Combined energy -- diffraction data refinement of decagonal AlNiCo

We incorporate realistic pair potential energies directly into a non-linear least-square fit of diffraction data to quantitatively compare structure models with experiment for the Ni-rich $d$(AlNiCo) quasicrystal. The initial structure models are derived from a few {\it a priori} assumptions (gross features of the Patterson function) and the pair potentials. In place of the common hyperspace approach to the structure refinement of quasicrystals, we use a real-space tile decoration scheme, which does not rely on strict quasiperiodicity, and makes it easy to enforce sensible local arrangements of the atoms. Inclusion of the energies provides information complementary to the diffraction data and protects the fit procedure from converging on spurious solutions. The method pinpoints sites which are likely to break the symmetry of their local environment.Comment: 7 pages, 5 figures, proceedings of the Internation Conference on Quasicrystals, Bangalore, India, August 200

Co-rich decagonal Al-Co-Ni: predicting structure, orientational order, and puckering

We apply systematic methods previously used by Mihalkovic et al. to predict the structure of the `basic' Co-rich modification of the decagonal Al70 Co20 Ni10 layered quasicrystal, based on known lattice constants and previously calculated pair potentials. The modelling is based on Penrose tile decoration and uses Monte Carlo annealing to discover the dominant motifs, which are converted into rules for another level of description. The result is a network of edge-sharing large decagons on a binary tiling of edge 10.5 A. A detailed analysis is given of the instability of a four-layer structure towards $c$-doubling and puckering of the atoms out of the layers, which is applied to explain the (pentagonal) orientational order.Comment: IOP LaTex; 7 pp, 2 figures. In press, Phil. Mag. A (Proc. Intl. Conf. on Quasicrystals 9, Ames Iowa, May 2005

Clusters, phason elasticity, and entropic stabilisation: a theory perspective

Personal comments are made about the title subjects, including: the relation of Friedel oscillations to Hume-Rothery stabilisation; how calculations may resolve the random-tiling versus ideal pictures of quasicrystals; and the role of entropies apart from tile-configurational.Comment: IOP macros; 8pp, 1 figure. In press, Phil. Mag. A (Proc. Intl. Conf. on Quasicrystals 9, Ames Iowa, May 2005

Temperature-dependent "phason" elasticity in a random tiling quasicrystal

Both ``phason'' elastic constants have been measured from Monte Carlo simulations of a random-tiling icosahedral quasicrystal model with a Hamiltonian. The low-temperature limit approximates the ``canonical-cell'' tiling used to describe several real quasicrystals. The elastic constant K2 changes sign from positive to negative with decreasing temperature; in the ``canonical-cell'' limit, K2/K1 appears to approach -0.7, about the critical value for a phason-mode modulation instability. We compare to the experiments on i-AlPdMn and i-AlCuFe.Comment: 5 pages, 2 Postscript figures, LaTeX, uses revtex4, submitted to PR

Symmetry-broken crystal structure of elemental boron at low temperature

The crystal structure of boron is unique among chemical elements, highly complex, and imperfectly known. Experimentalists report the beta-rhombohedral (black) form is stable over all temperatures from absolute zero to melting. However, early calculations found its energy to be greater than the energy of the alpha-rhombohedral (red) form, implying beta cannot be stable at low temperatures. Furthermore, beta exhibits partially occupied sites, seemingly in conflict with the thermodynamic requirement that entropy vanish at low temperature. Using electronic density functional theory methods and an extensive search of the configuration space we find a unique, energy minimizing pattern of occupied and vacant sites that can be stable at low temperatures but that breaks the beta-rhombohedral symmetry. Even lower energies occur within larger unit cells. Alternative configurations lie nearby in energy, allowing the entropy of partial occupancy to stabilize the beta-rhombohedral structure through a phase transition at moderate temperature.Comment: 12 pages, 5 figure

Empirical oscillating potentials for alloys from ab-initio fits

By fitting to a database of ab-initio forces and energies, we can extract pair potentials for alloys, with a simple six-parameter analytic form including Friedel oscillations, which give a remarkably faithful account of many complex intermetallic compounds. As examples we show results for (crystal or quasicrystal) structure prediction and phonon spectrum for three systems: Fe--B, Al--Mg--Zn, and Al--Cu--Fe.Comment: 5 pages 3 figures 2 table

First-principles prediction of a decagonal quasicrystal containing boron

We interpret experimentally known B-Mg-Ru crystals as quasicrystal approximants. These approximant structures imply a deterministic decoration of tiles by atoms that can be extended quasiperiodically. Experimentally observed structural disorder corresponds to phason (tile flip) fluctuations. First-principles total energy calculations reveal that many distinct tilings lie close to stability at low temperatures. Transfer matrix calculations based on these energies suggest a phase transition from a crystalline state at low temperatures to a high temperature state characterized by tile fluctuations. We predict B$_{38}$Mg$_{17}$Ru$_{45}$ forms a decagonal quasicrystal that is metastable at low temperatures and may be thermodynamically stable at high temperatures.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let