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Stabilization of extended stacking faults by {111}/{112} twin junction interactions
Abstract
Extended stacking faults, with lengths of up to 10 nm, that join {1 1 1}/{1 1 2} twin-boundary junctions were observed by high-resolution transmission electron microscopy (HRTEM) in gold thin films. Circuit analysis shows that these defects possess a Burgers vector of 1/3〈1 1 1〉. In order to explain the generation of these extended defects, we consider the behavior of 1/3〈1 1 1〉 dislocations at {1 1 1}- and {1 1 2}-type twin boundaries and near {1 1 1}/{1 1 2} twin-boundary junctions using HRTEM observations and theoretical modeling. By establishing the interaction forces that lead to this defect configuration, our analysis shows that the relief of intrinsic strain at the junction corners, which results from the incompatibility of the translation states at the intersecting boundaries, is sufficient to stabilize the stacking fault extension. Because grain–boundary junctions possess intrinsic strain fields whenever they join boundaries with incompatible translation states, similar mechanisms for stacking fault emission may arise between other closely spaced grain–boundary junctions.
... 1,4,5 Twin boundaries with {111} and {112} planes in fcc metals are often designated as coherent twin boundaries (CTBs) and incoherent twin boundaries (ITB), respectively. 6 The structure and energy of the twin boundaries have been extensively investigated by theoretical simulation and experiments. [7][8][9][10][11][12][13] CTBs, serving as strong barriers to dislocation movement and as dislocation emission sources, play a significant role in strengthening and maintaining the ductility. ...
... This suggests a different dissociation process here. As we discussed previously, when the 1/3[111] partial exchanges position with the partial dislocation Cd, the 1/3[111] partial Dd dissociates into a full dislocation BD T and two partial dislocations according to Eq. (6). Nevertheless, when the dislocation Dd reaches the end of the ITB, the 1/3[111] partial Dd also has the possibility to dissociate into a full dislocation DA and a partial dislocation dA according to Eq. (1), which is more energetically favorable than reaction Eq. ...
The atomic structure of Σ3 {112} ITBs in nanotwinned Cu is investigated by using aberration-corrected high resolution transmission electron microscopy (HRTEM) and in situ HRTEM observations. The Σ3 {112} ITBs are consisted of periodically repeated three partial dislocations. The in situ HRTEM results show that 1/3[111] partial dislocation moves on the Σ3 {112} incoherent twin boundary (ITB), which was accompanied by a migration of the ITB. A dislocation reaction mechanism is proposed for the motion of 1/3[111] Frank partial dislocation, in which the 1/3[111] partial dislocation exchanges its position with twin boundary dislocations in sequence. In this way, the 1/3[111] dislocation can move on the incoherent twin boundary in metals with low stacking fault energy. Meanwhile, the ITB will migrate in its normal direction accordingly. These results provide insight into the reaction mechanism of 1/3[111] dislocations and ITBs and the associated migration of ITBs.
... The free surface provides an additional degree of freedom for structural relaxation, resulting in delay in creation of a trailing partial dislocation and promoting extension of the initial partial dislocation. This hypothesis is corroborated by a recent report of stabilization of an extended SF in Au thin films [22]. On the other hand, s as well as the ratio of c us /c ut are higher in nanofilms, indicating greater twinnability of the films. ...
... Twinning has also been observed in nanowires of fcc metals [17,23]. The emission of twins and SFs from grain boundaries has also been demonstrated in many atomistic simulations of nanocrystalline deformation [24] and some observations and simulations have even suggested that twin-boundary defects can, themselves, serve as sources for dislocations [22]. ...
The energies of stacking and twinning faults in nanofilms of Ni with 7, 13 and 19-layers of (1 1 1) planes were determined using first-principles density functional theory total energy calculations. The ratios of energy barriers relevant to nucleation of dislocations and twinning as obtained from the generalized planar fault energy curves suggest an enhanced tendency for extended partial dislocation formation and twinning in the nano-thin films vis-à-vis the bulk.
... Other experimental techniques additionally focus on using nanoindentation methods to determine locally induced effects from nearby GBs but are still unable to directly sample and isolate individual GBs with the requisite precision or GB character sampling [12,13]. Although some recent work demonstrates new experimental techniques able to isolate GB structures with increased accuracy [14][15][16][17][18][19], such techniques are not yet widely utilized, and significant explorations to the mechanical response with a dedicated GB study have not been conducted. ...
The influence of grain boundaries (GBs) on the mechanical behavior and deformation of crystalline materials is well documented. Specifically, intergranular failure within the microstructure often is due to GB fracture or decohesion under load. By analyzing the incipient failure response of individual GBs (e.g., decohesion), as a function of GB character, a more fundamental understanding of microstructure failure can be uncovered. Accordingly, this work leverages atomistic modeling and simulations of GBs in Al to ascertain the governing role of GB character on decohesion behavior. A range of GB characters are studied by using a newly developed GB structure database to develop trends and identify fundamental decohesion behaviors using macroscopic GB descriptors (e.g., energy, misorientation, and excess volume). However, we find that no clear correlations exist between GB decohesion and these descriptors, indicating that the origins of decohesion are missed by GB descriptors that ignore the underlying spectrum of atomic environments that compose a GB. Our results further indicate that GB decohesion behavior may be driven by atomic environments and/or dynamics specific to individual GBs, potentially independent of the macroscopic descriptions of GBs commonly employed for identification and model development.
... 15,29 In the first mechanism, dislocations interact with the twin boundaries and result in the generation of new dislocations and stacking faults. 31 The dissociation debris, especially the sessile Frank partial dislocations and stacking faults, have been demonstrated to effectively impede the motion of other dislocations and thus contribute to the work hardening. 15 However, for those twin boundaries which are parallel to the tensile direction (accounting for about 8.8% in this study counted from the TEM images), threading dislocations dominate their plastic deformation process inside the nanotwins, which reduces this dislocation storage capacity. ...
A CoCrFeNiMn high entropy alloy with a novel nanostructure consisting of ultrafine grains, TiO(C) nanoparticles and nanotwins has been fabricated. It achieves an ultrahigh tensile yield strength of 1507 MPa by coupling multiple strengthening mechanisms, including grain boundary strengthening, twin boundary strengthening, nanoparticle strengthening and dislocation strengthening. The work hardening ability is also improved by coupling the interactions of dislocations with nanoparticles and nanotwins during plastic deformation, leading to a good tensile ductility with a uniform elongation of 4.7%.
... 15,29 In the first mechanism, dislocations interact with the twin boundaries and result in the generation of new dislocations and stacking faults. 31 The dissociation debris, especially the sessile Frank partial dislocations and stacking faults, have been demonstrated to effectively impede the motion of other dislocations and thus contribute to the work hardening. 15 However, for those twin boundaries which are parallel to the tensile direction (accounting for about 8.8% in this study counted from the TEM images), threading dislocations dominate their plastic deformation process inside the nanotwins, which reduces this dislocation storage capacity. ...
Ultrafine-grained CoCrFeNiMn high entropy alloy matrix nanocomposites reinforced by nanoparticles were fabricated by thermomechanical consolidation of high energy mechanically milled powders. TiO(C) nanoparticles in the CoCrFeNiMnTi0.15 sample make the FCC matrix grains clearly finer than those in the CoCrFeNiMnNb0.1 sample with NbC and (Cr, Mn)3O4 nanoparticles (average grain size: 503 ± 184 vs 778 ± 274 nm). Quantitative analysis reveals that drag force for grain growth during consolidation in the CoCrFeNiMnTi0.15 sample is higher than that in the CoCrFeNiMnNb0.1 sample due to the higher Zener force from the TiO(C) nanoparticles. The microstructural difference renders the yield strength of the CoCrFeNiMnTi0.15 sample to be almost 50% higher than that of CoCrFeNiMnNb0.1 sample (1243 vs. 831 MPa). To elucidate this phenomenon, the strengthening mechanisms are systematically analyzed and a model considering grain boundary dislocation emission is established to account for the interaction between grain boundary strengthening and nanoparticle strengthening. This model explains the different effects of NbC, (Cr, Mn)3O4 and TiO(C) nanoparticles, and estimates the yield strength better than the existing models.
... The twin planes of Cu was along (111) planes, however, amounts of (111) twin planes could not reach both ends of the grain boundary of the untwined region, as shown in Fig. 4a. Two parallel (111) twin boundaries, which had a mirror lattice symmetry and were named as coherent twin boundaries (CTB), might stop in the middle of the grain at an incoherent twin boundary (ITB) [12][13][14][15], which was normal to these two (111) twin boundaries and possessed a relatively disordered atomic arrangement. As a result, a butttype or step-type boundary was generated at the twin interface. ...
We reported on the study of the thermal mechanical reliability of Cu-filled through silicon via (TSV) under 450 °C thermal loading. It was found that the voids could be generated at twin boundaries in TSV-Cu after thermal process. To study the mechanism of void formation at twin boundaries, the voided regions were characterized by focused ion beam—scanning electron microscope (FIB-SEM), the crystallographic orientation of Cu grains and the microstructure of twin boundaries was analyzed by means of electron backscattered diffraction (EBSD) and transmission electron microscope (TEM). Stress induced voids were considered to be generated at twin boundaries because of the stress concentration induced by three possible factors: crystallographic orientation differences of Cu grains near the twin boundary, interface decohesion of twin boundary and morphology of twin boundary.
... Twin boundaries with {111} and {112} planes in f.c.c. metals are often designated as coherent twin boundaries (CTBs) and incoherent twin boundaries (ITBs), respectively [50]. Regions A and B circled in Fig. 11a show typical ITBs. ...
... Thus, a large number of Frank partials formed during irradiation may exist along ITBs. Others have also shown that ITB could consist of an array of Frank loops [39]. ...
... Thus, a large number of Frank partials formed during irradiation may exist along ITBs. Others have also shown that ITB could consist of an array of Frank loops [39]. ...
Twin boundary migration is usually observed during annealing or plastic deformation. We report on in situ observation of Kr ion irradiation-induced microstructure evolution in epitaxial nanotwinned Ag films with an average twin thickness of 70 nm. Kr ion irradiation-induced defect clusters are absorbed by coherent and incoherent twin boundaries. Frequent interactions between defect clusters and twin boundaries lead to continuous migration of twin boundaries. The potential mechanisms of twin boundary migration are discussed. Published by Elsevier Ltd. on behalf of Acta Materialia Inc.
... Deformation twinning usually occurs simultaneously with the slip of perfect and partial dislocations, making it inevitable to have interactions between twins and gliding dislocations at twin boundaries, which have been observed both experimentally [40][41][42][43][44]218,280,281] and by molecular dynamics simulations [45][46][47][48][49][50]282]. These interactions are believed to make twins effective in simultaneously increasing the strength and ductility of nc materials [40,47,51,153,221,282,283]. ...
Nanocrystalline (nc) materials can be defined as solids with grain sizes in the range of 1–100 nm. Contrary to coarse-grained metals, which become more difficult to twin with decreasing grain size, nanocrystalline face-centered-cubic (fcc) metals become easier to twin with decreasing grain size, reaching a maximum twinning probability, and then become more difficult to twin when the grain size decreases further, i.e. exhibiting an inverse grain-size effect on twinning. Molecular dynamics simulations and experimental observations have revealed that the mechanisms of deformation twinning in nanocrystalline metals are different from those in their coarse-grained counterparts. Consequently, there are several types of deformation twins that are observed in nanocrystalline materials, but not in coarse-grained metals. It has also been reported that deformation twinning can be utilized to enhance the strength and ductility of nanocrystalline materials. This paper reviews all aspects of deformation twinning in nanocrystalline metals, including deformation twins observed by molecular dynamics simulations and experiments, twinning mechanisms, factors affecting the twinning, analytical models on the nucleation and growth of deformation twins, interactions between twins and dislocations, and the effects of twins on mechanical and other properties. It is the authors’ intention for this review paper to serve not only as a valuable reference for researchers in the field of nanocrystalline metals and alloys, but also as a textbook for the education of graduate students.
... Postmortem TEM investigation was carried out to understand the detailed structure of the curved TB2 shown in Fig. 2͑d͒. Figure 3͑a͒ shows that there are some nanometer-sized steps 24,25 and hampered dislocations at the TB. Diffraction contrast experiments ͑not shown here͒ using the invisibility criterion g · b = 0 suggest that the Burgers vector of these dislocations is 1 2 ͓101͔ T , i.e., DЈA represented by double Thomp-son's tetrahedron in Fig. 3͑a͒, while the electron beam direction is along AB ͑ 1 2 ͓110͔͒. ...
In situ tensile straining transmission electron microscopy investigation of electrodeposited copper with high density of nanoscale growth twins reveals that twin boundaries (TBs) can serve as dislocation sources. Atomic steps at TBs formed by sessile Frank partial dislocations are beneficial for TBs serving as dislocation sources. The underlying mechanism that includes dislocation reactions with TBs is discussed.
Incoherent twin boundary (ITB) evolution and migration induced by nanoindentation in Au nanocrystalline films were systematically investigated by Cs-corrected transmission electron microscopy (TEM). With a gradient stress distribution at various indentation depths, 9R/3R phase nucleation is greatly facilitated at the ITBs. The 9R/3R phase formation can be achieved by collective glide of triple partial dislocations with different Burgers vectors at two phase boundaries. With 9R/3R phase at ITBs, atoms on consecutive {111} planes shear in a helical manner, generating zero macroscopic strain during ITB migration. Dislocation interactions with ITBs were further analyzed by combining atomic-scale high angle annular dark-field scanning TEM (HAADF-STEM) with geometric phase analysis method. ITBs can both absorb partial dislocations or emit partial dislocations from the junctions between coherent twin boundaries and ITBs, providing complementary mechanisms for ITB migration in Au nanocrystalline films under nanoindentation. These results suggest the critical role of 9R/3R phase nucleation in ITB migration and provide a deeper understanding of nanoindentation-induced deformation twinning in nanocrystalline films.
The single-crystalline copper (Cu) thin film is a platform substrate for the growth of numerous materials and has been a significant issue for the scientific community. The primary concern is the inevitable presence of stacking faults and twin boundary formation in inherent face-centered-cubic (FCC) structures. Here, we report a method for growing single-crystalline Cu(111) thin films on an Al2O3 substrate using conventional sputtering deposition. The desired growth configuration is induced by hidden incoherent twin boundaries (HITBs) embedded during the early growth stages. Two possible FCC stacking orders of Cu atoms, A-B-C-A and A-C-B-A rotated by 60˚, give rise to HITBs between islands, as confirmed by X-ray diffraction phi-scan mapping. Such islands merge every three layers, triggering layer-by-layer growth that subsequently leads to an inverse Stranski–Krastanov growth mode. Single-crystalline Cu(111) thin film growth is confirmed by high-resolution transmission electron microscopy and electron backscatter diffraction mapping. Our approach paves the way for mass production of single-crystalline metal thin film and thus leads to substantial advanced research and electronic device application.
Low-mobility twin grain boundaries dominate the microstructure of grain boundary-engineered materials and are critical to understanding their plastic deformation behaviour. The presence of solutes, such as hydrogen, has a profound effect on the thermodynamic stability of the grain boundaries. This work examines
the case of a 3 grain boundary at inclinations from 0° ≤ Φ ≤ 90°.The angle corresponds to the rotation of the Σ3 (1 1 1) ⟨1 1 0⟩ (coherent) into the Σ3 (1 1 2) ⟨1 1 0⟩ (lateral) twin boundary. To this end, atomistic models of inclined grain boundaries, utilizing empirical potentials, are used to elucidate the finite-temperature boundary structure while grand canonical Monte Carlo models are applied to determine the degree of hydrogen segregation. In order to understand the boundary structure and segregation behavior of hydrogen, the structural unit description of inclined twin grain boundaries is found to provide insight into explaining the observed variation of excess enthalpy and excess hydrogen concentration on inclination angle, but the explanatory power is limited by how the enthalpy of segregation is affected by hydrogen concentration. At higher concentrations, the grain boundaries undergo a defecting transition. In order to develop a more complete mesoscale model of the interfacial behaviour, an analytical model of boundary energy and hydrogen segregation that relies on modelling the boundary as arrays of discrete ⅓ ⟨1 1 1⟩ disconnections is constructed. Furthermore, the complex interaction of boundary reconstruction and concentration- dependent segregation behaviour exhibited by inclined twin grain boundaries limits the range of applicability of such an analytical model and illustrates the fundamental limitations for a structural unit model description of segregation in lower stacking fault energy materials.
Severe plastic deformation (SPD) was performed on AISI304 stainless steel by surface mechanical attrition treatment (SMAT). The microstructure evolution of the specimens along the depth direction were examined by transmission electron microscope (TEM) and electron backscattered diffraction (EBSD) associated with field emission scanning electron microscope (FESEM). The results show that the specimens by SMAT can be divided into three regions. Region I is the untreated one, where a large number of annealing twins exist. Region II is the small plastic-deformed one, where the grains are deformed by dislocation slipping. Region III is the severe plastic-deformed one, where the grains are deformed by mechanical twinning. The hardness of the untreated and the treated specimens were determined, which shows that the hardness of the untreated specimen (including region I) is about 250HV, while the hardness is uniformly increased from region II to region III, and the largest value appears on the surface. The untreated and the 600 N-treated specimens were determined and observed by X-ray diffractometer (XRD) and confocal laser scanning microscope (CLSM), which shows that the SMAT treated specimen exhibits a layer of ultra-fined γ-Fe grains on the treated surface.
Interfaces are a critical determinant of the full range of materials properties, especially at the nanoscale. Computational and experimental methods developed a comprehensive understanding of nanograin evolution based on a fundamental understanding of internal interfaces in nanocrystalline nickel. It has recently been shown that nanocrystals with a bi-modal grain-size distribution possess a unique combination of high-strength, ductility and wear-resistance. We performed a combined experimental and theoretical investigation of the structure and motion of internal interfaces in nanograined metal and the resulting grain evolution. The properties of grain boundaries are computed for an unprecedented range of boundaries. The presence of roughening transitions in grain boundaries is explored and related to dramatic changes in boundary mobility. Experimental observations show that abnormal grain growth in nanograined materials is unlike conventional scale material in both the level of defects and the formation of unfavored phases. Molecular dynamics simulations address the origins of some of these phenomena.
The growth and annealing behavior of strongly twinned homoepitaxial films on Ir(111) have been investigated by scanning tunneling microscopy, low-energy electron diffraction, and surface x-ray diffraction. In situ surface x-ray diffraction during and after film growth turned out to be an efficient tool for the determination of twin fractions in multilayer films and to unravel the nature of lateral twin crystallite boundaries. The annealing of the twin structures is shown to take place in a two-step process; first, the length of the lateral twin crystallite boundaries is reduced, without affecting the amount of twinned material, and then, at much higher temperatures, the twins themselves anneal. Within moderately annealed films lateral twin crystallite boundaries are visible at the film surface as fractional steps from which strain fields extend. The nature of these boundaries is discussed.
Synthetic CdZnTe or “CZT” crystals are highly suitable for γ-spectrometers operating at the room temperature. Secondary phases (SP) in CZT are known to inhibit detector performance, particularly when they are present in large numbers or dimensions. These SP may exist as voids or composites of non-cubic phase metallic Te layers with bodies of polycrystalline and amorphous CZT material and voids. Defects associated with crystal twining may also influence detector performance in CZT. Using transmission electron microscopy, we identify two types of defects that are on the nano scale. The first defect consists of 40 nm diameter metallic Pd/Te bodies on the grain boundaries of Te-rich composites. Although the nano-Pd/Te bodies around these composites may be unique to the growth source of this CZT material, noble metal impurities like these may contribute to SP formation in CZT. The second defect type consists of atom-scale grain boundary dislocations. Specifically, these involve inclined “finite-sized” planar defects or interfaces between layers of atoms that are associated with twins. Finite-sized twins may be responsible for the subtle but observable striations that can be seen with optical birefringence imaging and synchrotron X-ray topographic imaging.
We present a continuum model for the core relaxation of incoherent twin boundaries based on the Peierls–Nabarro framework, incorporating both the long-range strain field and the local atomic structure. The continuum model is applied to the finite size effect of twin boundaries and interactions of dislocations with twin boundaries. The obtained results agree well with the experimental and atomistic simulation results. This model provides a basis for quantitative study of structures and collective behaviors of twin boundaries within the continuum framework.
Twin boundaries (TBs) in ultra-fine grained (UFG) copper prepared by powder metallurgy were investigated using high-resolution transmission electron microscopy (HRTEM) and geometric phase analysis (GPA). Specimens were analyzed both before and after mechanical deformation (compression of 40%) and emphasis placed on the study of TB defects. Twin boundaries in the as-processed specimens are mainly disoriented from the perfect Σ3 coincidence. They present a faceted structure with coherent {111} and incoherent {112} facets. The latter have a 9R structure and the {111}/{112} junctions are associated with sessile dislocations of Frank type . Shockley glissile dislocations with Burgers vector of type are also present. This microstructure is interpreted in terms of the absorption and decomposition at room temperature of lattice dislocations (60° type). After mechanical deformation, an enrichment of twins at dislocations and a decrease of step density and height is observed and quantified by statistical analysis. Deformation mechanisms of UFG copper are discussed in light of these observations.
The results of a computer simulation of the structure of periodic grain boundaries between twin related crystals of aluminium are described. An interatomic potential derived on the basis of pseudo-potential theory was used. The algorithm employed allows simultaneous local atomic relaxation and rigid body translation of the adjacent grains. It was found that rigid body translation is a dominant contribution to relaxation, and that the energy of a boundary, gamma , is not simply related to boundary periodicity. In addition, annealing twins in aluminium were observed by using transmission electron microscopy and detailed correspondence with theoretical predictions was found in two areas; the calculated gamma 's of experimentally observed boundary planes were lower than those of geometrically possible alternatives, and excellent agreement between predicted and experimentally measured rigid body translations was obtained for two types of tilt boundary.
The present work deals with the atomic mechanism responsible for the emission of partial dislocations from grain boundaries (GB’s) in nanocrystalline metals. It is shown that in 12 and 20 nm grain size samples GB’s containing GB dislocations can emit a partial dislocation during deformation by local atomic shuffling and stress-assisted free volume migration. The free volume is often emitted or absorbed in a neighboring triple junction. It is further suggested that the degree of delocalization surrounding the grain boundary dislocation determines whether atomic shuffling can associate displacements into the Burgers vector necessary to emit a partial dislocation. Temporal analysis of atomic configurations during dislocation emission indicates that creation and propagation of the partial might be separate processes.
Bulk Cu foils have been synthesized via magnetron sputtering with an average twin spacing of 5 nm. Twin interfaces are of {111} type and normal to the growth direction. Growth twins with such high twin density and preferred orientation have never been observed in elemental metals. These Cu foils exhibited tensile strengths of 1.2 GPa, a factor of 3 higher than that reported earlier for nanocrystalline Cu, average uniform elongation of 1%–2%, and ductile dimple fracture surfaces. This work provides a route for the synthesis of ultrahigh-strength, ductile pure metals via control of twin spacing and twin orientation in vapor-deposited materials.
Magnetron-sputter-deposited austenitic 330 stainless steel (330 SS) films, several microns thick, were found to have a hardness ∼6.5 GPa, about an order of magnitude higher than bulk 330 SS. High-resolution transmission electron microscopy revealed that sputtered 330 SS coatings are heavily twinned on {111} with nanometer scale twin spacing. Molecular dynamics simulations show that, in the nanometer regime where plasticity is controlled by the motion of single rather than pile-ups of dislocations, twin boundaries are very strong obstacles to slip. These observations provide a new perspective to producing ultrahigh strength monolithic metals by utilizing growth twins with nanometer-scale spacing. © 2004 American Institute of Physics.
The partial-dislocation-mediated processes have so far eluded high-resolution transmission electron microscopy studies in nanocrystalline (nc) Ni with nonequilibrium grain boundaries. It is revealed that the nc Ni deformed largely by twinning instead of extended partials. The underlying mechanisms including dissociated dislocations, high residual stresses, and stress concentrations near stacking faults are demonstrated and discussed.
Molecular dynamics simulations have recently shown that the presence of grown-in twin boundaries in nc-Al promotes slip activity in the form of twin boundary migration. In this letter we investigate the effect of grown-in twin boundaries on the plastic deformation mechanism in nc-Ni and Cu, and show that (1) for these particular fcc metals twin boundary migration is not the favored deformation mechanism and (2) that the Schmid factors of the grown-in twin plane play a correspondingly important role. The results are explained in terms of the different ratios of the extrema of the generalized planar fault curves.
Junction lines, where three or more interfaces meet in polycrystalline materials, are analysed from a topological point of view. Using circuit mapping methods, it is shown that, in contiguous polyerystals, the dislocations constituting the interfaces always react at junctions according to topological conservation principles. This conclusion is at variance with recent suggestions in the literature. In addition, it is shown that, in certain circumstances, junction lines can themselves exhibit defect character, i.e., dislocation and/or disclination character. Such defects arise in order to accommodate the coexistence of the abutting crystals. Simple examples are illustrated.
We report transmission electron microscope observations that provide evidence of deformation twinning in plastically deformed
nanocrystalline aluminum. The presence of these twins is directly related to the nanocrystalline structure, because they are
not observed in coarse-grained pure aluminum. We propose a dislocation-based model to explain the preference for deformation
twins and stacking faults in nanocrystalline materials. These results underscore a transition from deformation mechanisms
controlled by normal slip to those controlled by partial dislocation activity when grain size decreases to tens of nanometers,
and they have implications for interpreting the unusual mechanical behavior of nanocrystalline materials.
Methods used to strengthen metals generally also cause a pronounced decrease in electrical conductivity, so that a tradeoff must be made between conductivity and mechanical strength. We synthesized pure copper samples with a high density of nanoscale growth twins. They showed a tensile strength about 10 times higher than that of conventional coarse-grained copper, while retaining an electrical conductivity comparable to that of pure copper. The ultrahigh strength originates from the effective blockage of dislocation motion by numerous coherent twin boundaries that possess an extremely low electrical resistivity, which is not the case for other types of grain boundaries.
The search for deformation mechanisms in nanocrystalline metals has profited from the use of molecular dynamics calculations. These simulations have revealed two possible mechanisms; grain boundary accommodation, and intragranular slip involving dislocation emission and absorption at grain boundaries. But the precise nature of the slip mechanism is the subject of considerable debate, and the limitations of the simulation technique need to be taken into consideration. Here we show, using molecular dynamics simulations, that the nature of slip in nanocrystalline metals cannot be described in terms of the absolute value of the stacking fault energy-a correct interpretation requires the generalized stacking fault energy curve, involving both stable and unstable stacking fault energies. The molecular dynamics technique does not at present allow for the determination of rate-limiting processes, so the use of our calculations in the interpretation of experiments has to be undertaken with care.
Publisher Summary This chapter discusses the crystallographic features of dislocations, with emphasis on their topological characteristics as constrained by the symmetry of their hosts. Microscopic observations of metallic, ceramic, semiconducting, superconducting, and composite materials have confirmed that dislocations are ubiquitous features in interfaces, occurring both as isolated discrete defects and in organized arrays. The chapter presents several crystallographic tools and methodology. It reviews several important (infinite) crystal structures and their space groups and outlines the assignment of space groups to (1) crystals exhibiting a planar surface and (2) bicrystals. The chapter also discusses the topological properties of defects in single crystals together with surface discontinuities and isolated interfacial defects. Only line defects arise in the class of manifest symmetry, namely, dislocations, disclinations, and dispirations. A broad range of defect types can arise in the broken symmetry class, and it is convenient to subdivide these into surface-like features (steps, demisteps, and facet junctions), and bulk-like defects (dislocations, disclinations, and dispirations). Finally, the chapter discusses several interface structures modeled by dislocation arrays.
The nucleation and growth of twins in a 78% Ni-Fe alloy were investigated by electron transmission microscopy. The twins nucleated at migrating grain boundaries during primary recrystallization, in the form of stacking faults or a small packet of stacking faults. Stacking faults gliding into the recrystallized grain constituted edgewise growth, and the nucleation of contiguous layers of stacking fault at the grain boundary constituted sidewise growth. In the final stage of growth the partial dislocations which border the stacking faults interact to form planar low energy interfaces, the so-called “non-coherent twin boundary.” The non-coherent twin planes were of the type {531}, {353}, and {110}.
The role of vicinal twin boundaries in tensile deformation of nanocrystalline materials is investigated using molecular dynamics. Lattice dislocations are emitted from the intersection of the step structures with general grain boundaries, resulting in significant dislocation activity. The results are discussed in terms of the mechanical properties of twin dominated structures.
A crystallographic treatment is developed which clarifies the relation
between the structure of a grain boundary and its location between
relatively translated crystals. Characterization of line defects which
can exist in grain boundaries is also facilitated by using this
treatment, and the following topics are considered: (1) the computed
structures in part I of this work; (2) steps at the cores of perfect
grain boundary dislocations; (3) boundary structures related by c.s.l.
symmetry; (4) partial grain boundary dislocations. Transmission electron
microscope observations of topic 4 are presented.
In a combined theoretical and experimental study, the energies and structures of σ = 3, [011] tilt boundaries in Cu were investigated. Equilibrium atomistic structures and grain-boundary energies were calculated by static energy minimization using an embedded-atom potential. Cu bicrystals of the same boundary orientations were fabricated by welding of Cu single crystals. Grain-boundary energies were measured by the thermal grooving technique. The atomistic structure of the {211} twin boundary was investigated by high-resolution transmission electron microscopy (HRTEM).The calculated grain-boundary energies γb plotted against the inclination of the boundary plane show a minimum for the {111} twin boundary and a second minimum at an inclination of about 82° to the {111} boundary. The calculated dependence of γb on inclination is confirmed by the measured energies over the entire range. Common to all calculated boundary structures is a microfaceting into {111} and {211} twin facets. The structures calculated for grain boundaries around the second energy minimum show significant atomic rearrangements extending over several planes normal to the boundary together with large translations. A striking feature of these structures is a bending of the {111} planes that run continuously through the boundary. This is confirmed by HRTEM. The structures are explained in terms of a rhombohedral 9R phase of Cu forming a thin (1–2 nm) layer at the boundary.
Low- and high-angle grain boundaries, and twin boundaries in aluminium and copper have been observed during in-situ electron irradiation using a high-voltage electron microscope. Evidence is presented for dislocation mechanisms of point-defect absorption in all three types of interface. In grain boundaries, climb of extrinsic dislocation structures leading to equilibration and final inclusion in the intrinsic structure is observed. Any movement of the intrinsic dislocations in a fully equilibrated array would usually be too small to observe using this technique. In coherent twin boundaries, dislocation loops are formed : these grow, coalesce and annihilate, and then renucleate, unlike matrix loops for which nucleation ends at an early stage of irradiation.
High-resolution transmission electron microscopy observations are presented of the motion of grain-boundary dislocations within an aluminium Σ = 3[011] bicrystal. The observations show the glide of dissociated a/3[111] grain-boundary dislocations on the incoherent Σ = 3(211) boundary. These dislocations are subsequently incorporated into a growing coherent two lamella where further motion occurs by climb. Analysis of the tip of the advancing twin suggests that nucleation of coherent twin segments may be initiated by the absorption of a lattice dislocation in the boundary with the subsequent dissociation to form a/3[111] and a/6[211] grain-boundary dislocations.
We investigate the structure of 1/3111 disconnections at Σ3 {111} twin boundaries in gold. Our high-resolution transmission electron microscopy (HREM) observations and atomistic simulations show that the core relaxation of this defect is dramatically affected by reversing the sign of the Burgers vector, as oriented with respect to the twin boundary. In particular, we find two distinct, relaxed structures: one with a localized core and the other with a dissociated core composed of a stacking fault terminated by a Shockley partial dislocation. An analysis of the specific pathways available for the defect to relax and of the elastic interactions of the components of the dissociated dislocation for these cases explains the structural difference.
The atomic structure of secondary dislocations at Σ = 3, [ī10]—(ī1) grain boundaries in pure aluminium have been studied by high-resolution electron microscopy. In defect-free regions, the grain boundary coincident-site lattice is continuous across the interface but several different secondary grain-boundary dislocations are observed in the vicinity of interplanar steps.
Twinning is ubiquitous in electroplated metals. Here, we identify and discuss unique aspects of twinning found in electrodeposited Ni–Mn alloys. Previous reports concluded that the twin boundaries effectively refine the grain size, which enhances mechanical strength. Quantitative measurements from transmission electron microscopy (TEM) images show that the relative boundary length in the as-plated microstructure primarily comprises twin interfaces. Detailed TEM characterization reveals a range of length scales associated with twinning beginning with colonies (1000 nm) down to the width of individual twins, which is typically <50 nm. We also consider the connection between the crystallographic texture of the electrodeposit and the orientation of the twin planes with respect to the plating direction. The Ni–Mn alloy deposits in this work possess a {110}-fiber texture. While twinning can occur on {111} planes either perpendicular or oblique to the plating direction in {110}-oriented grains, plan-view TEM images show that twins form primarily on those planes parallel to the plating direction. Therefore, grains enclosed by twins and multiply twinned particles are produced. Another important consequence of a high twin density is the formation of large numbers of twin-related junctions. We measure an area density of twin junctions that is comparable to the density of dislocations in a heavily cold-worked metal.
Defect structures of plastically deformed nanocrystalline Pd investigated by high-resolution transmission electron microscopy are presented. Material with an average grain size of about 15 nm was prepared by inert-gas condensation, and this was plastically deformed by cold rolling up to a true strain of 0.32 at a strain rate of about 0.3 s−1. Abundant deformation twinning on {111} planes was found and Shockley partial dislocations identified. Remarkably, in each grain, twinning occurs only on a single set of parallel planes. This implies that only one out of the five independent slip systems required for the general deformation of a grain is active, a finding which suggests that grain rotation and grain-boundary sliding must be active together with twinning.
We present here a study of the Σ=3 {112} incoherent twin boundary in aluminum. Atomistic studies of this boundary indicate that several high energy boundary structures may exist, with the lowest energy structure exhibiting a small rigid body shift parallel to the boundary. The observations presented here indicate that the rigid body shift does in fact occur and that its magnitude, as well as the local grain boundary structure, is well predicted by atomistic calculations using the Embedded Atom Method. The low energy boundary configuration is much narrower than the equivalent boundaries that have been observed in the lower stacking fault energy FCC metals.
A theoretical model is suggested that describes emission of partial Shockley dislocations from triple junctions of grain boundaries (GBs) in deformed nanocrystalline materials. In the framework of the model, triple junctions accumulate dislocations due to GB sliding along adjacent GBs. The dislocation accumulation at triple junctions causes partial Shockley dislocations to be emitted from the dislocated triple junctions and thus accommodates GB sliding. Ranges of parameters (applied stress, grain size, etc) are calculated in which the emission events are energetically favourable in nanocrystalline Al, Cu and Ni. The model accounts for the corresponding experimental data reported in the literature.
Nanocrystalline solids, in which the grain size is in the nanometre range, often have technologically interesting properties such as increased hardness and ductility. Nanocrystalline metals can be produced in several ways, among the most common of which are high-pressure compaction of nanometre-sized clusters and high-energy ball-milling. The result is a polycrystalline metal with the grains randomly orientated. The hardness and yield stress ofthe material typically increase with decreasing grain size, a phenomenon known as the Hall-Petch effect,. Here we present computer simulations of the deformation of nanocrystalline copper, which show a softening with grain size (a reverse Hall-Petch effect,) for the smallest sizes. Most of the plastic deformation is due to a large number of small `sliding' events of atomic planes at the grain boundaries, with only a minor part being caused by dislocation activity in the grains; the softening that we see at small grain sizes is therefore due to the larger fraction of atoms at grain boundaries. This softening will ultimately impose a limit on how strong nanocrystalline metals may become.
The structure and motion via climb of twin dislocations along a coherent twin boundary in aluminum are examined via a combination of high resolution transmission electron microscopy (HRTEM) and computer simulation. Climb of these defects increases the thickness of the twin and is a possible alternative to the more familiar glide mechanism. Detailed analysis of the observed defect structure and comparison with atomistic modeling shows that the twin dislocations exist in a dissociated configuration. This structure can be interpreted as the relaxation of the dislocation into two dislocations, a Shockley partial and a stair-rod dislocation, which are separated by a short segment of stacking fault. The atomistic mechanism of the climb of the dislocations is analyzed.
Large-scale production of high purity (99.999%), nano-twinned, and ultrafine-grained copper foils (22 mu m thick) was successfully implemented by the use of nanoscale multilayer technology. The process allows the production of up to fourteen 10 cm diameter foils during a single deposition run with high levels of reproducibility. Mechanical tests demonstrate that the strength of the Cu foils (alpha(y) similar to 540-690 MPa) compares favorably to ultratine-grained copper samples produced by other methods. (c) 2006 Elsevier B.V. All rights reserved.
We present an experimental approach to systematically produce nanostructures with various grain sizes and twin densities in
the Ni-Co binary system. Using electrodeposition with various applied current densities and organic additive contents in the
deposition bath, we synthesize nanostructured fcc and hcp solid solutions with a range of compositions. Due to the low stacking
fault energy (SFE) of these alloys, growth twins are readily formed during deposition, and by adjusting the deposition conditions,
a range of twin boundary densities is possible. The resulting nanostructured alloys cannot be described by a single characteristic
length scale, but instead must be characterized in terms of (1) a true grain size pertaining to general high-angle grain boundaries
and (2) an effective grain size that incorporates twin boundaries. Analysis of Hall-Petch strength scaling for these materials
is complicated by their dual length scales, but the hardness trends found in Ni-80Co are found to be roughly in line with
those seen in pure nanocrystalline nickel.
We develop the embedded-atom method [Phys. Rev. Lett. 50, 1285 (1983)], based on density-functional theory, as a new means of calculating ground-state properties of realistic metal systems. We derive an expression for the total energy of a metal using the embedding energy from which we obtain several ground-state properties, such as the lattice constant, elastic constants, sublimation energy, and vacancy-formation energy. We obtain the embedding energy and accompanying pair potentials semiempirically for Ni and Pd, and use these to treat several problems: surface energy and relaxation of the (100), (110), and (111) faces; properties of H in bulk metal (H migration, binding of H to vacancies, and lattice expansion in the hydride phase); binding site and adsorption energy of hydrogen on (100), (110), and (111) surfaces; and lastly, fracture of Ni and the effects of hydrogen on the fracture. We emphasize problems with hydrogen and with surfaces because none of these can be treated with pair potentials. The agreement with experiment, the applicability to practical problems, and the simplicity of the technique make it an effective tool for atomistic studies of defects in metals.
We use a recently developed, massively parallel molecular-dynamics code for the simulation of polycrystal plasticity to elucidate the intricate interplay between dislocation and GB processes during room-temperature plastic deformation of model nanocrystalline-Al microstructures. Our simulations reveal that under relatively high stresses (of 2.5 GPa) and large plastic strains (of ~12%), extensive deformation twinning takes place, in addition to deformation by the conventional dislocation-slip mechanism. Both heterogeneous and homogeneous nucleation of deformation twins is observed. The heterogeneous mechanism involves the successive emission of Shockley partials from the grain boundaries onto neighboring slip planes. By contrast, the homogeneous process takes place in the grain interiors, by a nucleation mechanism involving the dynamical overlap of the stacking faults of intrinsically and/or extrinsically dissociated dislocations. Our simulations also reveal the mechanism for the formation of a new grain, via an intricate interplay between deformation twinning and dislocation nucleation from the grain boundaries during the deformation. The propensity for deformation twinning observed in our simulations is surprising, given that the process has never been observed in coarse-grained Al and that the well-known pole mechanism cannot operated for such a small grain size. It therefore appears that the basic models for deformation twinning should be extended with particular emphasis on the role of grain-boundary sources in nanocrystalline materials.
The concepts of twinning shears and twinning modes are introduced. The early attempts to predict these features are presented. This is followed by a detailed discussion of the formal theories of Bilby and Crocker and Bevis and Crocker for predicting these elements. Their formalisms are applied to predict twinning modes in single lattice structures, superlattices, hexagonal close packed structure and other double lattice structures. Wherever possible the predicted modes are compared with those observed.The description of fully coherent, rational twin interfaces is presented, and the concepts of elementary, zonal, complementary and partial twinning dislocations are discussed. It is suggested that the irrational K1 twin interfaces may be faceted on the microscopic scale, and these facets may be coherent.Homogeneous and heterogeneous nucleation of twins are discussed. The growth of twins by the nucleation of twinning dislocations on planes parallel and contiguous to the coherent twin boundary is considered. Various dislocation models proposed for the formation of twins in b.c.c., f.c.c., diamond cubic, zinc-blende and h.c.p. structures are critically reviewed. In some cases the supporting experimental evidence is presented. Additionally, the effects of deformation temperature, imposed strain-rate, alloying and doping, prestrain, precipitates and second phase disperions on deformation twinning are discussed.Mechanistic details regarding the accommodation processes occurring at twins terminating within a crystal, slip-twin, twin-slip and twin-twin intersections are reviewed and are compared with the experimental results. The role of twins in the nucleation of fracture in materials is also considered.
The nucleation and propagation of dissociated full dislocations from grain boundaries in nanocrystalline fcc metals is discussed in terms of the splitting distance between two partial dislocations. It is demonstrated that the use of the splitting distance assumes the existence of the partial dislocations and therefore can not account for nucleation criteria. Moreover, even once both partial dislocations are nucleated, the local stress distribution seems to play an important role in the separation of the partials.
Deformation twins and stacking faults have been observed in nanocrystalline Ni, for the first time under uniaxial tensile test conditions. These partial dislocation mediated deformation mechanisms are enhanced at cryogenic test temperatures. Our observations highlight the effects of deformation conditions, temperature in particular, on deformation mechanisms in nanograins.
We have investigated the rate sensitivity of flow stress and the extent of strengthening in polycrystalline copper containing different volume fractions of nano-sized twins, but having the same average grain size. The specimens were produced by pulsed electrodeposition, wherein the concentration of twins was varied systematically by varying the processing parameters. Depth-sensing instrumented indentation experiments performed at loading rates spanning three orders of magnitude on specimens with the higher density of twins (twin lamellae width ∼20 nm) revealed an up to sevenfold increase in rate-sensitivity of hardness compared to an essentially twin-free pure Cu of the same grain size. A reduction in twin density for the same grain size (with twin lamellae width ∼90 nm) also resulted in a noticeable reduction in rate-sensitivity and hardness. The presence of a high density of nano-scale twins is also seen to impart significant hardness, which is comparable to that achieved in nano-grained Cu. Post-indentation analyses of indented Cu with nano-scale twins in the transmission electron microscope reveal deformation-induced displacement of coherent twin boundaries (CTBs), formation of steps and jogs along CTBs, and blockage of dislocations at CTBs. These processes appear to significantly influence the evolution of thermal activation volume for plastic flow which is some three orders of magnitude smaller than that known for microcrystalline Cu. Transmission electron microscopy also reveals CTBs with a high density of dislocation debris and points to the possibility that displaced CTBs may serve as barriers to dislocation motion and that they may also provide sources for dislocation nucleation, especially near stress concentrations, very much like grain boundaries. Possible consequences of these trends for deformation are explored.
This paper describes mechanistic models that seek to rationalize experimentally determined low values for the activation volume associated with the high strain rate sensitivity of nanocrystalline metals. We present models for the emission of partial or perfect dislocations from stress concentrations at a grain boundary or twin boundary. The emission of deformation twins is likewise examined as a competing mechanism to perfect dislocation emission. The approach illustrates the important roles of both the intrinsic stacking fault energy and the unstable stacking energy. We find that the models lead to estimates of activation volumes in the range 3 − 10b3 for truly nanocrystalline metals. Activation volumes are found to increase monotonically with increasing grain size. The findings are found to be in accord with available experimental evidence in both a quantitative and qualitative manner. Deficiencies in the available experimental evidence are noted, specifically in the context of explaining some of the difficulties in comparing theoretical predictions to experimental observation.
High resolution transmission electron microscopy (HRTEM) observations and atomistic simulations of facets in a gold 90° tilt boundary show the presence of a ∼10 Å wide layer with stacking faults distributed one to every three close-packed planes. This interfacial reconstruction, which forms the rhombohedral 9R stacking arrangement, is similar to that found previously for near−Σ=3{112} boundaries in low stacking fault energy metals. We discuss a general approach for partitioning grain boundary orientation into a set of Shockley partial dislocations and then apply this description to the interface. The analysis explains both the distribution of faults and the geometry of the local plane bending and shows, further, that the 9R stacking occurs in both the Σ=3{112} and interfaces due to the similar ratios of 30° and 90° Shockleys in both cases. Finally, we discuss limitations of this description, in particular concerning a relaxation that is predicted by the atomistic simulations.
A new, semiempirical model of metals and impurities (embedded atom method) makes possible a static treatment of the brittle fracture of a transition metal in the presence of hydrogen. Results indicate that hydrogen can reduce the fracture stress in nickel.
Molecular-dynamics simulations of the Sigma3(211) twin boundary in Ag predict a thin (1 nm) boundary phase of the 9R (alpha-Sm) structure. High-resolution electron microscopy shows the presence of the predicted structure. We also calculate the energy ab initio for several hypothetical structures of Cu and Ag. Low energies of the 9R structure and other polytypes, low experimental stacking-fault energies, and the hcp-fcc energy difference are correlated and explained in terms of an effective nearest-neighbor Ising interaction.
The plane-wave pseudopotential (PWPP) method is used to perform density-functional-theory (DFT) calculations for two grain boundaries in aluminum studied previously using the embedded-atom method (EAM) and high-resolution transmission electron microscopy: (1) a [Sigma]=11 (1[bar 1]3)129[degree] symmetric tilt boundary and (2) a [Sigma]=3 (112) twin boundary. Results are presented for the grain-boundary energies and the electron-density distributions in the boundary regions. The DFT results confirm that the EAM provides a good description of structural properties. However, the DFT grain-boundary energies are a factor of 2 larger than the EAM values, consistent with discrepancies found previously for (111) stacking faults in aluminum. In addition, two sources of instability are identified in the Teter-Payne-Allan preconditioned conjugate-gradients algorithm [Phys. Rev. B 40, 12 255 (1989)] used to perform the PWPP calculations. Simple techniques are proposed that eliminate these instabilities and their utility is demonstrated for these grain-boundary calculations.
The mechanical behaviour of nanocrystalline materials (that is, polycrystals with a grain size of less than 100 nm) remains controversial. Although it is commonly accepted that the intrinsic deformation behaviour of these materials arises from the interplay between dislocation and grain-boundary processes, little is known about the specific deformation mechanisms. Here we use large-scale molecular-dynamics simulations to elucidate this intricate interplay during room-temperature plastic deformation of model nanocrystalline Al microstructures. We demonstrate that, in contrast to coarse-grained Al, mechanical twinning may play an important role in the deformation behaviour of nanocrystalline Al. Our results illustrate that this type of simulation has now advanced to a level where it provides a powerful new tool for elucidating and quantifying--in a degree of detail not possible experimentally--the atomic-level mechanisms controlling the complex dislocation and grain-boundary processes in heavily deformed materials with a submicrometre grain size.
We present a combined experimental and theoretical analysis of the structure of finite-sized Sigma 3 [112] grain boundaries in Au. High-resolution electron microscopy shows lattice translations at the grain boundary, with the magnitude of the translation varying along the finite-sized grain boundaries. The presence of this structural profile is explained using continuum elasticity theory and first-principles calculations as originating from a competition between elastic energy and the energy cost of forming continuous [111] planes across the boundary. This competition leads to a structural transition between offset-free and nontrivial grain boundary structures at a critical grain boundary size, in agreement with the experiments. We also provide a method to estimate the energy barrier of the gamma surface.
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