How ab initio numerical simulation methods can be used to check and improve structure models for i(Al-Pd-Mn) is presented. By focusing on the optimization of a small approximant, a number of general structural and compositional rules simple enough to be applicable to the quasicrystalline structure were obtained.

We introduce a growth model for entropically stabilized quasicrystals. The dominating feature of this model is a fluctuating growth front which enables growth near equilibrium with small phason components. We summarize the results obtained for 2D and give a first presentation of 3D calculations.

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.

Finite alphabets of at least three letters permit the construction of square-free words of infinite length. We show that the entropy density is strictly positive and derive reasonable lower and upper bounds. Finally, we present an approximate formula which is asymptotically exact with rapid convergence in the number of letters. Finite alphabets of at least three letters permit the construction of square-free words of infinite length. We show that the entropy density is strictly positive and derive reasonable lower and upper bounds.

A structure model, based on a rhombohedral random tiling, is proposed for the ‘perfect’ Al-Cu-Fe and Al-Pd-Mn icosahedral phases. Locally, the model has much in common with six-dimensional models, with over 78% of all atoms belonging to an edge-sharing network of Bergman dodecahedra. The size of the tiles in the model is sufficiently small that relatively little atomic motion is required to implement an elementary rearrangement of tiles. Periodic arrangements of the tiles are consistent with known approximant phases. © 1996 Taylor & Francis Group, LLC.

The possibility of π-electron ring currents in C60 has been of interest since the initial identification of the fullerenes and the recent synthesis of these compounds has provided an experimental impetus to magnetic studies. We calculated a vanishingly small π-electron ring-current magnetic susceptibility for C60 and this prediction has recently received experimental verification. We attributed this behavior to a near cancellation of the diamagnetic and Van Vleck paramagnetic terms. The higher fullerenes may become available for study in the near future and recent work by Diedrich et al.

We present an atomic-structure model for high-quality AlCuFe icosahedral quasicrystals which is simple and yet incorporates most of what is known about the microscopic structure of the AlCuFe alloy. Using realistic image simulations, we compare this model with actual lattice-image micrographs of thermodynamically stable quasicrystal. We find good agreement between the micrographs and the models, although we find that lattice imaging is incapable of distinguishing small differences in the atomic structure.

Large, single-quasicrystalline grains, both cooled from the melt and annealed on cooling at ≈825°, were ground approximately into spheres with a resultant diameter of ≈0.2 mm. These crystal were then studied at the NSLS where, using λ = 1 A ̊, integrated intensities on more than 1300 (inequivalent) reflections were collected out to Q⊥ greater than 1.7 Å-1 (Q|| units). A crucial aspect of this work has been the careful characterization of crystal quality.

High quality Al-Cu-Fe quasicrystals have been studied at the atomic level with a high resolution microscope operating at 400 kV. When the incident beam is parallel to the fivefold axis, experimental bright-field images in thin regions of the specimen are found to be of two types, depending on the electron optical parameters employed. One of these images is of greater contrast than the other, but both types yield decagon-like image features. Close agreement is found between both types of contrast-enhanced micrographs and microscope image simulations of a realistic atomic model.

BY analogy with the positively curved carbon networks that comprise the fullerenes1-3, it has been suggested4 that negative curvature might be possible in graphitic carbon sheets, giving rise to extended structures corresponding to periodic minimal surfaces5 that divide space into two disjoint labyrinths. Whereas the positive curvature of fullerenes results from the presence of five-membered rings, negative curvature would derive from seven-membered rings. Here we present calculations of the cohesive energy and bulk moduli of two such hypothetical, negatively curved carbon networks.