Nucleation Of Loops Research Articles

Deformation behavior of Ni 3Al single crystals during nanoindentation

The deformation behavior of (1 1 1), (1 1 0) and (0 0 1) oriented Ni 3Al single crystals was investigated by means of nanoindentation. Upon loading with the blunt and sharp indenter tips, the crystal deforms elastically in the initial stage followed by plastic deformation of which the onset is characterized by an obvious displacement burst (or pop-in) in the loading curve. This pop-in corresponds to homogeneous nucleation of dislocation loops under the indenter. When a sharp indenter tip was used, a major pop-in can be identified at a large load (∼7 mN for (1 1 1) crystal) in the plastic regime on loading. The major pop-in may be correlated with the special dislocation structure of the K–W locks in the Ni 3Al crystals that are formed during loading. The pop-in behavior during plastic deformation of Ni 3Al crystals is found to be closely related to the crystal orientation, pre-existing dislocation density in the sample surface, loading rate, and holding (at a constant sub-critical load) time as well. Pop-ins were also observed at critical loads in unloading processes.

Theory of Frank loop nucleation at elevated temperatures

The nucleation of Frank loops from immobile primary interstitial clusters produced by irradiation in collision cascades is considered. Owing to the thermal instability of primary vacancy clusters at elevated temperatures, interstitial clusters receive, on the average, a net vacancy flux acting against their further growth. However, it has been shown previously that, under the combined action of the dislocation bias and continuous loop coalescence, sufficiently large interstitial loops manage to grow despite the net flux of vacancies. The nucleation of a growing interstitial loop, then, constitutes the growth, beyond a critical loop size, of an individual small cluster in an ensemble of clusters that are shrinking on the average. In this paper, the rate of interstitial loop nucleation based on this theory is developed analytically. We show that fluctuations in point-defect fluxes produced by the random (in time and space) generation of point defects in packets during cascade irradiation may significantly increase, that is by orders of magnitude, the probability of a small cluster to survive and grow. It is found that this flux is sufficient to explain the loop number densities experimentally observable in stainless steels at elevated temperatures, as well as to provide through the dislocation climb the steady-state swelling rate of about 1% (NRT)−1 (displacements per atom)−1.

Anomalous dislocation multiplication in FCC metals.

Direct atomistic simulations of dislocation multiplication in fcc aluminum reveal an unexpected mechanism, in which a Frank-Read source emits dislocations with Burgers vectors different from that of the source itself. The mechanism is traced to a spontaneous nucleation of partial dislocation loops within the stacking fault. Understanding and a quantitative description of this unusual process are achieved through the development of a continuum model for dislocation nucleation based on the coarse-grained dislocation dynamics approach and a minimal amount of atomistic input.

Pop-in effect as homogeneous nucleation of dislocations during nanoindentation

Using advanced depth-sensitive hardness measurements, the homogenous nucleation of dislocations has been observed in dislocation-free single crystals. This process is related to a sudden displacement jump in the force-displacement curve. The mechanical stress for the set-in of this pop-in effect has been estimated with the Hertzian elastic contact theory. Experimental results of dislocation loop nucleation show good agreement with the continuum theory of dislocations. Electron microscopy provides a direct proof of dislocation nucleation during nanoindentation.

Microstructure of high-pressure-synthesized diamonds under rapid quenching and electron irradiation

A type of synthetic diamond single crystal about 0.4–0.5 mm in dimension prepared under high pressure–high temperature (HPHT) in the presence of a FeNi molten catalyst was quenched from HPHT and irradiated with 300 keV electrons at room temperature. Transmission electron microscopy was employed to examine the microstructure of the diamond single crystal before and after electron irradiation. It was found that there exists a large amount of cellular interfaces in the quenched diamond sample, which indicates the growth condition of the diamond under HPHT. Hexagonal dislocation loops about several tens of nanometers in dimension were observed in the high-pressure-synthesized diamond single crystal before electron irradiation, which strongly suggests that a number of vacancies were quenched-in due to rapid quenching from high temperature at the end of diamond synthesis, and were aggregated in the synthetic diamond to form vacancy disks on the (111) plane, the collapse of such vacancy disks forming vacancy-type dislocation loops. After electron irradiation, it was found that defect clusters present as interstitial-character dislocation loops were formed in the electron-irradiated region of the diamond. The interstitial dislocation loops grow with increase of the irradiation time. The present study, in comparison to previous work on ion implantation on diamond, indicates that electron irradiation does not induce a phase transformation but produces interstitial dislocation loops due to the migration of interstitial atoms and vacancies. The result of the study directly indicates that interstitials and vacancies in diamond are mobile at room temperature under electron irradiation. Nitrogen, as the most important kind of impurity contained in the HPHT as-grown diamond, probably acts as nucleation of the interstitial loops.

Laser-induced shock compression of monocrystalline copper: characterization and analysis

Controlled laser experiments were used to generate ultra-short shock pulses of approximately 5 ns duration in monocrystalline copper specimens with [001] orientation. Transmission electron microscopy revealed features consistent with previous observations of shock-compressed copper, albeit at pulse durations in the μs regime. At pressures of 12 and 20 GPa, the structure consists primarily of dislocation cells; at 40 GPa, twinning and stacking-fault bundles are the principal defect structures; and at a pressure of 55–60 GPa, the structure shows micro-twinning and the effects of thermal recovery (elongated sub-grains). The results suggest that the defect structure is generated at the shock front; the substructures observed are similar to the ones at much larger durations. The dislocation generation is discussed, providing a constitutive description of plastic deformation. It is proposed that thermally activated loop nucleation at the front is the mechanism for dislocation generation. A calculational method for dislocation densities is proposed, based on nucleation of loops at the shock front and their extension due to the residual shear stresses behind the front. Calculated dislocation densities compare favorably with experimentally observed results. It is proposed that simultaneous diffraction by Laue and Bragg of different lattice planes at the shock front can give the strain state and the associated stress level at the front. This enables the calculation of the plastic flow resistance at the imposed strain rate. An estimated strength of 435 MPa is obtained, for a strain rate of 1.3×10 7 s −1. The threshold stress for deformation twinning in shock compression is calculated from the constitutive equations for slip, twinning, and the Swegle–Grady relationship. The calculated threshold pressure for the [001] orientation is 16.3 GPa.

Effect of undersized solute atoms on point defect behavior in V–A (A=Fe, Cr and Si) binary alloys studied by using HVEM

Point defect behavior in pure vanadium and V–A binary alloys, which contain undersized solute atoms, are examined by using high voltage electron microscope. In alloys, the number densities of self-interstitial (SIA) loops are found to be much higher than that in vanadium, indicating that solute atoms trap SIAs and enhance loop nucleation. Moreover, in contrast to the case of pure vanadium, several stages are observed in the Arrhenius-type plot of the loop density. From the temperature dependence of the loop density in each alloy, the activation energies of 0.81, 0.65 and 0.99 eV for V– xFe ( x⩾0.1 at.%), V– yCr ( y⩾1 at.%) and V–1Si have been obtained, respectively. Complex loop shapes have been observed in all alloys. Those become more significantly with increasing solute concentration, indicating solute segregation to loops. Various observed phenomena are discussed in terms of the obtained activation energy.

Energetics of nucleation of half dislocation loops at a surface crack

Energetics of nucleation of half dislocation loops at a surface crack

Energetics of nucleation of half dislocation loops at a surface crack

Abstract A previously developed variational boundary integral method in the Peierls-Nabarro framework is extended to analyse nucleation of half dislocation loops at a semicircular surface crack of near-atomic dimensions. The saddle-point configurations of embryonic dislocations and their associated thermal activation energies are determined. The influence of the crack on the energetics of dislocation nucleation is ascertained by calculating these activation energies for cracks of various radii. As the radius of the crack approaches zero, the result naturally converges to that for homogeneous nucleation of a half dislocation loop from the perfect surface. Compared with previous studies of this problem based on continuum elastic dislocation theory, the model presented in this paper provides a more definitive solution because it eliminates the uncertain core cutoff parameter and presumption that the dislocation loop is of semicircular shape.

A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals

A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals is developed. The theory accounts for: an arbitrary number and arrangement of dislocation lines over a slip plane; the long-range elastic interactions between dislocation lines; the core structure of the dislocations resulting from a piecewise quadratic Peierls potential; the interaction between the dislocations and an applied resolved shear stress field; and the irreversible interactions with short-range obstacles and lattice friction, resulting in hardening, path dependency and hysteresis. A chief advantage of the present theory is that it is analytically tractable, in the sense that the complexity of the calculations may be reduced, with the aid of closed form analytical solutions, to the determination of the value of the phase field at point-obstacle sites. In particular, no numerical grid is required in calculations. The phase-field representation enables complex geometrical and topological transitions in the dislocation ensemble, including dislocation loop nucleation, bow-out, pinching, and the formation of Orowan loops. The theory also permits the consideration of obstacles of varying strengths and dislocation line-energy anisotropy. The theory predicts a range of behaviors which are in qualitative agreement with observation, including: hardening and dislocation multiplication in single slip under monotonic loading; the Bauschinger effect under reverse loading; the fading memory effect, whereby reverse yielding gradually eliminates the influence of previous loading; the evolution of the dislocation density under cycling loading, leading to characteristic ‘butterfly’ curves; and others.

Superlattice stacking fault formation and twinning during creep in γ/γ′ single crystal superalloy CMSX-4

This paper describes further insight which has been gained into the formation of deformation twins during high temperature creep in a high volume fraction single crystal superalloy (CMSX-4) and correlation with the nature of superlattice stacking faults also observed. In general it is found that the formation of high temperature twinning can always be associated with the loading orientation in which SESF formation is expected from a determination of the sign of the shear stress. One can rationalise the reason for this twinning being associated with extrinsic stacking faults, by consideration of the critical radius of stacking fault loop nucleation. In particular calculations at 1223 K demonstrate a minimum in radius being associated with four overlapping faulted planes for the extrinsic case. Although the process by which twin formation occurs has not been observed, it is shown that twin formation can take place by the passage of extrinsic stacking faults within the precipitate which operate on every alternate plane of the structure. If one considers formation to occur via a pole mechanism similar to that in a face centred cubic structure a mechanism for this occurrence is postulated due to the fact that climb of the helix structure as it rotates around a pair of suitable matrix dislocations, will amount to double that which occurs in the single pole case.

Dislocation loops in overheated free-standing smectic films.

Static and dynamic phenomena in overheated free-standing smectic-A films are studied theoretically. The work is based on a generalization, introduced recently by the authors, of de Gennes' theory for a confined presmectic liquid. In this approach, smectic ordering in an overheated film is caused by an intrinsic surface contribution to the film free energy and vanishes at some temperature depending on the number of layers. Here the theory is further generalized to study the dynamics of films with planar inhomogeneities. A static application is to determine the profile of the film meniscus and the meniscus contact angle, the results being compared with those of a recent study employing de Gennes' original theory. The dynamical generalization of the theory is based on a time-dependent Ginzburg-Landau approach. This is used to compare two modes for layer-thinning transitions in overheated free-standing films, namely, "uniform thinning" versus nucleation of dislocation loops. It is concluded that the nucleation mechanism dominates provided there is a sufficiently large pressure difference arising from meniscus curvature. Properties such as the line tension and velocity of a moving dislocation line are evaluated self-consistently by the theory.

Cooperative nucleation of shear dislocation loops.

The mean elastic interaction between randomly distributed transient subcritical shear loops of the same sign, formed in the presence of an applied shear stress, is the "image stress." This stress is proportional to the volume density of loops and has the same sign as the applied stress. The image stress promotes the cooperative nucleation of shear loops, and leads to an instability in which the number of loops and the image stress increase rapidly, leading to the generation of stable expanding loops. The critical stress at which the instability is predicted is relatively high.

Dislocation emission around nanoindentations on a (001) fcc metal surface studied by scanning tunneling microscopy and atomistic simulations.

We present a combined study by scanning tunneling microscopy and atomistic simulations of the emission of dissociated dislocation loops by nanoindentation on a (001) fcc surface. The latter consist of two stacking-fault ribbons bounded by Shockley partials and a stair-rod dislocation. These dissociated loops, which intersect the surface, are shown to originate from loops of interstitial character emitted along the <110> directions and are usually located at hundreds of angstroms away from the indentation point. Simulations reproduce the nucleation and glide of these dislocation loops.

Modeling Dislocation Loop Nucleation and Evolution in Germanium, Arsenic and Boron Implanted Silicon

AbstractA loop nucleation and evolution model in Si+ implanted Silicon was previously introduced [1]. In this study, the model is extended to predict end of range (EOR) and projected range defect nucleation and evolution created by different ion implant species such as Germanium, Arsenic and Boron. The model assumes that all the nucleated loops come from {311} unfaulting and the loop density and average loop radius follow a log normal distribution. The model is verified with the experimental data obtained from literature for Germanium [2], Arsenic [3] and Boron [4] implanted Silicon for different implant doses and energies. Modeling results are in agreement with the experimental results.

Fundamentals of dislocation nucleation at nanoindentation

Microelectronics and micromechanics dominate the development of modern techniques now and in the future. Investigations of the mechanical properties in this field are done favourably by nanoindentation, that means the penetration of the surface to nanometer depths using an indentation device. Indentation of perfect solids at nanometer scale is connected to formation of high local stresses. Using this advantage one can observe besides others the homogenous nucleation of dislocations in locally dislocations-free monocrystals. The mechanical stresses responsible for this process can be estimated in the framework of elastic contact theory from Hertz and Sneddon. Experimental results of the loop nucleation measurements shows a good agreement with the theory of dislocations within the isotropic approach. The Pop-in-effect has been observed in metals (Al, Cu, Ni, W), ionic crystals ( \\hbox{CaF}_2, \\hbox{BaF}_2 ) and semiconductors (CdTe, GaAs, GaP, InP, ZnSe). Corresponding dislocations were proved by means of microscopy imaging techniques (transmission electron microscopy TEM, cathodoluminescence imaging CL, and imaging of dislocation-etched surfaces).

Energetics of homogeneous nucleation of dislocation loops under a simple shear stress in perfect crystals

We present an analysis of homogeneous nucleation of a dislocation loop under an applied simple shear stress in a perfect crystal. By using a variational boundary integral method together with an interlayer potential in the Peierls-Nabarro (P-N) framework, we have determined the saddle-point configurations of embryonic dislocation loops and their associated activation energies under stress levels up to the ideal shear strength. The results, for typical materials such as Au, Cu, Al, and Si, indicate that energy barriers are far too high to suggest that thermal motion could play a role in nucleation of a dislocation loop in perfect crystals under usual stress levels, markedly below the ideal shear strength. These new findings broaden the earlier understanding of homogeneous nucleation of dislocations in crystalline materials and have significant implications on a number of existing models based on the mechanism of dislocation nucleation in deformation and fracture.

Modeling of microstructure evolution in austenitic stainless steels irradiated under light water reactor condition

A model for microstructure development in austenitic alloys under light water reactor irradiation conditions is described. The model is derived from the model developed by Stoller and Odette to describe microstructural evolution under fast neutron or fusion reactor irradiation conditions. The model is benchmarked against microstructure measurements in 304 and 316 SS irradiated in a boiling water reactor core using one material-dependent and three irradiation-based parameters. The model is also adapted for proton irradiation at higher dose rate and higher temperature and is calibrated against microstructure measurements for proton irradiation. The model calculations show that for both neutron and proton irradiations, in-cascade interstitial clustering is the driving mechanism for loop nucleation. The loss of interstitial clusters to sinks by interstitial cluster diffusion was found to be an important factor in determining the loop density. The model also explains how proton irradiation can produce an irradiated dislocation microstructure similar to that in neutron irradiation.

Is plastic flow always controlled by dislocation mobility? An answer from in situ transmission electron microscopy straining tests.

In situ transmission electron microscopy (TEM) straining experiments are used to illustrate in two extreme cases the possible role of dislocation nucleation and exhaustion as a controlling factor in plastic flow. In the first example (FeAl intermetallic compounds), a thermally activated dislocation exhaustion is responsible for an anomalous stress-temperature dependence and an associated small strain rate sensitivity, the latter being evidenced during in situ experiments through unstable localized slip. The second example (heavily drawn pearlite) shows specific dislocation loop nucleation processes that may account for the Hall-Petch law breakdown characteristic of fine scale nanostructures.

Kinetic Monte Carlo modeling of dislocation motion in BCC metals

We present a kinetic Monte Carlo (kMC) simulation method for modeling screw dislocation motion in BCC metals on the micron–second scales, using inputs from atomistic simulations of core mechanisms on the angstrom–picosecond scale. The simulations use atomistic input such as double-kink nucleation energy and kink mobility, include linear elastic (Peach–Koehler) interactions between dislocation segments, and predict overall dislocation velocity at different temperature and stress states. In addition, an important mechanism, namely, the spontaneous superjog growth and debris loop nucleation, is identified in the kMC simulation as an important factor controlling the dislocation motion in the high stress and medium temperature regime.