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QUASICRYSTALS The end of the beginning Cesar Pay
Gómez
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Outline

• History of Quasicrystals
• Where are the atoms?
• Past, present and future

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Dan Shechtman

• The Nobel Prize in Chemistry 2011 is awarded to
• Dan Shechtman
• for the discovery of quasicrystals.

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Crystal
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The discovery
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Crystal
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Quasicrystals

• Long-range ordered, aperiodic crystals with sharp
  diffraction peaks.
• Exhibit crystallographically forbidden symmetries
  (such as 5-, 8-, 10- or 12-fold rotational
  symmetry)
• Lack periodicity (no unit cell) in 3 dimensions.
• The diffraction patterns cannot be indexed with 3
  integers (6 are needed for icosahedral QCs).
• The structures can be described as projections
  from a high dimensional space.

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Quasicrystals

• Long-range ordered, aperiodic crystals with sharp
  diffraction peaks.
• Exhibit crystallographically forbidden symmetries
  (such as 5-, 8-, 10- or 12-fold rotational
  symmetry)
• Lack periodicity (no unit cell) in 3 dimensions.
• The diffraction patterns cannot be indexed with 3
  integers (6 are needed for icosahedral QCs).
• The structures can be described as projections
  from a high dimensional space.

Shechtman et al. Phys. Rev. Lett., 53, 1951 (1984)
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Quasicrystals

• Long-range ordered, aperiodic crystals with sharp
  diffraction peaks.
• Exhibit crystallographically forbidden symmetries
  (such as 5-, 8-, 10- or 12-fold rotational
  symmetry)
• Lack periodicity (no unit cell) in 3 dimensions.
• The diffraction patterns cannot be indexed with 3
  integers (6 are needed for icosahedral QCs).
• The structures can be described as projections
  from a high dimensional space.

Shechtman et al. Phys. Rev. Lett., 53, 1951 (1984)
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Quasicrystals

• Long-range ordered, aperiodic crystals with sharp
  diffraction peaks.
• Exhibit crystallographically forbidden symmetries
  (such as 5-, 8-, 10- or 12-fold rotational
  symmetry)
• Lack periodicity (no unit cell) in 3 dimensions.
• The diffraction patterns cannot be indexed with 3
  integers (6 are needed for icosahedral QCs).
• The structures can be described as projections
  from a high dimensional space.

Shechtman et al. Phys. Rev. Lett., 53, 1951 (1984)
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Icosahedral Quasicrystals
Quenched Al-Mn alloy
Icosahedron
Shechtman et al. Phys. Rev. Lett., 53, 1951 (1984)
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QC families
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Approximants

• Conventional crystals with periodic long-range
  order and 3D unit cells.
• Should have similar compositions and local atomic
  arrangements (clusters) as the quasicrystals.
• The structures can be solved by standard
  diffraction techiques.

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Where are the atoms?
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Building blocks and linkages in Yb-Cd type
approximants
2/1 approximant Yb13Cd76
1/1 approximant YbCd6
H. Takakura, C. Pay Gómez, A. Yamamoto, M. de
Boissieu, A. P. Tsai Nature Materials. 2007, 6,
58 C. Pay Gómez, S. Lidin Angew. Chem., Int.
Ed. Engl. 2001, 40, 4037
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C. Pay Gómez, S. Lidin Angew. Chem., Int. Ed.
Engl. 2001, 40, 4037
Qisheng Lin, John D. Corbett, Proc. Nat. Acad.
Sci. 2006, 103, 13589
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QC families
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Conclusions

• Due to the discovery of QCs, the definition of
  crystal had to be changed.
• QCs have long-range order but lack periodicity in
  3D space.
• Approximants are normal crystals containing the
  same atomic clusters as QCs.
• Icosahedral QCs can be described as periodic
  structures in 6D space.

Thank you!