1989 Fiscal Year Annual Research Report

準結晶の構造とその秩序化過程の理論的研究

Research Project

Project/Area Number	01630002
Research Institution	University of Tsukuba
Principal Investigator	小川泰筑波大学, 物理工学系, 教授 (10025364)
Co-Investigator(Kenkyū-buntansha)	宮島佐介中部大学, 工学部, 教授 (80029173) 米沢富美子慶応義塾大学, 理工学部, 教授 (10027344) 石井靖東京大学, 物性研究所, 助手 (60143541) 渡辺泰成理化学研究所, 研究員 (70087401) 新関駒二郎東北大学, 理学部, 助教授 (90004407)
Keywords	準結晶 / ペンローズ・タイリング / 非周期秩序 / フェイゾン / 秩序化過程 / グラフ測地線 / パーコレーション / フラクタル
Research Abstract	石井は、準結晶におけるフェイゾン歪みの理論を発展させた。従来の構造の理論的研究は、幾何学的側面に偏りがちであったが、群論に基づくこの研究によって、実験事実の構造解析の一つの手段が得られたといえよう。新関は、同じく群論的な対称性の議論から、射影法による2・3次元準結晶構造について、局所対称構造の変換性の分類を行った。電子状態の研究にも役立つ研究であり、今後の発展が期待される。また、原子が理想配置からずれている場合の回析強度を計算する一般式を導いた。渡辺らは、以前から立方対称性をもち、射影物が8回対称となるような新しい型の準結晶の可能性を研究していたが、デフレーション則の発見に成功した。宮島らは、いろいろなモデルについて、2次元の5回あるいは10回対称構造の成長のシミュレーションを行った。ある種の方向秩序は得られるが、準結晶的な長距離秩序を成長させるには、長距離の位置相関を強いるような特別な相互作用が必要と思われる。川崎らは、準結晶におけるフェイゾン凍結をはじめ、さまざまな系における秩序化過程の研究を行った。米沢らは、準結晶における電子状態、パーコレーションの研究を行った。小川は、二次元の三角形綱を特徴づける一般的な方法として、グラフ測地線という概念を導入し、ペンローズ構造に適用したみた。中間距離での構造のゆらぎが浮き彫りされる。また正20面体的な対称性をもつ調和関数を求めたり、フラクタルをタイリングの観点からとらえるなど、形の科学の観点からの研究を行った。

Research Products
(25 results)

All Other

All Publications (25 results)

[Publications] Masahiro Inoue: "Theory of Self-Similarity in Reflectiveity Spectrum of Thue-Morse Superlattice" Solid State Communications. 71. 631-739 (1989)
[Publications] 小川泰: "空間分割とフラクタル" 統計数理. 37. 107-117 (1989)
[Publications] Komajiro Niizeki: "A Classification of Special Points of Quasilattices in Two Dimensions" J.Phys.A:Math.Gen.22. 4281-4293 (1989)
[Publications] Komajiro Niizeki: "A Classification of Special Points of Icosahedral Quasilattices" J.Phys.A:Math.Gen.22. 4295-4302 (1989)
[Publications] Komajiro Niizeki: "The Reciprocal Space Properties and Localization Properties of the Electronic Wave Functions in Quasicrystals" Journal of Noncrystalline Solids.
[Publications] Tohru Ogawa: "Chains,Flowers,Rings and Peanuts-Graphical Geodesic Line and Its Application to Penrose Tiling" “Quasicrystals"Ed,T.Fujiwara and T.Ogawa(Springer). (1990)
[Publications] Yutaka Okabe: "Monte Calro Study of spin Statistics in Two-and Three-Dimensional Quasicrystals" “Quasicrystals"Ed.T.fujiwara and T.Ogawa(Springer Ser.Mat.Sci.). (1990)
[Publications] Yasunari Watanabe: "Modeling of Quasicrystal" Proc.Third Int.Conf.on Quasicrystal and Incommensurate Structure. (1990)
[Publications] Tohru Ogawa: "Ehrenfest Process,A Rational Representation of Spin Operators and Explicit Forms of Rotational Operators-Miscellaneous in Preparing Tools Towards Icosahedral Harmonics" “Quasicrystals"Ed.T.Fujiwara and T.Ogawa(Springer Ser.Mat.Sci.). (1990)
[Publications] Sasuke Miyajima: "A Simulation Approach to Form a Quasicrystal" Journal of Physical Cociety ofJapan.
[Publications] Yasushi Ishi: "Mode-locking in Quasicrystals" Physical Review B. 39. 11862-11871 (1989)
[Publications] Yasushi Ishii: "Structural Modulation Iduced by Phasons in Quasicrystals" J.Non-cryst.Solids.
[Publications] Yasushi Ishii: "Elastic Instability Induced by Phasons in Icosahedral Quasicrystals" “Quasicrystals"Ed.T.Fujiwara and T.Ogawa(Springer Ser.Mat.Sci.).
[Publications] Ken Sekimoto: "Phason Freezing" “Quasicrystals"Ed.T.Fujiwara and T.Ogawa(Springer Ser.Mat.Sci.).
[Publications] Katsuya Nakashima: "Scaling Behavior of Two-Dimensional Domain Growth:Computor Simulation of Vertex Models" Journal of Statistical Physics. 57. 759-787 (1989)
[Publications] Kyoji Kawasaki: "Vertex Models for Two-Dimensional Grain Growth" Philosophical Magazine B. 60. 399-421 (1989)
[Publications] Ken Sekimoto: "Sponge-like Domain Structure of Two-Dimensional Model Gel System Undergoing Volume-Phase Transition" Physical Review A. 39. 4912-4915 (1989)
[Publications] Ken Sekimoto: "Elastic Instabilities and Phase Coexistence of Gels" Phisica A. 154. 389-420 (1989)
[Publications] Tatsuya Nagao: "A Formulation of Electronic Properties in Quasicrystals-Transformation to the Study of Higher Dimensional Periodic Lattice" Journal of Physics C.
[Publications] 長尾辰哉: "準結晶の電子状態ー高次元への拡張ー" 固体物理. 25. 46-52 (1990)
[Publications] Fumiko Yonezawa: "Theoretical Study of Metal-Nonmetal Transition in Microclusters" J.Non-cryst,Solids.
[Publications] Shoichi Sakamoto: "Molecular Orbital Study for Electronic Structures of Metallic Microclusters" J.Non-cryst.Solids.
[Publications] Fumiko Yonezawa: "Theoretical Study for Electronic Structure of Metallic Microcluster" J.Non-cryst.Solids.
[Publications] 小川泰: "フラクタルとは何か" 岩波書店, (1989)
[Publications] Takeo Fujiwara(Ed.): "“Quasicrystals"" Springer(Springer Ser.Mat.Sci.),

1989 Fiscal Year Annual Research Report

準結晶の構造とその秩序化過程の理論的研究

Principal Investigator

小川 泰 筑波大学, 物理工学系, 教授 (10025364)

Research Products

[Publications] Masahiro Inoue: "Theory of Self-Similarity in Reflectiveity Spectrum of Thue-Morse Superlattice" Solid State Communications. 71. 631-739 (1989)

[Publications] 小川泰: "空間分割とフラクタル" 統計数理. 37. 107-117 (1989)

[Publications] Komajiro Niizeki: "A Classification of Special Points of Quasilattices in Two Dimensions" J.Phys.A:Math.Gen.22. 4281-4293 (1989)

[Publications] Komajiro Niizeki: "A Classification of Special Points of Icosahedral Quasilattices" J.Phys.A:Math.Gen.22. 4295-4302 (1989)

[Publications] Komajiro Niizeki: "The Reciprocal Space Properties and Localization Properties of the Electronic Wave Functions in Quasicrystals" Journal of Noncrystalline Solids.

[Publications] Tohru Ogawa: "Chains,Flowers,Rings and Peanuts-Graphical Geodesic Line and Its Application to Penrose Tiling" “Quasicrystals"Ed,T.Fujiwara and T.Ogawa(Springer). (1990)

[Publications] Yutaka Okabe: "Monte Calro Study of spin Statistics in Two-and Three-Dimensional Quasicrystals" “Quasicrystals"Ed.T.fujiwara and T.Ogawa(Springer Ser.Mat.Sci.). (1990)

[Publications] Yasunari Watanabe: "Modeling of Quasicrystal" Proc.Third Int.Conf.on Quasicrystal and Incommensurate Structure. (1990)

[Publications] Tohru Ogawa: "Ehrenfest Process,A Rational Representation of Spin Operators and Explicit Forms of Rotational Operators-Miscellaneous in Preparing Tools Towards Icosahedral Harmonics" “Quasicrystals"Ed.T.Fujiwara and T.Ogawa(Springer Ser.Mat.Sci.). (1990)

[Publications] Sasuke Miyajima: "A Simulation Approach to Form a Quasicrystal" Journal of Physical Cociety ofJapan.

[Publications] Yasushi Ishi: "Mode-locking in Quasicrystals" Physical Review B. 39. 11862-11871 (1989)

[Publications] Yasushi Ishii: "Structural Modulation Iduced by Phasons in Quasicrystals" J.Non-cryst.Solids.

[Publications] Yasushi Ishii: "Elastic Instability Induced by Phasons in Icosahedral Quasicrystals" “Quasicrystals"Ed.T.Fujiwara and T.Ogawa(Springer Ser.Mat.Sci.).

[Publications] Ken Sekimoto: "Phason Freezing" “Quasicrystals"Ed.T.Fujiwara and T.Ogawa(Springer Ser.Mat.Sci.).

[Publications] Katsuya Nakashima: "Scaling Behavior of Two-Dimensional Domain Growth:Computor Simulation of Vertex Models" Journal of Statistical Physics. 57. 759-787 (1989)

[Publications] Kyoji Kawasaki: "Vertex Models for Two-Dimensional Grain Growth" Philosophical Magazine B. 60. 399-421 (1989)

[Publications] Ken Sekimoto: "Sponge-like Domain Structure of Two-Dimensional Model Gel System Undergoing Volume-Phase Transition" Physical Review A. 39. 4912-4915 (1989)

[Publications] Ken Sekimoto: "Elastic Instabilities and Phase Coexistence of Gels" Phisica A. 154. 389-420 (1989)

[Publications] Tatsuya Nagao: "A Formulation of Electronic Properties in Quasicrystals-Transformation to the Study of Higher Dimensional Periodic Lattice" Journal of Physics C.

[Publications] 長尾辰哉: "準結晶の電子状態ー高次元への拡張ー" 固体物理. 25. 46-52 (1990)

[Publications] Fumiko Yonezawa: "Theoretical Study of Metal-Nonmetal Transition in Microclusters" J.Non-cryst,Solids.

[Publications] Shoichi Sakamoto: "Molecular Orbital Study for Electronic Structures of Metallic Microclusters" J.Non-cryst.Solids.

[Publications] Fumiko Yonezawa: "Theoretical Study for Electronic Structure of Metallic Microcluster" J.Non-cryst.Solids.

[Publications] 小川泰: "フラクタルとは何か" 岩波書店, (1989)

[Publications] Takeo Fujiwara(Ed.): "“Quasicrystals"" Springer(Springer Ser.Mat.Sci.),

小川泰筑波大学, 物理工学系, 教授 (10025364)