Constructing Penrose-like tilings from a single prototile and the implications for quasicrystals

Journal Article · Fri Jan 31 23:00:00 EST 1997 · Physical Review, B: Condensed Matter

DOI:https://doi.org/10.1103/PhysRevB.55.3520· OSTI ID:489110

Jeong, H ^[1]; Steinhardt, P J ^[2]

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1. Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (United States)
2. Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (United States)

We present two sets of rules for constructing quasiperiodic tilings that suggest a simpler structural model of quasicrystals and a more plausible explanation of why quasicrystals form. First, we show that quasiperiodic tilings can be constructed from a single prototile with matching rules which constrain the way that neighbors can overlap. Second, we show that maximizing the density of a certain cluster of fat and thin tiles can force a Penrose tiling without imposing the usual Penrose matching rules. {copyright} {ital 1997} {ital The American Physical Society}

• Research Organization: University of Pennsylvania
• DOE Contract Number: AC02-76ER03071
• OSTI ID: 489110
• Journal Information: Physical Review, B: Condensed Matter, Journal Name: Physical Review, B: Condensed Matter Journal Issue: 6 Vol. 55; ISSN PRBMDO; ISSN 0163-1829
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ANHARMONIC CRYSTALS
ATOMIC CLUSTERS
GROUND STATES
STRUCTURAL MODELS
THERMODYNAMICS