Effect of doping with divalent cationic impurities on relative mobility of edge and screw dislocations in NaCl crystals

In NaCl:Ca and NaCl:Pb crystals, we have investigated the effect of the impurity concentration and temperature on the parameter ξ=l _e /l _s where l _e and l _s are the path lengths traveled by edge and screw dislocations in the stress field of an indenter. The results obtained are explained taking into account additional inhibition of screw dislocations by debris. State Medical University, Moldavian Republic. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 98–102, May, 1996.     

The velocity of acoustic phonons in crystals with edge dislocations and point impurities

The velocity of longitudinal long-wave phonons in crystals with a small number of randomly distributed static edge dislocations was shown to be the same as in ideal crystals. The correction to the velocity of phonons is determined by their interaction with the field of lattice deformations caused by the presence of dislocations. The field of deformations of dislocation displacements is long-range. In addition, these deformations experience sign reversal when the sign of the coordinate perpendicular to the dislocation line and Burgers vector changes. It follows that a crystal contracts or expands in this direction because of the interaction of phonons with dislocations as the defect deformation sign alters. Such an anisotropic volume (and density) change over the whole crystal should however be balanced somehow. For this reason, the density of samples with edge dislocations should remain constant, and the correction δc to the velocity of phonons should be zero. The procedure for averaging that gives δc = 0 is based on the independence of this macro value from the orientation of phonon momemtum incident on randomly distributed dislocations, the unaveraged correction being a diverging value because of the long-range character of the field of defect deformations. For comparison, the correction to the velocity of phonons in crystals with point impurities was calculated. Lattice deformation caused by such defects is isotropic. For this reason, the mean density of crystals with point impurities and the velocity of phonons in them are different from those in ideal crystals. All calculations were performed using the Dyson equation derived on the basis of the Keldysh diagram technique.     

The influence of thermal processing on the relative mobility of edge and screw dislocations in NaCl crystals

The effect of thermal processing on the mobility of dislocations is investigated in NaCl crystals doped with impurities of various types—high-solubility impurities (Ca²⁺) and low-solubility impurities (Pb²⁺). The results obtained after aging and thermal processing indicate that the type of impurity and its state (e.g., level of aggregation) in the crystal have a strong effect on the relative mobility of edge and screw dislocations, and also on the parameters of double transverse slip. Fiz. Tverd. Tela (St. Petersburg) 41, 1041–1043 (June 1999)     

Stable edge dislocations in finite crystals

Dislocations have been considered as mechanically unstable defects in bulk crystals, ignoring the Peierls oscillations. Eshelby [J. Appl. Phys. 24 (1953) p.176] had showed that a screw dislocation can be stable in a thin cylinder. In the current work, considering Eshelby's example of an edge dislocation in a single crystalline plate, we show that an edge dislocation can be stable in a finite crystal. Using specific examples, we also show that the position of stability of an edge dislocation can be off-centre. This shift in the stability from the centre marks the transition from a stable dislocation to an unstable one. The above-mentioned tasks are achieved by simulating edge dislocations using the finite element method.     

Energy characteristics of edge dislocations in quasicrystals

A model is developed for describing phason defects in quasicrystals in the form of dilation filaments. This model is used to calculate the energy of edge dislocations in quasicrystals including the interaction of this type of dislocation with its “intrinsic” phason defects and with the equilibrium phason defects present in a quasicrystal. It is shown that the contribution of “intrinsic” phason defects to the total energy of an edge dislocation in a quasicrystal is substantial. Fiz. Tverd. Tela (St. Petersburg) 39, 2003–2007 (November 1997)     

The gauge theory of dislocations: Static solutions of screw and edge dislocations

We investigate the T(3)-gauge theory of static dislocations in continuous solids. We use the most general linear constitutive relations in terms of the elastic distortion tensor and dislocation density tensor for the force and pseudomoment stresses of an isotropic solid. The constitutive relations contain six material parameters. In this theory, both the force and pseudomoment stresses are asymmetric. The theory possesses four characteristic lengths ?₁, ?₂, ?₃ and ?₄, which are given explicitly. We first derive the three-dimensional Green tensor of the master equation for the force stresses in the translational gauge theory of dislocations. We then investigate the situation of generalized plane strain (anti-plane strain and plane strain). Using the stress function method, we find modified stress functions for screw and edge dislocations. The solution of the screw dislocation is given in terms of one independent length ?₁ = ?₄. For the problem of an edge dislocation, only two characteristic lengths ?₂ and ?₃ arise with one of them being the same ?₂ = ?₁ as for the screw dislocation. Thus, this theory possesses only two independent lengths for generalized plane strain. If the two lengths ?₂ and ?₃ of an edge dislocation are equal, we obtain an edge dislocation, which is the gauge theoretical version of a modified Volterra edge dislocation. In the case of symmetric stresses, we recover well-known results obtained earlier.     

Influence of monovalent cationic impurities on plasticity of AgCl

The hardening effect of Li⁺, Na⁺, K⁺ and Rb⁺ impurities in polycrystalline AgCl was investigated. With increasing concentration of the impurities the flow stress increases and the plasticity decreases. By doping with a few ppm of Rb⁺ AgCl becomes very brittle. Comparing the results with the statistical theory of solid solution hardening, deviations were found.     

Correlation effects in an ensemble of edge dislocations

A kinetic theory of correlation interaction in an ensemble of edge dislocations is developed taking into account the effects of the fluctuation dynamics of dislocations. Equations of evolution of a dislocation ensemble are derived including the correlation interaction between dislocations. A criterion of instability of a uniform dislocation distribution is established. It is shown that the nucleation of spatially nonhomogeneous dislocation structures due to correlation instability is mainly determined by the specific features of the elastic interaction between dislocations and depends only slightly on the mechanism of dislocation kinetics. The theory is applied to calculating the dispersion of an internal stress field.     

Interaction of two edge dislocations in free-space propagation

This paper studies in detail the interaction of two edge dislocations nested in a Gaussian beam propagating in free space. It shows that in free-space propagation the edge dislocations are unstable and vanish, and two noncanonical vortices with opposite topological charge take place when off-axis distances c₁ and c₂ of two edge dislocations are non-zero, and the condition k²w₀⁸+32c₁c₂(w₀²-2c₁c₂)z²>0 is fulfilled (k-wave number, w₀-waist width). A noncanonical vortex appears when one off-axis distance is zero. However, one edge dislocation is stable when two edge dislocations are perpendicular and one off-axis distance is zero. Two perpendicular edge dislocations both with zero off-axis distance are also stable. The analytical results are illustrated by numerical examples.     

Electron-trapping centers in additively colored alkali halide crystals doped with divalent impurities

A study has been made of the temperature dependences of the dielectric loss and structure-sensitive conductivity of additively colored KCl single crystals having a Sr²⁺ impurity. The optical absorption spectra were recorded before and after heat treatment of the colored crystals. A model for Z-centers is proposed on the basis of the results.Translated from Izvestiya VUZ. Fizika, No. 10, pp. 26–29, October, 1969.In conclusion the author thank Professor E. K. Zavadovskaya for suggesting thistopic and for discussion of the results.     

The optical absorption of hydroxyl ions associated with divalent calcium in NaCl

The measurements confirmed the association of Ca²⁺ and OH^– in NaCl: CaCl₂ + NaOH, which causes an increase and a shift +0·031 of the OH^– absorption at 2·8, the extinction of the OH^– UV-absorption at 184 nm and the occurrence of new absorption bands between 160 and 210 nm.The measurements were performed at the II. Physikalisches Institut of the University of Stuttgart.     

Deflection of quadratic solitons at edge dislocations

We report the observation of deflection of optical solitons generated in the frequency doubling of light beams containing edgelike topological amplitude and phase dislocations. The angular deflection of the solitons was found to be controllable through the position of the dislocation. The experiments were conducted near phase matching in a bulk potassium titanyl phosphate crystal pumped with picosecond light pulses at 1064 nm.     

Smectic-A edge dislocations in a very thin cell

We study stable “bookshelf” smectic-A structures within a very thin plane-parallel cell of thickness L in which the mismatch between surface preferred (d _s) and intrinsic (d₀) smectic layer thicknesses occurs. The Landau-Ginzburg approach based on a complex smectic order parameter is used. For a weak enough smectic positional anchoring strength W smectic layers adopt the modified bookshelf profile. In a thick enough cell with increasing W a lattice of edge dislocations is continuously formed at the confining surfaces and then depinned from them. The structure with dislocations is formed when the condition d ₀/( d ₀/d _s - 1) ∼ 2 is fulfilled, where is the positional surface anchoring extrapolation length. If the cell is thin enough the dislocations formed at opposite cell plates annihilate and consequently the smectic layers adopt a locked bookshelf structure. This transition is discontinuous and takes place when d ₀/(L d ₀/d _s - 1) ∼ 5 is realized. To observe these transitions in a cell of thickness L∼ 1μm the conditions W∼ 10^-6 J/m ² and d ₀/d _s - 1∼ 5 ^. 10^-4 have to be fulfilled. All the three qualitatively different structures coexist at the triple point. Received 21 February 2002     

Ionic thermocurrents in LiF and NaF containing substitutional divalent cation impurities

Abstract

By means of ITC and EPR we study the symmetry of the impurity vacancy dipoles in LiF and NaF.     

Observation of edge dislocations in helical smectic liquid crystals

We report the observation of elementary edge dislocations in smectic liquid crystals possessing helical structure. The dislocations were observed in the entire temperature range of helical phases, including ferroelectric, ferrielectric and antiferroelectric phases. The mechanism for visualizing the dislocations is based on the phenomenon of selective reflection of circularly polarised light. The performed observations of dislocations deliver not only information on the mechanisms of defect creation in various chiral smectic phases, but also on the structure and properties of the investigated smectics, often inaccessible using standard methods.     

Duration of stoppage of dislocations at obstacles in NaCl crystals

The method of selective etching is employed to investigate the time for which dislocations are stopped in front of obstacles under conditions of constant loading of the investigated samples. It is shown that in NaCl crystals the obstacles have an impurity origin and that they have a wide range of strengths.Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 51–54, May, 1976.