Abstract
Several techniques for visualizing and analyzing scatterer densities of quasiperiodic quasicrystals, both in the physical space and in the associated hyperspace, are discussed. In particular, a method for analyzing quasicrystal densities in terms of tilings is introduced and illustrated for the icosahedral Ammann tiling. A specific application to the x-ray and neutron scattering data of i(Al0.570Cu0.108Li0.322) is made. The six-dimensional hyperspace density of i(Al0.570Cu0.108Li0.322) is found to be consistent with the presence of hyperatoms on vertices, edge centers, and body centers of the hypercubic lattice. Some gross features of the hyperatom shapes are suggested. In the physical space, it is shown that densities around some high symmetry points are similar to those in R(Al0.564Cu0.116Li0.320) crystal, while around others, they suggest new atomic clusters. The Ammann tiling is found to be a useful template for the structure of i(Al0.570Cu0.108Li0.322), with the rhombic dodecahedra as important building units. While several structural models of i(Al0.570Cu0.108Li0.322) are generally consistent with the results of the density analysis, some differences are detected. A symmetric decoration of the rhombic dodecahedron, similar to the one found in R(Al0.564Cu0.116Li0.320), that is a basis for several structural models, is not consistent with the density analysis. No sign of the pure Al inside the rhombic dodecahedra, nor of the related Al hyperatom at the body center of the hypercrystal, could be detected.
| Original language | English |
|---|---|
| Pages (from-to) | 154-173 |
| Number of pages | 20 |
| Journal | Computers in Physics |
| Volume | 10 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Mar 1996 |
| Externally published | Yes |
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Visualization and analysis of quasicrystal densities. / Qiu, Shi Yue; Rowell, Corbett R.; Vukobrat Jaric, Marko.
In: Computers in Physics, Vol. 10, No. 2, 03.1996, p. 154-173.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Visualization and analysis of quasicrystal densities
AU - Qiu, Shi Yue
AU - Rowell, Corbett R.
AU - Vukobrat Jaric, Marko
PY - 1996/3
Y1 - 1996/3
N2 - Several techniques for visualizing and analyzing scatterer densities of quasiperiodic quasicrystals, both in the physical space and in the associated hyperspace, are discussed. In particular, a method for analyzing quasicrystal densities in terms of tilings is introduced and illustrated for the icosahedral Ammann tiling. A specific application to the x-ray and neutron scattering data of i(Al0.570Cu0.108Li0.322) is made. The six-dimensional hyperspace density of i(Al0.570Cu0.108Li0.322) is found to be consistent with the presence of hyperatoms on vertices, edge centers, and body centers of the hypercubic lattice. Some gross features of the hyperatom shapes are suggested. In the physical space, it is shown that densities around some high symmetry points are similar to those in R(Al0.564Cu0.116Li0.320) crystal, while around others, they suggest new atomic clusters. The Ammann tiling is found to be a useful template for the structure of i(Al0.570Cu0.108Li0.322), with the rhombic dodecahedra as important building units. While several structural models of i(Al0.570Cu0.108Li0.322) are generally consistent with the results of the density analysis, some differences are detected. A symmetric decoration of the rhombic dodecahedron, similar to the one found in R(Al0.564Cu0.116Li0.320), that is a basis for several structural models, is not consistent with the density analysis. No sign of the pure Al inside the rhombic dodecahedra, nor of the related Al hyperatom at the body center of the hypercrystal, could be detected.
AB - Several techniques for visualizing and analyzing scatterer densities of quasiperiodic quasicrystals, both in the physical space and in the associated hyperspace, are discussed. In particular, a method for analyzing quasicrystal densities in terms of tilings is introduced and illustrated for the icosahedral Ammann tiling. A specific application to the x-ray and neutron scattering data of i(Al0.570Cu0.108Li0.322) is made. The six-dimensional hyperspace density of i(Al0.570Cu0.108Li0.322) is found to be consistent with the presence of hyperatoms on vertices, edge centers, and body centers of the hypercubic lattice. Some gross features of the hyperatom shapes are suggested. In the physical space, it is shown that densities around some high symmetry points are similar to those in R(Al0.564Cu0.116Li0.320) crystal, while around others, they suggest new atomic clusters. The Ammann tiling is found to be a useful template for the structure of i(Al0.570Cu0.108Li0.322), with the rhombic dodecahedra as important building units. While several structural models of i(Al0.570Cu0.108Li0.322) are generally consistent with the results of the density analysis, some differences are detected. A symmetric decoration of the rhombic dodecahedron, similar to the one found in R(Al0.564Cu0.116Li0.320), that is a basis for several structural models, is not consistent with the density analysis. No sign of the pure Al inside the rhombic dodecahedra, nor of the related Al hyperatom at the body center of the hypercrystal, could be detected.
UR - http://www.scopus.com/inward/record.url?scp=0030104580&partnerID=8YFLogxK
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U2 - 10.1063/1.168566
DO - 10.1063/1.168566
M3 - Article
VL - 10
SP - 154
EP - 173
JO - Computers in Physics
JF - Computers in Physics
SN - 0894-1866
IS - 2
ER -