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

Energy-based Structure Prediction for d(Al70Co20Ni10)

We use energy minimization principles to predict the structure of a decagonal quasicrystal - d(AlCoNi) - in the Cobalt-rich phase. Monte Carlo methods are then used to explore configurations while relaxation and molecular dynamics are used to obtain a more realistic structure once a low energy configuration has been found. We find five-fold symmetric decagons 12.8 A in diameter as the characteristic formation of this composition, along with smaller pseudo-five-fold symmetric clusters filling the spaces between the decagons. We use our method to make comparisons with a recent experimental approximant structure model from Sugiyama et al (2002).Comment: 10pp, 2 figure

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

Phason elasticity of a three-dimensional quasicrystal: transfer-matrix method

We introduce a new transfer matrix method for calculating the thermodynamic properties of random-tiling models of quasicrystals in any number of dimensions, and describe how it may be used to calculate the phason elastic properties of these models, which are related to experimental measurables such as phason Debye-Waller factors, and diffuse scattering wings near Bragg peaks. We apply our method to the canonical-cell model of the icosahedral phase, making use of results from a previously-presented calculation in which the possible structures for this model under specific periodic boundary conditions were cataloged using a computational technique. We give results for the configurational entropy density and the two fundamental elastic constants for a range of system sizes. The method is general enough allow a similar calculation to be performed for any other random tiling model.Comment: 38 pages, 3 PostScript figures, self-expanding uuencoded compressed tar file, LaTeX using RevTeX macros and epsfig.st

Phonon-phason coupling in icosahedral quasicrystals

From relaxation simulations of decoration-based quasicrystal structure models using microscopically based interatomic pair potentials, we have calculated the (usually neglected) phonon-phason coupling constant. Its sign is opposite for the two alloys studied, i-AlMn and i-(Al,Cu)Li; a dimensionless measure of its magnitude relative to the phonon and phason elastic constants is of order 1/10, suggesting its effects are small but detectable. We also give a criterion for when phonon-phason effects are noticeable in diffuse tails of Bragg peaks.Comment: 7 pages, LaTeX, uses Europhys Lett macros (included

Compact z=2z=2 Electrodynamics in 2+1 dimensions: Confinement with gapless modes

We consider 2+1 dimensional compact U(1) gauge theory at the Lifshitz point with dynamical critical exponent $z=2$. As in the usual $z=1$ theory, monopoles proliferate the vacuum for any value of the coupling, generating a mass scale. The theory of the dilute monopole gas is written in terms a non-relativistic Sine-Gordon model with two real fields. While monopoles remove some of the massless poles of the perturbative field strength propagator, a gapless mode representing the incomplete screening of monopoles remains, and is protected by a shift invariance of the original theory. Timelike Wilson loops still obey area laws, implying that minimal charges are confined, but the action of spacelike Wilson loops of linear size L goes instead as $L^3$.Comment: 4 pages, RevTeX. Some equations simplified. Version to appear in Physical Review Letter

Echolocation by Quasiparticles

It is shown that the local density of states (LDOS), measured in an Scanning Tunneling Microscopy (STM) experiment, at a single tip position contains oscillations as a function of Energy, due to quasiparticle interference, which is related to the positions of nearby scatterers. We propose a method of STM data analysis based on this idea, which can be used to locate the scatterers. In the case of a superconductor, the method can potentially distinguish the nature of the scattering by a particular impurity.Comment: 4+ page

Stability of a hard-sphere binary quasicrystal

The stability of a quasicrystalline structure, recently obtained in a molecular-dynamics simulation of rapid cooling of a binary melt, is analyzed for binary hard-sphere mixtures within a density-functional approach. It is found that this quasicrystal is metastable relative to crystalline and fluid phases for diameter ratios above 0.83. Such trend is partially reversed for lower diameter ratios, since the quasicrystal becomes stable with respect to the crystal but does not reach a coexistence with the fluid.Comment: 14 pages, 6 eps figures included. Revised version to appear in Phil. Mag.