V. Paidar

The Czech Academy of Sciences | AVCR · Institute of Physics

The occurrence of the regions with different compositions of particular elements in refractory high entropy alloys can be rationalized using the binary phase diagrams. The composition range and the temperature interval related to the solidification and the existence of solid solution above the occurrence of hexagonal phase are used to evaluate the...

When plastic deformation cannot be carried by dislocations, mechanical twinning is often activated. This situation often takes place in hexagonal materials. In addition to general grain boundaries, twin boundaries as special interfaces play an important role not only for mechanical properties but for other properties of materials as well. This shor...

Dislocation content of various interfaces in twinned hexagonal crystals has been studied. The analysis of their crystallography shows that the so-called disconnections play an essential role and determine the properties of special planar defects in hexagonal materials.

The energies of grain boundaries with different inclination of the boundary plane for a misorientation close to 90° about the axis in hexagonal close packed metals are discussed. On the basis of large scale computer simulations with an empirical potential for magnesium, it can be illustrated that the basal/prismatic interfaces possess special prope...

The mechanical properties are directly influenced by the properties of dislocation. In the relatively simple ordered structure of B2 type, the dislocation core structure is controlled by the stacking-fault-like defects as antiphase boundaries. It will be shown, that three types of B2 alloys can be distinguished differing by the degeneracy of antiph...

The mechanism of phase transitions in magnesium dihydrides is explored with the aim how to find the ways for lowering crystal structure stability and facilitate hydrogen desorption. After recapitulation of transition metal hydrides properties, a possible mechanism of fluorite-rutile type displacive phase transition is proposed.

Identical atomic planes of transition-metal disilicides can form different stacking when they are ordered in several combinations of four different positions A, B, C, D. The following arrangements can be formed: AB in C11(b) structure of e.g. MoSi2, ABC in C40 structure of e.g. VSi2 and ABDC in C54 structure of e.g. TiSi2 disilicides. The ABC atomi...

Professor Petr Kratochvil initiated a modern investigation of this class of materials in our country. He has been interested in various methods how to improve iron aluminides by alloying, precipitation and insertion of hard particles. He also restored the results obtained already in fifties of the last century in the development of so called PyroFe...

The 1/2〈3 3 1] dislocations in the tetragonal C11b structure of disilicides may possess a threefold non-planar core structure inherited from the BCC lattice. Due to non-metallic bonding, the dislocation splitting is intrinsically asymmetrical what has large consequences for dislocation properties. The 1/2〈3 3 1] slip on the {0 1 3) planes was obser...

Non-planar dislocation dissociations and cores play a fundamental role in mechanical properties of many materials. In this contribution, we concentrate on the complex structures arising from a large number of possible metastable stacking faults in disilicides with the C11(b) structure, specifically MoSi2. First, gamma-surfaces for the planes with h...

Atomic planes at three different positions ABC form the stacking along the < 111 > directions in the FCC lattice and similarly along the < 0001 > hexagonal axis in the C40 structure in transition metal silicides. However, the structures of suicides are constituted of several stacking of identical atomic planes at four different positions: AB in C11...

Transition metal disilicides have received considerable attention for their potential ultra-high temperature applications. The structures of silicides are constituted of stacking of several identical atomic planes at four different positions A, B, C, D: AB in C11b of e.g. MoSi2, ABC in C40 of e.g. VSi2 and ABDC in C54 of e.g. TiSi2. In comparison w...

Density functional theory based calculations of segregation energies at interfaces are often unreliable when the bulk solid solubility of the segregant is lower than that corresponding to one solute atom per computational repeat cell. In this case, the calculated energy of a solute in the bulk cannot be used when evaluating segregation energies. We...

Stability of the crystal structure is determined by the competition between attractive and repulsive interatomic forces. Using many-body exponential potentials it can be shown that the bcc structure corresponding to austenitic phases is more stable for low values of the q-parameter characterising the attractive forces for a fixed value of the p-par...

Transition metal disilicides have received considerable attention for their potential ultra-high temperature applications. The structures of silicides are constituted of stacking of several identical atomic planes at four different positions A, B, C, D: AB in C11b of e.g. MoSi2, ABC in C40 of e.g. VSi2 and ABDC in C54 of e.g. TiSi2. In comparison w...

The displacive phase transformations can be considered as composed of two processes, namely, pure displacements, shuffling or shearing of atomic planes, and supplementary homogeneous lattice deformation changing also the dimensions of the moving planes. Such deformation causes shape memory effect when the structural transformation is reversed. Gene...

Discussion of the austenite-single-variant martensite interfaces in Cu-Al-Ni alloy is performed in the frame of a topological model of martensite interfaces. This model takes into account admissible defects lying in the interface. The results are compared with the experimental data obtained on the foils of Cu-Al-Ni alloys deformed in situ in a tran...

The dominant slip directions in different intermetallic alloys with B2 structure are different, either h0 0 1i or h1 1 1i. The elastic energy of h1 1 1i dislocations is usually significantly higher than that of h0 0 1i dislocations and it is commonly assumed that h1 1 1i slip occurs if h1 1 1i dislocations can dissociate on {1 1 0} planes into ½h1...

Adequate mechanical properties are important for both structural and functional applications of materials. There are significant differences in mechanical behaviour of different B2 ordered alloys and these are related to the properties of superlattice dislocations. Several types of dislocations can be activated, in particular 〈111〉 and 〈001〉 disloc...

The changes of sample shape are caused by plastic deformation or by martensitic phase transformations. In both cases the mechanisms of atomic rearrangements are based on collective displacements of atomic aggregates. The internal structure of dislocations, carriers of plastic deformation, can be examined using the energies of generalized stacking f...

A simple model of dissipative processes originally developed for magnetic materials is extended to ferroelastic materials, in particular to shape memory alloys that display a pseudoelastic behaviour. The model based on non-equilibrium dissipative dynamics leads to kinetic equations. The characteristic feature of the model is a three-level response...

The Peierls stress for 1/6〈111〉 twinning dislocations and 1/2〈111〉 perfect dislocations in a bcc structure has been evaluated. The calculations have been performed using the Peierls-Nabarro formalism. The Peierls stresses have been determined from the migration energy of a twin boundary γtbm and the energy of an unstable stacking fault γus. The val...

Recent in situ and post mortem observations in Ni3Al and Ni3Ga alloys have yielded consistent results concerning the structure and the movement of screw superdislocations in {111} planes. The different stresses involved in the observed cross-slip processes have been computed, and the outline of a new model of stress anomaly has been formulated on t...

In a kinetic model [1] for the phenomenon of dynamic embrittlement, the cracking rate is predicted to be proportional to the diffusivity of the embrittling species along the grain boundary. To test this model, bicrystals of Cu-Sn and Fe-Si with Σ5 symmetrical tilt boundaries are used in which tin and sulfur, respectively, are the embrittling elemen...

A large number of different lattice clusters has been analyzed according to the occurrence of low index atomic planes in the clusters. A relationship of this analysis to the classification of symmetrical grain boundaries is discussed. The classification is based on the combinations of structural units that describe the structure of different grain...

The misfit between 120° rotational variants of the lamellar structure in y-phase TiAl with the ordered L10 lattice is analysed. It is shown that such a misfit on the (111) interface plane, which has a shear character, can be accommodated by one, two or three arrays of interface intrinsic dislocations. One example of interface dislocation structure...

The structures of {121} twin boundary in orthorhombic 2H martensite are modeled using Finnis-Sinclair type many-body interatomic potentials. The boundary corresponds to type-I twinning in 2H martensite of Cu-Al-Ni, Cu-Zn-Al and Au-Cd alloys. Three possible configurations of the {121} boundary are found. The structure with the lowest energy possesse...

Due to a lower symmetry of the tetragonal C11b structure when compared with the cubic BCC lattice, the 1/2<331] dislocation cores are split asymmetrically contrary to the 1/2<111> BCC dislocations. This has essential impact on their behaviour and, consequently, on mechanical properties. Various types of dislocation dissociations are analyzed in the...

The slip system in FeAl at low temperatures is <111>{110}. However, while in B2 compounds the slip plane is {110}, the slip direction is often <001> which is the shortest lattice vector in this structure. Differences among various B2 systems are obviously rooted in the nature of chemical bonds and it has often been assumed that it is the antiphase...

Due to a lower symmetry of the tetragonal C11 b structure when compared with the cubic BCC lattice, the 1/2<331] dislocation cores are split asymmetrically contrary to the 1/2<111> BCC dislocations. This has essential impact on their behaviour and, consequently, on mechanical properties. Various types of dislocation dissociations are analyzed in th...

Two basic displacive processes can be considered, namely displacements of crystal parts as rigid blocks and shuffling of atomic planes. The many-body potentials are used for the interatomic forces. General displacements of atomic planes are examined, i.e. γ-surface type calculations are applied to single plane shuffling and alternate shuffling of e...

A set of many-body potentials of Finnis-Sinclair type is used for modelling of several displacive processes in the bcc structures. The twinning process on the {112} plane and bcc-hcp transformation by Burgers mechanism are considered. The energy barriers on both paths are compared and Peierls stresses for partials responsible for movements of the t...

Geometrical analysis of interfaces in a Cu-Al-Ni alloy is performed on the basis of the phenomenological theory of martensite. The austenite-martensite interfaces in the foils of the Cu-Al-Ni alloy are faceted. In order to assess possible facet planes, lattice invariant deformation in the form of a simple shear is included into the phenomenological...

Martensitic transformations originate from the interaction of the short-wave (atomic plane shuffling) and long-wave (homogeneous deformation) processes. The mutual role of these movements is examined with the aim to elucidate formation mechanisms of the structures with lower symmetry at the atomic level. Generic many-body potentials differing in th...

The properties of A-B binary alloys are controlled by the mixed AB interaction potentials. The interfaces between two different metals are investigated for fictive mixed potentials spreading from A-type to B-type nature. The elemental AA and BB potentials are fixed. The tendencies towards formation of ordered structures on one side, and separation...

Geometrical analysis of austenite-marten site interfaces in foils of a CuAlNi alloy is performed on the basis of the phenomenological theory of martensite. The inter-faces in the foils of the CuAlNi alloy are faceted. In order to assess possible facet planes, lattice invariant deformation in the form of a simple shear is included into the phenomeno...

Shear deformation and shuffling of atomic planes are elementary mechanisms of collective atomic motion that take place during displacive phase transformations. General displacements of atomic planes are examined, i.e. γ-surface type calculations extensively used for the stacking faults and crystal dislocations are applied to single plane shuffling...

Phase transformation behaviour of Ti-rich and Ni-rich NiTi SMAs subjected to two rounds of heat treatments are compared. The first group of samples, received as straight-annealed, was subjected to a series of heat treatments in the temperature range from n the text as 1st round of heat treatments). A tments in the temperature range from Phase trans...

The intermetallic compound MoSi2 crystallises in the body-centred-tetragonal C11b structure and while it is brittle when loaded in tension, it deforms plastically in compression even at and below the room temperature. The ductility of MoSi2 is controlled by the mobility of 1/2<3311] dislocations on {013) planes but the critical resolved shear stres...

A set of exponential many-body potentials of Finnis-Sinclair type was chosen to be tested for application to atomistic simulations of extended crystal defects. The selected potentials lead to stability of different lattices, fee, hep or bcc. The aim of this work is to test behaviour of the models based on such potentials in the cases when phase tra...

Non-planar dislocation cores are widespread and frequently control the mechanical properties of materials. Most prominent phenomena related to non-planar cores are unusually strong temperature and orientation dependencies of yielding, the breakdown of the Schmid law and anomalous increase of the yield stress with increasing temperature. This chapte...

Two basic processes, namely shear and shuffling of atomic planes can be considered as elementary mechanisms of displacive phase transformations. The atomistic models suitable to investigate the role of interfaces in the structural changes are tested. The many-body potentials are used for the description of interatomic forces. General displacements...

With the aim to elucidate the transformation paths producing complex martensitic structures, the elementary mechanisms of collective atomic motion in diffusionless phase transformations are investigated using simple geometrical models. Relationships of the structures created by different mechanisms are summarized and the role of various planar crys...

The parameters of exponential many-body Finnis-Sinclair potentials corresponding to qualitatively different crystal lattice stability were selected and their behaviour was studied. Furthermore, a model with pairwise Lennard-Jones potential was also considered. The attention was paid to the stability of different crystal structures and the propertie...

The behavior of the surface segregation in infinitely diluted bimetallic alloys is addressed by calculating the segregation energy, local pressure and relative changes in the volume of atomic sites. The atomic interactions are described by a Finnis-Sinclair semi-empirical N-body potential derived from the second moment approximation of the tight bi...

The properties of intermetallics are affected by various types of two-dimensional (planar) defects, interfaces. The external free surfaces influence the crystal growth, grain boundaries have essential impact on material strength and fracture phenomena etc. The behaviour of dislocations as displacive line defects is primarily determined by the stack...

The ideal cleavage strength is calculated for the many-body potentials describing weakly stable cubic structures. The cleavage strength is compared with the ideal shear strength that is discussed from the point of view of the energetically lowest shear path to break the crystal. The exponential semiempirical interatomic potentials have been chosen...

Lamellar interfaces are efficient obstacles for propagating plastic deformation and can force the total strain to be parallel with the interfaces even if the shear stress acting on the interface plane is zero. This phenomenon of channelling plastic deformation deserves specific attention as it has important technological impacts. However, it is als...

The effect of the deformation constraints is examined for the lamellar structure of TiAl where the unconstrained plastic deformation occurs parallel to the lamellae. The constraints generally redistribute the stresses in such a way that the resolved shear stresses are decreased on the most stressed systems and increased on other systems. This behav...

Materials based on Ni–Al intermetallics are prospective high temperature materials. Properties of these intermetallics can often be improved by surface diffusion layers enriched by various metals. In this contribution results of a study are presented about microstructure and composition of Mn enriched diffusion layers on a NiAl alloy. A pure Mn pla...

Internal interfaces are decisive for many properties of materials. Both functional and structural properties of interfaces are briefly reviewed on selected examples. Approaches to the grain boundary classification are discussed in the context of the complex relationship between microstructure and material properties. Implications for grain boundary...

Intergranular segregation is studied in the limit of infinitely diluted solution for eight dilute metallic systems made of four face centred cubic metals, one transition metal, nickel, and three noble metals, copper, silver and gold. The grain boundary (GB) chosen is the symmetrical tilt Σ = 11′ {332} 〈110〉 GB with its characteristic “zigzag” struc...

The study of migration of well-characterized grain boundaries (GBs) in bicrystals of an Fe–Si alloy by in situ synchrotron radiation (SR) topography is described. The differences in migration behaviour of the (100)/(110) asymmetrical tilt GB and {hk0} symmetrical tilt GB in the 45° [001] bicrystal at 1293 K are evidently connected with intersection...

The most widely used characteristic of grain boundary type in grain boundary engineering (GBE) is the reciprocal density of coincidence sites Σ. Low values of Σ are supposed to indicate special boundaries. A systematic study of segregation at well characterised grain boundaries in Fe–Si alloys resulted in detailed classification of [100] tilt grain...

The mechanical properties of TiAl with lamellar structure depend strongly on the interaction of crystal dislocations with the lamellar interfaces. This phenomenon is discussed with the emphasis on the role of various types of the crystal and interfacial dislocations. Strengthening by the interfaces is caused by the dislocation processes occurring a...

Operation of a deformation mode on the plane inclined to the parallel interfaces is significantly affected by the interfaces that act as strong obstacles to plastic flow. This general phenomenon is demonstrated on the lamellar structure of TiAl where twinning in the direction inclined to the interface plane can be associated with the glide of ordin...

The behaviour with respect to segregation is studied for two qualitatively different symmetrical tilt grain boundaries (GBs): a low energy boundary with mirror-symmetric structure on the {113} plane and the high energy {332} GB with a “zigzag” structural pattern. These two structures have been confirmed by high resolution transmission electronic mi...

The behaviour with respect to segregation is studied for two qualitatively different symmetrical tilt grain boundaries (GBs): a low energy boundary with mirror-symmetric structure on the {1 1 3} plane and the high energy {3 3 2} GB with a ''zigzag'' structural pattern. These two structures have been confirmed by high resolution transmission electro...

Two qualitatively different interfaces can be encountered in TiAl intermetallics: crystallographic rotational interfaces between parallel lamellae and grain boundaries between differently oriented lamellar colonies. The effect of these crystal boundaries on propagation of plastic deformation is discussed and various occurring phenomena are describe...

Within past ten years, the importance of cellular automata (CA) models of both recrystallization and grain boundary migration has been recognized. It can be shown that CA provides a computationally efficient mathematical framework for simulations of physically relevant models of the above processes. Generally, CA works in such models with a vast nu...

A complete classification of [100] tilt grain boundaries into the categories of special, vicinal and general resulting from measurements of grain boundary segregation in α-iron is presented. In contrast to the coincidence site lattice approach at least one special grain boundary was found to exist for each misorientation of adjoining grains irrespe...

Materials based on Ni–Al intermetallics are prospective materials for high temperature applications. They often show good resistance to oxidation and lower specific gravity than nickel based superalloys. High temperature resistance of Ni–Al intermetallics to oxidation can often be improved by aluminium enriched surface layers. Microstructure and ch...

Polarization of deformation twinning (its propagation in a certain sense but not in the opposite one) is taken for granted. However, the same phenomenon can occur for a superdislocation glide as well, as is demonstrated in this paper. The consequences for plastic deformation of polysynthetically twinned TiAl crystals with the lamellar interfaces pa...

IntroductionGeneralized Stacking Faults, γ-surfaces and Metastable Stacking-Fault-Like DefectsStacking-Fault-Like Defects in Intermetallic Compounds with Specific Crystal StructuresProblems in Determining Energies of Stacking-Fault-Like DefectsSummary and Conclusions AcknowledgmentsReferences

Plastic deformation in the lamellar microstructure of the L10 tetragonal phase is strongly affected by special rotational lamellar interfaces on the {111} close packed planes and by general grain boundaries separating the lamellar colonies. The activity of possible deformation modes in Ti-rich TiAl alloys is explained considering in addition to gen...

The microstructure of TiAl alloys contains two types of interfaces. First, the interfaces between rotational domains misoriented by the multiples of 60°. They lie on the planes parallel to the close packed lattice planes and form the blocks separated by the interfaces of the second type, the grain boundaries in commonly used sense. The misorientati...

The phenomena involving the grain boundaries of two types are discussed for polysynthetically twinned TiAl. The interfaces separating parallel lamellae are special twist boundaries and their influence on plastic deformation is treated on the mesoscopic level. The boundaries between differently oriented lamellar colonies are grain boundaries in a co...

Changes of the grain shapes caused by the grain boundary migration are modelled by a cellular automaton in a quadricrystal. It is shown that a simple local transition rule is sufficient to describe the grain boundary migration also in the configurations containing triple junctions. A process during which two grains shrink and finally disappear is q...

A simple model of the cross-slip of the ½ (111) superpartials in B2 intermetallics is analysed with the purpose of evaluating the importance of this mechanism for explanation of the anomalous flow stress increase in iron aluminides. The orientation dependence of the forces that act on the fractional dislocations of the threefold-split screw superpa...

Two types of interfaces can be distinguished in TiAl polycrystals: special rotational interfaces on the {111} planes for which the misorientation angles about the normal to the interface plane are multiples of 60°; and grain boundaries in common sense with arbitrary orientations of the boundary plane and rotation axis. The former are the boundaries...

Tangential interaction forces acting between superlattice partial dislocations in the L12 ordered alloys affect decisively the cross-slip of the dislocations and are thus a fundamental part of the models, explaining the so-called anomalous dependence of the flow stress with increasing temperature. A complex nature of the interaction forces between...

The temperature dependence of dislocation density and its relationship with the anomalous growth of the flow stress are presented. A pronounced density increase of about one order of magnitude in a temperature range below the peak of anomalous flow stress growth has been clearly established experimentally. The correlation with different components...

The applicability and characteristics of the central force many-body potentials of Finnis-Sinclair-type for NiAl and TiAl are investigated by studying the variation of the energy of these compounds with structural transformations that correspond to three distinct paths: tetragonal (B2L10), trigonal (B2L11) and hexagonal (B2B19). The energy was comp...

A mechanism of the phase transition between two different structures of the Sigma 5 36.87 degrees (100) (013) symmetrical tilt grain boundary in BCC metals has been studied using a molecular dynamics method. For both grain boundary structures, the boundary plane is a plane of mirror symmetry; however, in one case the atomic density at the boundary...

The elastic constants of fcc transition metals are studied as functions of the exponential parameters of a many-body potential based on the second moment approximation of the d-electron density of states. It is shown that this model gives a reasonable agreement with the experimental values not only for all three independent elastic constants but al...

A systematic study of solute segregation in numerous bicrystals of an Fe-3.5at.%Si alloy enabled us to find all special [100] tilt grain boundaries. Various plots of segregation enthalpy vs. grain boundary orientation were compared to the grain boundary plane classification. From the correlation obtained we conclude that the {012}, {013} and {015}...

Structures of the (340)/(010) asymmetrical grain boundary with the [001] rotation axis in the bcc lattice are discussed. Four low energy atomic configurations of this boundary were found by computer simulation. Local properties such as atomic volume and pressure were determined in order to find atomic sites, which might be important for solute segr...

The interfaces of lamellar structure in γ-phase TiAl are analysed. The misfit between 120° rotation domains with the ordered L10 lattice on the (111) plane, and the arrays of interface intrinsic dislocations observed by transmission electron microscopy are investigated. It is shown that a triangular dislocation network of screw Shockley partials ca...

Antiphase domain boundaries (APBs) have been studied by means of transmission electron microscopy in a D03 long-range ordered Fe3Al single crystal. Two types of APB contrasts have been observed. The normal π-type APB contrast was imaged with superlattice reflections. This type of contrast is caused by the basic displacement R0=1/4〈111〉 or 1/2〈111〉...

NiAl base intermetallic is one of the prospective materials for high temperature applications. Technological use, however, requires knowledge of the behavior of all structural constituents in order to avoid the weak ones. Since grain boundaries in these intermetallics represent such weak links, it is necessary to study their properties and to impro...

Measurements of the temperature dependencies of the chemical composition of 45°[100] incommensurate tilt grain boundaries in an Fe-3.55at.%Si alloy revealed large differences between the segregation behaviour of {Okl} symmetrical and asymmetrical grain boundaries. The low negative values of the segregation enthalpies of Si, P and C determined at th...

Relationships between the ordered crystal structures and dislocations that control the plastic deformation of intermetallics are briefly discussed. An emphasises is put on those aspects of high temperature deformation which can be considered as general for the ordered structures on both fee and bcc cubic lattices. In particular, the indications tha...

In situ straining experiments in an Ni-25.9at.% Al alloy at room temperature indicate that the density of incomplete Kear-Wilsdorf locks is high during deformation. The model of mechanical properties which is based on their unlocking by an intrinsic cross-slip process is described, and compared with the alternative kink model. The results indicate...

Two superdislocation configurations consisting in an asymmetric planar dissociation on one octahedral plane, and symmetric wedge shape dissociation on two inclined octahedral planes are analysed using anisotropic elasticity. The presented results can be used to evaluated the stacking fault energies from the measured widths of dissociation.

The intermetallic phase NiAl is a perspective material for high-temperature and shape memory effect applications. Formation of Ni5Al3, Ni2Al, Ni3Al phases which influence the extent of martensitic transformation in NiAl have been studied up to now with controversial results. We have investigated (using SEM and local elemental analyses) the microstr...

Five different structures of the Σ1150.48° $[\overline 1 01]$ {131} grain boundary in the bcc lattice, obtained by computer simulation, are analysed on the basis of their symmetry. It is demonstrated that the singular character of a grain boundary is not determined by the macroscopic geometrical degrees of freedom, but is associated with a partic...

Two different descriptions of the deviation of a real bicrystal fromthe singular coincidence grain boundary are compared. It isdemonstrated using the electron microscopy observations ofdislocation structure that the description derived from the requireddeviation with respect to the [001] tilt axis is not correct since itdoes not take into account t...

A new model has been set up with the aim of explaining the mechanical properties of L1(2) nickel base alloys, in particular their anomalous increase of yield-stress with increasing temperature. In agreement with recent microscopic observations, dislocations movements are assumed to be controlled by a series of double cross-slip mechanisms between o...

Symmetry analysis of dichromatic pattern of an ideal non-relaxed bicrystal is used to determine the symmetry of Σ5 36.87°<100> grain boundary structures in bcc lattice situated at different positions with respect to a reference plane. It is shown that the vectors of rigid body translations corresponding to the bicrystals with higher symmetry select...

The extent to which the moving dislocations interact with the lattice depends on the character of their core. Planar dislocation cores can easily move on a glide plane, providing that this glide plane is identical with the plane of dislocation dissociation, while the cores with a spatial character are sessile and are subjected to large friction for...

The behaviour of dislocations dissociated into two partials, dislocations which are not freely mobile on the plane of dissociation has been studied in the frame of a model where the frictional force is described by a simple Peierls-Nabarro potential. In addition to the dislocations exhibiting the equilibrium separation of the partial dislocations,...