Preparation, structural analysis and dielectric properties of Bi x La1−x FeO3 perovskite

Rare earth element substituted bismuth ferrites (BiFeO₃) are of enormous importance as magnetoelectric materials. The polycrystalline samples of Bi _x La_1−x FeO₃ (x=0, 0.2, 0.4, 0.6, 0.8) were prepared by solid-state reaction using standard ceramic method. The single-phase formation of these compounds was confirmed by X-ray diffraction (XRD) studies. The samples with x=0, 0.2, 0.4, 0.6 are found to be orthorhombic while the sample with x=0.8 is triclinic. The dielectric constant (ε′) and dissipation factor (tan δ) were measured in the frequency range 100 Hz to 1 MHz at room temperature and as a function of temperature at certain fixed frequencies (1 kHz, 10 kHz, 100 kHz, 1 MHz). All the samples showed dielectric dispersion. The dielectric constant with temperature shows a broad peak; the peak temperature shifts with frequency which reflects the relaxor-type behavior. The peak above 600 K in the measured temperature range corresponds to antiferromagnetic ordering temperature (Néel temperature). The broadness of the peak changes with composition. The ac conductivity as well as ε′ are found to be maximum for the sample x=0.2 at room temperature.     

Plastic deformation under high-rate loading: The multiscale approach

A two-level approach has been proposed for describing the plastic deformation under high-rate loading of metals. The characteristics of the motion of dislocations under shear stresses have been investigated at the atomistic level by using the molecular dynamics simulation. The macroscopic motion of a material has been described at the continuum level with the use of the model of continuum mechanics with dislocations, which uses information obtained at the atomistic level on the dislocation dynamics. The proposed approach has been used to study the evolution of the dislocation subsystem under shock-wave loading of an aluminum target. The behavior of the dynamic yield stress with an increase in the temperature has been analyzed. The results of the calculations are in good agreement with experimental data.     

On thermodynamic similarity of the stability boundaries of metastable metal states

The data on the thermodynamic and kinetic stability boundaries of liquid and solid Pb, Li, Al, Cu, and Fe metals over a wide range of pressures and temperatures accumulated by the authors are analyzed and compared. Molecular-dynamics models using the embedded atom and Lennard-Jones potentials are considered. Examples of assuredly absent similarity are given, and the possibility of constructing approximate similarity is discussed. The following variants for constructing dimensionless parameters are considered: the use of critical point parameters (for the liquid phase), the use of Simon parameters, and the use of parameters reached at the stability boundary at zero pressure (the latter variant was most effective for ordering the stability boundaries of crystals).     

Infinite Töplitz–Lipschitz matrices and operators

We introduce a class of infinite matrices , which are asymptotically (as |s| + |s′| → ∞) close to Hankel–T?plitz matrices. We prove that this class forms an algebra, and that flow-maps of nonautonomous linear equations with coefficients from the class also belong to it.     

A KAM theorem for space-multidimensional Hamiltonian PDEs

We describe a method of translating a Lambek grammar with one division into an equivalent context-free grammar whose size is bounded by a polynomial in the size of the original grammar. Earlier constructions by Buszkowski and Pentus lead to exponential growth of the grammar size.     

Influence of plastic deformation on fracture of an aluminum single crystal under shock-wave loading

The plastic deformation and the onset of fracture of single-crystal metals under shock-wave loading have been studied using aluminum as an example by the molecular dynamics method. The mechanisms of plastic deformation under compression in a shock wave and under tension in rarefaction waves have been investigated. The influence of the defect structure formed in the compression wave on the spall strength and the fracture mechanism has been analyzed. The dependence of the spall strength on the strain rate has been obtained.