On the role of solute atom — dislocation elastic interaction in solid solution hardening of Cu single crystals

Elastic interaction of solute atoms with dislocations has been reconsidered in Labusch's theory of solid solution hardening. New interaction parametersε are suggested and tested on dΤ/dc ^2/3 dependence onε ^4/3 for Cu base solid solutions.     

On the integrated density of states for crystals with randomly distributed impurities

In the present paper, we discuss spectral properties of a periodic Schrödinger operator which is perturbed by randomly distributed impurities; such operators occur as simple models for crystals (or semi-conductors) with impurities. While the spectrum itself is independent of the concentrationp of impurities, for 0<p<1, we focus our attention on the limiting behavior of the integrated density of states _p of the random Schrödinger operator, inside a spectral gap of the periodic operator, asp0. Denoting byU ₀ the set of eigenvalues (in the gap) of the reference problem having precisely one impurity (located at the origin, say), we show that the integrated density of states concentrates around the points ofU ₀, in the sense that _p (U ) is of orderp, for any fixed -neighborhoodU ofU ₀, while _p (K)C·p ², for any compact subsetK of the gap which does not intersectU .Research partially supported by Deutsche Forschungsgemeinschaft     

Surface deformation due to non-homogeneous distribution of solute atoms in crystals

Deformation caused by a modulated distribution of solute atoms, periodic in one dimension, in a plate-like crystal is studied within the framework of the isotropic theory of elasticity. The exact formulae for the strain and displacement field, which changes near the surface due to relaxation of the internal concentration stresses, can be used for determination of the distribution of the solute atoms by X-ray diffraction techniques.     

Localisation of elastic waves in two-dimensional randomly disordered solid phononic crystals

Combined with the supercell technique, the plane wave expansion method is used to calculate the band structures of the two-dimensional solid–solid phononic crystals with the random disorders in either radius or location of the scatterers. Phononic systems with plumbum scatterers embedded in an epoxy matrix are calculated in detail. The influences of the disorder degree on the band structures for both anti-plane and in-plane wave modes are investigated. It is found that, with increase of the disorder degree, the band gaps become narrower with more flat bands appearing in the gaps. Both displacement distribution and response spectra show that at the flat bands, elastic waves are localised due to the presence of the disorder. Wave localisation is more pronounced at the flat bands near the lower/upper edge for the radius/location disorder. Wave propagation and localisation in a randomly disordered system with a point defect is also studied. The influence of the disorder on the point-defect state is discussed. The results show that the disorder can tune the frequencies of the defect states. It is particularly noticed that the double degenerate mode appearing within the gap of the mixed in-plane waves is split up into two separated ones when the random disorder is introduced into the system. Generally, the influence of the disorder is more pronounced for the mixed in-plane modes than the anti-plane modes. The analysis of this paper is relevant to the assessment of the influences of manufacture errors on wave behaviours in phononic crystals as well as the possible control of wave propagation by intentionally introducing disorders into periodic systems.     

Misoriented surfaces with randomly distributed steps

Models for surfaces with randomly distributed steps having a peferred direction, i.e., an unequal probability of encountering an up or down step when going from one lattice site to the adjacent one, are constructed. The terrace widths obey a geometric distribution function. A closed-form solution is obtained for the angular distribution of the electron diffraction beam intensity. We show that both the angular width of the diffracted beam and the Bragg peak position oscillate as a function of the incident electron energy. Practical implications of these results are discussed.     

Flame spread along a thin solid randomly distributed combustible and noncombustible areas

Flame spread route in fire strongly depends on distribution of combustible materials. Two types of scenario are considered in flame spread when combustible materials randomly distributed; one case is that flame spreads and combustible materials burn out, and the other case is that flame self-extinguishes on the way. The threshold of burning out or self-extinguishing may be determined by quantity of combustible materials and their placement in space. Our objectives are to clarify the characteristics and threshold of flame spread. In this paper, we examine non-uniform flame spread in open air along a thin combustible solid with randomly distributed pores, which are considered as noncombustible space. Experimental results show that the flame spread rate for S ≦ 1 (S ≡ d/L_h, S: scale ratio, d: pore-scale, L_h: pre-heat length ahead of flame leading edge measured by using a shadowgraph method) increases with increasing the porosity and reaches maximum value approximately at 20–30% of porosity, while the flame spread rate for S > 1 is almost constant. Over 40% of porosity, the flame spread rate for both S ≦ 1 and S > 1 decreases. The flame cannot spread and completely self-extinguish over 60% of porosity independently with pore-scale and shape. The threshold of flame spread is related with the average-number of slit, N_s, which is made by connecting each pores. The N_s as the threshold of flame spread is unity for S > 1, while the modified average-number of slit (N_s × S) becomes two for S ≦ 1.     

On the particle hardening in Cu-Cd alloy single crystals

The transmission electron microscopy of Cu-Cd single crystals deformed previously was performed to explain the hardening effect measured. The increment of the critical resolved shear stress is explained by the size misfit effect of the observed particles.     

Diffraction from surfaces with randomly distributed steps

A closed-form solution is obtained for the angular distribution of intensity in diffraction from a surface on which the terrace size distribution is given by the geometric distribution, i.e. a surface in which the occurrence of steps is random. Several distributions of step heights that are integral multiples of the monatomic step height are considered. It is shown that a random occurrence of monatomic steps will cause some multiatomic steps. If a very broad distribution of step heights is assumed, the beam width no longer oscillates with energy but approaches a constant value except at the characteristic energies of zero width. Comparisons are made with a previous model and with measurements on GaAs(110).     

Interaction between interstitial hydrogen and substitutional solute atoms in solid solutions of niobium-base ternary alloys

The interaction between interstitial hydrogen and substitutional solute atoms has been investigated by the measurements of the hydrogen solubility and the influence of hydrogen charging on the half-width of the X-ray reflection lines in pure Nb, Nb-5%V, Nb-5%Mo and Nb-5%Ta alloys. In Nb-5%V and Nb-5%Mo alloys, the solubility considerably increases with respect to pure Nb. On the other hand, the solubility hardly changes in Nb-5%Ta alloy. With addition of hydrogen, the half-widths in pure Nb and Nb-5%Ta alloy show a monotonic increase, but in Nb-5%V and Nb-5%Mo alloys they show a minimum. The results are explained by the interaction of hydrogen with substitutional solute atoms. The interaction is considered to be caused by the internal strain induced by the difference in atomic radii between substitutional and solvent (Nb) atoms.     

Electronic structure of titanium monoxide with randomly distributed vacancies

The electronic structure of titanium monoxide TiO _y (0.810 ≤ y ≤ 1.262) in the high-temperature cubic phase with vacancies randomly distributed over the titanium and oxygen sublattices is calculated in the coherent potential approximation. The changes in the electronic spectra with the concentration of vacancies are retraced. The calculated spectra are compared to the available experimental data.     

Entangling atoms in photonic crystals

We propose a method for entangling a system of two-level atoms in photonic crystals. The atoms are assumed to move in void regions of a photonic crystal. The interaction between the atoms is mediated either via a defect mode or via a resonant dipole-dipole interaction. We show that these interactions can produce pure entangled atomic states. We analyze the problem with parameters typical for currently existing photonic crystals and Rydberg atoms and we show that the atoms can emerge from photonic crystals in entangled states. Depending on the linear dimensions of the crystal we estimate that a pair of atoms entangled in a photonic crystal can be separated by tens of centimeters. Receive 11 June 1999 and Received in final form 4 October 1999     

Fast solute diffusion in solid and supersaturated solid solutions

In this paper, we review the experimental data concerning fast diffusion of solute in Pb matrix and Pb (solute) solid solutions. Using both calorimetric and radiotracer techniques the temperature dependence of solute diffusion coefficients in Pb (solute) supersaturated solid solutions is determined. On the basis of experimental results it is shown that these coefficients can only be understood by assuming different defect states for solutes in solid and supersaturated solid solutions.     

Work hardening of alloys with short range order of atoms

The study presents analysis of the experimental flow curves for polycrystals of fcc concentrated solid solutions Ni-Cr and Ni-Mn. It was demonstrated that the flow curves of these alloys can be divided into a number of stages of work hardening, and stage II bisects into two substages: with parabolic, and linear hardening. It was demonstrated that the shape of the curves of work hardening is determined by the type of dependence L = f(σ), where L is the average path length of the motion of the dislocation;σ is flow stress. Some possible critical stresses of transition from stage to stage are discussed.     

On the strength distribution of a field created by randomly distributed dipoles

The probability distribution of the strength of a field created by parallel dipoles arranged randomly, on average, uniformly is considered. The problem of divergence at small distances is analyzed. It is shown that, for any, including an arbitrarily small, number of dipoles ε in the cutoff sphere, the average field value is zero. In the case ε ? 1, the field distribution consists of a central part, whose half-width is of an order of the average polarization of a medium, and a very wide and structured background. An interpolation formula for the Fourier image of the field distribution applicable for arbitrary values of ε is proposed. An analogy with the theory of spectral line broadening is established. The connection with the problems of molecular optics and inhomogeneous Stark broadening of spectral lines is discussed.     

Magnetic properties of nonmagnetic metals with randomly distributed paramagnetic impurities

A generalized mean field theory for disordered systems with the RKKY interaction is constructed on the basis of calculation and analysis of distribution functions for random magnetic fields produced by magnetic moments with an irregularly spatial distribution. These distribution functions are determined by two methods: (i) analytically and (ii) numerically by statistical processing of the results of calculation of random fields in a model system. For metals diluted by magnetic impurities, it is shown that the ground state of the system becomes magnetically ordered when the impurity concentration exceeds a certain critical value depending on the type of crystal lattice of the metal and the sample shape. The magnetic phase diagram of the system is determined and the temperature dependence of its magnetic susceptibility, the concentration dependence of the Curie temperature, and the temperature and concentration dependences of the magnetization and magnetic part of the heat capacity of the system are established.     

Bombardment of alkali halide crystals with medium-energy atoms

The sputtering characteristics of KCl and NaCl alkali halide single crystals by bombardment with argon and mercury atoms are investigated. The sputtering coefficients are measured in the energy range 0.5–3 keV. Anisotropy is found in sputtering at various incident angles of the beam. The yield of charged particles during bombardment of thin specimens (of the order of 8–20 m) of KCl single crystals is investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 55–59, July, 1984.