Revealing the Maximum Strength in Nanotwinned Copper

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Science  30 Jan 2009:
Vol. 323, Issue 5914, pp. 607-610
DOI: 10.1126/science.1167641


The strength of polycrystalline materials increases with decreasing grain size. Below a critical size, smaller grains might lead to softening, as suggested by atomistic simulations. The strongest size should arise at a transition in deformation mechanism from lattice dislocation activities to grain boundary–related processes. We investigated the maximum strength of nanotwinned copper samples with different twin thicknesses. We found that the strength increases with decreasing twin thickness, reaching a maximum at 15 nanometers, followed by a softening at smaller values that is accompanied by enhanced strain hardening and tensile ductility. The strongest twin thickness originates from a transition in the yielding mechanism from the slip transfer across twin boundaries to the activity of preexisting easy dislocation sources.

The strength of polycrystalline materials increases with decreasing grain size, as described by the well-known Hall-Petch relation (1, 2). The strengthening originates from the fact that grain boundaries block the lattice dislocation motion, thereby making plastic deformation more difficult at smaller grain sizes. However, below a certain critical size, the dominating deformation mechanism may change from lattice dislocation activities to other mechanisms such as grain boundary–related processes, and softening behavior (rather than strengthening) is expected (3, 4). Such a softening phenomenon has been demonstrated by atomistic simulations, and a critical grain size of maximum strength has been predicted (57). In pure metals, an impediment to determining the grain size that yields the highest strength is the practical difficulty of obtaining stable nanostructures with extremely small structural domains (on the order of several nanometers). The driving force for growth of nanosized grains in pure metals, originating from the high excess energy of numerous grain boundaries, becomes so large that grain growth may take place easily even at ambient temperature or below.

Coherent twin boundaries (TBs), which are defined in a face-centered cubic structure as the (111) mirror planes at which the normal stacking sequence of (111) planes is reversed, are known to be as effective as conventional grain boundaries in strengthening materials. Strengthening has been obtained in Cu when high densities of nanometer-thick twins are introduced into submicrometer-sized grains (810). In addition, coherent TBs are much more stable against migration (a fundamental process of coarsening) than conventional grain boundaries, as the excess energy of coherent TBs is one order of magnitude lower than that of grain boundaries. Hence, nanotwinned structures are energetically more stable than nanograined counterparts with the same chemical composition. The stable nanotwinned structure may provide samples for exploring the softening behavior with very small domain sizes. Here, we prepared nanotwinned pure Cu (nt-Cu) samples with average twin thickness ranging from a few nanometers to about 100 nm.

High-purity (99.995%) Cu foil samples composed of nanoscale twin lamellae embedded in submicrometer-sized grains were synthesized by means of pulsed electrodeposition. By increasing the deposition rate to 10 nm/s, we succeeded in refining the mean twin thickness (i.e., the mean spacing between adjacent TBs, hereafter referred to as λ) from a range of 15 to 100 nm down to a range of 4 to 10 nm (see supporting online material). The as-deposited Cu foils have an in-plane dimension of 20 mm by 10 mm and a thickness of 30 μm with a uniform microstructure. Shown in Fig. 1, A to C, are transmission electron microscopy (TEM) plane-view images of three as-deposited samples with λ values of 96 nm, 15 nm, and 4 nm, respectively. The TEM images indicate that some grains are irregular in shape, but low-magnification scanning electronic microscopy images, both cross section and plane view, show that the grains are roughly equiaxed in three dimensions. Grain size measurements showed a similar distribution and a similar average diameter of about 400 to 600 nm for all nt-Cu samples. Twins were formed in all grains (see the electron diffraction pattern in Fig. 1D), and observations of twins in a large number of individual grains revealed no obvious change in the twin density from grain to grain. Note that in all samples, the edge-on twins that formed in different grains are aligned randomly around the foil normal (growth) direction (8, 11), in agreement with a strong [110] texture determined by x-ray diffraction (XRD). For each sample, twin thicknesses were measured from a large number of grains, which were detected from numerous TEM and high-resolution TEM (HRTEM) images, to generate a distribution. Figure 1E illustrates the 492 measurements for the sample with the finest twins; the majority yielded spacings between twins smaller than 10 nm, with a mean of 4 nm. For simplicity, each nt-Cu sample is identified by its mean twin thickness; for example, the sample with λ = 4 nm is referred to as nt-4.

Fig. 1.

TEM images of as-deposited Cu samples with various mean twin thicknesses. (A) λ = 96 nm. (B) λ = 15 nm. (C) λ = 4 nm. (D) The same sample as (C) but at higher resolution, with a corresponding electron diffraction pattern (upper right inset) and a HRTEM image of the outlined area showing the presence of Shockley partials at the TB (lower right inset). (E) Distribution of the lamellar twin thicknesses determined from TEM and HRTEM images for λ = 4 nm.

Figure 2 shows the uniaxial tensile true stress–true strain curves for nt-Cu samples of various λ values. Also included are two stress-strain curves obtained from a coarse-grained Cu (cg-Cu) and an ultrafine-grained Cu (ufg-Cu) that has a similar grain size to that of nt-Cu samples but is free of twins within grains. Two distinct features are observed with respect to the λ dependence of the mechanical behavior of nt-Cu. The first is the occurrence of the λ giving the highest strength. All stress-strain curves of nt-Cu samples in Fig. 2, A and B, are above that of the ufg-Cu, indicating a strengthening by introducing twins into the submicrometer grains. However, such a strengthening does not show a linear relationship with λ. For λ > 15 nm (Fig. 2A), the stress-strain curves shift upward with decreasing λ, similar to the strengthening behavior reported previously in the nt-Cu (9, 11) and nanocrystalline Cu (nc-Cu) (1215) samples (Fig. 3A). However, with further decreases of λ down to extreme dimensions (i.e., less than 10 nm), the stress-strain curves shift downward (Fig. 2B). As plotted in Fig. 3A, the measured yield strength σy (at 0.2% offset) shows a maximum value of 900 MPa at λ ≈ 15 nm.

Fig. 2.

Uniaxial tensile true stress–true strain curves for nt-Cu samples tested at a strain rate of 6 × 10–3 s–1. (A) Curves for samples with mean twin thickness varying from 15 to 96 nm; (B) curves for samples with mean twin thickness varying from 4 to 15 nm. For comparison, curves for a twin-free ufg-Cu with a mean grain size of 500 nm and for a cg-Cu with a mean grain size of 10 μm are included.

Fig. 3.

Variation of (A) yield strength and (B) strain hardening coefficient n as a function of mean twin thickness for the nt-Cu samples. For comparison, the yield strength and n values for nc-Cu [▲ (12), ◂ (13), ▸ (14), and ♦ (15)], ufg-Cu [▾ (9)], and cg-Cu samples reported in the literature are included. A maximum in the yield stress is seen for the nt-Cu with λ = 15 nm, but this has not been observed for the nc-Cu, even when the grain size is as small as 10 nm.

The second feature is a substantial increase in tensile ductility and strain hardening when λ <15 nm. As seen in Fig. 2, the tensile elongation of the nt-Cu samples increases monotonically with decreasing λ. When λ < 15 nm, the uniform tensile elongation exceeds that of the ufg-Cu sample, reaching a maximum value of 30% at the finest twin thickness. Strain-hardening coefficient (n) values were determined for each sample by fitting the uniform plastic deformation region to σ = K1 + K2ϵn, where K1 represents the initial yield stress and K2 is the strengthening coefficient (i.e., the strength increment due to strain hardening at strain ϵ = 1) (16, 17). The n values determined for all the nt-Cu samples increase monotonically with decreasing λ (Fig. 3B), similar to the trend of uniform elongation versus λ. When λ < 15 nm, n exceeds the value for cg-Cu (0.35) (16, 17) and finally reaches a maximum of 0.66 at λ = 4 nm. The twin refinement–induced increase in n is opposite to the general observation in ultrafine-grained and nanocrystalline materials, where n continuously decreases with decreasing grain size (Fig. 3B).

The strength of the nt-Cu samples has been considered to be controlled predominantly by the nanoscale twins via the mechanism of slip transfer across the TBs (10, 18), and it increases with decreasing λ in a Hall-Petch–type relationship (9) similar to that of grain boundary strengthening in nanocrystalline metals (12). Our results show that such a relationship breaks down when λ < 15 nm, although other structural parameters such as grain size and texture are unchanged. The grain sizes of the nt-Cu samples are in the submicrometer regime, which is too large for grain boundary sliding to occur at room temperature, as expected for nanocrystalline materials with grain sizes below 20 nm (3). Therefore, the observed softening cannot be explained by the initiation of grain boundary–mediated mechanisms such as grain boundary sliding and grain rotation, as proposed by molecular dynamics (MD) simulations for nanocrystalline materials (3).

To explore the origin of the twin thickness giving the highest strength, we carried out detailed structural characterization of the as-deposited samples. HRTEM observations showed that in each sample TBs are coherent Σ3 interfaces associated with the presence of Shockley partial dislocations (as steps), as indicated in Fig. 1D. These partial dislocations have their Burgers vector parallel to the twin plane and are an intrinsic structural feature of twin growth during electrodeposition. The distribution of the preexisting partial dislocations is inhomogeneous, but their density per unit area of TBs is found to be rather constant among samples with different twin densities. This suggests that the deposition parameters and the twin refinement have a negligible effect on the nature of TBs. Therefore, as a consequence of decreasing λ, the density of such TB-associated partial dislocations per unit volume increases.

We also noticed that grain boundaries in the nt-Cu samples with λ ≤ 15 nm are characterized by straight segments (facets) that are often associated with dislocation arrays (19), whereas in samples with coarser twins, grain boundaries are smoothly curved, similar to conventional grain boundaries. The microstrain measured by XRD was a negligible 0.01% for samples with λ ≥ 15 nm, but increased gradually from 0.038% to 0.057% when λ decreased from 10 to 4 nm, which also indicates a gradual increase in the defect density.

Recent experimental studies and MD simulations (3, 20, 21) have shown that an increase in the density of preexisting dislocations in nanoscale materials will cause softening. In the nt-Cu samples studied, both the dislocation arrays associated with the grain boundaries and the steps associated with the preexisting partial dislocations along TBs could be potential dislocation sources, which are expected to affect the initiation of plastic deformation (22) and to provide the dislocations required for the dislocation-TB interactions that cause work hardening. The preexisting partial dislocations can act as readily mobile dislocations, and their motion may contribute to the plastic yielding when an external stress is applied to the sample. The plastic strains induced by the motion of preexisting partial dislocations can be estimated as ϵ = ρ0bsd/M (where ρ0 is the initial dislocation density, bs is the Burgers vector of Shockley partial dislocation, d is the grain size, and M is the Taylor factor). Calculations showed that for the samples with λ > 15 nm, the preexisting dislocations induce a negligibly small plastic strain (<0.05%). However, for the nt-4 specimen, a remarkable amount of plastic strain, as high as 0.1 to 0.2%, can be induced just by the motions of high-density preexisting dislocations at TBs (roughly 1014 m–2), which could control the macroscopic yielding of the sample. The above analysis suggests that for extremely small values of λ, a transition in the yielding mechanism can result in an unusual softening phenomenon in which the preexisting easy dislocation sources at TBs and grain boundaries dominate the plastic deformation instead of the slip transfer across TBs.

Shockley partial dislocations are always involved in growth of twins during crystal growth, thermal annealing, or plastic deformation. Shockley partials might be left at TBs when the twin growth is interrupted. Therefore, the presence of Shockley partials at some TBs is a natural phenomenon. Although these preexisting dislocations may have a small effect on the mechanical behavior of the samples with thick twins, the effect will be much more pronounced in the samples with nanoscale twins and/or with high preexisting TB dislocation densities such as those seen in deformation twins (23).

To understand the extraordinary strain hardening, we analyzed the deformation structures of the tensile-deformed samples. In samples with coarse twins, tangles and networks of perfect dislocations were observed within the lattice between the TBs (Fig. 4A), and the dislocation density was estimated to be on the order of 1014 to 1015 m–2. In contrast, high densities of stacking faults and Shockley partials associated with the TBs were found to characterize the deformed structure of the nt-4 sample (Fig. 4, B and C), indicating the interactions between dislocations and TBs. Recent MD simulations (18, 24, 25) showed that when an extended dislocation (two Shockley partials connected by a stacking fault ribbon) is forced by an external stress into a coherent TB, it recombines or constricts into a perfect dislocation configuration at the coherent TB and then slips through the boundary by splitting into three Shockley partials. Two of them glide in the slip plane of the adjacent twin lamella, constituting a new extended dislocation, whereas the third one, a twinning partial, glides along the TB and forms a step. It is expected that with increasing strain, such an interaction process will generate a high density of partial dislocations (steps) along TBs and stacking faults that align with the slip planes in the twin lamellae, which may (or may not) connect to the TBs. Such a configuration of defects was observed, as shown in Fig. 4C. The density of partial dislocations in the deformed nt-4 sample was estimated to be 5 × 1016 m–2 on the basis of the spacing between the neighboring partials and λ. This is two orders of magnitude higher than that of the preexisting dislocations and the lattice dislocations stored in the coarse twins. Such a finding suggests that decreasing the twin thickness facilitates the dislocation-TB interactions and affords more room for storage of dislocations, which sustain more pronounced strain hardening in the nt-Cu (26, 27).

Fig. 4.

(A) A typical bright TEM image of the deformed nt-96 sample showing the tangling of lattice dislocations. (B) An HRTEM image of the nt-4 sample tensile-deformed to a plastic strain of 30%, showing a high density of stacking faults (SF) at the TB. (C) The arrangement of Shockley partials and stacking faults at TBs within the lamellae in the nt-4 sample. Triangles, Shockley partial dislocations associated with stacking faults; ⊥, partials with their Burgers vector parallel to the TB plane.

These observations suggest that the strain-hardening behavior of nt-Cu samples is governed by two competing processes: dislocation-dislocation interaction hardening in coarse twins, and dislocation-TB interaction hardening in fine twins. With a refining of λ, the contribution from the latter mechanism increases and eventually dominates the strain hardening, as revealed by the continuous increase of n values (Fig. 3B). However, the former hardening mechanism usually leads to an inverse trend, diminishing with size refinement (17).

Twins are not uncommon in nature, and they appear in various metals and alloys with different crystallographic structures. Extremely thin twin lamellae structures can possibly be achieved under proper conditions during crystal growth, plastic deformation, phase transformations, or thermal annealing of deformed structures. Our finding of the twin thickness giving maximum strength illustrates that the scale-dependent nature of plastic deformation of nanometer-scale materials is not necessarily related to grain boundary–mediated processes. This finding also provides insight into the development of advanced nanostructured materials.

Supporting Online Material

Materials and Methods

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