Quasicrystals: What are they, and why do they exist? Outline • What is a crystal? – Symmetries, periodicity, (quasiperiodicity) • How can you tell for sure? – Diffraction patterns, indexing • Higher-dimensional representation – Cut and project – phason fluctuations + diffuse scattering • Thermodynamic stability
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Quasicrystals: What are they, and why do they exist? Outline What is a crystal? –Symmetries, periodicity, (quasiperiodicity) How can you tell for sure?
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Quasicrystals: What are they, and why do they exist?
Outline• What is a crystal?
– Symmetries, periodicity, (quasiperiodicity)
• How can you tell for sure?– Diffraction patterns, indexing
Shared tile edge types must match to achieve perfect quasiperiodicity
Levine and Steinhardt proposed as mechanism of stability
Bachelor Hall, Miami University of Ohio, 1979
Storey Hall, Royal Melbourne Institute of Technology (1998)
Penrose Quilt, Newbold (2005) Penrosette doily, Jason (1999)
Penrose arts & crafts
(C.S. Kaplan)
“The Pentalateral Commission”“Busby Berkeley Chickens”
Penrose “Escher” designs
Toys: ZomeTool® and SuperMag®
“True technological advances are welcome in any field. Cybernox stick-resistant cookware is such an advance. The cooking surface of Cybernox pans is Quasi-Crystal, a patented metal alloy that is super hard (10 times harder than stainless steel), extremely durable, distributes heat rapidly and evenly, and has low adhesion properties. The French government owns the patent, and ……”