Recent advances in the fabrication of quasicrystals in soft matter systems have increased the length scales for quasicrystals1 into the mesoscale range (20 to 500 ångströms). Thus far, dendritic liquid crystals2, ABC-star polymers3, colloids4 and inorganic nanoparticles5 have been reported to yield quasicrystals. These quasicrystals offer larger length scales than intermetallic quasicrystals (a few ångströms)1,6, thus potentially leading to optical applications through the realization of a complete photonic bandgap induced via multiple scattering of light waves in virtually all directions7,8,9. However, the materials remain far from structurally ideal, in contrast to their intermetallic counterparts, and fine control over the structure through a self-organization process has yet to be attained. Here we use the well-established self-assembly of surfactant micelles to produce a new class of mesoporous silicas, which exhibit 12-fold (dodecagonal) symmetry in both electron diffraction and morphology. Each particle reveals, in the 12-fold cross-section, an analogue of dodecagonal quasicrystals in the centre surrounded by 12 fans of crystalline domains in the peripheral part. The quasicrystallinity has been verified by selected-area electron diffraction and quantitative phason strain analyses on transmission electron microscope images obtained from the central region. We argue that the structure forms through a non-equilibrium growth process, wherein the competition between different micellar configurations has a central role in tuning the structure. A simple theoretical model successfully reproduces the observed features and thus establishes a link between the formation process and the resulting structure.
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Shechtman, D., Blech, I., Gratias, D. & Cahn, J. W. Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53, 1951–1953 (1984)
Zeng, X. et al. Supramolecular dendritic liquid quasicrystals. Nature 428, 157–160 (2004)
Hayashida, K., Dotera, T., Takano, A. & Matsushita, Y. Polymeric quasicrystal: mesoscopic quasicrystalline tiling in ABC star polymers. Phys. Rev. Lett. 98, 195502 (2007)
Fischer, S. et al. Colloidal quasicrystals with 12-fold and 18-fold diffraction symmetry. Proc. Natl Acad. Sci. 108, 1810–1814 (2011)
Talapin, D. V. et al. Quasicrystalline order in self-assembled binary nanoparticle superlattices. Nature 461, 964–967 (2009)
Steurer, W. Twenty years of structure research on quasicrystals. Part I. Pentagonal, octagonal, decagonal and dodecagonal quasicrystals. Z. Kristallogr. 219, 391–446 (2004)
Zoorob, M. E., Charlton, M. D. B., Parker, G. J., Baumberg, J. J. & Netti, M. C. Complete photonic bandgaps in 12-fold symmetric quasicrystals. Nature 404, 740–743 (2000)
Man, W., Megens, M., Steinhardt, P. J. & Chaikin, P. M. Experimental measurement of the photonic properties of icosahedral quasicrystals. Nature 436, 993–996 (2005)
Chan, Y. S., Chan, C. T. & Liu, Z. Y. Photonic band gaps in two dimensional photonic quasicrystals. Phys. Rev. Lett. 80, 956–959 (1998)
Gao, C., Sakamoto, Y., Terasaki, O. & Che, S. Formation of diverse mesophases templated by a diprotic anionic surfactant. Chem. Eur. J. 14, 11423–11428 (2008)
Ishimasa, T., Nissen, H. U. & Fukano, Y. New ordered state between crystalline and amorphous in Ni-Cr particles. Phys. Rev. Lett. 55, 511–513 (1985)
Frank, F. C. & Kasper, J. S. Complex alloy structures regarded as sphere packings. II. Analysis and classification of representative structures. Acta Crystallogr. 12, 483–499 (1959)
Sullivan, J. M. in Foams and Emulsions (eds Sadoc, J. F. & Rivier, N. ) 379–402 (Kluwer Academic, 1998)
Borén, B. Röntgenuntersuchung der Legierungen von Silicium mit Chrom, Mangan, Kobalt und Nickel. Ark. Kemi. Miner. Geol. 11, 1–28 (1933)
Bergman, G. & Shoemaker, D. P. The determination of the crystal structure of the sigma phase in the iron-chromium and iron-molybdenum systems. Acta Crystallogr. 7, 857–865 (1954)
Ye, H. Q., Li, D. X. & Kuo, K. H. Structure of the H phase determined by high-resolution electron microscopy. Acta Crystallogr. B 40, 461–465 (1984)
Grunbaum, B. & Shephard, G. C. Tilings and Patterns (Freeman, 1986)
Baake, M., Klitzing, R. & Schlottmann, M. Fractally shaped acceptance domains of quasiperiodic square-triangle tilings with dodecagonal symmetry. Physica A 191, 554–558 (1992)
Stampfli, P. A. dodecagonal quasiperiodic lattice in two dimensions. Helv. Phys. Acta 59, 1260–1263 (1986)
Leung, P. W., Henley, C. L. & Chester, G. V. Dodecagonal order in a two-dimensional Lennard-Jones system. Phys. Rev. B 39, 446–458 (1989)
Miyasaka, K., Han, L., Che, S. & Terasaki, O. A lesson from the unusual morphology of silica mesoporous crystals: growth and close packing of spherical micelles with multiple twinning. Angew. Chem. 118, 6666–6669 (2006)
Oxborrow, M. & Henley, C. L. Random square-triangle tilings: a model for twelvefold-symmetric quasicrystals. Phys. Rev. B 48, 6966–6998 (1993)
Yamamoto, A. Crystallography of quasiperiodic crystals. Acta Crystallogr. A 52, 509–560 (1996)
Cockayne, E. Nonconnected atomic surfaces for quasicrystalline sphere packings. Phys. Rev. B 49, 5896–5910 (1994)
Ziherl, P. & Kamien, R. D. Maximizing entropy by minimizing area: towards a new principle of self-organization. J. Phys. Chem. B 105, 10147–10158 (2001)
Weaire, D. & Phelan, R. A counter-example to Kelvin's conjecture on minimal surfaces. Phil. Mag. Lett. 69, 107–110 (1994)
Kusner, R. & Sullivan, J. M. in The Kelvin Problem: Foam Structures of Minimal Surface Area (ed. Weaire, D. ) 71–80 (Taylor and Francis, 1996)
Eden, M. in Symposium on Information Theory in Biology (ed. Yockey, P. H. ) 359–370 (Pergamon, Symposium Publications Division, 1958)
Meakin, P. Noise-reduced and anisotropy-enhanced Eden and screened-growth models. Phys. Rev. A 38, 418–426 (1988)
Durian, D. J. & Raghavan, S. R. Making a frothy shampoo or beer. Phys. Today 63, 62–63 (2010)
We thank K. Niizeki, T. Dotera, A. E. Garcia-Bennett, S. Che and C. Gao for discussions, O. M. Yaghi and M. O’Keeffe for critical reading of the manuscript, and J. Shen for encouragement and support. This work was supported by the Swedish Research Council (VR), the Japan Science and Technology Agency (JST) and Berzelii EXSELENT. SEM and TEM studies were performed at the Electron Microscopy Center (EMC) at Stockholm University, which is supported by the Knut and Alice Wallenberg Foundation. Support from the WCU programme, Korea (R-31-2008-000-10055-0; K.M. and O.T.), Grants-in-Aid for Young Scientists (B) of JSPS (no. 23710132; Y.S.), and Special Coordination Funds for Promoting Science and Technology of MEXT, Japan (Y.S.) is also acknowledged.
The authors declare no competing financial interests.
About this article
Cite this article
Xiao, C., Fujita, N., Miyasaka, K. et al. Dodecagonal tiling in mesoporous silica. Nature 487, 349–353 (2012). https://doi.org/10.1038/nature11230
Physical Review Research (2020)
Science Advances (2020)
Growth modes of quasicrystals involving intermediate phases and a multistep behavior studied by phase field crystal model
Physical Review Materials (2020)
Chemistry of Materials (2020)