Prismatic Loops Research Articles

Generation and interaction mechanisms of prismatic dislocation loops in FCC metals

We investigate the mechanisms of prismatic loop formation, motion, interactions, and large-scale patterning in fcc metals utilizing Discrete Dislocation Dynamics (DDD). We identify two main formation mechanisms; both enabled by cross-slip of screw dislocations. The first is termed Super-Jog-Drag-Truncation (SJDT), and the second is the Offset-Double-Cross-Slip (ODCS) mechanism. DDD simulations show that the ODCS mechanism is a precursor to the SJDT mechanism, which then leads to the formation of prismatic loop arrays. It is shown that successive SJDT events enable a knitting mechanism that can generate long strings of prismatic loop arrays, consistent with experiments. We show that fully sessile dislocation segments arise in several loop-loop interactions, leading to Frank-Read and single-arm type sources. A new stable butterfly configuration is found when two {11¯1}<011> prismatic loops interact to form glissile segments on conjugate glide planes, joined by one sessile segment that pins this structure. Absorption of prismatic loops by screw segments and the formation of helical turns is reproduced by DDD simulations, consistent with earlier MD results. An efficient new tripolar transport mechanism is found to contribute to the clustering of prismatic loops near Persistent Slip Band (PSB) channel walls during fatigue loading.

Effect of orientation of prismatic dislocation loops on interaction with free surfaces in BCC iron

The prismatic loops appear in metals as a result of high-energy irradiation. Understanding their formation and interaction is important for quantification of irradiation-induced deterioration of mechanical properties. Characterization of dislocation loops in thin foils is commonly made using transmission electron microscopy (TEM), but the results are inevitably influenced by the proximity of free surfaces. The prismatic loops are attracted to free surfaces by image forces. Depending on the type, shape, size, orientation and depth of the loop in the foil, they can escape to the free surface creating denuded loop-free zones and thus invalidating TEM observations. In our previous studies we described a simple general method to determine the critical depth and the critical stress to move prismatic dislocation loops. The critical depths can be further used to correct measurements of the loop density by TEM. Here, we use this procedure to compare 〈100〉 loops and 12〈111〉 loops in body-centered cubic (BCC) iron. The influences of the interatomic potential and the loop orientation are studied in detail. The difference between interstitial and vacancy type loop is also investigated.

Formation of prismatic loops in AlN and GaN under nanoindentation

The formation of prismatic loops in metals has been studied extensively, but the corresponding research related to ceramics can rarely be found in the literature. In this article, the formation of prismatic loops in B4 ceramics under nanoindentation were investigated with molecular dynamics (MD) simulations. The indentation directions are respectively in the normal of the basal plane and the two prismatic planes in AlN and GaN single crystals. Two mechanisms for the formation of prismatic loop in B4 ceramics are found. One is the “lasso”-like mechanism, which is similar to that observed in metals, and the other is “nested-loops” mechanism, which has never been reported in the literature. MD simulations show that the screw segments of the two different shear loops, be adjacent to each other, can intersect with each other and finally produce a prismatic dislocation loop. The pile-up symmetry after unloading, associated with dislocation loops propagation, can be found, which is consistent with experimental results. More detailed analysis of dislocation patterns and directions indicate that plastic deformation is dominated by the shuffle-set dislocations along 13〈112¯0〉, and the glide-set dislocations along 13〈1¯010〉 are asymmetric.

Mechanism of damage buildup in ion bombarded ZnO

Ion beam induced defect processes in wide bandgap compound semiconductors are rather complex because of the formation of different types of defects and their transformations. In this paper, we report results of the study on the mechanism of defect formation, migration and agglomeration in 300 keV Ar-ion bombarded ZnO single crystals. RBS/c analysis performed with the use of the unique McChasy code allowed determination of depth distributions for different defect types separately. Complementary HRXRD analysis was applied to study lattice deformation due to ion bombardment. It has been observed that migration of simple defects and their agglomeration lead to the formation of two types of dislocation loops: basal loops located at the depth corresponding to the range of incident Ar ions and prismatic loops located beyond the ion range. The stress induced by defects in the bombarded layer has been identified as the driving force for defect migration and loop formation. As soon as the critical stress is attained bombarded layer undergoes plastic deformation resulting in the formation of a dense dislocation tangle.

Interlayer vacancy defects in AA-stacked bilayer graphene: density functional theory predictions

AA-stacked graphite and closely related structures, where carbon atoms are located in registry in adjacent graphene layers, are a feature of graphitic systems including twisted and folded bilayer graphene, and turbostratic graphite. We present the results of ab initio density functional theory calculations performed to investigate the complexes that are formed from the binding of vacancy defects across neighbouring layers in AA-stacked bilayers. As with AB stacking, the carbon atoms surrounding lattice vacancies can form interlayer structures with sp2 bonding that are lower in energy than in-plane reconstructions. The sp2 interlayer bonding of adjacent multivacancy defects in registry creates a type of stable sp2 bonded ‘wormhole’ or tunnel defect between the layers. We also identify a new class of ‘mezzanine’ structure characterised by sp3 interlayer bonding, resembling a prismatic vacancy loop. The V6 hexavacancy variant, where six sp3 carbon atoms sit midway between two carbon layers and bond to both, is substantially more stable than any other vacancy aggregate in AA-stacked layers. Our focus is on vacancy generation and aggregation in the absence of extreme temperatures or intense beams.

Initial dislocation density effect on strain hardening in FCC aluminium alloy under laser shock peening

The effect of initial dislocation density on subsequent dislocation evolution and strain hardening in FCC aluminium alloy under laser shock peening (LSP) was investigated by using three-dimension discrete dislocation dynamics (DD) simulation. Initial dislocations were randomly generated and distributed on slip planes for three different dislocation densities of 4.21 × 1012, 8.12 × 1012 and 1.26 × 1013 m−2. Besides, variable densities of prismatic loops were introduced into the DD cells as nanoprecipitates to study the dislocation pinning effect. The flow stresses as a function of strain rate obtained by DD simulation are compared with relevant experimental data. The results show a significant dislocation density accumulation in the form of dislocation band-like structures under LSP. The overall yield strength in FCC aluminium alloy decreases with increasing initial dislocation density and forest dislocation strengthening becomes negligible under laser induced ultra-high strain rate deformation. In addition, yield strength is enhanced by increasing the nanoprecipitate density due to dislocation pinning effect.

Simulation of Helium Behavior Near Subsurface Prismatic Dislocation Loops in Tungsten

We analyze the effect of subsurface prismatic dislocation loops on the surface morphology and helium clustering behavior of plasma-facing tungsten through the use of molecular dynamics simulations that are moderately large in scale, consisting of approximately 830 000 atoms, and extend to times on the order of 1 μs. This approach eliminates some finite-size effects common in smaller simulations and reduces the flux to ∼5.5 × 1026 m−2 s−1, including ions that reflect back into the plasma—this flux is a factor of ∼15 lower than is typically used in smaller simulations. These results indicate that prismatic loops with radii of ∼3 nm that are centered 10 nm below the surface with Burgers vectors parallel to the surface cause helium atom clusters to accumulate at the edge of the dislocation core relatively quickly—within 100 to 150 ns of the onset of plasma exposure. Subsequent growth of these clusters, however, is relatively minimal even out to 1 μs or more. This is partially explained by the relatively high helium implantation flux, which causes bubbles to accumulate 0 to 7 nm below the surface and block the region of the metal containing the dislocation, but this is only part of the explanation. Another effect results from the strain field around the loop itself. The compressive regions along the direction of the Burgers vector repel helium, but the tensile region initially attracts helium and traps it. However, we believe that the attractive tensile stress region is effectively shielded by the formation of helium clusters on and above it, and these bubbles subsequently experience relatively slow growth.

Dislocation climb models from atomistic scheme to dislocation dynamics

We develop a mesoscopic dislocation dynamics model for vacancy-assisted dislocation climb by upscalings from a stochastic model on the atomistic scale. Our models incorporate microscopic mechanisms of (i) bulk diffusion of vacancies, (ii) vacancy exchange dynamics between bulk and dislocation core, (iii) vacancy pipe diffusion along the dislocation core, and (iv) vacancy attachment-detachment kinetics at jogs leading to the motion of jogs. Our mesoscopic model consists of the vacancy bulk diffusion equation and a dislocation climb velocity formula. The effects of these microscopic mechanisms are incorporated by a Robin boundary condition near the dislocations for the bulk diffusion equation and a new contribution in the dislocation climb velocity due to vacancy pipe diffusion driven by the stress variation along the dislocation. Our climb formulation is able to quantitatively describe the translation of prismatic loops at low temperatures when the bulk diffusion is negligible. Using this new formulation, we derive analytical formulas for the climb velocity of a straight edge dislocation and a prismatic circular loop. Our dislocation climb formulation can be implemented in dislocation dynamics simulations to incorporate all the above four microscopic mechanisms of dislocation climb.

Interaction of irradiation-induced prismatic dislocation loops with free surfaces in tungsten

The prismatic dislocation loops appear in metals as a result of high-energy irradiation. Understanding their formation and interaction is important for quantification of irradiation-induced deterioration of mechanical properties. Characterization of dislocation loops in thin foils is commonly made using transmission electron microscopy (TEM), but the results are inevitably influenced by the proximity of free surfaces. The prismatic loops are attracted to free surfaces by image forces. Depending on the type, size and depth of the loop in the foil, they can escape to the free surface, thus invalidating TEM observations and conclusions. In this article small prismatic hexagonal and circular dislocation loops in tungsten with the Burgers vectors 1/2〈111〉 and 〈100〉 are studied by molecular statics simulations using three embedded atom method (EAM) potentials. The calculated image forces are compared to known elastic solutions. A particular attention is paid to the critical stress to move edge dislocations. The escape of the loop to the free surface is quantified by a combination of atomistic simulations and elastic calculations. For example, for the 1/2〈111〉 loop with diameter 7.4nm in a 55nm thick foil we calculated that about one half of the loops will escape to the free surface. This implies that TEM observations detect only approx. 50% of the loops that were originally present in the foil.

Molecular dynamics simulation of nano-indentation on Ti-V multilayered thin films

We developed a second nearest-neighbor modified embedded-atom method potential for binary Ti-V system. The potential parameters were identified by fitting the lattice parameter, cohesive energy and elastic constants of CsCl-type TiV, and further validated by reproducing the fundamental physical and mechanical properties of Ti-V systems with other crystal structures. In addition, we also performed molecular dynamics simulations of nano-indentation processes of pure Ti film, pure V film, and two kinds of four-layer Ti-V films, V-Ti-V-Ti and Ti-V-Ti-V. We found that the indentation force-depth curve for the pure V film turns flat at an indentation depth of 2.8nm, where a prismatic loop was observed. Such prismatic loop is not found in the V/Ti/V/Ti multilayer because the thickness of each layer is insufficient for the formation of such prismatic loops, which accounts for the increase of stress in the multilayer.

Fast, vacancy-free climb of prismatic dislocation loops in bcc metals.

Vacancy-mediated climb models cannot account for the fast, direct coalescence of dislocation loops seen experimentally. An alternative mechanism, self climb, allows prismatic dislocation loops to move away from their glide surface via pipe diffusion around the loop perimeter, independent of any vacancy atmosphere. Despite the known importance of self climb, theoretical models require a typically unknown activation energy, hindering implementation in materials modeling. Here, extensive molecular statics calculations of pipe diffusion processes around irregular prismatic loops are used to map the energy landscape for self climb in iron and tungsten, finding a simple, material independent energy model after normalizing by the vacancy migration barrier. Kinetic Monte Carlo simulations yield a self climb activation energy of 2 (2.5) times the vacancy migration barrier for 1/2〈111〉 (〈100〉) dislocation loops. Dislocation dynamics simulations allowing self climb and glide show quantitative agreement with transmission electron microscopy observations of climbing prismatic loops in iron and tungsten, confirming that this novel form of vacancy-free climb is many orders of magnitude faster than what is predicted by traditional climb models. Self climb significantly influences the coarsening rate of defect networks, with important implications for post-irradiation annealing.

Orbital-free density functional theory study of the energetics of vacancy clustering and prismatic dislocation loop nucleation in aluminium

In the present work, we conduct large-scale orbital-free density functional theory calculations to study the energetics of vacancy clustering in aluminium from electronic structure calculations by accurately accounting for both the electronic structure and long-ranged elastic fields. Our results show positive binding energies for a range of vacancy clusters considered. However, the binding energies for the various quad-vacancy clusters considered in this study are vastly different, and only some of these clusters are found to be stable with respect to dissociation into divacancies. This suggests that, while vacancy clustering is an energetically feasible mechanism, this happens preferentially through the formation of certain vacancy clusters. Among the vacancy clusters considered in this study, the 19 vacancy hexagonal cluster lying in plane has a very large binding energy with the relaxed atomic structure representative of a prismatic dislocation loop. This suggests that vacancy prismatic loops as small as those formed from 19 vacancies are stable, thus providing insights into the nucleation sizes of these defects in aluminium.

Formation of extended prismatic dislocation structures under indentation

Prismatic dislocation structures are often observed after indentation experiments. These structures usually start from the zone of high dislocation density underneath an indenter tip, but extend far beyond. Three dimensional Discrete Dislocation Dynamics simulations show how these complex structures can be formed from preexisting dislocations. The specifics of the indentation stress field and the crystallographic orientation play an important role for the formation of these structures. The mechanism of formation of the prismatic dislocations loops is dominated by stress controlled cross slip events, with cross slip locations reflecting the symmetry of the indentation stress field.

Lattice expansion by intrinsic defects in uranium by molecular dynamics simulation

A re-formulated and re-parameterized interatomic potential for uranium metal in the Charge-Optimized Many-Body (COMB) formalism is presented. Most physical properties of the orthorhombic α and bcc γ phases are accurately reproduced. In particular, this potential can reproduce the negative thermal expansion of the b axis in α-U while keeping this phase as the most stable phase at low temperatures, in accord with experiment. Most of the volume expansion in α-U by intrinsic defects is shown to come from the b axis, due to the formation of prismatic loops normal to this direction. Glide dislocation loops forming stacking faults are also observed. Structures of both loop types are analyzed. An expansion simulation is conducted and the results are verified by using the Norgett-Robinson-Torrens model. Rather than forming extended defect structures as in α-U, the γ phase forms only isolated defects and thus results in a much smaller and isotropic expansion.

Nanoindentation of hcp metals: a comparative simulation study of the evolution of dislocation networks

Using molecular dynamics simulation, we study the nanoindentation of three hcp metals: Mg, Ti, and Zr. Both the basal and two prismatic surface planes are considered. We focus on the characterization of the plasticity generated in the crystal. The similarities to, and the differences from, the behavior of the more commonly investigated fcc and bcc metals are highlighted. We find that hcp metals show a larger variety than the fcc and bcc metals studied up until now. The prolific emission of prismatic loops can lead to extended plastic zones. The size of the plastic zone is quantified by the ratio f of the plastic zone radius to the radius of the contact area. We find values of between 1.6 (an almost collapsed zone) and >5; in the latter case, complex dislocation networks build up which are extended in the direction of easy glide.

The stability of precepitates and the role of lattice defects in Fe-1at%Cu-1at%Ni-1at%Mn alloy: A phase-field model study

In the first part of this study, the stability of Cu precipitates, up to 2 nm in diameter, in Fe-1at%Cu-1at%Ni-1at%Mn system was evaluated within the framework of phase-field modeling by utilizing a thermodynamic database. The implanted precipitates either in isolated or in clustered arrangements, were unstable and dissolved into the matrix. The dissolution rate decreases with increasing precipitate size; however, it is strongly influenced by the spatial arrangements of the implants and the overall alloy content. In the second part, the precipitation/segregation behavior at a circular dislocation, and square prismatic loops was parametrically studied. While precipitates formed at the dislocation loop, a significant segregation of Cu was observed at prismatic loops with either vacancy or interstitial character. Although, the both types of prismatic loops provide the spatial evolution of the stress-fields with the same absolute magnitude, the vacancy loops appears to be stronger sinks and their sink strength increases with decreasing loop size. The results clearly show the necessity of inclusion of the underlying lattice defects in the microstructure modeling of materials under the irradiation environments.

Giant isochoric compressibility of solidHe4: The bistability of superclimbing dislocations

A significant accumulation of matter in solid Helium-4 observed during the superflow events, dubbed as the giant isochoric compressibility (or the syringe effect), is discussed within the model of dislocations with superfluid core. It is shown that solid Helium-4 in a contact with superfluid reservoir can develop a bistability with respect to the syringe fraction, with the threshold for the bias by chemical potential determined by a typical free length of dislocations with superfluid core. The main implications of this effect are: hysteresis and strongly non-linear dynamical behavior leading to growth, proliferation and possibly exiting from a crystal of superclimbing dislocations. Three major channels for such dynamics are identified: i) injection and inflation of the prismatic loops from the boundary; ii) Bardeed-Herring generation of the loops in the bulk; iii) helical instability of the screw dislocations. It is argued that the current experiments are likely to be well in this regime. Several testable predictions for the time and the bias dependencies of the dynamics are suggested

Interactions of prismatic dislocation loops with free surfaces in thin foils of body-centered cubic iron

We employ molecular statics simulations to investigate the interactions of circular and hexagonal 1/2〈111〉 prismatic loops in body-centered cubic iron with two parallel {111} free surfaces of a free-standing foil. If the presence of two surfaces is taken into account, these results agree well with the isotropic elastic solutions of Bastecka (1964) for circular loops and of Groves and Bacon (1970) for square loops with the Burgers vector of the loop perpendicular to the surface. By varying the size and shape of the loop, we identify the critical depth at which the image stresses overcome the internal lattice friction and thus drive the loop towards the surface. We investigate how this depth and the corresponding critical stress on the dislocation depend on the shape and size of the loop and outline how these results can be used to correct transmission electron microscope (TEM) measurements of the densities of prismatic dislocation loops in thin foils. For example, for the loops of 5nm in diameter in a 50nm thick foil, the loop density corrected for the existence of denuded zones adjacent to the surfaces of the foil is shown to be nearly 49% higher than that obtained by direct TEM measurements.

Displacement fields and self-energies of circular and polygonal dislocation loops in homogeneous and layered anisotropic solids

There are large classes of materials problems that involve the solutions of stress, displacement, and strain energy of dislocation loops in elastically anisotropic solids, including increasingly detailed investigations of the generation and evolution of irradiation induced defect clusters ranging in sizes from the micro- to meso-scopic length scales. Based on a two-dimensional Fourier transform and Stroh formalism that are ideal for homogeneous and layered anisotropic solids, we have developed robust and computationally efficient methods to calculate the displacement fields for circular and polygonal dislocation loops. Using the homogeneous nature of the Green tensor of order −1, we have shown that the displacement and stress fields of dislocation loops can be obtained by numerical quadrature of a line integral. In addition, it is shown that the sextuple integrals associated with the strain energy of loops can be represented by the product of a pre-factor containing elastic anisotropy effects and a universal term that is singular and equal to that for elastic isotropic case. Furthermore, we have found that the self-energy pre-factor of prismatic loops is identical to the effective modulus of normal contact, and the pre-factor of shear loops differs from the effective indentation modulus in shear by only a few percent. These results provide a convenient method for examining dislocation reaction energetic and efficient procedures for numerical computation of local displacements and stresses of dislocation loops, both of which play integral roles in quantitative defect analyses within combined experimental–theoretical investigations.

Resilient ZnO nanowires in an irradiation environment: An in situ study

ZnO nanowires (NWs) have been extensively studied for various device applications. Although these nanowires are often suspected to be impractical and highly unstable under hostile radiation environments, to date little is known on their radiation tolerance. Here, we show outstanding resilience of ZnO NWs by using in situ Kr ion irradiation at room temperature inside a transmission electron microscope. Our studies show that ZnO nanowires with certain diameters become nearly immune to radiation damage due to the existence of dislocation loop denuded zones. A remarkable size effect also holds: the smaller the nanowire diameter, the lower the defect density. Rate theory modeling suggests that the size effect arises from fast interstitial migration and a limit in size to which interstitial loops can grow. In situ studies also revealed a surprising phenomenon: the pristine prismatic loops can prevail over the strongest known defect sinks, free surfaces, to trap radiation-induced defect clusters. This study comprises the first critical step toward in-depth understanding of radiation response of functional oxide nanowires for electronic device applications in extreme environments.