Phason

About: Phason is a research topic. Over the lifetime, 1142 publications have been published within this topic receiving 16913 citations.

Elasticity and dislocations in pentagonal and icosahedral quasicrystals.

Abstract: Theories for elasticity and dislocation defects in two-dimensional pentagonal and three-dimensional icosahedral quasicrystals are presented.

Phonons, phasons, and dislocations in quasicrystals.

Abstract: In this paper we examine the detailed relationship between the density-wave and unit-cell descriptions of quasicrystals. We show that phonons, phasons, and dislocations correspond to translations, distortions, and rearrangements of unit cells. The associated density-wave images closely resemble experimental electron micrographs of the icosahedral phase of aluminum-manganese and related alloys. Partial dislocations are also discussed and a natural classification scheme for partials is proposed.

Crystallography of quasiperiodic crystals

Abstract: The aim of this review is to describe many approaches to modulated crystals and quasicrystals developed in two decades after the introduction of higher-dimensional crystallography in a unified way. Much attention is focused on higher-dimensional crystallography of quasi-crystals, which is under development. After discussions on symmetries of modulated crystals and methods of their structure analysis, many subjects on the analysis of quasicrystals are discussed, which include methods of generating quasiperiodic tilings, their diffraction patterns, similarity transformations, indexing problems, point density of quasicrystals, phason distortion, relations between quasicrystals and their crystalline approximants, model constructions, Patterson, refinement and maximum-entropy methods for quasicrystals, and superstructures in quasicrystals. In particular, the theories for octagonal, decagonal, dodecagonal and icosahedral quasicrystals are given in detail.

Symmetry, stability, and elastic properties of icosahedral incommensurate crystals.

Abstract: The symmetry and stability of icosahedral incommensurate structures and generalized two-dimensional Penrose pentagonal structures are studied. The crystallographic properties of Penrose lattices are described by five-dimensional (5D) super space groups, and the icosahedral structures are described by 6D space groups, with or without improper translations. The density in real space is given as the density along a three-dimensional plane in this 6D space. The fivefold symmetry of the diffraction spectrum of Mn-Al alloys, which is inconsistent with three-dimensional translational invariance, reflects a fivefold rotation axis of the 6D space group. The six continuous degrees of freedom associated with the 6D space represent the usual three orthogonal rigid displacements of the crystal, plus three phase shifts associated with internal rearrangements, leading to three acoustic-phonon modes and three phason modes. There are two independent elastic constants, which is fewer than in any regular crystal, representing one-dimensional and five-dimensional irreducible strains, respectively. If the phase degrees of freedom are included, there are five generalized elastic constants. The stability of icosahedral structures and ``lyotropic'' Penrose structures can be understood from a phenomenological Landau theory. The ideal icosahedral crystal has perfect positional order, which is stable with respect to thermal fluctuations at low temperatures. The melting transition is first order.

Hydrodynamics of icosahedral quasicrystals

Abstract: The equations governing long-wavelength, low-frequency excitations in icosahedral quasicrystals are derived. It is found that while the speeds of the propagating modes are isotropic, the attenuations are not, implying that purely macroscopic experiments can in principle distinguish quasicrystals from crystals, glasses, or conventional incommensurate systems. The coefficient of the anisotropy is, regrettably, quite small. The complete spectrum consists of three diffusive phasons, two pairs of transverse and one pair of longitudinal sound modes, a vacancy diffusion mode, a heat diffusion mode, and, in a material with n atomic species, n-1 additional particle diffusion modes. The diffusion times of the vacancy and phason modes are expected to be comparable and very long. It is shown that propagating phasons, even at short wavelength, are an unlikely prospect. The static, equilibrium elastic properties are also anisotropic, but are approached very slowly, and in many situations, the elastic response is isotropic on experimentally accessible time scales. Our results also imply that nonlinear fluctuation corrections to the linearized hydrodynamics presented here are finite as q and \ensuremath{\omega}\ensuremath{\rightarrow}0, i.e., there is no breakdown of conventional hydrodynamics in icosahedral quasicrystals.