Tiling of Canonical Cells: Large
                    <i>Pa</i>
                    3 Approximants

Mihalkovič, M.; Mrafko, P.

doi:10.1209/0295-5075/21/4/014

Cited by 22 publications

(10 citation statements)

References 6 publications

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“…Local? decorations rhombohedral [20,21] ico yes i(AlPdMn): [38] canonical cells [39,40,41] ico no i(AlMn): [33,42] binary [43,44] 10 yes d(AlCuCo): [45] hexagon-boat-star [46] 10 yes d(AlMn): [47] d(AlPdMn): [47] d(AlCuCo): [48] d(AlNiCo): [49] rectangle-triangle [50] 10 no d(AlPdMn): [50] d(AlNiCo) [51] square-triangle [23,52] 12 no dd(VNiSi) [53] dd(Ta 1:6 Te) [54] discover by this technique.) Each tile is decorated in a deterministic way by candidate sites: these sites take the place of the quasilattice defined in the plain lattice-gas technique.…”

Section: Tilingmentioning

confidence: 99%

Structure determinations for random-tiling quasicrystals

Henley

Elser²,

Mihalkovič³

2000

Zeitschrift Für Kristallographie - Crystalline Materials

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How, in principle, could one solve the atomic structure of a quasicrystal, modeled as a random tiling decorated by atoms, and what techniques are available to do it? One path is to solve the phase problem first, obtaining the density in a higher dimensional space which yields the averaged scattering density in 3-dimensional space by the usual construction of an incommensurate cut. A novel direct method for this is summarized and applied to an i(AlPdMn) data set. This averaged density falls short of a true structure determination (which would reveal the typical unaveraged atomic patterns.) We discuss the problematic validity of inferring an ideal structure by simply factoring out a ªperp-spaceº Debye-Waller factor, and we test this using simulations of rhombohedral tilings. A second, ªunifiedº path is to relate the measured and modeled intensities directly, by adjusting parameters in a simulation to optimize the fit. This approach is well suited for unifying structural information from diffraction and from minimizing total energies derived ultimately from ab-initio calculations. Finally, we discuss the special pitfalls of fitting random-tiling decagonal phases.

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Section: Tilingmentioning

confidence: 99%

Structure determinations for random-tiling quasicrystals

Henley

Elser²,

Mihalkovič³

2000

Zeitschrift Für Kristallographie - Crystalline Materials

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“…A69, 322-340 3 Computational techniques for generating CCTs with large periods have been developed by several authors(Mihalkovic & Mrafko, 1993;Newman et al, 1995). (2013).…”

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confidence: 99%

“…(2013). A69, 322-340 3 Computational techniques for generating CCTs with large periods have been developed by several authors(Mihalkovic & Mrafko, 1993;Newman et al, 1995). These techniques search possible arrangements of canonical cells under preset periodic boundary conditions, where the amount of computations will expand exponentially as the periods are increased.…”

mentioning

confidence: 99%

Cluster-packing geometry for Al-based F-type icosahedral alloys

et al. 2013

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This paper presents a new, highly stable, periodic approximant to the Al-based F-type icosahedral quasicrystals, i-Al-Pd-TM (TM = transition metals). The structure of this intermetallic Al-Pd-Cr-Fe compound is determined ab initio using single-crystal X-ray diffraction, where the space group is identified to be Pa3 and the lattice constant 40.5 Å . The structure is well described as a dense packing of clusters of two kinds, which are called the pseudo-Mackay-type and the mini-Bergman-type clusters. Adjacent clusters can be markedly interpenetrated, while the structure requires no glue atoms to fill in the gaps between the clusters. It is shown that the clusters are centred at the vertices of a canonical cell tiling, which corresponds to a 2 Â 2 Â 2 superstructure of Henley's cubic 3/2 packing, and that the parity of each vertex determines the kind of associated cluster. The proper quasi-lattice constant for describing the cluster packing is 1/ ( = golden mean) times the conventional one used to describe Al-based P-type icosahedral alloys. The superstructure ordering of the present approximant turns out to be of a different kind from the P-type superstructure ordering previously reported in i-Al-Pd-Mn. The present results will greatly improve the understanding of atomic structures of F-type icosahedral quasicrystals and their approximants.

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“…7). Though lower approximants can be constructed today [21], the long range quasiperiodic tiling is still waiting to be found [23]. This quasiperiodic tiling is highly desirable because together with a decoration rule it would be an outright description for an i quasicrystal.…”

Section: Methodsmentioning

confidence: 99%

Local 3D Real Space Atomic Structure of the Simple Icosahedral Ho₁₁Mg₁₅Zn₇₄ Quasicrystal from PDF Data.

et al. 2004

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Structure Structure D 2000Local 3D Real Space Atomic Structure of the Simple Icosahedral Ho 11 Mg 15 Zn 74 Quasicrystal from PDF Data. -A novel complementary strategy to quasicrystalline local structure determination is presented, which uses the atomic pair distribution function (PDF) of the quasicrystal derived from powder XRD data for refinement of the local structure. -(BRUEHNE*, S.; UHRIG, E.; GROSS, C.; ASSMUS, W.; Cryst.

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Tiling of Canonical Cells: Large Pa 3 Approximants

Cited by 22 publications

References 6 publications

Structure determinations for random-tiling quasicrystals

Structure determinations for random-tiling quasicrystals

Cluster-packing geometry for Al-based F-type icosahedral alloys

Local 3D Real Space Atomic Structure of the Simple Icosahedral Ho₁₁Mg₁₅Zn₇₄ Quasicrystal from PDF Data.

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Tiling of Canonical Cells: Large Pa 3 Approximants

Cited by 22 publications

References 6 publications

Structure determinations for random-tiling quasicrystals

Structure determinations for random-tiling quasicrystals

Cluster-packing geometry for Al-based F-type icosahedral alloys

Local 3D Real Space Atomic Structure of the Simple Icosahedral Ho11Mg15Zn74 Quasicrystal from PDF Data.

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Product

Resources

About

Local 3D Real Space Atomic Structure of the Simple Icosahedral Ho₁₁Mg₁₅Zn₇₄ Quasicrystal from PDF Data.