Electronic transport in quasicrystals

Mobility of electrons in quasicrystals is considered in the framework of the fractional Fermi surface (FS) model, i.e., a multiconnected FS with many electron-hole pockets. The Mott law for the variable range hopping conductivity is obtained when intervalley scattering processes with small momentum transfer are taken into account. The transition to the power-law temperature dependence is discussed.     

Electronic conduction in quasicrystals at low temperatures

At low temperatures, a perfect quasicrystal is in the “critical” state of metal-insulator transition. A power-law temperature dependence of conductivity, which was experimentally observed at T<5 K in the icosahedral phase of Al-Pd-Re, was obtained using the critical wave functions. Mott’s hopping law was also observed in the Al-Pd-Re samples and explained by the delocalization of electronic states in the momentum space.     

Thermodynamics of equilibrium properties of quasicrystals

Thermodynamics of equilibrium properties of crystals has been generalized to the case of quasicrystals. Based on it, relations between direct and converse effects, and some relations between the coefficients measured under different conditions have been derived. By group representation theory, physical property tensors have been derived for two-dimensional pentagonal, octagonal, decagonal and dodecagonal, and three-dimensional icosahedral and cubic quasicrystals.     

Unconventional properties of dislocations in quasicrystals

Dislocations in quasicrystals are defined as the intersections of dislocations in a high dimensional lattice with an irrational cut which figures the physical space. This definition confers to them a number of unusual geometrical properties which can be studied either by suitable extensions of the Volterra process, or by topological approaches, which often offer complementary points of view and are presented in this paper. Amongst these unusual properties, the production of stacking faults under shear at low temperature, reshuffling processes on stacking faults, and properties of non-commutativity which could have some incidences on the interplay between dislocations in deformation processes are mentioned.Dedicated to Dr. Frantiek Kroupa in honour of his 70^th birthday.Unité de Recherche Associée 009 du CNRS, associée aux Universités de Paris VI at Paris VIIWe are very grateful to Dr. Vladimir Dmitrienko for discussions and useful remarks.     

Electronic crystals: an experimental overview

This article reviews the static and dynamic properties of spontaneous superstructures formed by electrons. Representations of such electronic crystals are charge density waves (CDW) and spin density waves in inorganic as well as organic low-dimensional materials. A special attention is paid to the collective effects in pinning and sliding of these superstructures, and the glassy properties at low temperature. Charge order and charge disproportionation which occur in organic materials resulting from correlation effects are analysed. Experiments under magnetic field, and more specifically field-induced CDWs are discussed. Properties of meso- and nanostructures of CDWs are also reviewed.     

Isotropic and anisotropic physical properties of quasicrystals

Since quasicrystals have positional and orientational long-range order, they are essentially anisotropic. However, the researches show that some physical properties of quasicrystals are isotropic. On the other hand, quasicrystals have additional phason degrees of freedom which can influence on their physical behaviours. To reveal the quasicrystal anisotropy, we investigate the quasicrystal elasticity and other physical properties, such as thermal expansion, piezoelectric and piezoresistance, for which one must consider the contributions of the phason field. The results indicate that: for the elastic properties, within linear phonon domain all quasicrystals are isotropic, and within nonlinear phonon domain the planar quasicrystals are still isotropic but the icosahedral quasicrystals are anisotropic. Moreover, the nonlinear elastic properties due to the coupling between phonons and phasons may reveal the anisotropic structure of QCs. For the other physical properties all quasicrystals behave like isotropic media except for piezoresistance properties of icosahedral quasicrystals due to the phason field.     

Dislocations and mechanical properties of icosahedral quasicrystals

In this article we interpret the mechanical properties of icosahedral quasicrystals with the dislocation theory. After having defined the concept of dislocation in a periodic crystal, we extend this notion to quasicrystals in the 6-dimensional space. We show that perfect dislocations and imperfect dislocations trailing a phason fault can be defined and observed in transmission electron microscopy (TEM). In-situ straining TEM experiments at high temperature show that dislocations move solely by climb, a non-conservative motion-requiring diffusion. This behavior at variance with that of crystals which deform mainly by glide is explained by the atypical nature of the atomic structure of icosahedral quasicrystals.     

High-temperature electronic and thermal properties of icosahedral quasicrystals

We discuss the high-temperature electronic and thermal properties of an icosahedral quasicrystal within the framework of the fractional multicomponent Fermi-surface model. When intervalley electron-phonon scattering sets in above a characteristic temperature T^∗ of the order of the Debye temperature ΘD the quasicrystal becomes more “metallic”. In this regime the electrical conductivity and the electronic contribution to the thermal conductivity vary as T and T², respectively. We predict that at elevated temperatures the electronic specific heat will vary faster than γT and the low-frequency Drude-type component of the optical conductivity σ₁(ω) will gain weight.     

Photonic bandgap properties of 8-fold symmetric photonic quasicrystals

The bandgap properties of 2D 8-fold symmetric photonic quasicrystals (PQCs) composed of a set of rods are numerically investigated for various fill factors, dielectric constants and propagation angles using the finite difference time domain (FDTD) method. Some interesting properties are found besides the known results: (i) the central frequency of the bandgap shifts to low frequency as r/a increases; (ii) an optimum fill factor to obtain the largest gap width exists, which decreases with increasing dielectric constant; (iii) compared with the behavior for a given fill factor, the variation of bandgap width for the optimum fill factor increases much more significantly with the dielectric constant. Selection guidelines for 8-fold symmetric PQC designs are provided for optimum fill factors and variation of the relative bandgap width at different dielectric constants.     

Continuity properties of the electronic spectrum of 1D quasicrystals

In this paper we consider operatorsH(,x) defined onl ²() by

A parametric study of the lensing properties of dodecagonal photonic quasicrystals

We present a study of the lensing properties of two-dimensional (2-D) photonic quasicrystal (PQC) slabs made of dielectric cylinders arranged according to a 12-fold-symmetric square-triangle aperiodic tiling. Our full-wave numerical analysis confirms the results recently emerged in the technical literature and, in particular, the possibility of achieving focusing effects within several frequency regions. However, contrary to the original interpretation, such focusing effects turn out to be critically associated to local symmetry points in the PQC slab, and strongly dependent on its thickness and termination. Nevertheless, our study reveals the presence of some peculiar properties, like the ability to focus the light even for slabs with a reduced lateral width, or beaming effects, which render PQC slabs potentially interesting and worth of deeper investigation.     

Crystallization of quasicrystals

Abstract

We present an overview of our work on the crystallization of the icosahedral phase in Al_100?xMn_x, Ti_100?xMn_x, and Pd_58.8U_20.6Si_20.6 alloys and compare our results with those of others. Evidence presented suggests that the icosahedral phase in Ti₆₀Mn₃₇Si₃ may be stable below 1100 K. The origin of arcs of diffuse scattering in TEM diffraction patterns is discussed in light of new experimental data in i-phase Ti-Mn. A model that simulates directly the i-phase transformation under isothermal and nonisothermal conditions is presented and used to analyze kinetic data for Al₈₆Mn₁₄ alloys to obtain the first estimate for the interfacial energy between the i-phase and the crystal: σ_i-c = 0.03 J/m². This is similar to the interfacial energies between crystalline metals and their liquids at the interfacial melting temperature.     

AlCuFe quasicrystals: Local electronic properties of these new industrial materials

We present room temperature ⁵⁷Fe Mössbauer centre (isomer) shift and electric field gradient (EFG) results in the Al_100-x-yCu_xFe_y icosahedral-quasicrystalline (i-) and crystalline phases. We have investigated the local electronic properties and atomic order along the existence domains of the quasicrystalline and approximant phases given by two close-lying parallel lines in the concentration diagram: the I-line, where the quasicrystal is stable, and the A-line, where the rhombohedral approximant is stable, and other high-order approximants (orthorhombic and pentagonal) as well as the quasicrystal phase are metastable. We have also studied a series of intermediate concentrations situated between the I- and A-lines retained in the metastable i-phase by quenching. It is found that the centre shift and EFG are linearly correlated to each other over the range of compositions and structures for both the I- and A-lines as well as the intermediate samples. This correlation results from systematic changes in the orbital occupations on Fe atoms with composition. We have investigated as well the new low-order cubic approximant phase containing Si. The results for this phase fall near to but not on the correlation line indicating small changes in the atomic binding as compared to the i- and high order approximant phases. In addition, we have studied several non-approximant phases which lie close to these phases in composition. The results for the non-approximant structures do not fall near the correlation line, indicating very different atomic binding.