Detwinning mechanism of ITBs

Detwinning, a process of reversed twinning widely occurring in the deformation process of hcp metals,^{Reference Wu, Jain, Brown, Stoica, Agnew, Clausen, Fielden and Liaw76} has recently received a great deal of attention in face-centered-cubic (fcc) and body-centered-cubic (bcc) metals. In fcc metals especially, the detwinning process can directly eliminate the twin lamella and decrease the density of TBs,^{Reference Anderoglu, Misra, Wang, Hoagland, Hirth and Zhang77} thus, it greatly influences the material’s mechanical performance.^{Reference Lu, Chen, Huang and Lu78} The underlying mechanism has been explored through in situ TEM studies on nanotwinned (NT) Cu: The detwinning mechanism of ultrafine twins is fulfilled through the migration of Σ3 {112} ITBs.^{Reference Wang, Li, Anderoglu, Zhang, Misra, Huang and Hirth67,Reference Liu, Jian, Chen, Wang and Zhang69}

Based on topological analysis, ITBs in fcc metals can be represented as an array of Shockley partial dislocations (a pair of dislocations resulting in stacking faults) on every {111} plane. Furthermore, a structural unit of three Shockley partials, containing a pure-edge partial (b₁) and two mixed partials (b₂ and b₃), is identified with a net Burgers vector equal to zero.^{Reference Wang, Anderoglu, Hirth, Misra and Zhang79,Reference Lucadamo and Medlin80} Due to its singular dislocation structure, the migration of the boundary can be realized through the collective glide of partial dislocations, thus the migration barrier is rather low.

Figure 1a presents a typical indentation stress versus displacement (and time) plot captured during loading (red) and unloading (blue) processes for epitaxial NT Cu. The inset presents the MD results of detwinning of thin twins with an end of ITBs.^{Reference Wang, Li, Anderoglu, Zhang, Misra, Huang and Hirth67} The loading segment can be grouped into three regimes corresponding to three different microstructural evolution events: ITB migration at very low stress (∼0.1 GPa); dislocation nucleation at median stress state (∼0.5 GPa); and dislocation transmission across the CTB at a higher stress (∼0.8 GPa). The corresponding defect evolution events are presented in Figure 1b–d. Compared to dislocation nucleation and transmission, the barrier stress for migration of fine ITBs is relatively low.

Figure 1.

In situ nanoindentation studies of nanotwinned Cu.^{Reference Li, Wang, Huang, Misra and Zhang68,Reference Liu, Jian, Chen, Wang and Zhang69} (a) Indentation stress versus displacement (time) plot during the loading (red) and unloading (blue) process. Inset: Molecular dynamics results of detwinning of thin twins with an end of incoherent twin boundaries (ITBs).^{Reference Wang, Li, Anderoglu, Zhang, Misra, Huang and Hirth67} Atoms are colored by common-neighbor analysis. The blue atoms represent face-centered-cubic (fcc) structure, and the red ones correspond to stacking faults relative to fcc. The Shockley partial dislocation b₁ (indicated by dislocation symbols) moves ahead of the two other partials. The whole boundary migrates ahead by a distance of d. (b–d) Correspond to the starting of the phenomena of ITB migration, dislocation nucleation, and transmission to CTB, respectively. (e–g) Correspond to the microstructure evolution afterward. T1, T2, and T3 mark the position and morphology of different TBs. (h–i) Structure-related migration behavior of ITBs. Locally generated Frank partial (pointed by arrow) could suppress the migration. Note: “tip” refers to the position of indentation tip.

When the ITB is subjected to an applied shear stress (e.g., τ_yx), it is easier for the partial edge dislocation b₁ to migrate than the other two partial dislocations, because it experiences smaller Peierls barrier, and the Peach–Koehler glide force (i.e., the force on a dislocation produced by applied or internal stresses, on the pure edge partial [b₁]) can be described as:

(1)$${F_{{b_1}}} = - {\tau _{yx}}{b_1} + {F_{{b_1} - {b_2}{b_3}}} + {\gamma _{SF}},$$

where ${F_{{b_1}}}$ represents the contribution from the shear stress, ${F_{{b_1} - {b_2}{b_3}}}$ is the interaction between b₁ and the paired partials, b₂ and b₃, and γ_SF is the stacking-fault energy (SFE). The glide force on the paired partials, b₂ and b₃, equals:

(2)$${F_{{b_2}{b_3}}} = {\tau _{yx}}{b_1} - {F_{{b_1} - {b_2}{b_3}}} - {\gamma _{SF}} \cdot$$

Although the net force on the ITB is zero, a slight increase in stress would overcome the attractive force between b₁ and the paired partials, b₂ and b₃, and disturb the equilibrium position of b₁, and thus drive b₁ to one direction. In parallel, the paired partials experience attractive forces due to SFE (γ_SF) and the interaction with b₁, both of which pull them toward b₁ until they again reach an equilibrium state. The repeat of this process could result in the migration of ITBs in the direction favored by the applied force acting on b₁. Such collective glide of groups of Shockley partials has been confirmed by in situ nanoindentation studies, as shown in Figure 1h.^{Reference Li, Wang, Huang, Misra and Zhang68} It is noticed that several three-{111}-plane steps compose the migration front of the ITB in Figure 1h. As the net Burgers vector of one triple unit is zero, the migration of ITBs of nanotwins is expected to produce insignificant macroscopic strain.

In addition, the migration behavior of Σ3 {112} ITBs may change due to their interactions with dislocations. For instance, the transmission of a glide dislocation across the ITB locally changes the dislocation structure and generates a Frank partial dislocation (which is a sessile, immobile defect with a Burgers vector of 1/3[111] in fcc metals) along the ITB (as shown by the white arrow in Figure 1i), thereby pinning it against stress-induced migration.^{Reference Li, Wang, Huang, Misra and Zhang68} At higher local shear stress, depinning could happen due to the dissociation of the Frank partial,^{Reference Lu, Du, Lu and Ye81,Reference Medlin, Carter, Angelo and Mills82} permitting continuous migration of the ITB segment. This finding benefits the explanation of the intrinsically enhanced fatigue cracking resistance of ITBs.^{Reference Li, Zhang, Zhang and Zhang83}

Interface-disconnection-glide mechanism at ITBs in nanotwinned Al

The migration behavior of Σ3 {112} ITBs is closely correlated with the SFE of metals. For metals with higher SFE, the width of the dissociated equilibrium boundary is small, and the stress required to break the equilibrium is high. MD simulations found that when the SFE is ultrahigh, like in Al, the Σ3 {112} ITBs are prone to shear by coupling the nucleation of a Frank partial (interface disconnection) from the edge and shuffling on the boundary planes along [111] direction.^{Reference Wang, Misra and Hirth84} However, verification of these predictions can be challenging, due to the difficulty of introducing high-density growth twins in Al.^{Reference Zhang, Misra, Wang, Shen, Nastasi, Mitchell, Hirth, Hoagland and Embury6}

By manipulating the low SFE buffer layer as twin seed and interface design, high-density twins have been successfully fabricated in Al (see the Introductory article in this issue).^{Reference Bufford, Liu, Zhu, Bi, Jia, Wang and Zhang85} Multiple in situ nanoindentation cycles have been performed at the same location in NT Al to investigate deformation mechanisms. The compiled indentation stress-displacement curves for four consecutive indentation cycles on NT Al are presented in Figure 2a.^{Reference Bufford, Liu, Wang, Wang and Zhang70} During the first and second indentation cycles, the dislocations are nucleated and confined by the ITB. During the third cycle, at 40 s (Figure 2b), the new dislocations propagate left and pile up at the ITB, causing the distortion of a small portion of the ITB (marked by a red dotted line as step 1). Upon additional indentation, more dislocations are nucleated and pile up against the further distorted ITB, resulting in the work hardening observed in Figure 2a. The first dislocation transmission event across the ITB occurs in the fourth indentation cycle, as shown in Figure 2c–d. The repetitive indentation cycles clearly reveal accumulative work-hardening behavior in NT Al. The schematic diagram in Figure 2e shows the orientation of the adjacent domains, ITB geometry, and slip systems. It is worth pointing out that ITB migration in NT Al has been observed at a stress level of 0.5 GPa, which is higher than the yield strength of NT Al (0.3 GPa), and much higher than the stress necessary for ITB migration in NT Cu (0.1 GPa).^{Reference Liu, Jian, Chen, Wang and Zhang69}

Figure 2.

In situ nanoindentation of highly twinned Al.^{Reference Bufford, Liu, Wang, Wang and Zhang70} (a) Compiled curves for several cycles of successive indentations at the same location, showing nominal indentation stress as a function of indentation depth. (b–d) Structural evolution of indented incoherent twin boundaries (ITBs) under continuous loading cycles. (e) Schematic showing orientations of the twin and matrix separated by an ITB. (f–g) Molecular dynamics simulations of nanoindentation of nanotwinned (NT) Al and NT Cu. Atoms are colored according to common-neighbor analysis (red = stacking fault; blue = normal face-centered cubic (fcc); green = defected fcc structure).

MD simulations have uncovered that the extent of dissociation of the ITBs in NT Al is negligible, and when lattice dislocations are nucleated, the interaction of lattice dislocations with ITBs causes the nucleation and migration of interface disconnections (Figure 2f–g).^{Reference Bufford, Liu, Wang, Wang and Zhang70} During indentation of the NT Cu, ITBs dissociate readily into two tilt walls, thereby bounding a volume of a 9R crystal phase^{Reference Medlin, Campbell and Carter86} before absorbing lattice dislocations (Figure 2h–i). The 9R regions can accommodate plastic deformation by allowing frequent transmission of lattice dislocations. Therefore, the ITB barrier resistance for the transmission of lattice dislocations in NT Cu is much lower than in NT Al. Correspondingly, ITBs in NT metals with high SFE could induce significant work hardening and plasticity.

Defects multiplication at CTBs

CTBs are known to be a strong barrier to the transmission of dislocations due to the slip discontinuity across CTBs. In general, after the interaction of an incoming dislocation with a CTB, one twinning dislocation (TD) with step height of one {111} d-spacing is left at the boundary, the glide of which causes the migration of the CTB forward one step. However, in situ TEM experiments revealed these interactions could lead to the formation of Lomer–Cottrell (L–C) locks at the TBs, causing significant work hardening,^{Reference Lee, Holland, Mukherjee, Zhang and Wang71} or multiple TDs, causing the formation of significant ITB steps, which could be sources for mobile dislocations.^{Reference Li, Wang, Misra, Zhang, Huang and Hirth72} Similar to the migration of Σ3 {112} ITBs, the multiplication behavior of defects at CTBs may be influenced by the SFE as well: Full dislocation interaction induces the formation of L–C locks more prevalently in high-SFE metals.

Figure 3a shows multiple force-displacement plots obtained from three consecutive indentation cycles for twinned Ni. The area of interest marked by the white box in Figure 3b comprises a CTB (T1) and is enlarged in Figure 3c–d. The former shows the two dislocations (A₀ and B) on different sets of {111} planes intercepting at T1. During continuous indentation, the two dislocations interact and form an L–C lock at the CTB (Figure 3d). The corresponding mechanism is shown schematically in Figure 3e–f. Higher stress is necessary to promote the interaction of these dislocations with the CTB. The sequential repetitive loadings at the same location reveal the prominent work-hardening behavior due to the formation of L–C locks along TBs in NT Ni.

Figure 3.

(a–f) In situ nanoindentation studies on work hardening arising from coherent twin boundaries (CTBs) in Ni and the formation of Lomer–Cottrell (L–C) locks at twin boundaries.^{Reference Lee, Holland, Mukherjee, Zhang and Wang71} (b) Top to bottom: grains, G1 and G2, and twin, T1, are marked. (c) At 28.30 s, two dislocations A₀ and B from different sets of {111} planes intercept and react to form the L–C lock. (g–h) In situ nanoindentation on twinned Cu and the multiplication of twinning dislocations at CTBs.^{Reference Li, Wang, Misra, Zhang, Huang and Hirth72} (i) Schematic diagram to present the multiplication process at CTBs.

On the other hand, the formation of ITB steps can be fulfilled through the multiplication of Shockley partials during dislocation-CTB interactions. Figure 3g–h presents inverse fast Fourier transforms of high-resolution TEM (HRTEM) snapshots of the interaction of a glide dislocation with a CTB taken during dynamical loading of NT Cu.^{Reference Li, Wang, Misra, Zhang, Huang and Hirth72} After the interaction, the CTB is divided into two segments separated by a disconnection with the height of three {111} atomic planes. The height of the step changes under the loading and can be explained by a dislocation multiplication mechanism at CTBs. As illustrated in Figure 3i,^{Reference Li, Wang, Misra, Zhang, Huang and Hirth72} under compressive and local shear stresses, the full lattice dislocation dissociates into a sessile Frank partial dislocation and a TD at the CTB. The TD moves away, resulting in the migration of the TB upward by one atomic layer. The Frank partial could continuously dissociate into a full dislocation and a TD, and these dissociation processes can be repeated, causing the formation of ITB steps. These ITB steps could act as sources for mobile partials.

Twin-density-dependent heterogeneous-to-homogeneous dislocation nucleation

Although nanoscaled TBs in fcc bulk metals remarkably improve the mechanical strength, ductility, and tolerance to fatigue cracking, in one-dimensional metallic nanowires (NWs), the introduction of TBs could induce unexpected but intriguing mechanical responses.^{Reference Wang, Sansoz, Huang, Liu, Sun, Zhang and Mao75} A heterogeneous-to-homogeneous dislocation nucleation phenomenon has been identified in ultratwinned Au NWs, when the critical twin size is less than 2.8 nm.^{Reference Wang, Sansoz, Huang, Liu, Sun, Zhang and Mao75}

Figure 4a shows the microstructure of ultratwinned Au NWs with growth direction along 〈111〉. The parallel TBs are perpendicular to the wire axis, and tensile loading along the axis has been applied. The mechanical responses of four types of NWs with various twin densities have been explored and corresponding stress–strain curves are plotted in Figure 4b.^{Reference Wang, Sansoz, Huang, Liu, Sun, Zhang and Mao75} The ultimate strength of Au NWs without twins is ∼1.43 GPa, with no strain hardening after yielding. The mechanical response of Au NWs with low-density twins is characterized by significant strain hardening, with an ultimate strength of ∼2.05 GPa after yielding (∼1.7 GPa), as well as by considerable ductility (∼35%). As presented in Figure 4c, the deformation and fracture of Au NWs with either low-density twins or no twins is dominated by dislocations nucleated from free surfaces. In the Au NWs with low-density twins, uniform plastic elongation followed by necking primarily occurs between TBs with the largest twin spacing. TBs are also found to act as barriers for partial dislocation motion, thus contributing to the observed strengthening and strain-hardening effects.

Figure 4.

Structure-mechanical property-deformation mechanism relationships in ultrathin Au nanowires (NWs) with different structures.^{Reference Wang, Sansoz, Huang, Liu, Sun, Zhang and Mao75} (a) Morphology and high-resolution TEM image of Au NW with ultrahigh-density twins. (b) Representative stress–strain curves of Au NWs with different structures, including no twins (green curve), low-density twins (LDTs, blue curve), bimodal twins (red curve), and ultrahigh-density twins (UDTs, black curve). (c) Heterogeneous dislocation nucleation from the free surface in Au NWs with LDTs (λ > 5.6 nm). During uniaxial tensile loading (marked by σ above the double-headed arrow). Red arrows point to the location of dislocation nucleation. (d) Homogeneous dislocation nucleation and semi-brittle fracture in a Au NW with bimodal twins.

In contrast, Au NWs with ultrahigh-density twins show little strain hardening, considerably reduced ductility, and their elastic limit increases to ∼3.12 GPa. In Figure 4d, plastic deformation starts in the region with the largest spacing (between TB₃ and TB₇ with TB spacing of 2.4–3.3 nm), and dislocations and stacking faults nucleate directly inside the crystal (Figure 4d). Under tensile loading, deformation proceeds via the homogeneous nucleation of partial dislocations in the twin with the largest size; further deformation induces detwinning, shear localization, and necking, leading to semi-brittle fracture with detwinned tips.

The observed ductile-to-brittle transition controlled by the heterogeneous-to-homogeneous dislocation nucleation with increasing twin densities is in large contrast to the change from brittle fracture to ductile plasticity recently reported in NT Cu nanopillars,^{Reference Jang, Li, Gao and Greer8} in which the deformation was found to be dominated by the heterogeneous nucleation of dislocations from the TBs/surface intersections. The distinctive behavior may result from the SFE of the materials, which is correlated with the stress required to nucleate new dislocations; the sample size (diameter of NWs), which is correlated with the image effect; the difference of the ideal strength limit between Cu and Au; and possible different surface structures.

Size-dependent deformation twinning in tungsten

A prior study on fcc Au NWs uncovered the size dependence of TB-related deformation mechanisms. By using in situ HRTEM nanomechanical testing, the phenomenon of dominant deformation twinning has been probed in W NWs with a diameter of ∼20 nm at room temperature and low strain rates.^{Reference Wang, Zeng, Weinberger, Zhang, Zhu and Mao74} As presented in Figure 5a, the diameter of the W nanowire is 14.7 nm, and the loading direction is along $\left[ {\overline 1 10} \right]$. Pseudoelastic deformation twinning has been captured in a W bicrystal nanowire under loading-unloading cycles (Figure 5a). Under compressive loading, a deformation twin nucleates from the intersection between the surface and grain boundary, and then expands to about 4 nm before unloading; upon unloading, the W bicrystal deforms via a layer-by-layer detwinning process that returns the NW to its original shape after full detwinning. The corresponding fast Fourier transform pattern and the enlarged detwinning process are shown in Figure 5b. In addition to the 〈110〉 loading, deformation twinning dominates for several other loading orientations tested, including 〈100〉 tension and 〈111〉 compression (shown in Figure 5c–d). Except for the surface nucleation, grain-boundary-mediated twinning nucleation has also been captured under 〈110〉 compression, as shown in Figure 5e.

Figure 5.

Twinning-dominated deformation in body-centered-cubic W nanowires (NWs).^{Reference Wang, Zeng, Weinberger, Zhang, Zhu and Mao74} (a) Pseudoelastic deformation twinning in a W bicrystal NW under loading-unloading cycles. (b) Fast Fourier transform pattern of the deformation twin and the magnified detwinning process. (c–d) Twinning-dominated deformation under 〈001〉 and 〈111〉 loadings, respectively. (e) Grain-boundary-mediated twinning nucleation and growth in a W NW.

Challenges and future prospects

Generally, in situ nanomechanical testing provides us with a deeper understanding of the fundamental deformation mechanisms, and such knowledge may ultimately enable the development of design principles for synthesizing required microstructure for tailored mechanical response. TBs, as one of the simplest structurally defective boundaries, bring complicated but intriguing mechanical properties to materials. In situ mechanical straining in a TEM provide us the opportunity to explore the influence of a material’s intrinsic characteristics, such as SFE, nature of TBs (CTBs versus ITBs), and twin spacing, on the mechanical responses of TBs in fcc and bcc metals.

In addition to these intrinsic characteristics, the external mechanical straining environments, including local stress state, strain rate, and testing temperatures, are equally important. Uncovering the mechanical response of TBs under different deformation environments remains a challenge. In order to solve this problem, more advanced in situ mechanical testing tools are necessary:^{Reference Zheng, Meng and Zhu87,Reference Zhu and Durr88} (1) to obtain three-dimensional (3D) stress–strain configurations under in situ straining; (2) to capture high-quality micrographs with ultrashort exposure time; and (3) to perform straining under a wide range of environments, such as at elevated temperatures, in a liquid cell, under different gas flow, etc.

First, the stress–strain information is of great importance in any mechanical test. Through in situ nanoindentation on TEM samples with regular shapes, the recorded force and displacement signal can be used to calculate the stress–strain curves. However, the calculated stress typically reflects the overall stress state of the entire specimen. In comparison, the information of local stress–strain state correlated with the occurrence of defect-TB interactions (which may be more instructive to understand deformation mechanisms) is often missing. Minor’s group at Berkeley used advanced nanobeam electron diffraction to develop a nanoscale strain-mapping technique.^{Reference Ozdol, Gammer, Sarahan and Minor89,Reference Ozdol, Gammer, Jin, Ercius, Ophus, Ciston and Minor90} On the other hand, extended attempts have been made to obtain local strain information through tracking of the displacement of individual atomic columns shown in the HRTEM images.^{Reference Li, Misra, Shao and Wang91–Reference Wang, Liu, Guan, Yang, Sun, Cheng, Hirata, Zhang, Ma, Chen and Han93} However, special attention should be paid to handle the artifacts arising from the projection of 3D objects onto the two-dimensional planes.

Second, stabilized high-quality micrographs are critical for subsequent analyses of deformation processes. During dynamic loading, capturing stabilized images remains an issue.^{Reference Stach, Zakharov, Rivas, Longo, Lent, Gubbens and Czarnik94,Reference Kim, LaGrange, Reed, Taheri, Armstrong, King, Browning and Campbell95} In order to obtain clear micrographs during deformation, the strain rate is typically limited to 10^–3 s^–1 or less. Even so, the mechanism of ultrafast events such as dislocation nucleation from TBs still cannot be explored. Under the current quasistatic straining conditions, high strain-rate deformation, such as shock loading, cannot be investigated. The development of superfast electron detectors is required for extending the range of strain rate for in situ testing.^{Reference Stach, Zakharov, Rivas, Longo, Lent, Gubbens and Czarnik94,Reference Kim, LaGrange, Reed, Taheri, Armstrong, King, Browning and Campbell95}

Third, most current in situ mechanical straining tests are performed at ambient temperature or under vacuum condition. Through integrating the thermal actuator connected to a temperature controller into the MEMS tensile testing stage, elevated temperatures, up to 475 K, can be achieved.^{Reference Chen, He, Shin, Richter and Gianola96} However, further modifications are necessary to suppress thermal strain due to the difference of thermal expansion coefficients between the sample and stage. To date, there are very few in situ studies on the influence of liquid or gas flow on mechanical response during in situ straining, as it is challenging to integrate the straining stage into a liquid or gas cell.

In summary, in situ TEM nanomechanical testing provides a unique opportunity to investigate the interaction of dislocations with TBs, and new technology developed in the field of in situ TEM will enable us to push the frontiers of fundamental understanding of TB-dictated deformation mechanisms. Such fundamental knowledge will be useful to guide the design of advanced structural materials with significantly enhanced mechanical performance.