Random cluster models for icosahedral phase alloys

Robertson, J. L.; Moss, S. C.

doi:10.1007/bf01313410

Cited by 24 publications

(7 citation statements)

References 53 publications

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“…Transformations from the A1MnSi I phase to the cubic a-AlMnSi (Cooper & Robinson, 1966) or the orthorhombic A16Mn (Nicol, 1953) phase were studied by Pannetier, Dubois, Janot & Bride (1987), Koskenmaki, Chen & Rao (1986) and others. Similarities in the intensity distribution in their diffraction patterns were taken as an indication that the I and a phases contain the same basic building block, viz the Mackay icosahedron; an object consisting of 54 atoms: 12Mn + 42(A1 + Si) (Guyot & Audier, 1985;Cahn, Gratias & Mozer, 1988a,b;Duneau & Oguey, 1989;Robertson & Moss, 1991;Yamamoto & Hiraga, 1988). The a phase is termed an approximant to the A1-Mn-Si quasicrystal (Mukhopadyay, Ishihara & Ranganathan 1991), and is used as a guide to the atomic decoration on the quasilattice.…”

Section: Introductionmentioning

confidence: 99%

Approximants and Intermediate Stages during Transformation from a Quasicrystalline to a Crystalline Phase in an Al–Mn–Si Alloy

Hansen¹,

Gjønnes²

1996

Acta Cryst Sect A

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In precipitate particles formed by heat treatment of industrially cast Al-(1.8-1.6wt%)Mn alloys, a sequence of stages intermediate between the quasicrystalline I phase and the cubic a-A1MnSi phase have been found. Their electron diffraction patterns and images can be interpreted in terms of faults on { 110}~ planes, with a fault vector [350]/16 or [iTO]/2T 2, where 7-= 1.618 is the golden mean. A lattice generated by such faults on every (110)~ plane has as its unit cell a prolate rhombohedron (a') that is complementary to the oblate rhombohedron (a) that describes the packing of the MacKay icosahedra in a-A1MnSi. Domains of this new lattice have been observed. Based on the two rhombohedra, a cubic Pa3 structure model (a") with cell dimension 7-times aA1MnSi and nearest-neighbour intericosahedral vectors along all threefold axes of the icosahedron is proposed as a second approximant to the I phase in the system, with a-A1MnSi as the first approximant. Calculations of diffraction patterns and Patterson sections are presented as support for this proposal.

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Section: Introductionmentioning

confidence: 99%

Approximants and Intermediate Stages during Transformation from a Quasicrystalline to a Crystalline Phase in an Al–Mn–Si Alloy

Hansen¹,

Gjønnes²

1996

Acta Cryst Sect A

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“…2, slightly ͑''elastically''͒ distorting these cells so that their surfaces are brought into contact, and then ''gluing'' these contacting surfaces in such a way that the coinciding atoms at the ''glued together'' surfaces are united and shared by neighboring units. In order to fill the hollow places in the corners of the construction obtained, let us introduce one more basic unit D 16 (1) by adding 28 atoms above the faces of the 16-coordinated first neighbor shell of Z16. The resulting second shell, shown in Fig.…”

Section: Construction Schemementioning

confidence: 99%

“…This is done either analytically, by defining some ''basic'' atomic clusters and then arranging them in space, [11][12][13][14][15][16] or by molecular dynamics ͑MD͒ cooling down of a ''melt.'' 17,18 The advantage of the MD approach is the immediate determination of the relevant atomic positions without any additional assumptions on the geometric laws governing atomic packing.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional model of quasicrystalline atomic structure

1996

Phys. Rev. B

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A three-dimensional model of quasicrystalline atomic structure is proposed. The model originates from a 33-atom dodecahedral cluster and involves a strategy allowing us to progressively increase the size of the system using only three basic clusters as building blocks. The structure obtained is characterized simultaneously by dense local atomic packing and by global quasicrystalline properties ͑intrinsic icosahedral symmetry, the absence of translational order, and self-similarity at different length scales͒. A 439-atom computer model has been built following the proposed strategy and has demonstrated the possibility to combine global quasicrystalline symmetry with a reasonable local packing of atoms. In order to elucidate the hierarchical nature of the long-range order in the proposed model, it is also analyzed using the disclination network approach.

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“…Until now, the location of specific elemental species in the structure has been deduced only indirectly, for example, by the analysis of Patterson functions derived from x-ray and neutron diffraction peak intensities of single-domain samples [3] or by powder diffraction peak intensities [4]. We report here the first observations of x-ray standing waves (XSW) in an aperiodic mediumquasicrystals-and their use to test directly the positions of specific elements in the structure.…”

Section: (Received 28 August 1998)mentioning

confidence: 99%

“…The determination of the atomic structure of quasicrystals remains one of the most important questions about these remarkable materials. Present theory is concerned with the relationship between cluster models, which give insights into growth and bonding, and planar models, which are testable by diffraction [1][2][3][4]. Even the symmetry of quasicrystals remains a major question.…”

Section: (Received 28 August 1998)mentioning

confidence: 99%