Four-phonon model of soft-matter quasicrystals for studying thermodynamics

Four-phonon model of soft-matter quasicrystals is proposed, in which there are three solid phonons and one fluid phonon. With this model, the vibration spectrum of soft-matter quasicrystals can be obtained. The generalized Debye frequency, generalized Debye temperature and the thermodynamic functions of soft-matter quasicrystals are observed. The results on the specific heat of soft-matter quasicrystals demonstrate the contributions of both solid phonons and fluid phonon, respectively.     

Structure of Al–Co–Ni pentagonal quasicrystal studied by HAADF-STEM and ab initio calculations

Using a combination of atomic-resolution high-angle annular dark-field (HAADF) Z-contrast imaging and ab initio calculations, atomic models of clusters 2 nm in diameter and 0.8 nm in height are proposed for the Al–Co–Ni pentagonal quasicrystal. This quasicrystal has 5-fold symmetry (the so-called 5f state) without superstructures, and is one of numerous modifications of the Al–Co–Ni decagonal quasicrystal. HAADF results reveal that the two-dimensional quasi-periodic lattice contains mainly Penrose pentagonal tiling. The centres within the decorated pentagonal tiles, i.e. the so-called pentagonal super-clusters, show structural characteristics having both a satellite-orbit shape and a pentagon-symmetry shape. The proposed atomic models, based directly on the HAADF images, are subjected to ab initio total energy calculations. After relaxation, the calculations demonstrate that the models with 5-fold symmetry are energetically more favourable than those with 10-fold symmetry.     

An analytic solution of initial boundary value problem for 3D quasicrystals in half space

In this article, initial boundary value problem for 3D quasicrystals in half space is considered. An analytic method is proposed for special form of initial conditions and nonhomogeneous term. It is explained that a weak solution of the problem can be constructed in the similar form of data by using symbolic calculations.     

A general solution of elasto-hydrodynamics of two-dimensional quasicrystals

Dynamic problems of quasicrystals are analysed within the framework of continuum mechanics. Phonon excitations yield wave propagation while phason excitations yield atomic diffusion. Phonon fields obey the equations of motion and phason fields obey the diffusion equations. Governing equations of elasto-hydrodynamics of decagonal quasicrystals combine characteristics of the equations of motion and diffusion. A general solution is derived in terms of two introduced auxiliary functions. It provides an easy-to-use approach to solve initial-boundary value problems encountered in elasticity problems for quasicrystals. Explicit expressions for displacements and stresses in the phonon and phason fields can be directly obtained. A derived general solution is also applicable to some planar quasicrystals such as pentagonal quasicrystals with fivefold symmetry.