A ``universal' dynamical system generated by a continuous map of the interval

In this paper we show that there is a continuous map of the interval such that any -limit set of any continuous map can be transformed by a homeomorphism to an -limit set of . Consequently, any nowhere-dense compact set and any finite union of compact intervals is a homeomorphic copy of an -limit set of .

     

Ab initio calcuation of ideal strength for cubic crystals under three-axial tension

Ab initio calculation of ideal strength of cubic crystals under three-axial tension was performed using the LMTO-ASA method. Computed values are in a good agreement with those obtained previously by means of semi-empirical polynomial approach. The values of equilibrium lattice parameter obtained in the framework of ab initio method are well comparable with the experimental data whereas a less satisfactory agreement was achieved in the case of bulk moduli.     

The origin of lattice instability in bcc tungsten under triaxial loading

Abstract

Stability of ideal bcc tungsten crystal under triaxial tensile loading was explored from first principles using an analysis of both elastic and dynamic stability. The triaxial stress state was considered as a superposition of axial and biaxial transverse stresses. The region of attainable stresses which was delimited using the computed tensile stress maxima was marginally reduced by occurrence of soft phonons in the crystal lattice. While, under purely hydrostatic tension, the crystal was predicted stable up to 48 GPa, greater magnitude of a differential stress reduced the value of a mean (hydrostatic) stress associated with first phonon instabilities to about 35 GPa. This value is rather close to that recently determined in experiment. Computed phonon spectra were successfully verified with the help of atomistic models of microscopic lattice deformation.     

Dynamic stability of fcc crystals under isotropic loading from first principles

Lattice dynamics and stability of four fcc crystals (Al, Ir, Pt and Au) under isotropic (hydrostatic) tensile loading are studied from first principles using the linear response method and the harmonic approximation. The results reveal that, contrary to former expectations, strengths of all the studied crystals are limited by instabilities related to soft phonons with finite or vanishing wavevectors. The critical strains associated with such instabilities are remarkably lower than those related to the volumetric instability. On the other hand, the corresponding reduction of the tensile strength is by 20% at the most. An analysis of elastic stability conditions is also performed and the results obtained by means of both approaches are compared.     

Solute segregation at 46.8°(111) twist grain boundary of a phosphorus doped Fe–2.3%V alloy

The Auger electron spectroscopy study on chemistry of the 46.8°(111) twist grain boundary of an Fe–2.3%V alloy showed an extended phosphorus enrichment at temperatures in range of 500 °C and 800 °C. Simultaneously, slight but nearly independent segregation of vanadium was also detected. The standard enthalpy and entropy of grain boundary segregation of phosphorus and vanadium were determined according to the Guttmann model of multicomponent interfacial segregation. Obtained data clearly show that this Σ = 19 coincidence boundary is special (i.e. low energy interface). The data also fit well with the predictive model of grain boundary segregation and confirm that phosphorus segregates interstitially at the grain boundary while vanadium substitutes iron atoms in the interface structure.