TY - JOUR
T1 - New perspectives on forbidden symmetries, quasicrystals, and Penrose tilings
AU - Steinhardt, Paul Joseph
PY - 1996/12/10
Y1 - 1996/12/10
N2 - Quasicrystals are solids with quasiperiodic atomic structures and symmetries forbidden to ordinary periodic crystals - e.g., 5-fold symmetry axes. A powerful model for understanding their structure and properties has been the two-dimensional Penrose tiling. Recently discovered properties of Penrose tilings suggest a simple picture of the structure of quasicrystals and shed new light on why they form. The results show that quasicrystals can be constructed from a single repeating cluster of atoms and that the rigid matching rules of Penrose tilings can be replaced by more physically plausible cluster energetics. The new concepts make the conditions for forming quasicrystals appear to be closely related to the conditions for forming periodic crystals.
AB - Quasicrystals are solids with quasiperiodic atomic structures and symmetries forbidden to ordinary periodic crystals - e.g., 5-fold symmetry axes. A powerful model for understanding their structure and properties has been the two-dimensional Penrose tiling. Recently discovered properties of Penrose tilings suggest a simple picture of the structure of quasicrystals and shed new light on why they form. The results show that quasicrystals can be constructed from a single repeating cluster of atoms and that the rigid matching rules of Penrose tilings can be replaced by more physically plausible cluster energetics. The new concepts make the conditions for forming quasicrystals appear to be closely related to the conditions for forming periodic crystals.
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U2 - 10.1073/pnas.93.25.14267
DO - 10.1073/pnas.93.25.14267
M3 - Article
C2 - 8962037
AN - SCOPUS:0029965051
VL - 93
SP - 14267
EP - 14270
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
SN - 0027-8424
IS - 25
ER -