Skip to main content
Top

2022 | OriginalPaper | Chapter

2. Discovery of Soft-Matter Quasicrystals and Their Properties

Authors : Tian-You Fan, Wenge Yang, Hui Cheng, Xiao-Hong Sun

Published in: Generalized Dynamics of Soft-Matter Quasicrystals

Publisher: Springer Nature Singapore

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Quasicrystals have long-range orientational order but no translational symmetry. As a consequence, sharp diffraction spots can occur but are unable to be described by 230 crystallographic space groups in both real and reciprocal spaces. There are three types of quasicrystals: one-, two- and three-dimensional quasicrystals. In one-dimensional quasicrystals, the quasiperiodic arrangement of atoms is along one direction, while the plane perpendicular to which has a regular two-dimensional periodic arrangement.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Abe, E., Yan, Y., Pennycook, S.J.: Quasicrystals as cluster aggregates. Nat. Mater. 3, 759–767 (2004)ADSCrossRef Abe, E., Yan, Y., Pennycook, S.J.: Quasicrystals as cluster aggregates. Nat. Mater. 3, 759–767 (2004)ADSCrossRef
2.
go back to reference Yamamoto, A.: Crystallography of quasiperiodic crystals. Acta Crystallogr. A 52, 509–560 (1996)CrossRef Yamamoto, A.: Crystallography of quasiperiodic crystals. Acta Crystallogr. A 52, 509–560 (1996)CrossRef
3.
go back to reference Graef, M.D., Mchenry, M.E.: Structure of Materials: an Introduction to Crystallography, Diffraction and Symmetry, 2nd edn. Cambridge University Press, Cambridge (2012)CrossRef Graef, M.D., Mchenry, M.E.: Structure of Materials: an Introduction to Crystallography, Diffraction and Symmetry, 2nd edn. Cambridge University Press, Cambridge (2012)CrossRef
4.
go back to reference Zeng, X., Ungar, G., Liu, Y., Percec, V., Dulcey As, E., Hobbs, J.K.: Supramolecular dendritic liquid quasicrystals. Nature 428, 157–160 (2004)ADSCrossRef Zeng, X., Ungar, G., Liu, Y., Percec, V., Dulcey As, E., Hobbs, J.K.: Supramolecular dendritic liquid quasicrystals. Nature 428, 157–160 (2004)ADSCrossRef
5.
go back to reference Gillard, T.M., Lee, S., Bates, F.S.: Dodecagonal quasicrystalline order in a diblock copolymer melt. Proc. Natl. Acad. Sci. 113, 5167–5172 (2016)ADSCrossRef Gillard, T.M., Lee, S., Bates, F.S.: Dodecagonal quasicrystalline order in a diblock copolymer melt. Proc. Natl. Acad. Sci. 113, 5167–5172 (2016)ADSCrossRef
6.
go back to reference Ye, X., Chen, J., Eric Irrgang, M., Engel, M., Dong, A., Glotzer, S.C., Murray, C.B.: Quasicrystalline nanocrystal superlattice with partial matching rules. Nat. Mater. 16, 214–219 (2017)ADSCrossRef Ye, X., Chen, J., Eric Irrgang, M., Engel, M., Dong, A., Glotzer, S.C., Murray, C.B.: Quasicrystalline nanocrystal superlattice with partial matching rules. Nat. Mater. 16, 214–219 (2017)ADSCrossRef
7.
go back to reference Yue, K., Huang, M., Marson, R.L., He, J., Huang, J., Zhou, Z., Wang, J., Liu, C., Yan, X., Wu, K., Guo, Z., Liu, H., Zhang, W., Ni, P., Wesdemiotis, C., Zhang, W.B., Glotzer, S.C., Cheng, S.Z.D.: Geometry induced sequence of nanoscale Frank-Kasper and quasicrystal mesophases in giant surfactants. Proc. Natl. Acad. Sci. 113, 14195–14200 (2016)ADSCrossRef Yue, K., Huang, M., Marson, R.L., He, J., Huang, J., Zhou, Z., Wang, J., Liu, C., Yan, X., Wu, K., Guo, Z., Liu, H., Zhang, W., Ni, P., Wesdemiotis, C., Zhang, W.B., Glotzer, S.C., Cheng, S.Z.D.: Geometry induced sequence of nanoscale Frank-Kasper and quasicrystal mesophases in giant surfactants. Proc. Natl. Acad. Sci. 113, 14195–14200 (2016)ADSCrossRef
8.
go back to reference Feng, X., Liu, G., Guo, D., Lang, K., Zhang, R., Huang, J., Su, Z., Li, Y., Huang, M., Li, T., Cheng, S.Z.D.: Transition kinetics of self-assembled supramolecular dodecagonal quasicrystal and Frank-Kasper σ Phases in ABn Dendron-like giant molecules. ACS Macro Lett. 8, 875–881 (2019)CrossRef Feng, X., Liu, G., Guo, D., Lang, K., Zhang, R., Huang, J., Su, Z., Li, Y., Huang, M., Li, T., Cheng, S.Z.D.: Transition kinetics of self-assembled supramolecular dodecagonal quasicrystal and Frank-Kasper σ Phases in ABn Dendron-like giant molecules. ACS Macro Lett. 8, 875–881 (2019)CrossRef
9.
go back to reference Ungar, G., Zeng, X.: Frank-Kasper, quasicrystalline and related phases in liquid crystals. Soft Matter 1, 95–106 (2005)ADSCrossRef Ungar, G., Zeng, X.: Frank-Kasper, quasicrystalline and related phases in liquid crystals. Soft Matter 1, 95–106 (2005)ADSCrossRef
10.
go back to reference Ishimasa, T.: Dodecagonal quasicrystals still in progress. Isr. J. Chem. 51, 1216–1225 (2011)CrossRef Ishimasa, T.: Dodecagonal quasicrystals still in progress. Isr. J. Chem. 51, 1216–1225 (2011)CrossRef
11.
go back to reference Baake, M., Klitzing, R., Schlottman, M.: Fractally shaped acceptance domains of quasiperiodic square-triangle tilings with dodecagonal symmetry. Physica A 191, 554–558 (1992)ADSMathSciNetCrossRef Baake, M., Klitzing, R., Schlottman, M.: Fractally shaped acceptance domains of quasiperiodic square-triangle tilings with dodecagonal symmetry. Physica A 191, 554–558 (1992)ADSMathSciNetCrossRef
12.
go back to reference Oxborrow, M., Henley, C.: Random square-triangle tilings: a model for twelvefold-symmetric quasicrystals. Phys. Rev. B 48, 6966–6998 (1993)ADSCrossRef Oxborrow, M., Henley, C.: Random square-triangle tilings: a model for twelvefold-symmetric quasicrystals. Phys. Rev. B 48, 6966–6998 (1993)ADSCrossRef
13.
go back to reference Leung, P., Henley, C., Chester, G.: Dodecagonal order in a two-dimensional Lennard-Jones system. Phys. Rev. B 39, 446–458 (1989)ADSMathSciNetCrossRef Leung, P., Henley, C., Chester, G.: Dodecagonal order in a two-dimensional Lennard-Jones system. Phys. Rev. B 39, 446–458 (1989)ADSMathSciNetCrossRef
14.
go back to reference Asai, Y., Takano, A., Matsushita, Y.: Creation of cylindrical morphologies with extremely large oblong unit lattices from ABC block terpolymer blends. Macromolecules 48, 1538–1542 (2015)ADSCrossRef Asai, Y., Takano, A., Matsushita, Y.: Creation of cylindrical morphologies with extremely large oblong unit lattices from ABC block terpolymer blends. Macromolecules 48, 1538–1542 (2015)ADSCrossRef
15.
go back to reference Hayashida, K., Dotera, T., Takano, A., Matsushita, Y.: polymeric quasicrystal: mesoscopic quasicrystalline tiling in star polymers. Phys. Rev. Lett. 98, 195502 (2007) Hayashida, K., Dotera, T., Takano, A., Matsushita, Y.: polymeric quasicrystal: mesoscopic quasicrystalline tiling in star polymers. Phys. Rev. Lett. 98, 195502 (2007)
16.
go back to reference Zeng, X., Kieffer, R., Glettner, B., Nurnberger, C., Liu, F., Pelz, K., Prehm, M., Baumeister, U., Hahn, H., Lang, H., Gehring, G.A., Weber, C.H.M., Hobbs, J.K., Tschierske, C., Ungar, G.: Complex multicolor tilings and critical phenomena in tetraphilic liquid crystals. Science 331, 1302–1306 (2011)ADSCrossRef Zeng, X., Kieffer, R., Glettner, B., Nurnberger, C., Liu, F., Pelz, K., Prehm, M., Baumeister, U., Hahn, H., Lang, H., Gehring, G.A., Weber, C.H.M., Hobbs, J.K., Tschierske, C., Ungar, G.: Complex multicolor tilings and critical phenomena in tetraphilic liquid crystals. Science 331, 1302–1306 (2011)ADSCrossRef
17.
go back to reference Nagaoka, Y., Zhu, H., Eggert, D., Chen, O.: Single-component quasicrystalline nanocrystal superlattices through flexible polygon tiling rule. Science 362, 1396–1400 (2018)ADSMathSciNetCrossRef Nagaoka, Y., Zhu, H., Eggert, D., Chen, O.: Single-component quasicrystalline nanocrystal superlattices through flexible polygon tiling rule. Science 362, 1396–1400 (2018)ADSMathSciNetCrossRef
18.
go back to reference Fischer, S., Exner, A., Zielske, K., Perlich, J., Deloudi, S., Steurer, W., Lindner, P., Foerster, S.: Colloidal quasicrystals with 12-fold and 18-fold diffraction symmetry. Proc. Nat. Acad. Sci. 108, 1810–1814 (2011)ADSCrossRef Fischer, S., Exner, A., Zielske, K., Perlich, J., Deloudi, S., Steurer, W., Lindner, P., Foerster, S.: Colloidal quasicrystals with 12-fold and 18-fold diffraction symmetry. Proc. Nat. Acad. Sci. 108, 1810–1814 (2011)ADSCrossRef
19.
go back to reference Engel, M., DamascenoP, F., Phillips, C.L., Glotzer, S.C.: Computational self-assembly of a one-component icosahedral quasicrystal. Nat. Mater. 14, 109–116 (2014)ADSCrossRef Engel, M., DamascenoP, F., Phillips, C.L., Glotzer, S.C.: Computational self-assembly of a one-component icosahedral quasicrystal. Nat. Mater. 14, 109–116 (2014)ADSCrossRef
20.
go back to reference de Nijs, B., Dussi, S., Smallenburg, F., Meeldijk, J.D., Groenendijk, D.J., Filion, L., Imhof, A., van Blaaderen, A., Dijkstra, M.: Entropy-driven formation of large icosahedral colloidal clusters by spherical confinement. Nat. Mater. 14, 56–60 (2015)ADSCrossRef de Nijs, B., Dussi, S., Smallenburg, F., Meeldijk, J.D., Groenendijk, D.J., Filion, L., Imhof, A., van Blaaderen, A., Dijkstra, M.: Entropy-driven formation of large icosahedral colloidal clusters by spherical confinement. Nat. Mater. 14, 56–60 (2015)ADSCrossRef
21.
go back to reference Lifshitz, R., Diamant, H.: Soft quasicrystals-Why are they stable? Phil. Mag. 87, 3021–3030 (2007)ADSCrossRef Lifshitz, R., Diamant, H.: Soft quasicrystals-Why are they stable? Phil. Mag. 87, 3021–3030 (2007)ADSCrossRef
22.
go back to reference Barkan, K., Diamant, H., Lifshitz, R.: Stability of quasicrystals composed of soft isotropic particles, Phys. Rev. B 83, 172201 (2011) Barkan, K., Diamant, H., Lifshitz, R.: Stability of quasicrystals composed of soft isotropic particles, Phys. Rev. B 83, 172201 (2011)
23.
go back to reference Fan, T.Y., Sun, J.J.: Four phonon model for studying thermodynamics of soft-matter quasicrystals. Phil. Mag. Lett. 94, 112–117 (2014)ADSCrossRef Fan, T.Y., Sun, J.J.: Four phonon model for studying thermodynamics of soft-matter quasicrystals. Phil. Mag. Lett. 94, 112–117 (2014)ADSCrossRef
24.
go back to reference Fan, T.Y.: Equation system of generalized hydrodynamics of soft-matter quasicrystals. Appl. Math Mech. 37, 331–347, in Chinese (2016); arXiv:1908.06425[cond-mat.soft]. 15 Oct 2019 Fan, T.Y.: Equation system of generalized hydrodynamics of soft-matter quasicrystals. Appl. Math Mech. 37, 331–347, in Chinese (2016); arXiv:1908.06425[cond-mat.soft]. 15 Oct 2019
25.
go back to reference Cheng, H., Fan, T.Y.: Dynamics of decagonal soft-matter quasicrystals. Sci. China-Phys. Mech. Astron. submitted (2021) Cheng, H., Fan, T.Y.: Dynamics of decagonal soft-matter quasicrystals. Sci. China-Phys. Mech. Astron. submitted (2021)
26.
go back to reference Cheng, H., Fan, T.Y., Wei, H.: Solutions of hydrodynamics of quasicrystals with 5- and 10-fold symmetry. Appl. Math. Mech. 37, 1393–1404 (2016)CrossRef Cheng, H., Fan, T.Y., Wei, H.: Solutions of hydrodynamics of quasicrystals with 5- and 10-fold symmetry. Appl. Math. Mech. 37, 1393–1404 (2016)CrossRef
27.
go back to reference de Gennes, P.D.: Soft matter. Mod. Phys. Rev. 64,544–548 (1992); Angw. Chem. 31, 842–845 (1992) de Gennes, P.D.: Soft matter. Mod. Phys. Rev. 64,544–548 (1992); Angw. Chem. 31, 842–845 (1992)
28.
go back to reference Witten, T.A., Pincus, P.A.: Structured Fluids: Polymers Colloids, Surfactants. Oxford University Press, New York (2004) Witten, T.A., Pincus, P.A.: Structured Fluids: Polymers Colloids, Surfactants. Oxford University Press, New York (2004)
29.
go back to reference Kleman, M.: Soft Matter Physics: An Introduction. Springer, Berlin (2003) Kleman, M.: Soft Matter Physics: An Introduction. Springer, Berlin (2003)
30.
go back to reference Motiv, M.: Sensitive Matter: Foams Gels, Liquid Crystals and Other Materials. Harvard University Press, New York (2010) Motiv, M.: Sensitive Matter: Foams Gels, Liquid Crystals and Other Materials. Harvard University Press, New York (2010)
31.
go back to reference Israelachvili, N.J.: Intermolecular and Surface Forces. Academic Press, New York (2010) Israelachvili, N.J.: Intermolecular and Surface Forces. Academic Press, New York (2010)
32.
go back to reference Lifshitz, E.M., Pitaevskii, L.: Statistical Physics, Part 2. Pergamon, Oxford (1980) Lifshitz, E.M., Pitaevskii, L.: Statistical Physics, Part 2. Pergamon, Oxford (1980)
33.
go back to reference Fan, T.Y., Tang, Z.Y.: Three-dimensional generalized dynamics of soft-matter quasicrystals. Appl. Math. Mech. 38, 1195–1207 (2017), in Chinese; Adv. Mat. Sci. Eng. 2020, Article 1D 4875854 (2020) Fan, T.Y., Tang, Z.Y.: Three-dimensional generalized dynamics of soft-matter quasicrystals. Appl. Math. Mech. 38, 1195–1207 (2017), in Chinese; Adv. Mat. Sci. Eng. 2020, Article 1D 4875854 (2020)
34.
go back to reference Fan, T.Y.: Generalized hydrodynamics of soft-matter second kind of two-dimensional quasicrystals. Appl. Math. Mech. 38, 189–199, in Chinese (2017); arXiv: 1908.06430[cond-mat.soft]. 15 Oct 2019 Fan, T.Y.: Generalized hydrodynamics of soft-matter second kind of two-dimensional quasicrystals. Appl. Math. Mech. 38, 189–199, in Chinese (2017); arXiv: 1908.06430[cond-mat.soft]. 15 Oct 2019
35.
go back to reference Hu, C.Z., Ding, D.H., Yang, W.G., Wang, R.H.: Possible two-dimensional quasicrystals structures with six-dimensional embedding space. Phys. Rev. B 49, 9423–9427 (1994) Hu, C.Z., Ding, D.H., Yang, W.G., Wang, R.H.: Possible two-dimensional quasicrystals structures with six-dimensional embedding space. Phys. Rev. B 49, 9423–9427 (1994)
36.
go back to reference Tang, Z.Y., Fan, T.Y.: Point groups and group representation theory of second kind of two-dimensional quasicrystals, unpublished work (2017) Tang, Z.Y., Fan, T.Y.: Point groups and group representation theory of second kind of two-dimensional quasicrystals, unpublished work (2017)
Metadata
Title
Discovery of Soft-Matter Quasicrystals and Their Properties
Authors
Tian-You Fan
Wenge Yang
Hui Cheng
Xiao-Hong Sun
Copyright Year
2022
Publisher
Springer Nature Singapore
DOI
https://doi.org/10.1007/978-981-16-6628-5_2

Premium Partners