Mater. 15, 1679 (2003)CrossRefGoogle Scholar
  3. 3.
    C.M. Soukoulis, Photonic band gap materials (Kluwer Academic Publishers, Dordrecht, 1996)CrossRefGoogle Scholar
  4. 4.
    U. Gasser, E.R. Weeks, A. Schofield, P.N. Pusey, D.A. Weitz, Real-space imaging of nucleation and growth in colloidal crystallization. Science 292, 258 (2001)ADSCrossRefGoogle Scholar
  5. 5.
    Z.Y. Zhong, Y.D. Yin, B. Gates, Y.N. Xia, Preparation of mesoscale hollow spheres of TiO2 and SnO2 by templating against crystalline arrays of polystyrene beads. Adv. Mater. 12, 206 (2000)CrossRefGoogle Scholar
  6. 6.
    D.K. Yi, D.Y. Kim, Polymer nanosphere lithography: fabrication of an ordered trigonal polymeric nanostructure. Chem. Commun. 8, 982 (2003)CrossRefGoogle Scholar
  7. 7.
    K.M. Kulinowski, P. Jiang, H. Vaswani, V.L. Colvin, Porous metals from colloidal templates. Adv. Mater. 12, 833 (2000)CrossRefGoogle Scholar
  8. 8.
    G.I.N. Waterhouse, M.R. Waterland, Opal and inverse opal photonic crystals: fabrication and characterization. Polyhedron 26, 356 (2007)CrossRefGoogle Scholar
  9. 9.
    Y.A. Vlasov, V.N. Astratov, A.V. Baryshev, A.A. Kaplyanskii, O.Z. Karimov, M.F. Limonov, Manifestation of intrinsic defects in optical properties of self-organized opal photonic crystals. Phys. Rev. E 61, 5784 (2000)ADSCrossRefGoogle Scholar
  10. 10.
    J.M. Meijer, V.W.A. De Villeneuve, A.V. Petukhov, In-plane stacking disorder in polydisperse hard sphere crystals. Langmuir 23, 3554 (2007)CrossRefGoogle Scholar
  11. 11.
    T.A. Taton, D.J. Norris, Device physics: defective promise in photonics. Nature 416, 685 (2002)ADSCrossRefGoogle Scholar
  12. 12.
    P. Masse, S. Reculusa, K. Clays, S. Ravaine, Tailoring planar defect in three-dimensional colloidal crystals. Chem. Phys. Lett. 422, 251 (2006)ADSCrossRefGoogle Scholar
  13. 13.
    S.A. Rinne, F. Garcia-Santamaria, P.V. Braun, Embedded cavities and waveguides in three-dimensional silicon photonic crystals. Nat. Photonics 2, 52 (2008)ADSCrossRefGoogle Scholar
  14. 14.
    L. Woodcock, Entropy difference between the face-centred cubic and hexagonal close-packed crystal structures. Nature 385, 141 (1997)ADSCrossRefGoogle Scholar
  15. 15.
    A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S.W. Leonard, C. Lopez, F. Meseguer, H. Miguez, J.P. Mondia, G.A. Ozin, O. Toader, H.M. Van Driel, Large-scale synthesis of a silicon photonic crystal with a complete three-dimensional bandgap near 1.5 micrometres. Nature 405, 437 (2000)ADSCrossRefGoogle Scholar
  16. 16.
    Y.N. Fu, Z.G. Jin, G.Q. Liu, Y.X. Yin, Self-assembly of polystyrene sphere colloidal crystals by in situ solvent evaporation method. Synth. Met. 159, 1744 (2009)CrossRefGoogle Scholar
  17. 17.
    S. Hu, J. Rieger, Z. Yi, J. Zhang, X. Chen, S.V. Roth, R. Gehrke, Y. Men, Structural evolution of a colloidal crystal fiber during heating and annealing studied by in situ synchrotron small angle X-ray scattering. Langmuir 26, 13216 (2010)CrossRefGoogle Scholar
  18. 18.
    D.J. Norris, E.G. Arlinghaus, L. Meng, R. Heiny, L.E. Scriven, Opaline photonic crystals: how does self-assembly work? Adv. Mater. 16, 1393 (2004)CrossRefGoogle Scholar
  19. 19.
    L. Meng, H. Wei, A. Nagel, B.J. Wiley, L.E. Scriven, D.J. Norris, The role of thickness transitions in convective assembly. Nano Lett. 6, 2249 (2006)ADSCrossRefGoogle Scholar
  20. 20.
    P. Schall, I. Cohen, D.A. Weitz, F. Spaepen, Visualization of dislocation dynamics in colloidal crystals. Science 305, 1944 (2004)ADSCrossRefGoogle Scholar
  21. 21.
    L. Zhang, D.Y. Li, S.Q. Luo, Non-invasive microstructure and morphology investigation of the mouse lung: qualitative description and quantitative measurement. PLoS ONE 6, e17400 (2011)CrossRefGoogle Scholar
  22. 22.
    J.H. Duan, C.H. Hu, H. Chen, High-resolution micro-CT for morphologic and quantitative assessment of the sinusoid in human cavernous hemangioma of the liver. PLoS ONE 8, e53507 (2013)ADSCrossRefGoogle Scholar
  23. 23.
    Z. Xing, M.H. Wang, G.H. Du, T.Q. Xiao, W.H. Liu, Q. Dou, G.Z. Wu, Preparation of microcellular polystyrene/polyethylene alloy foams by supercritical CO2 foaming and analysis by X-ray micro tomography. J. Supercrit. Fluids 82, 50 (2013)CrossRefGoogle Scholar
  24. 24.
    M. Born, E. Wolf, Principles of optics, 7th edn. (Cambridge University Press, Cambridge, 1999)CrossRefGoogle Scholar
  25. 25.
    D. Paganin, S.C. Mayo, T.E. Gureyev, P.R. Miller, S.W. Wilkins, Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object. J. Microsc. 206, 33 (2002)CrossRefMathSciNetGoogle Scholar
  26. 26.
    X.Z. Wu, H. Liu, A.M. Yan, X-ray phase-attenuation duality and phase retrieval. Opt. Lett. 30, 379 (2005)ADSCrossRefGoogle Scholar
  27. 27.
    R.C. Chen, L. Rigon, R. Longo, Comparison of single distance phase retrieval algorithms by considering different object composition and the effect of statistical and structural noise. Opt. Express 21, 7384 (2013)ADSCrossRefGoogle Scholar
  28. 28.
    R.C. Chen, L. Rigon, R. Longo, Quantitative 3D refractive index decrement reconstruction using single-distance phase-contrast tomography data. J. Phys. D Appl. Phys. 44, 495401 (2011)ADSCrossRefGoogle Scholar
  29. 29.
    X.J. Guo, X.L. Liu, M. Gu, C. Ni, S.M. Huang, B. Liu, Polychromatic X-ray in-line phase-contrast tomography for soft Tissue. EPL 98, 14001 (2012)ADSCrossRefGoogle Scholar
  30. 30.
    B.D. Arhatari, F.D. Carlo, A.G. Peele, Direct quantitative tomographic reconstruction for weakly absorbing homogeneous phase objects. Rev. Sci. Instrum. 78, 053701 (2007)ADSCrossRefGoogle Scholar
  31. 31.
    M. Langer, P. Cloetens, F. Peyrin, Regularization of phase retrieval with phase-attenuation duality prior for 3-D holotomography. IEEE Trans. Image Process. 19, 9 (2010)CrossRefMathSciNetGoogle Scholar
  32. 32.
    R.C. Chen, X-ray quantitative micro-CT and its biomedical applications (Chinese Academy of Sciences, Beijing, 2010)Google Scholar
  33. 33.
    R.C. Chen, D. Dreossi, L. Mancini, R. Menk, L. Rigon, T.Q. Xiao, R. Longo, PITRE software for phase-sensitive X-ray image processing. J. Synchrotron Rad. 19, 836 (2012)CrossRefGoogle Scholar
  34. 34.
    J.D. O’Sullivan, A fast sinc function gridding algorithm for Fourier inversion in computer tomography. IEEE Trans. Med. Imaging 4, 200 (1985)CrossRefGoogle Scholar
  35. 35.
    R.A. Ketcham, Computational methods for quantitative analysis of three-dimensional features in geological specimens. Geosphere 1, 32 (2005)ADSCrossRefGoogle Scholar
  36. 36.
    R.A. Ketcham, T. Ryan, Quantification and visualization of anisotropy in trabecular bone. J. Microsc. 213, 158 (2004)CrossRefMathSciNetGoogle Scholar
  37. 37.
  38. 38.
    V. Prasad, D. Semwogerere, E.R. Weeks, Confocal microscopy of colloids. J. Phys. Condens. Matter 19, 113102 (2007)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Yanan Fu
    • 1
  • Honglan Xie
    • 1
  • Biao Deng
    • 1
  • Guohao Du
    • 1
  • Rongchang Chen
    • 1
  • Tiqiao Xiao
    • 1
  1. 1.Shanghai Institute of Applied PhysicsChinese Academy of ScienceShanghaiChina

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