Transition of deformation mechanisms in nanotwinned single crystalline SiC

ABSTRACT

The ability to experimentally synthesise ceramic materials to incorporate nanotwinned microstructures can drastically affect the underlying deformation mechanisms and mechanics through the complex interaction between stress state, crystallographic orientation, and twin orientation. In this study, molecular dynamics simulations are used to examine the transition in deformation mechanisms and mechanical responses of nanotwinned zinc-blende SiC ceramics subjected to different stress states (uniaxial compressive, uniaxial tensile, and shear deformation) by employing various twin spacings and loading/crystallographic orientations in nanotwinned structures, as compared to their single crystal counterparts. The simulation results show that different combinations of stress states and crystal/twin orientation, and twin spacing trigger different deformation mechanisms: (i) shear localised deformation and shear-induced fracture, preceded by point defect formation and dislocation slip, in the vicinity of the twin lamellae, shear band formation, and dislocation (emission) avalanche; (ii) cleavage and fracture without dislocation plasticity, weakening the nanotwinned ceramics compared to their twin-free counterpart; (iii) severe localised deformation, generating a unique zigzag microstructure between twins without any structural phase transformations or amorphisation, and (iv) atomic disordering localised in the vicinity of coherent twin boundaries, triggering dislocation nucleation and low shearability compared to twin-free systems.     

Deformation-induced excitation of the luminescence centres in coloured alkali halide crystals

The present paper reports the deformation-induced excitation of the luminescence centres in coloured alkali halide crystals. The peaks of the mechanoluminescence (ML) in γ-irradiated KCl, KBr, KI, NaCl and LiF crystals lie at 455, 463, 472, 450 and 485 nm, i.e. at 2.71, 2.67, 2.62, 2.75 and 2.56 eV, respectively. From the similarity between the ML spectra and the thermoluminescence (TL) and afterglow spectra, the ML of KCl, KBr, KI, NaCl and LiF crystals can be assigned to the deformation-induced excitation of the halide ions in V₂-centres or any other hole centres. For the deformation-induced excitation of the halide ions in V₂-centres, or in other centres, the following four models may be considered: (i) free electron generation model, (ii) electron–hole recombination model, (iii) dislocation exciton radiative decay model and (iv) dislocation exciton energy transfer model. The dislocation exciton energy transfer model is found to be suitable for the coloured alkali halide crystals. According to the dislocation exciton energy transfer model, during the deformation of solids the moving dislocations capture electrons from the F-centres and then they capture holes from the hole centres and consequently the formation of dislocation excitons takes place. Subsequently, the energy released during the decay of dislocation excitons excites the halide ions of the V₂-centres or any other hole centres and the light emission occurs during the de-excitation of the excited halide ions, which is the characteristic of halide ions. The mechanism of ML in irradiated alkali halide crystals is different from that of the TL in which the electrons released form F-centres due to the thermal vibrations of lattices reach the conduction band and the energy released during the electron–hole recombination excites the halide ions in V₂-centres or in any other hole centres. It is shown that the phenomenon of ML may give important information about the dislocation bands in coloured alkali halide crystals.     

Thermoluminescence dosimetry: State-of-the-art and frontiers of future research

The state-of-the-art in the use of thermoluminescence for the measurement of energy imparted by ionizing radiation is discussed. Emphasis is on the advantages obtainable by the use of computerized glow curve analysis in (i) quality control, (ii) low dose environmental dosimetry, (iii) medical applications (especially precision) and microdosimetric applications, and (iv) mixed field ionization-density–dosimetry. Possible frontiers of future research are highlighted: (i) vector representation in glow curve analysis, (ii) combined OSL/TL measurements, (iii) detection of sub-ionization electrons, (iv) requirements for new TL materials and (v) theoretical subjects involving kinetic modeling invoking localized/delocalized recombination applied to dose response and track structure theory including creation of defects.     

Debye screening of dislocations

Debye-like screening by edge dislocations of some externally given stress is studied by means of a variational approach to coarse grained field theory. Explicitly given are the force field and the induced geometrically necessary dislocation (GND) distribution, in the special case of a single glide axis in 2D, for (i) a single edge dislocation and (ii) a dislocation wall. Numerical simulation demonstrates that the correlation in relaxed dislocation configurations is in good agreement with the induced GND in case (i). Furthermore, the result (ii) well predicts the experimentally observed decay length for the GND developing close to grain boundaries.     

Ordered step arrays on evaporated As (0001) vicinal surfaces

A computational procedure dealing with a one-dimensional epitaxial monolayer model was developed in part I. In this part it is extended and applied to the two-dimensional case, allowing for misfit along two perpendicular interfacial directions. The model employed differs slightly from that used by van der Merwe in that the overgrowth film is simulated by a plane of atoms linked to each other by elastic springs. This allows for an exact determination of the equilibrium boundary conditions. The results show (i) that the rectangular boundary edge is slightly deformed, lateral contractions occurring where the misfit dislocations intersect the boundary edge, (ii) that the dependence of stable structures on misfit is in good agreement with the analytical results of van der Merwe, (iii) that misfit dislocations are introduced alternately at the mutually perpendicular edges of a system having quadratic symmetry, (iv) that a segmented dependence of lowest energy on crystal size is obtained, one segment for each additional dislocation, (v) that a saw-toothed dependence of average strain on crystal size, in qualitative agreement with the experimental work of Vincent, results and (vi) that a fine structure in the energy curves results from discrete adatom peripheral growth.     

Orientation-dependent deformation mechanisms of bcc niobium nanoparticles

Nanoparticles usually exhibit pronounced anisotropic properties, and a close insight into the atomic-scale deformation mechanisms is of great interest. In present study, atomic simulations are conducted to analyse the compression of bcc nanoparticles, and orientation-dependent features are addressed. It is revealed that surface morphology under indenter predominantly governs the initial elastic response. The loading curve follows the flat punch contact model in [1 1 0] compression, while it obeys the Hertzian contact model in [1 1 1] and [0 0 1] compressions. In plastic deformation regime, full dislocation gliding is dominated in [1 1 0] compression, while deformation twinning is prominent in [1 1 1] compression, and these two mechanisms coexist in [0 0 1] compression. Such deformation mechanisms are distinct from those in bulk crystals under nanoindentation and nanopillars under compression, and the major differences are also illuminated. Our results provide an atomic perspective on the mechanical behaviours of bcc nanoparticles and are helpful for the design of nanoparticle-based components and systems.     

Dislocation motion in high strain-rate deformation

We present a systematic investigation of dislocation motion, dislocation interactions, and the collective behaviour of dislocations in high strain-rate deformation. Based on results from three-dimensional dislocation dynamics simulations, we find that employing the accurate, full-dynamics, equation of motion (i.e. that includes inertial effects) significantly changes the predictions of microstructural evolution and the macroscopic response compared to the commonly used overdamped equation of motion (i.e. with no inertial effects), especially at high strain rates (10³–10⁶ s^?1). While we find that inertial effects cannot be neglected, the net velocities are not high enough that ‘relativistic’ effects are important. We also present results on the effects of high strain rates on single-crystal deformation, which show good agreement with experimental trends, including increased hardening with increasing strain rate.     

Arbitrary full-state hybrid projective synchronization for chaotic discrete-time systems via a scalar signal

In this paper we present a new projective synchronization scheme,where two chaotic(hyperchaotic) discretetime systems synchronize for any arbitrary scaling matrix.Specifically,each drive system state synchronizes with a linear combination of response system states.The proposed observer-based approach presents some useful features:i) it enables exact synchronization to be achieved in finite time(i.e.,dead-beat synchronization);ii) it exploits a scalar synchronizing signal;iii) it can be applied to a wide class of discrete-time chaotic(hyperchaotic) systems;iv) it includes,as a particular case,most of the synchronization types defined so far.An example is reported,which shows in detail that exact synchronization is effectively achieved in finite time,using a scalar synchronizing signal only,for any arbitrary scaling matrix.     

铝-0.5%铜合金中反常振幅效应内耗峰的进一步实验和位错弯结气团模型

用低频扭摆进一步研究了在Al-0.5％Cu合金中观察到反常位错内耗峯的条件。结果指出,对于完全退火的试样来说,需要有适当的冷加工量,但是对于高温淬火试样则不需要冷加工。用位错气团模型定性地解释了过去所观测到的表现反常振幅效应的时效内耗峯和温度内耗峯;同时指出,简单的气团模型在作定量的解释时,遇到了下述的困难:(i)在测量内耗所用的交变应力的作用下,位错线所能够拖着气团移动的距离太短。(ii)为了气团能够被位错拖着移动,组成气团的溶质原子必须具有比通常大很多个数量级的扩散系数。(iii)根据气团模型,从理论上计算出来的使位错拖着气团以临界速度而移动时,所需的临界应力比观测值大几百倍。提出了溶质原子沿着位错弯结而扩散的气团模型,这个改进模型能够初步解决上述困难,并能定性地解释所观测的结果。这个模型所依据的基本假设是,要观测到反常内耗现象,位错线上必须具有一定数目的弯结。要得到这种弯结,可以对于退火试样进行适量的冷加工,或者把试样从高温淬火。带着弯结的位错线能够通过弯结的沿边运动而实现垂直于位错线方向的移动。可以假定,气团只在弯结两端的直位错段处形成,在弯结本身上并不形成气团。在弯结的沿边振动的过程中,聚集在弯结两端的溶质原子可以沿着位错管道进行来回的短程扩散。已知沿着位错管道的扩散具有比在正常晶体点阵中扩散时大得多的扩散系数。     

Sound wave propagation in weakly polydisperse granular materials

Dynamic simulations of wave propagation are performed in dense granular media with a narrow polydisperse size-distribution and a linear contact-force law. A small perturbation is created on one side of a static packing and its propagation, for both P- and S-waves, is examined. A size variation comparable to the typical contact deformation already changes sound propagation considerably. The transmission spectrum becomes discontinuous, i.e., a lower frequency band is transmitted well, while higher frequencies are not, possibly due to attenuation and scattering. This behaviour is qualitatively reproduced for (i) Hertz non-linear contacts, for (ii) frictional contacts, (iii) for a range of smaller amplitudes, or (iv) for larger systems. This proves that the observed wave propagation and dispersion behaviour is intrinsic and not just an artifact of (i) a linear model, (ii) a frictionless packing, (iii) a large amplitude non-linear wave, or (iv) a finite size effect.     

Effect of dose on irradiation-induced loop density and Burgers vector in ion-irradiated ferritic/martensitic steel HT9

Samples of F/M steel HT9 were irradiated to 20?dpa at 420°C, 440°C and 470°C in a transmission electron microscope with 1?MeV Kr ions so that the microstructure evolution could be followed in situ and characterised as a function of dose. Dynamic observations of irradiation-induced defect formation and evolution were made at the different temperatures. Irradiation-induced loops were characterised in terms of their Burgers vector, size and density as a function of dose and similar observations and trends were found at the three temperatures: (i) both a/2 <111> and a <100> loops are observed; (ii) in the early stage of irradiation, the density of irradiation-induced loops increases with dose (0–4?dpa) and then decreases at higher doses (above 4?dpa), (iii) the dislocation line density shows an inverse trend to the loop density with increasing dose: in the early stages of irradiation, the pre-existing dislocation lines are lost by climb to the surfaces while at higher doses (above 4?dpa), the build-up of new dislocation networks is observed along with the loss of the radiation-induced dislocation loops to dislocation networks; (iv) at higher doses, the decrease of number of loops affects more the a/2 <111> loop population; the possible loss mechanisms of the a/2 <111> loops are discussed. Also, the ratio of a <100> to a/2 <111> loops is found to be similar to cases of bulk irradiation of the same alloy using 5?MeV Fe²⁺ ions to similar doses of 20?dpa at similar temperatures.     

Nucleation of misfit dislocations and plastic deformation in core/shell nanowires

During fabrication of metal nanowires, an oxide layer (shell) that surrounds the metal (core) may form. Such an oxide-covered nanowire can be viewed as a cylindrical core/shell nanostructure, possessing a crystal lattice mismatch between the core and shell. Experimental evidence has shown that, in response to this mismatch, mechanical stresses induce plastic deformation in the shell and misfit dislocations nucleate at the core/shell interface. As a result, the mechanical, electrical and optoelectronic properties of the nanowire are affected. It is therefore essential to be able to predict the critical conditions at which misfit dislocation nucleation at the nanowire interface takes place and the critical applied load at which the interface begins deforming plastically. Two approaches are explored in order to analyze the stress relaxation processes in these oxide-covered nanowires: (i) energy considerations are carried out within a classical elasticity framework to predict the critical radii (of the core and shell) at which dislocation nucleation takes place at the nanowire interface; (ii) a strain gradient plasticity approach is applied to estimate the flow stress at which the interface will begin deforming plastically (this stress is termed “interfacial-yield” stress). The interfacial-yield stress, predicted by gradient plasticity, depends, among other material parameters, on the radii of the core and shell. Both approaches demonstrate how the geometric parameters of nanowires can be calibrated so as to avoid undesirable plastic deformation; in particular, method (i) can give the radii values that prevent misfit dislocation formation, whereas method (ii) can provide, for particular radii values, the critical stress at which interface deformation initiates.     

Elastic interaction between a dislocation and a near-by inclusion

The study of elastic interaction between a dislocation and an inclusion (i.e., a region transformed without change of elastic constants) in an elastic continuum is extended to the cases when the singular dislocation line intersects or touches the inclusion or is situated inside it. The interaction energy is shown to be a finite and continuous function of position of the inclusion. The interaction of an edge dislocation with a dilatation sphere and of a screw dislocation with a sphere transformed into ellipsoid in isotropic continuum are studied in detail. The spherical inclusion which is considered as a rough model of a point defect (e.g. of carbon atom in iron) has a maximum and minimum energy position near the dislocation line so that the binding energy can be calculated in a consistent way.     

Do moving basal dislocations in sapphire (α-Al2O3) have non-stoichiometric cores?

An idealized crystal structure for sapphire (α-Al₂O₃) (perfect oxygen hcp packing, flat cation planes perpendicular to [0 0 0 1]) has been used by Kronberg [Acta. Metall. 5 (1957)] and many others over the past 50 years to describe basal slip and basal twinning at the atomic level. However, it was recognized a decade ago [Bilde-Sørensen et al., Acta Mater. 44 2145 (1996); Pirouz et al., Acta Mater. 44 2153 (1996)] that the actual structure of sapphire allows much simpler atomic mechanisms to be postulated for basal slip and basal twinning. These models are supported by convincing arguments derived from chemical and structural considerations.

Recently, a climb-dissociated basal dislocation in the boundary of a manufactured bicrystal was observed by atomic resolution transmission electron microscopy [Shibata et al., Science 316 82 (2007)]. The images were interpreted as indicating non-stoichiometric charged dislocation cores and it was inferred that, during dislocation motion on the basal plane, the basal dislocations had to move according to a variant of Kronberg's mechanism. This conclusion is difficult to reconcile, with (i) the models based on the actual structure [Bilde-Sørensen et al., Acta Mater. 44 2145 (1996); Pirouz et al., Acta Mater. 44 2153 (1996)], (ii) weak beam TEM images [Lagerlöf et al., in Proceedings of the Electron Microscopy Society of America, edited by G.W. Baily (San Francisco Press, 1982), p.554], which contradict important implications of this variant of Kronberg's model, (iii) implications concerning dislocation motion in ionic materials, and (iv) the possibility that interface dislocations can be subject to entirely different constraints than apply to gliding lattice dislocations.     

Atomic scale investigation of grain boundary structure role on intergranular deformation in aluminium

The role that grain boundary (GB) structure plays on the directional asymmetry of an intergranular crack (i.e. cleavage behaviour is favoured along one direction, while ductile behaviour along the other direction of the interface) was investigated using atomistic simulations for aluminium 〈1 1 0〉 symmetric tilt GBs. Middle-tension (M(T)) and Mode-I crack propagation specimens were used to evaluate the predictive capability of the Rice criterion. The stress–strain response of the GBs for the M(T) specimens highlighted the importance of the GB structure. The observed crack tip behaviour for certain GBs (Σ9 (2 2 1), Σ11 (3 3 2) and Σ33 (4 4 1)) with the M(T) specimen displayed an absence of directional asymmetry which is in disagreement with the Rice criterion. Moreover, in these GBs with the M(T) specimen, the dislocation emission from a GB source at a finite distance ahead of the crack tip was observed rather than from the crack tip, as suggested by the Rice criterion. In an attempt to understand discrepancy between the theoretical predictions and atomistic observations, the effect of boundary conditions (M(T), Mode-I and the edge crack) on the crack tip events was examined and it was concluded that the incipient plastic events observed were strongly influenced by the boundary conditions (i.e. activation of dislocation sources along the GB, in contrast to dislocation nucleation directly from the crack tip). In summary, these findings provide new insights into crack growth behaviour along GB interfaces and provide a physical basis for examining the role of the GB character on incipient event ahead of a crack tip and interface properties, as an input to higher scale models.     

Interface dislocation structures at the onset of coherency loss in nanoscale Ni–Cu bilayer films

We have performed a transmission electron microscopy study, using weak beam imaging, of the interface dislocation arrays that form initially at the (001) Ni–Cu interface during coherency loss. Interface dislocations were absent in the 2.5?nm Ni/100?nm Cu bilayers, but were present in the 3.0?nm Ni samples, indicating that the critical Ni film thickness for coherency loss is between 2.5 and 3?nm. The key features of the interface dislocation structure at the onset of coherency loss are: (i) the majority of interface dislocations are 60° dislocations, presumably formed by glide of threading dislocations in the coherently stressed Ni layer, and have Burgers vector in the {111} glide plane; (ii) the interface contained approximately 5% Lomer edge dislocations, with Burgers vector in the {001} interface plane, and an occasional Shockley partial dislocation and (iii) isolated segments of interface dislocations terminating at the surface are regularly observed. Possible mechanisms that lead to these dislocation configurations at the interface are discussed. This experimental study shows that near the critical thickness, accumulation of interface dislocations occurs in a somewhat stochastic fashion with favourable regions where coherency is first lost.     

Microstructural instabilities: dislocation substructures with pronounced mechanical effects

Microstructure evolution is largely dominated by the internal stress fields that appear upon the appearance of inhomogeneous structures in a material. The hardening behaviour of metals physically originates from such a complex microstructure evolution. As deformation proceeds, statistically homogeneous distributions of dislocations in grains become unstable, which constitutes the driving force for the development of a pronounced dislocation substructure. The dislocation structure already appears at early stages of deformation due to the statistical trapping of dislocations. Cell walls contain dislocation dipoles and multipoles with high dislocation densities and enclose cell-interior regions with a considerably smaller dislocation density. The presence and evolution of such a dislocation arrangement in the material influence the mechanical response of the material and is commonly associated with the transient hardening after strain path changes. This contribution introduces a micromechanical continuum model of the dislocation cell structure based on the physics of the dislocation interactions. The approximation of the internal stress field in such a microstructure and the impact on the macroscopic mechanical response are the main items investigated here.     

A dislocation dynamics study of the strength of stacking fault tetrahedra. Part I: interactions with screw dislocations

We present a comprehensive dislocation dynamics (DD) study of the strength of stacking fault tetrahedra (SFT) to screw dislocation glide in fcc Cu. Our methodology explicitly accounts for partial dislocation reactions in fcc crystals, which allows us to provide more detailed insights into the dislocation–SFT processes than previous DD studies. The resistance due to stacking fault surfaces to dislocation cutting has been computed using atomistic simulations and added in the form of a point stress to our DD methodology. We obtain a value of 1658.9 MPa, which translates into an extra force resolved on the glide plane that dislocations must overcome before they can penetrate SFTs. In fact, we see they do not, leading to two well differentiated regimes: (i) partial dislocation reactions, resulting in partial SFT damage, and (ii) impenetrable SFT resulting in the creation of Orowan loops. We obtain SFT strength maps as a function of dislocation glide plane-SFT intersection height, interaction orientation, and dislocation line length. In general SFTs are weaker obstacles the smaller the encountered triangular area is, which has allowed us to derive simple scaling laws with the slipped area as the only variable. These laws suffice to explain all strength curves and are used to derive a simple model of dislocation–SFT strength. The stresses required to break through obstacles in the 2.5–4.8-nm size range have been computed to be 100–300 MPa, in good agreement with some experimental estimations and molecular dynamics calculations.     

Dislocation modeling in bcc lithium: A comparison between continuum and atomistic predictions in the modified embedded atoms method

In this study, the modified embedded-atom method (MEAM) was applied to compare the predictions of dislocation core properties obtained by molecular statics with the continuum predictions obtained in the framework of the simplified 1D-Peierls–Nabarro model. To this end, a set of four fictive Li potentials in the MEAM framework was proposed with the condition that all four potentials reproduce the same elastic constants, the same transition energies between bcc and fcc crystal structures, and between bcc and hcp crystal structures, while the unstable stacking fault energy on the plane {110} in the direction <111> was varied around the value predicted by first-principles. Within these potentials, direct atomistic calculations were performed to evaluate dislocation core properties such as dislocation half width and Peierls stress and the results were compared with continuum predictions. We found that the trends predicted by the Peierls–Nabarro model, i.e. (i) a decrease of the dislocation half width with increasing unstable stacking fault energy, and (ii) an increase of the Peierls stress with increasing the magnitude of the unstable stacking fault energy, were recovered using atomic calculations in the MEAM framework. Moreover, the magnitude of the dislocation half width and the Peierls stress calculated in the MEAM framework are in good agreement with the Peierls–Nabarro predictions when the dislocation half width is determined using a generic strategy. Specifically, the dislocation half width is defined as the distance for which the disregistery is included between b/4 and 3b/4. It was, therefore, demonstrated herein that the set of fictive potentials could be parameterized in the MEAM framework to validate or to disprove the continuum theory using atomistic methods.