Effect of phasons and magnetic fields on the electronic spectrum of a three-dimensional quasicrystal

The effect of phasons and magnetic fields on the electronic spectrum of an icosahedral quasicrystal is investigated in the tight-binding approximation. Phasons smooth the singular spectrum and produce a greater delocalization of the critical wave functions. A magnetic field shifts the limits of the spectrum, smooths the spectrum, lifts the degeneracy, and also delocalizes the wave functions. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 9, 659–661 (10 May 1999)     

Electron spectrum of inert gas crystals under pressure

Changes in zone structure of inert gas crystals with pressure are studied. The zone structure of solid Ne, Ar, Kr, and Xe are calculated over a wide pressure range using the combined plane wave method. Stability limits of the basic dielectric phase are determined by overlap of direct gaps in the electron spectrum with pressure increase. No loss of stability upon transition to the metallic state was observed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 68–74, March, 1984.     

Charge state and diffusion of hydrogen in the TiZrNi icosahedral alloy

The electronic structure of a hydrogen atom in a 1/1 approximant of the Ti-Zr-Ni icosahedral quasicrystal is investigated using ab initio methods based on the density functional theory. The charge state of the hydrogen atom in Ti₃₆Zr₃₂Ni₁₃ with different types of tetrahedral pores, as well as the charge state of hydrogen at a ratio H/M ≈ 1.7, is determined. The hydrogen atom is found to be in a nearly neutral state. The coefficient of hydrogen diffusion in Ti₃₆Zr₃₂Ni₁₃ is calculated.     

Effect of vanadium doping on the structure of TiAl: <Emphasis Type="Italic">Ab initio</Emphasis> calculations

The degree of tetragonality of TiAl and the effect of vanadium doping on it are studied theoretically in the framework of the coherent-potential approximation using ab initio potentials. It is shown that substitution of vanadium for Ti increases the degree of tetragonality, whereas substitution of vanadium for aluminum decreases the degree of tetragonality of the TiAl: V alloy and the lattice becomes virtually cubic when the vanadium content is about 8 at. %; this, in turn, can increase the plasticity of TiAl, which is brittle at low temperatures.     

Pressure-induced change of the Fermi surface topology in Al-based solid solutions

An ab initio study of the electronic structure and the Fermi surface is carried out for random Al-Si and Al-Ge solid solutions. At a 10 at. % Si content, a topological transition of the neck-formation type is revealed, which can account for the experimentally observed peculiarities of the transport properties of the Al-Si system. A similar transition is also found in the Al-Ge system, and the appearance of the anomalous transport coefficients at Ge concentrations of about 10 at. % is predicted. In addition, it is shown that the increase in the concentration of the dopants gives rise to nesting of the Fermi surface sheets (superposition of electron-hole pockets). This peculiarity of the Fermi surface can be responsible for the enhancement of the superconductivity and the instability of the crystal structure observed in the Al_1?xSi_x and Al_1?xGe_x solid solutions.     

Phase diagrams of transition metals and the pseudopotential method

Phase stability boundaries for transition metals are derived from the condition of electron spectrum degeneration with respect to an external field.     

Electron spectrum and wave functions of icosahedral quasicrystals

Electron spectra and wave functions of icosahedral quasicrystals have been investigated in the tight-binding approximation using the two-fragment structural model (the Amman-MacKay network) with “central” decoration. A quasicrystal has been considered as a limiting structure in a set of optimal cubic approximants with increasing lattice constants. The method of level statistics indicates that the energy spectrum of an icosahedral quasicrystal contains a singular (nonsmooth) component. The density of electron states has been calculated for the first four optimal cubic approximants of the icosahedral quasicrystal, and the respective Lebesgue measures of energy spectra of these approximants have been obtained. Unlike the case of a one-dimensional quasiperiodic structure, the energy spectrum of an icosahedral quasicrystal does not contain a hierarchical gap structure typical of the Cantor set of measure zero in a one-dimensional quasicrystal. Localization of wave functions in an icosahedral quasicrystal has been studied, and their “critical” behavior has been detected. The effect of disorder due to substitutional impurities on electron properties of icosahedral quasicrystals has been investigated. This disorder makes the electron spectrum “smoother” and leads to a tendency to localization of wave functions. Zh. éksp. Teor. Fiz. 113, 1009–1025 (March 1998)     

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.     

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.