Penrose patterns and related structures. II. Decagonal quasicrystals

Yamamoto, Akio; Ishihara, Keiichi N.

doi:10.1107/s010876738800296x

Cited by 125 publications

(51 citation statements)

References 10 publications

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“…[7][8][9][10] The decagonal quasilattice may be described as a projection from a five-dimensional periodic lattice. [11][12][13] The fivedimensional space consists of two orthogonal subspaces, the three-dimensional physical or parallel space and the twodimensional external or perpendicular space. All physicalspace reciprocal lattice vectors can be written as a linear combination of five basis vectors.…”

Section: Introductionmentioning

confidence: 99%

Dislocations and dislocation reactions in decagonal Al-Ni-Co quasicrystals

2004

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were studied by means of diffraction-contrast imaging and defocus convergent beam electron diffraction techniques in the transmission electron microscope. In addition to dislocations with Burgers vectors parallel to the periodic and quasiperiodic directions as first reported by Zhang and Urban ͓Z. Zhang and K. Urban, Philos. Mag. Lett. 60, 97 ͑1989͔͒, a type of dislocation was found possessing a Burgers vector with components in the periodic as well as the quasiperiodic direction. The parallel-space component of this Burgers vector has a length of 2.5 Å. The quasiperiodic Burgers vectors were found to have parallel-space lengths of 2.9 and 4.7 Å. The Burgers vectors determined are correlated with interatomic vectors of the structure of decagonal Al-Ni-Co. In addition, dislocation reactions were identified by the determination of Burgers vectors of dislocations in triple-node arrangements. A model for the dislocation reaction is proposed which is in accordance with the results of the microstructural studies.

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Section: Introductionmentioning

confidence: 99%

Dislocations and dislocation reactions in decagonal Al-Ni-Co quasicrystals

2004

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“…So far a lock-in energy of Q 4 +Q *4 has been considered in (3). But there may be a coupling between the primary order parameter Q and the macroscopic polarization P or strain S; (Q 2 +Q *2 )P or (Q 2 -Q *2 )S. These terms can stabilize a ferroelectric phase or a ferroelastic phase without supersymmetry.…”

Section: Discussionmentioning

confidence: 99%

“…Even if the relation is not a symmetry operation of space group, the unit cell is invariant under symmetry operations of so called groupoid. [3] In our previous report, the additional symmetry, which relates subunits with each other within a superstructure (a commensurate structure induced from a high symmetry prototype phase), was called as supersymmetry. [4] This symmetry operation was one of the element of the prototype phase.…”

Section: Introductionmentioning

confidence: 99%

A model of phase transition with breaking supersymmetry

Mashiyama

1998

Ferroelectrics

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A phenomenological model of free energy is presented to demonstrate a phase transition from a state with supersymmetry to a state without supersymmetry. The model is equivalent, in a commensurate phase, to the extended sublattice model for antiferroelectricity and ferrielectricity. In a selected set of parameters, the state with supersymmetry (antiferroelectric state) transforms to the symmetry broken state (ferrielectric state), with decreasing temperature. The transition is either first or second order one depending on the coefficients of the free energy. commensurate structure; additional symmetry operations; Landau theory of sublattice model

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“…Thus, the periodicity in this case is either a fraction or a multiple of the b parameter which is about 8 A. Yamamoto & Ishihara (1988) have discussed the theoretical possibility of polytypism in decagonal phases. This is because in the two-dimensional Penrose tilings (constituting the stacking layers of decagonal phases) one can distinguish four types of layers of atoms which were labelled as A, B, C and D. By varying the stacking sequence following certain rules such as that neighbouring layers cannot be of the same type, one can develop different polytypes.…”

Section: Discussionmentioning

confidence: 99%

Polytypism in a decagonal quasicrystalline Al–Co phase

Menon¹,

Suryanarayana²,

Singh³

1989

J Appl Cryst

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A decagonal quasicrystalline phase has been produced in rapidly solidified binary Al-14 to 25 at.% Co and ternary A1-20 at.% Co-5 at.% Si alloys. Observation of periodicity along one of the directions in the electron diffraction patterns has confirmed the decagonal nature of the phase. Variations in periodicity ranging from 4 to 16 A suggest that a polytypismlike phenomenon occurs in these phases. By in situ hot-stage electron microscopy, it can be shown that one polytype transforms into another. Reasons for the formation and transformation of polytypes in decagonal quasicrystalline phases are discussed.

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Penrose patterns and related structures. II. Decagonal quasicrystals

Cited by 125 publications

References 10 publications

Dislocations and dislocation reactions in decagonal Al-Ni-Co quasicrystals

Dislocations and dislocation reactions in decagonal Al-Ni-Co quasicrystals

A model of phase transition with breaking supersymmetry

Polytypism in a decagonal quasicrystalline Al–Co phase

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