The interaction between non-parallel {102} crystallographic shear planes in slightly reduced tungsten trioxides

The displacements of non-parallel {102} CS planes in slightly reduced WO₃ observed by electron microscopy were quantified with the theory of elasticity for an isotropic continum. By this calculation, the magnitude of the force between cations in CS planes was estimated. It was found that the principle force involved was an attractive one between cations in the CS plane which was calculated to be $\text{～ 1.2 × 10}{}^{13}\text{(}\text{dyne}\text{cm}{}^2\text{) = 7.8 (}\text{eV}\text{A}\text{?}{}^3\text{)}$. Using this value, the magnitude of the strain energy was also evaluated, and was found to be larger in value than the energy associated with the dissociation of oxygen atoms from WO₃ lattice. This suggests that the strain energy plays a dominant role in the behaviour of CS planes.     

Elastic interaction of point defects with dislocations

Elastic interaction between dislocation and point defects with spherical symmetry is investigated theoretically by means of the sphere-in-hole model. The interaction energy due to the different elastic moduli of the point defect and matrix is computed and then added to the interaction energy due to the size effect. The force on and the probable position of the point defect is determined. The numerical results for some selected solute atoms are computed by means of available experimental data.The results are compared with other recent papers and some experimental applications are briefly discussed.The author is much indebted to F. Kroupa, CSc., for fruitful discussions and valuable comments.     

Kinematics of edge dislocations. I. Involutive distributions of local slip planes

The geometry of continuous distributions of dislocations and secondary point defects created by these distributions is considered. Particularly, the dependence of a distribution of dislocations on the existence of secondary point defects is modeled by treating dislocations as those located in a time-dependent Riemannian material space describing, in a continuous limit, the influence of these point defects on metric properties of a crystal structure. The notions of local glide systems and involutive distributions of local slip planes are introduced in order to describe, in terms of differential geometry, some aspects of the kinematics of the motion of edge dislocations. The analysis leads, among others, to the definition of a class of distributions of dislocations with a distinguished involutive distribution of local slip planes and such that a formula of mesoscale character describing the influence of edge dislocations on the mean curvature of glide surfaces is valid.     

Elastic interaction between a dilatation centre and split dislocations in b.c.c. metals

The elastic interaction energy between a dilatation centre and 1/2[111] dislocation split on {110} planes in b.c.c. metals is calculated for sessile and planar splittings of screw dislocation and for planar splitting of edge dislocation; the splitting is considered as a model of the dislocation core. It is concluded that the interstitial impurity atom has three or four possible minimum energy positions in the dislocation core. A hypothesis on the impurity jumps in the dislocation core is proposed.On leave from theInstitute of Physics, Hanoi, VDR.     

On the dynamic interaction between moving dislocations

Received: 25 August 1997/Accepted: 23 October 1997     

Elastic interaction between small nuclei

The radial distribution of gold nuclei obtained by evaporation in UHV onto alkali halide surfaces is measured, and is analysed in terms of parameters such as the nature of the substrate and the mean diameter of nuclei. This analysis seems to prove the presence of repulsive elastic forces between nucleus pairs due to the overlap of the strain fields induced by the nuclei in the substrate.     

The incorporation of slip dislocations in twins

The conditions for the incorporation of slip dislocations either propagating into a twin or engulfed by a growing twin are studied from the geometrical point of view. The resulting dislocation formed in a twin is independent of the mechanism of the incorporation. Under suitable conditions no stacking faults are formed at the twin boundary. The decomposition of twinning dislocations forming the noncoherent twin boundary is described using complementary partial twinning dislocations. The theory is formulated for both type I and II twins. Compound twins are also briefly treated in the discussion. Using the tensor notation all the formulae are given in the form valid for all crystal structures.The author is greatly indebted to Mr. J. Koík for many helpful comments.     

The foundations of turbulent motion flow between parallel planes

It is suggested that turbulence is a kind of macroscopic viscosity; the usual turbulent motion being a combination of purely dynamical motion and (proper) turbulence. A flow in a channel is considered, the equation for the spectrum of (proper) turbulence and the expression for the spectrum are derived.     

On hydromagnetic turbulent shear flow between moving parallel planes

Hydromagnetic turbulent shear flow of viscous, incompressible, electrically conducting fluid between two infinite uniformly porous moving parallel planes in the presence of axial and transverse magnetic field has been studied by the semi-empirical method. The expressions for the mean distributions for velocity and magnetic field for turbulent shear flow have been obtained for both the cases. As particular cases, the results have been obtained if the planes are fixed. The solutions obtained when the magnetic field is axial have been shown graphically for turbulent and laminar flows.     

Interaction between slip dislocations and twins in α-uranium II. Interaction forces

The forces on dislocations propagating through twins are calculated using the anisotropic elasticity. The anisotropic boundary force is calculated assuming that the twin boundary is of the welded type. The stresses necessary for the passage of dislocations through twins are compared with the estimated stresses for a homogeneous thermally activated nucleation of twins.     

The equilibrium shape of a two-dimensional crystal between parallel planes

By applying rather standard techniques for equilibrium crystal shapes (Wulff construction), we derive a construction for the equilibrium shape of a 2D crystal grown between two parallel plane substrates. The critical distance of the substrates at which this crystal splits into two parts is computed as a function of the wall free energy of the substrates. This may open new perspectives for the measurement of wall free energies.     

The foundations of turbulent motion flow between parallel planes. III

It is suggested that the dynamical vibrations interact with (proper) turbulence which acts as a kind of kinetic damping force; this transformes the discrete vibrations into a continuous spectrum; it contains most of the turbulent energy. The theoretical spectrum is in satisfactory agreement withLaufer's measurements.     

The foundations of turbulent motion flow between parallel planes. II

It is suggested that turbulence should be treated as a kind of macroscopic viscosity whose main effect is dissipation of energy. It is shown that turbulent motion could only be accounted within the framework of threedimensional motion. The equation for the (proper) turbulence is derived.     

Interactions between slip dislocations and twins in α-uranium I. Geometrical and energetical considerations

The geometrical conditions for the propagation of dislocations through the twins are applied to the main slip and twinning systems in-uranium. The energy of dislocations moving through a twin is calculated using the isotropic elasticity. It is shown that the principal slip system with the Burgers vector [100] can easily propagate only through the {130} compound twins. The possibility of uncommon slip systems in twins crossed by slip bands is thoroughly discussed.     

On the interaction between dislocations and cracks in one-dimensional hexagonal quasi-crystals

The solution of elasticity problems involving the interaction between dislocations and cracks plays a fundamental role in many practical and theoretical applications. Although elasticity problems involving dislocation or cracks in quasi-crystals have been investigated in many papers, the analysis is limited to a single defect. This paper investigates the interaction of defects in one-dimensional hexagonal quasi-crystals using the complex variable function method. The interaction force between two parallel dislocations is presented and the analytic solutions of elastic fields of interaction between a dislocation and a crack are obtained. A version of the well-known Peach－Koehler formula in one-dimensional hexagonal quasi-crystals is given.     

Elastic stress of moving dislocations in finite crystals

The elastic stress of a single crystal with finite dimensions is investigated by means of the linear continuum theory; external forces and dislocation motion are assumed to be known. A formal solution is derived with a Green's dyadic. The dyadic is expanded in a series, the first term of which delivers the well-known solution for infinite crystals, the following terms describe successive reflections of sound at the surface of the finite crystal. They can be computed by iteration. This expansion corresponds to the physical situation of pulse-echo-experiments. Fourier transforms lead to analogous expressions describing the influence of the surface on time-periodic dislocation experiments.     

X-ray diffraction determination of easiest slip planes in amorphous-crystalline polymers

A simple X-ray diffraction technique for determining the easiest slip planes in amorphous-crystalline polymer grains is suggested. The efficiency of the technique was demonstrated with polyethylene and polyamide-6.     

Special interaction between quasiperiodic grain boundaries and lattice dislocations in crystalline solids

A theoretical model is suggested which describes phason imperfections (specific excitations) in a quasiperiodic grain boundary in a polycrystalline solid as dilatation flexes. In the framework of the model, an elastic stress field of the quasiperiodic grain boundary is calculated as a stress field created by an ensemble of dilatation flexes (phason imperfections) located in the boundary. It is shown that there is a special elastic interaction between crystal lattice defects and quasiperiodic grain boundaries comprising phason imperfections. The strengthening effect in plastically deformed polycrystalline solids is quantitatively described which is related to the special elastic interaction between lattice dislocations and quasiperiodic grain boundaries. Received: 29 October 1996 / Revised: 22 August 1997 / Accepted: 13 November 1997