Quasicrystal / crystal real-space structure
Diffraction pattern — |F̃(k)|² (log scale)
Structure
Quasicrystal facts:
• Long-range order but no periodicity
• Sharp Bragg peaks (like crystal)
• Forbidden symmetries (5,8,10,12-fold)
• Shechtman 1984 — Nobel Prize 2011
• Projection of 5D periodic lattice → 2D
Crystal: peaks on periodic reciprocal lattice
Quasicrystal: peaks dense, all sharp
Amorphous: diffuse rings only
• Long-range order but no periodicity
• Sharp Bragg peaks (like crystal)
• Forbidden symmetries (5,8,10,12-fold)
• Shechtman 1984 — Nobel Prize 2011
• Projection of 5D periodic lattice → 2D
Crystal: peaks on periodic reciprocal lattice
Quasicrystal: peaks dense, all sharp
Amorphous: diffuse rings only