A long-range hierarchical clustering model for constructing perfect quasicrystalline formations

References

• Shechtman , D , Blech , I , Gratias , D and Cahn , JW . 1984 . Phys. Rev. Lett. , 53 : 1951
   Web of Science ®Google Scholar
• Levine , D and Steinhardt , P . 1986 . Phys. Rev. B , 34 : 596
   PubMed Web of Science ®Google Scholar
• Yamamoto , A and Takakura , H . 2008 . “ Recent development of quasicrystallography ” . In Quasicrystals , Edited by: Fujiwara , T and Ishii , Y . 11 Amsterdam : Elsevier .
   Google Scholar
• Boissieu , M , Currat , R and Francoual , S . 2008 . “ Phason modes in aperiodic crystals ” . In Quasicrystals , Edited by: Fujiwara , T and Ishii , Y . 107 Amsterdam : Elsevier .
   Google Scholar
• Ishii , Y and Fujiwara , T . 2008 . “ Electronic structures and stability of quasicrystals ” . In Quasicrystals , Edited by: Fujiwara , T and Ishii , Y . 171 Amsterdam : Elsevier .
   Google Scholar
• Mikhael , J , Roth , J , Helden , L and Bechinger , C . 2008 . Nature , 454 : 501
   PubMed Web of Science ®Google Scholar
• Dubois , J . 2002 . “ Bulk and surface properties of quasicrystalline materials and their potential applications ” . In Quasicrystals: An Introduction to Structure, Physical Properties, and Applications , Edited by: Suck , J-B , Schreiber , M and Haussler , P . Vol. 55 , 507 Berlin : Springer-Verlag .
   Google Scholar
• Tsai , A and Gomez , CP . 2008 . “ Quasicrystals and approximants in Cd–M systems and related alloys ” . In Quasicrystals , Edited by: Fujiwara , T and Ishii , Y . 75 Amsterdam : Elsevier .
   Google Scholar
• Penrose , R . 1974 . Bull. Inst. Math. Appl. , 10 : 266
   Google Scholar
• Steinhardt , PJ . 2008 . Nature , 452 : 43
   PubMed Web of Science ®Google Scholar
• Keys , AS and Glotzer , SC . 2007 . Phys. Rev. Lett. , 99 : 235503
   PubMed Web of Science ®Google Scholar
• Peterson , I . 1996 . Sci. News , 15 : 232
   Google Scholar
• Senechal , M . 1995 . Quasicrystals and Geometry , New York : Cambridge University Press .
   Google Scholar
• Grunbaum , B and Shephard , GC . 1987 . Tilings and Patterns , New York : W.H. Freeman and Co. .
   Google Scholar
• W.F. Lunnon and P.A.B. Pleasants, J. Math. Pure Appl. (9) 66 (1987).
   Google Scholar
• de Bruijn , NG . 1981 . Indag. Math. (N.S.) , 43 : 53
   Google Scholar
• Gummelt , P . 1996 . Geom. Dedicata , 62 : 1
   Web of Science ®Google Scholar
• Steinhardt , PJ and Jeong , HC . 1996 . Nature , 382 : 433
   Web of Science ®Google Scholar
• de Bruijn , NG . 1981 . Indag. Math. (N.S.) , 43 : 27
   Google Scholar
• Kramer , P . 1982 . Acta Crystallogr. A , 38 : 257
   Web of Science ®Google Scholar
• Bak , P . 1986 . Phys. Rev. Lett. , 56 : 861
   PubMed Web of Science ®Google Scholar
• Socolar , JES , Steinhardt , PJ and Levine , D . 1985 . Phys. Rev. B , 32 : 5547
   Web of Science ®Google Scholar
• Abe , E , Yan , Y and Pennycook , SJ . 2004 . Nat. Mater. , 3 : 759
   PubMed Web of Science ®Google Scholar
• Lord , EA , Ranganathan , S and Kulkarni , UD . 2000 . Curr. Sci. , 78 ( 1 ) : 64
   Web of Science ®Google Scholar