Skip to main content
Log in

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

  • Published:
Applied Physics A Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Y.N. Xia, B. Gates, Y.D. Yin, Y. Lu, Monodispersed colloidal spheres: old materials with new applications. Adv. Mater. 12, 693 (2000)

    Article  Google Scholar 

  2. C. López, Materials aspects of photonic crystals. Adv. Mater. 15, 1679 (2003)

    Article  Google Scholar 

  3. C.M. Soukoulis, Photonic band gap materials (Kluwer Academic Publishers, Dordrecht, 1996)

    Book  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  6. D.K. Yi, D.Y. Kim, Polymer nanosphere lithography: fabrication of an ordered trigonal polymeric nanostructure. Chem. Commun. 8, 982 (2003)

    Article  Google Scholar 

  7. K.M. Kulinowski, P. Jiang, H. Vaswani, V.L. Colvin, Porous metals from colloidal templates. Adv. Mater. 12, 833 (2000)

    Article  Google Scholar 

  8. G.I.N. Waterhouse, M.R. Waterland, Opal and inverse opal photonic crystals: fabrication and characterization. Polyhedron 26, 356 (2007)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  11. T.A. Taton, D.J. Norris, Device physics: defective promise in photonics. Nature 416, 685 (2002)

    Article  ADS  Google Scholar 

  12. P. Masse, S. Reculusa, K. Clays, S. Ravaine, Tailoring planar defect in three-dimensional colloidal crystals. Chem. Phys. Lett. 422, 251 (2006)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  14. L. Woodcock, Entropy difference between the face-centred cubic and hexagonal close-packed crystal structures. Nature 385, 141 (1997)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  20. P. Schall, I. Cohen, D.A. Weitz, F. Spaepen, Visualization of dislocation dynamics in colloidal crystals. Science 305, 1944 (2004)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  24. M. Born, E. Wolf, Principles of optics, 7th edn. (Cambridge University Press, Cambridge, 1999)

    Book  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  26. X.Z. Wu, H. Liu, A.M. Yan, X-ray phase-attenuation duality and phase retrieval. Opt. Lett. 30, 379 (2005)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  32. R.C. Chen, X-ray quantitative micro-CT and its biomedical applications (Chinese Academy of Sciences, Beijing, 2010)

    Google Scholar 

  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)

    Article  Google Scholar 

  34. J.D. O’Sullivan, A fast sinc function gridding algorithm for Fourier inversion in computer tomography. IEEE Trans. Med. Imaging 4, 200 (1985)

    Article  Google Scholar 

  35. R.A. Ketcham, Computational methods for quantitative analysis of three-dimensional features in geological specimens. Geosphere 1, 32 (2005)

    Article  ADS  Google Scholar 

  36. R.A. Ketcham, T. Ryan, Quantification and visualization of anisotropy in trabecular bone. J. Microsc. 213, 158 (2004)

    Article  MathSciNet  Google Scholar 

  37. CXRO, http://henke.lbl.gov/optical_constants/getdb2.html

  38. V. Prasad, D. Semwogerere, E.R. Weeks, Confocal microscopy of colloids. J. Phys. Condens. Matter 19, 113102 (2007)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

The financial supports of the National Natural Science Foundation of China (No. U1332115, 51274054) and the Key grant Project of Chinese Ministry of Education (No. 313011), are gratefully acknowledged.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yanan Fu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fu, Y., Xie, H., Deng, B. et al. Three-dimensional structure of polystyrene colloidal crystal by synchrotron radiation X-ray phase-contrast computed tomography. Appl. Phys. A 115, 781–790 (2014). https://doi.org/10.1007/s00339-014-8432-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00339-014-8432-1

Keywords

Navigation