Diffusive fluxes associated with interfacial defeet motion and interaction

The diffusional flux associated with the motion of interfacial defects is described by an equation expressed in terms of the topological parameters which characterise defects, namely their Burgers vectors and step heights, the defect velocity and the concentration of each atomic species in the two adjacent crystals. This expression demonstrates that glide/climb behaviour of grain boundary defects is analogous to motion of dislocations in single crystals; climb motion results if a component of b is perpendicular to the interface plane. However, the situation is more complex in the case of interphase interface defects, but the present approach, which considers the step and dislocation portions of defects separately, enables a straightforward analysis. Several examples are illustrated to show the various possibilities, such as climb motion even when b is parallel to the interface, and glide motion when b is not. The latter case arises in martensitic transformation where the existence of an invariant-plane-strain relation at the interface leads to equal and opposite fluxes to the step and dislocation portions of transformation defects so that overall the motion is diffusionless.Interfacial processes involve the motion and interaction of defects. The present analysis facilitates the consideration of diffusive fluxes associated with defect interaction since the step and dislocation portions can be treated independently. A general expression is derived for the total flux arising, and a particular case, the interaction of transformation dislocations with crystal dislocations which have reached the interface during lattice-invariant deformation in martensite formation, is considered.     

In situ and tomographic observations of defect free channel formation in ion irradiated stainless steels

The effects of heavy-ion irradiation on dislocation processes in stainless steels were investigated using in situ irradiation and deformation in the transmission electron microscope as well as post mortem electron tomography to retrieve information on the three-dimensional dislocation state. Irradiation-induced defects were found to pose a strong collective barrier to dislocation motion, leading to dislocation pileups forming in grain interiors and at grain boundaries. The passage of multiple dislocations along the same slip plane removes the irradiation defects and leads to the eventual formation of a defect-free channel. These channels are composed of densely tangled dislocation networks which line the channel-matrix walls as well as residual dislocation debris in the channel interiors. The structures of the dislocation tangles were found to be similar to those encountered in later stages of deformation in unirradiated materials, with the exception that they developed earlier in the deformation process and were confined to the defect free channels. Also, defect free channels were found to widen through both source widening as well as complex cross-slip mechanisms.     

Molecular dynamics simulation of the interaction between a mixed dislocation and a stacking fault tetrahedron

A high number-density of nanometer-sized stacking fault tetrahedra are commonly found during irradiation of low stacking fault energy metals. The stacking fault tetrahedra act as obstacles to dislocation motion leading to increased yield strength and decreased ductility. Thus, an improved understanding of the interaction between gliding dislocations and stacking fault tetrahedra are critical to reliably predict the mechanical properties of irradiated materials. Many studies have investigated the interaction of a screw or edge dislocation with a stacking fault tetrahedron (SFT). However, atomistic studies of a mixed dislocation interaction with an SFT are not available, even though mixed dislocations are the most common. In this paper, molecular dynamics simulation results of the interaction between a mixed dislocation and an SFT in face-centered cubic copper are presented. The interaction results in shearing, partial absorption, destabilization or simple bypass of the SFT, depending on the interaction geometry. However, the SFT was not completely annihilated, absorbed or collapsed during a single interaction with a mixed dislocation. These observations, combined with simulation results of edge or screw dislocations, suggest that defect-free channel formation in irradiated copper is not likely by a single dislocation sweeping or destruction process, but rather by a complex mix of multiple shearing, partial absorption and defect cluster transportation that ultimately reduces the size of stacking fault tetrahedra within a localized region.     

Atomic modeling of irradiation-induced hardening

We review recent results obtained by Molecular Dynamics (MD) simulations on the elementary interaction mechanisms between dislocations and irradiation defects, with the aim to obtain a fundamental understanding of plasticity in irradiated metals. The reactions obtained included defect shear, drag and absorption in edge and screw dislocations. We present the state of the art in both FCC and BCC metals and discuss the challenges faced by MD simulations, in particular in BCC metals in order to realistically simulate the thermally-activated glide of screw dislocations in the presence of obstacles. To cite this article: D. Rodney, C. R. Physique 9 (2008).     

Radio-frequency paramagnetic resonance spectra, detected from dislocation displacement in NaCl single crystals

Results are reported here of a study of the resonance effect of a constant magnetic field and a variable magnetic field crossed with it on the rate of macroplastic deformation and motion of edge dislocations in NaCl crystals. The frequencies of the variable magnetic field at which the maximum variations in the plasticity of the crystals are observed correspond to the resonant frequencies for transitions between the Zeeman sublevels in paramagnetic complexes of point defects and complexes consisting of a point defect and a dislocation. Analysis of the radio-frequency spectra obtained enabled us to establish the role of intercrystal reactions in the formation of the mechanical properties of the crystals. Fiz. Tverd. Tela (St. Petersburg) 41, 1778–1784 (October 1999)     

Atomistic simulation of the interaction between mobile edge dislocations and radiation-induced defects in Fe-Ni-Cr austenitic alloys

The classical molecular dynamics method is employed to simulate the interaction of edge dislocations with interstitial Frank loops (2 and 5 nm in diameter) in the Fe-Ni₁₀-Cr₂₀ model alloy at the temperatures T = 300–900 K. The examined Frank loops are typical extended radiation-induced defects in austenitic steels adapted to nuclear reactors, while the chosen triple alloy (Fe-Ni₁₀-Cr₂₀) has the alloying element concentration maximally resembling these steels. The dislocation-defect interaction mechanisms are ascertained and classified, and their comparison with the previously published data concerning screw dislocations is carried out. The detachment stress needed for a dislocation to overcome the defect acting as an obstacle is calculated depending on the material temperature, defect size, and interaction geometry. It is revealed that edge dislocations more efficiently absorb small loops than screw ones. It is demonstrated that, in the case of small loops, the number of reactions accompanied by loop absorption increases with temperature upon interaction with both edge and screw dislocations. It is established that Frank loops are stronger obstacles to the movement of screw dislocations than to the movement of edge ones.     

Structure,impurity composition,and photoluminescence of mechanically polished layers of single-crystal silicon

The introduction of optically active defects (such as atomic clusters, dislocations, precipitates) into a silicon single crystal using irradiation, plastic deformation, or heat treatment has been considered a possible approach to the design of silicon-based light-emitting structures in the near infrared region. Defects were introduced into silicon plates by traditional mechanical polishing. The changes in the defect structure and the impurity composition of damaged silicon layers during thermal annealing (TA) of a crystal were examined using transmission electronic microscopy and x-ray fluorescence. Optical properties of the defects were studied at 77 K using photoluminescence (PL) in the near infrared region. It has been shown that the defects generated by mechanical polishing transform into dislocations and dislocation loops and that SiO₂ precipitates also form as a result of annealing at temperatures of 850 to 1000°C. Depending on the annealing temperature, either oxide precipitates or dislocations decorated by copper atoms, which are gettered from the crystal bulk, make the predominant contribution to PL spectra.     

Plasticization of face-centered metals under electron irradiation

The effect exerted by an electron beam with an energy of 0.5 MeV on the deformation of polycrystalline aluminum (99.5%) and copper (99.5%) under uniaxial tension at a rate of 2 × 10^?4 s^?1 in the temperature range from 40 to 100°C has been investigated. It has been established that the plasticity of the metal increases under irradiation with an electron beam: the level of the flow stress and the strain hardening coefficient in the irradiated state decrease, whereas the total resource of plasticity of the material increases. A mechanism of an increase in the plasticity of metals has been proposed. This mechanism is based on the radiation-induced generation of nonlinear strongly localized excitations of the crystal lattice, namely, discrete breathers, whose lifetime is significantly longer than the relaxation time of phonons. The interaction of discrete breathers with dislocations can stimulate the detachment of dislocations from stoppers and, consequently, an increase in the plasticity of the material.     

Kinetics of accumulation of vacancy complexes in dislocated silicon under 60Co γ-ray irradiation

Abstract

Radiation defect accumulation in ⁶⁰Co γ-ray-irradiated n-type Si single crystals (ρ=150ωcm) with various densities of dislocations (N_D = 1 × 10⁴ to 1 × 10⁷ cm ^?2) introduced at plastic deformation was studied. The temperature dependences of the Hall coefficient were measured. The probabilities of interaction of vacancies with oxygen, phosphorus atoms, and dislocation line elements were determined. It has been established that with the increase of N_D they can increase at the expense of complication of dislocation structure, decrease during formation of impurity atmosphere near dislocations and compensation of deformation fields, and they do not change if complex formation of vacancies with impurities occurs far from dislocations. Kinetics of A- and E-centre accumulation in the crystals containing dislocations with different impurity atmosphere was described.     

Precursor effects of the Rhombohedral-to-Cubic Phase Transition in Indium Selenide

We report on the observation of precursor effects of the rhombohedral-to-cubic phase transition in Indium Selenide (InSe) with several experimental techniques. The pressure at which these precursor defects are first observed depends on the sensitivity of the experimental technique. In transport measurements, which are very sensitive to low defect concentrations, precursor effects are observed 5 to 6 GPa below the phase transition pressure whereas in X-ray diffraction measurements precursor effects are only observed 2 GPa below the phase transition pressure. We report optical absorption measurements, in which the precursor effects are shown by the growth and propagation of dark linear defects appearing 3 GPa below the phase transition pressure. On the base of a simple model of the stress field around edge dislocations, we attribute the darkening of the InSe samples to local phase transitions to a high-pressure modification along linear dislocations. These results agree with room-pressure and high-pressure Raman spectra of samples compressed up to 7-8 GPa, which show new phonon lines not corresponding to the low-pressure phase.     

Atomistic and electronic structure calculation of defects at the surfaces of oxides

We present the results of simulations using both atomistic and density functional theory (DFT) approaches that illustrate the uses of these techniques for investigating the structure and electronic structure of defects at the surfaces of oxides. Atomistic simulation studies of the low index surfaces of spinel (MgAl 2 O 4 ) will show the role of vacancy configuration and surface rearrangement. Atomistic and DFT studies on Li doped MgO illustrate the importance of both the defect structure and its effect of morphology. We will also illustrate using DFT electronic defects at the surface of CeO 2 , which are of great importance in redox reactions and catalytic activity. Finally we will present a novel atomistic approach for predicting the structure of supported oxide nanoclusters giving rise to a wide range of defects including a range of surface terminations, grain formation, mixed screw edge dislocations and misfit dislocations. We will illustrate this using the structure of a BaO supported MgO nanocluster.     

Simulation of low energy displacement processes in a dilute cu-au alloy

Abstract

Research into displacement cascade processes in alloy systems has received little attention, yet is potentially of interest because issues such as the effect of solutes on the displacement threshold and the defect distribution and movement in cascades are important. As part of a wider study, we have initially considered the minor substitutional solute Au in a Cu matrix, and have used molecular dynamics to investigate the properties of point defects, the threshold displacement energy E_d, and temporal and spatial distribution of defects in low-energy (≤500 eV) displacement cascades. The results show that the influence of the solute on the properties of defects is important and that E_d is dramatically different from its form in pure copper. In comparison with pure copper, the recoil of the Au solute gives rise to a higher peak at longer times in the number of displaced atoms in the generation of a displacement cascade. The influence of this on defect density in the cascade and the final number and arrangement of defects has been investigated.     

Amplitude dependence of the internal friction and Young’s modulus defect of polycrystalline indium

The dependences of the internal friction and the Young’s modulus defect of polycrystalline indium on the oscillatory strain amplitude have been studied over a wide range of temperatures (7–320 K) and oscillatory strain amplitudes (10⁻⁷−3.5 × 10⁻⁴) at oscillatory loading frequencies of about 100 kHz. It has been revealed that the amplitude dependences of the internal friction and the Young’s modulus defect include stages associated with the interaction of dislocations with point defects and the interdislocation interaction. The temperature range characterized by the formation of point-defect atmospheres (the Cottrell atmospheres) near dislocations in indium has been determined.     

Defects in silicon: the role of vibrational entropy

Vibrational free energies are calculated from first-principles in the same Si periodic supercells routinely used to perform defect calculations. The specific heat, vibrational entropy, and zero-point energy obtained in defect-free cells are very close to the measured values. The importance of the vibrational part of the free energy is studied in the case of two defect problems: the relative energies of the H₂ and H₂^∗ dimers and the binding energy of a copper pair. In both cases, the vibrational entropy term causes total energy differences to change by about 0.2 eV between 0 and 800 K. We also comment on the rotational entropy in the case of H₂ and the configurational entropy in the case of the Cu pair. These examples illustrate the importance of extending first-principles calculations of defects in semiconductors to include free energy contributions.     

Dislocation density-based constitutive model for the mechanical behaviour of irradiated Cu

Performance degradation of structural steels in nuclear environments results from the formation of a high number density of nanometre-scale defects. The defects observed in copper-based alloys are composed of vacancy clusters in the form of stacking fault tetrahedra and/or prismatic dislocation loops that impede the motion of dislocations. The mechanical behaviour of irradiated copper alloys exhibits increased yield strength, decreased total strain to failure and decreased work hardening as compared to their unirradiated behaviour. Above certain critical defect concentrations (neutron doses), the mechanical behaviour exhibits distinct upper yield points. In this paper, we describe the formulation of an internal state variable model for the mechanical behaviour of such materials subject to these (irradiation) environments. This model has been developed within a multiscale materials-modelling framework, in which molecular dynamics simulations of dislocation–radiation defect interactions inform the final coarse-grained continuum model. The plasticity model includes mechanisms for dislocation density growth and multiplication and for irradiation defect density evolution with dislocation interaction. The general behaviour of the constitutive (homogeneous material point) model shows that as the defect density increases, the initial yield point increases and the initial strain hardening decreases. The final coarse-grained model is implemented into a finite element framework and used to simulate the behaviour of tensile specimens with varying levels of irradiation-induced material damage. The simulation results compare favourably with the experimentally observed mechanical behaviour of irradiated materials.     

Study of the effects of grain size on the mechanical properties of nanocrystalline copper using molecular dynamics simulation with initial realistic samples

Abstract

Molecular dynamics simulations have been performed to study the mechanical properties of a columnar nanocrystalline copper with a mean grain size between 9.0 and 24 nm. A melting–cooling method has been used to generate the initial samples: this method produces realistic samples that contain defects inside the grains such as dislocations and vacancies. The results of uniaxial tensile tests applied to these samples reveal the presence of a critical mean grain size between 16 and 20 nm, for which there is an inversion of the conventional Hall–Petch relation. The principal mechanisms of deformation present in the samples correspond to a combination of dislocations and grain boundary sliding. In addition, this analysis shows the presence of sliding planes generated by the motion of perfect edge dislocations that are absorbed by grain boundaries. It is the initial defects present inside the grains that lead to this mechanism of deformation. An analysis of the atomic configurations further shows that nucleation and propagation of cracks are localised on the grain boundaries especially on the triple grains junctions.     

The differential geometry of elementary point and line defects in Bravais crystals

Since line defects (dislocations) and point defects (vacancies, self-interstitials, point stacking faults) in Bravais crystals can mutually convert, only theories which comprise these two sorts of defects can be closed in the sense of general field theory. Since the pioneering work of Kondo and of Bilby, Bullough, and Smith it is clear that differential geometry is the appropriate mathematical tool to formulate a field theory of defects in ordered structures. This is done here on the example of the Bravais crystal, where the above-mentioned defects are the only elementary point and line defects. It is shown that point defects can be described by a step-counting procedure which makes it possible to include also point stacking faults as elementary point defects. The results comprise two equations with the appropriate interpretation of the mathematical symbols. The point defects are step-counting defects and are essentially described by a metric tensorg, which supplements the torsion responsible for the dislocations. The proposed theory is meant to form a framework for defect phenomena, in a similar way that Maxwell's theory is a framework for the electromagnetic world.     

Defect aggregates in neutron-irradiated β-Si3N4

Abstract

Microstructural analysis of the defect aggregates formed in bulk samples of polycrystalline β-Si₃N₄ neutron-irradiated to a dose of ～2.0 × 10²⁶n/m² at temperatures of 1100 K and 925 K has been carried out. This study has shown that the defect aggregates formed are faulted dislocation loops lying on the {1010} planes with a Burgers vector of b ? 1 /10<1125>. The vector is non-rational but corresponds to the insertion of an extra layer of [SiN4] tetrahedra on the {10l0} planes plus an additional shear in the loop plane. The formation of these loops is dependent upon the temperature of irradiation. In the sample irradiated at 1100 K their formation is additionally dependent upon whether or not a particular grain contains pre-existing c-axis dislocations. If no c-axis dislocations are present then independent nucleation of the loops is apparent; if there are pre-existing c-axis dislocations then the loops form from an apparent dissociation between the arcs of the irradiation-induced helical c-axis dislocation. In the sample irradiated at 925 K only independent nucleation of the loops occurs, regardless of whether or not there are any pre-existing c-axis dislocations in the grains.     

Fields of stress and electric displacement produced by dislocations and disclinations in three-dimensional,anisotropic, elastic,and piezoelectric media. II. Infinite straight dislocation and Frank disclination

The fields of stress and electric displacement caused by infinitely extended straight dislocations and Frank disclinations are deduced from the author's statements for the fields caused by a continuous distribution of dislocations and disclinations (S. Minagawa, Phil. Mag. 84 2229 (2004)). The multiple integrals in the original statements are converted into functions of space coordinates. Cauchy's theorem plays an important part. The improper integral that appears in computations of the fields around a Frank disclination is interpreted as its finite part by Hadamard. Examples are the fields around an infinite straight defect in caesium copper chloride, as well as those in gallium arsenide. The contours and zero lines are plotted to illustrate the fields caused by a dislocation and a disclination dipole.