Related papers: Modelling Quasicrystal Growth
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…
The description of almost periodic or quasiperiodic structures has a long tradition in mathematical physics, in particular since the discovery of quasicrystals in the early 80's. Frequently, the modelling of such structures leads to…
The discovery of quasicrystals has changed our view of some of the most basic notions related to the condensed state of matter. Before the age of quasicrystals, it was believed that crystals break the continuous translation and rotation…
Crystals are the materials which can be described by uniform periodic lattices. Traditionally, only the 1-, 2-, 3-, 4- and 6-fold rotation symmetries are allowed in crystals because other n-fold rotation symmetries are forbidden by the…
We review our recent modeling of crystal nucleation and polycrystalline growth using a phase field theory. First, we consider the applicability of phase field theory for describing crystal nucleation in a model hard sphere fluid. It is…
A new method for finding electronic structure and wavefunctions of electrons in quasiperiodic potential is introduced. To obtain results it uses slightly modified Schrodinger equation in spaces of dimensionality higher than physical space.…
We study crystal growth inside an infinite octant on a cubic lattice. The growth proceeds through the deposition of elementary cubes into inner corners. After re-scaling by the characteristic size, the interface becomes progressively more…
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…
Quasicrystals lack translational symmetry, but can still exhibit long-ranged order, promoting them to candidates for unconventional physics beyond the paradigm of crystals. Here, we apply a real-space functional renormalization group…
A formula of grain growth rate, based on a nonlinear capillarity-driven relation, is derived to predict and interpret realistic growth processes in polycrystalline systems. The derived formula reveals how the growth and stagnation of grains…
The various magnetic orders observed in approximant crystals of Tsai-type quasicrystal are important for deepening our understanding of mysterious magnetism in quasicrystals. Using an icosahedral cluster model with inter-cluster…
The theory of phase ordering dynamics -- the growth of order through domain coarsening when a system is quenched from the homogeneous phase into a broken-symmetry phase -- is reviewed, with the emphasis on recent developments. Interest will…
The detailed atomic structure of quasicrystals has been an open question for decades. Here, we present a quasilattice-conserved optimization method (quasiOPT), with particular quasiperiodic boundary conditions. As the atomic coordinates…
The dynamics of quasicrystal growth remains an unsolved problem in condensed matter. By means of synchrotron live imaging, facetted growth proceeding by the tangential motion of ledges at the solid-melt interface is clearly evidenced all…
A model for diffusion-controlled spherical particle growth is presented and solved numerically, showing how, on cooling at sufficient rate from a given fraction solid, growth velocity first increases, and then decreases rapidly when solute…
Several aspects of the theory of epitaxial crystal growth from atomic or molecular beams are developed from the perspective of statistical physics. Lectures are devoted to the rate equation theory of two-dimensional nucleation and its…
Studies of nucleation generally focus on the properties of the critical cluster, but the presence of defects within the crystal lattice means that the population of nuclei necessarily evolve through a distribution of pre-critical clusters…
The observation recently of 12-fold quasicrystals in polymers, nanoparticle mixture and 12-fold and 18-fold quasicrystals in colloidal solutions are important events for the study of quasicrystals. To describe the mechanical behaviour we…
Unlike atoms, colloidal particles are not identical, but can only be synthesised within a finite size tolerance. Colloids are therefore polydisperse, i.e. mixtures of infinitely many components with sizes drawn from a continuous…
In this notes, we survey the recent developments on theory of generalized quasidisks. Based on the more or less standard techniques used earlier, we also provide some minor improvements on the recorded results. A few nature questions were…