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.     

Orientation effects in interaction of screw dislocation with interstitial impurity atom in b.c.c. lattice

The cross-slip and pinning of a 1/2a〈111〉 screw dislocation in b.c.c. metals in the vicinity of an interstitial impurity atom are studied in dependence on crystal orientation. To this purpose, the interaction energy between the dislocation and an interstitial atom is calculated in an anisotropic elastic continuum and it is assumed that the screw dislocation moves microscopically on {112} or {110} planes between its stable configuration positions in b.c.c. lattice. It is found that the probability of induced cross-slip is orientation dependent. This result is used for discussion of orientation dependence of the change of CRSS due to increased carbon content which was experimentally determined for Fe-3.2% Si alloy single crystals in a previous paper (Blahovec J., Kade?ková S.: Czech. J. Phys.B 21 (1971), 846).     

Sessile splitting of screw dislocations in b.c.c. metals

The energies of six different sessile splittings of screw dislocation 1/2 [111], which can occur in b.c.c. metals assuming the stacking faults on {110} and {112} planes according to the hard sphere model, are compared. The regions of the values of stacking fault energies on {110} and {112} planes, in which a given splitting is favoured over the other five, are then shown.     

Ab initio study of screw dislocations in Mo and ta: A new picture of plasticity in bcc transition metals

We report the first ab initio density-functional study of <111> screw dislocation cores in the bcc transition metals Mo and Ta. Our results suggest a new picture of bcc plasticity with symmetric and compact dislocation cores, contrary to the presently accepted picture based on continuum and interatomic potentials. Core energy scales in this new picture are in much better agreement with the Peierls energy barriers to dislocation motion suggested by experiments.     

Atomic configurations of a screw dislocation in A b.c.c. lattice

The interaction energy between atomic rows is calculated in the approximation of pairwise interaction. (This approximation is only valid for normal metals). The asymptotic behaviour of this energy is discussed as a function of the conduction electron number. This method fits computing with an iterative process the atomic configurations of a screw dislocation in a lithium lattice. Two configurations are found with three-fold symmetry, showing an asymmetry in (112) planes.     

Peierls-Nabarro model of planar dislocation cores in b.c.c. crystals

Planar dislocation cores on {110} and {112} planes in b.c.c. crystals are studied using the Peierls-Nabarro model with force laws derived from four different interatomic potentials. A numerical iterative method suitable for solution of the Peierls-Nabarro equation is developed. The cores are represented by a continuous distribution of dislocations. The discussion of the correlation between the force laws and corresponding dislocation densities is based on the properties of the Hilbert transform.     

Interatomic forces in the b.c.c. transition metals

Using information obtained from X-ray scattering data, a model for the charge density in the transition metals is constructed. In this model the charge density is given by the sum of the charges situated at the ionic and bond centre sites. Within this framework, expressions for the second order elastic constants and the phonon frequencies in the cubic transition metals are obtained. These quantities have been calculated with and without the bond charge contributions for iron. The comparison with the experimental results shows that the introduction of bond charges, and hence angularity in the force-fields, in iron leads to distinctly better agreement with experiment. From a study of the elastic constants of the other b.c.c. transition metals some observations as to the nature of the angular force fields are made.     

Lattice dynamics of b.c.c. alkaline-earth metals: Barium

Summary The attractive short-range component of the interatomic potential screens the conventional Born-Mayer potential in the framework of the resonance pseudopotential model. The elastic constants are evaluated at the long-wavelength limit of the phonon spectrum and the obtained results are compared with previous experimental values. The numerical calculations show that the attractive component of the potential explains the soft modes in this body-centred cubic (b.c.c.) alkaline-earth metal barium.     

A model for the lattice dynamics of b.c.c. transition metals

Recent ideas proposed by Fielek for the lattice dynamics of f.c.c. noble and transition metals have been extended to b.c.c. transition metals. Phonon dispersion curves, calculated on the basis of this model, for chromium are in fairly good agreement with experimental ones and are far better than those reported so far.     

The non-pair forces and phonon dispersion in heavy alkali metals

Two types of the non-pair forces, one from the Born-Mayer and other from the Morse potential, are derived to discuss the response of the electrons in heavy alkali metals, i.e. rubidium and caesium. These potentials are added to the two-body potential of Morse to account for the ion-ion interactions as well. The potentials so obtained are employed to predict the phonon dispersion relations in the bcc metals, which are also compared with the recent precise neutron scattering data.     

Relaxation near transition metal surfaces

A simple calculation of the relaxation near transition metal surfaces is described. The d electrons are treated in a tight-binding approximation and Born-Mayer type potentials are used to simulate the repulsive part of the energy at short distances. The interplanar spacing is found to decrease at the center of the series and to increase on the wings. For almost empty or filled bands one obtains no relaxation.     

Strengthening at nanoscaled coherent twin boundary in f.c.c. metals

This paper analyses slip transfer at the boundary of nanoscaled growth twins in face-centred cubic (f.c.c.) metals for strengthening mechanism. The required stress for slip transfer, i.e. inter-twin flow stress, is obtained in a simple expression in terms of stacking fault energy and/or twin boundary (TB) energy, constriction energy and activation volume. For nanotwinned Al, Cu and Ni, inter-twin flow stress versus twin thickness remarkably shows Hall–Petch relationship. The Hall–Petch slope is rationalized for various reactions of screw and non-screw dislocations at the TB. Additionally, strengthening at the boundary of nanoscaled deformation twins in f.c.c. metals is analysed by evaluating required twinning stress. At small nanograin size, the prediction of deformation twin growth stress shows inverse grain-size effect on twinning, in agreement with recent experimental finding.     

Peierls-Nabarro model of non-planar screw dislocation cores

The Peierls-Nabarro model originally developed for dislocations with planar cores is modified to describe the cores of screw dislocations extended along two or three intersecting slip planes, under the action of external stress. This concept generalizes the simplified concept of sessile splitting of screw dislocations into singular partials and enables an instructive interpretation of fully atomistic models of screw dislocation cores developed recently for b.c.c. metals. As an example, a numerical solution of the modified Peierls-Nabarro equation is given for the equilibrium configuration of a 1/2 [111] screw dislocation core in -Fe extended along three {110} planes.     

Splitting of dislocations in b.c.c. metals on {110} planes

Three possible splittings of a screw dislocation on {110} planes of a metal with a b.c.c. lattice are proposed, their total elastic energy is calculated and the dependence of the splitting width on the stacking fault energy is studied.We wish to express our thanks to B. esták, CSc., and S. Libovický for valuable comments and M. Jiincová for her help in carrying out the numerical calculations.     

Tunneling of screw dislocations in α-Fe

A model of tunneling of 1/2 [111] screw dislocations in b.c.c. metals from sessile to glissile core configurations described by dislocation splittings is proposed and numerical estimates for α-Fe are derived. The critical shear stress of the order of 50 kp/mm² should be temperature independent up to 8 K.     

The effect of shear stress on the screw dislocation core in bcc metals

The screw dislocation core structure in bcc metals under an external shear stress is investigated using the model of generalized splitting as an approximation of the Peierls-Nabarro model of screw dislocation dissociated on three {110} slip planes. The shear stress for which the core structure in this model is unstable is found.     

Shielding effect and emission criterion of a screw dislocation near an interfacial blunt crack

Shielding effect and emission criterion of a screw dislocation near an interfacial blunt crack are dealt with in this paper. Utilizing the conformal mapping technique, the closed-form solutions are derived for complex potentials and stress fields due to a screw dislocation located near the interfacial blunt crack. The stress intensity factor on the crack tips and the critical stress intensity factor for dislocation emission are also calculated. The influence of the orientation of the dislocation and the morphology of the blunt crack as well as the material elastic dissimilarity on the shielding effect and the emission criterion is discussed in detail. The results show that positive screw dislocations can reduce the stress intensity factor of the interfacial blunt crack tip (shielding effect). The shielding effect increases with the increase of the shear modulus of the lower half-plane, but it decreases with the increase of the dislocation azimuth angle. The critical loads at infinity for dislocation emission increases with the increase of emission angle and curvature radius of blunt crack tip, and the most probable angle for screw dislocation emission is zero. The present solutions contain previous results as special cases.     

On the non-uniform motion of dislocations: the retarded elastic fields,the retarded dislocation tensor potentials and the Liénard–Wiechert tensor potentials

The topic of this paper is the fundamental theory of the non-uniform motion of dislocations in two and three space dimensions. We investigate the non-uniform motion of an arbitrary distribution of dislocations, a dislocation loop and straight dislocations in infinite media using the theory of incompatible elastodynamics. The equations of motion are derived for non-uniformly moving dislocations. The retarded elastic fields produced by a distribution of dislocations and the retarded dislocation tensor potentials are determined. New fundamental key formulae for the dynamics of dislocations are derived (Jefimenko type and Heaviside–Feynman type equations of dislocations). In addition, exact closed-form solutions of the elastic fields produced by a dislocation loop are calculated as retarded line integral expressions for subsonic motion. The fields of the elastic velocity and elastic distortion surrounding the arbitrarily moving dislocation loop are given explicitly in terms of the so-called three-dimensional elastodynamic Liénard–Wiechert tensor potentials. The two-dimensional elastodynamic Liénard–Wiechert tensor potentials and the near-field approximation of the elastic fields for straight dislocations are calculated. The singularities of the near-fields of accelerating screw and edge dislocations are determined.     

Dislocation dynamic modelling of the brittle–ductile transition in tungsten

Brittle–ductile transitions in metals, ceramics and semiconductors are closely connected with dislocation activity emanating near to crack-tips. We have simulated the evolution of crack-tip plasticity using a two-dimensional dislocation dynamics model which has been developed to include two symmetric slip planes intersecting the crack-tip, and applied to single-crystal tungsten. The dislocation mobility law used was physically based on double-kink nucleation on screw dislocations, with an activation energy reduced by the local stress. Even in the strong stress gradients near a crack-tip, the dislocations are found to self-organise so that the internal stress in the array is effectively constant with time and position over a wide range of strain rates and temperatures. The resultant net activation energy for dislocation motion is found to be constant and close to the activation energy experimentally measured for the brittle–ductile transition. Use of a fracture criterion based on the local crack-tip stress intensity factor, as modified by the stresses from the emitted dislocations, allows explicit prediction of the form and temperature of the brittle–ductile transition. Predictions are found to be in very close agreement with experiment.