Defective twin boundaries in nanotwinned metals

doi:10.1038/NMAT3646

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PUBLISHED ONLINE: 19 MAY 2013 | DOI: 10.1038/NMAT3646

Defective twin boundaries in nanotwinned metals

Y. Morris Wang

1

*

, Frederic Sansoz

2

, Thomas LaGrange

1

, Ryan T. Ott

3

, Jaime Marian

1

,

Troy W. Barbee Jr

1

and Alex V. Hamza

1

Coherent twin boundaries (CTBs) are widely described, both

theoretically and experimentally, as perfect interfaces that

play a signiﬁcant role in a variety of materials. Although

the ability of CTBs in strengthening, maintaining the ductility

and minimizing the electron scattering is well documented

1–3

,

most of our understanding of the origin of these properties

relies on perfect-interface assumptions. Here we report

experiments and simulations demonstrating that as-grown

CTBs in nanotwinned copper are inherently defective with

kink-like steps and curvature, and that these imperfections

consist of incoherent segments and partial dislocations.

We further show that these defects play a crucial role in

the deformation mechanisms and mechanical behaviour of

nanotwinned copper. Our ﬁndings offer a view of the structure

of CTBs that is largely different from that in the literature

2,4,5

,

and underscore the signiﬁcance of imperfections in nanotwin-

strengthened materials.

CTBs formed during growth, deformation or annealing exist

broadly in many crystalline solids with low or medium stacking-

fault energies

1,5,6

. The strengthening behaviour and other attractive

properties of CTBs have been studied in nanotwinned metals (with

an average twin spacing <100 nm; refs 7–9). One prevalent view

is that CTB-strengthened materials have certain advantages over

nanocrystalline or ultrafine-grained materials; that is, materials

strengthened through traditional grain boundaries (GBs) that

are considered incoherent and defective

10

. GBs not only scatter

electrons, but can migrate and slide under shear stresses

11

, leading to

a maximum in strength in nanocrystalline materials

12,13

. In contrast,

such migration/sliding mechanisms may not be operative in CTBs

despite some reports of detwinning evidence

7,14,15

and the obser-

vation of a similar maximum strength in a nanotwinned copper

3

(nt-Cu). Existing models widely assume perfect CTBs and rational-

ize flow softening due to CTB migrations and detwinning as caused

by nucleation and motion of partial dislocations parallel to CTBs

(ref. 4). These mechanisms are informative as long as CTB lengths

are limited to the tens of nanometres typically used in molecular

dynamics simulations

4,16–18

. It still remains difficult through molec-

ular dynamics simulations to validate the migrations/detwinning of

the much longer CTBs seen in experiments (500 nm; ref. 3). There

could be alternative mechanisms that are intricately related to the

potential structures of CTBs and the characteristics of GBs, both of

which are not accounted for in the literature.

Recent studies of nanotwinned copper pillars without GBs

revealed strong deformation anisotropy and a brittle-to-ductile

transition behaviour (where CTBs are considered intrinsically

brittle)

2

, suggesting that CTBs alone are not sufficient for increased

plasticity despite their strong strengthening effect, and that a

reasonable mix of GBs is helpful to mediate the plasticity and

achieve high ductility. Experiments and simulations have frequently

1

Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California 94550, USA,

2

School of Engineering, The University

of Vermont, Burlington, Vermont 05405, USA,

3

Division of Materials Sciences and Engineering, Ames Laboratory (USDOE), Ames, Iowa 50011, USA.

*e-mail: ymwang@llnl.gov

quoted GBs as one primary source of dislocations in nanotwinned

polycrystalline materials, the nature of which is expected to

have impacts on the mechanical behaviour; that is, experimental

evidence hints at the relevance of GBs in nanotwinned metals.

Unfortunately, limited information is available regarding the nature

of GBs and the roles they are playing in controlling the plasticity.

We have examined the nanometre structural features of many

twin boundaries (TBs) and the characteristics of GBs using a re-

cently developed inverse pole figure orientation mapping (IPFOM)

in a field-emission transmission electron microscope (TEM). This

nanodiffraction-based technique has a spatial resolution of ∼1 nm

that is comparable to the conical-scanning dark-field imaging

approach

19

. In a standard IPFOM image, 250,000 frames of

diffraction patterns were collected, each of which was indexed by

EDAX orientation-image-mapping indexing software and applied

to determine the crystallographic orientations. The orientation-

resolving ability of IPFOM allows us to identify many previously

unobserved microstructural defect features on preconceived-to-be

completely perfect TBs. The materials used in our studies are nt-Cu

synthesized by magnetron sputtering (see Methods and Supple-

mentary Information). Shown in Fig. 1a is the cross-sectional mi-

crostructure of an as-deposited material, indicating a twin spacing

of ∼5–70 nm with grain column width spanning from ∼0.3 to

1.8 µm. Most TBs appear rather straight without obvious evidence

of defective structures. Similar materials have been synthesized in

parallel by other groups albeit with clear variations in twin density

and columnar grain size

14,20

. To obtain statistical misorientations

of TBs and GBs, we carried out detailed IPFOM studies in TEM

using the NanoMegas Astar system

21

(the pixellation effect of this

technique can be seen in Supplementary Figs S1 and S2). As shown

in Fig. 1b, under low resolution the as-synthesized nt-Cu contains

at least two types of TB; that is, 63{111} CTBs normal or inclined

to the growth direction that often transverse the columns, and a

very limited number of 63{112} incoherent TBs (ITBs) that tend to

bond CTBs terminated inside grains (marked with circles). Owing

to their low frequency, the influence of these ITBs on the mechanical

behaviour is considered inconsequential until the twins become

very thin (<2 nm; ref. 17). However, a zoomed-in high-resolution

IPFOM image shown in Fig. 1c indicates that originally thought

perfect 63{111} CTBs contain many kink-like steps along the

interfaces (a few are marked with arrows). These steps are inco-

herent 63{11

¯

2} segments, as evidenced by their crystallographic

orientations, and their heights (∼1–5 nm) are visibly smaller than

the ITBs mentioned above. The CTBs observed in IPFOM analysis

are imperfect and comprise numerous partial dislocations, as com-

pared with those with perfectly straight lines in two-dimensional

images. For simplicity, we hereinafter refer to these steps as kinks in

two-dimensional descriptions. Note that these nanometre features

are substantially larger than the Burgers vector length (0.147 nm) of

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LETTERS

NATURE MATERIALS DOI: 10.1038/NMAT3646

ac d

350 nm

CTB

GD

ITB

001 011

112

111

b

350 nm

40 nm

5 µm

100 nm

Figure 1 | Microstructure of as-grown nanotwinned copper. a, A focused-ion-beam ion-channelling image of the as-grown nanotwinned copper. The

imaging condition is 30 keV, 9.7 pA. The orientations of representative TBs are marked with double-headed red arrows. b, An IPFOM image of growth

twins. The coherent and incoherent TBs are labelled as CTB and ITB (inside circles), respectively. The growth direction (GD) of the ﬁlm is marked with an

arrow. c, An edge-on high-resolution IPFOM image of CTBs. Some selected kinks are marked with white arrows. The portion of CTBs marked with an X is

perfect TBs without defects. Note that the TEM sample for IPFOM is prepared by electropolishing. d, An IPFOM image of a long GB (from top to the

bottom), which shows mixed segments of low- and high-angle GBs. The GBs are characterized by a coincidence site lattice (CSL) model. The interface

colour scheme in b–d is as follows: yellow, low-angle GBs with misorientation < 15

◦

; black, large-angle GBs; red, 63 CSL boundary; blue, 69 CSL boundary.

The orientations of grains are coloured according to the inverse (001) pole ﬁgure shown in the inset of b.

a single Shockley partial previously reported on CTBs (ref. 3); but

the existence of these defective structures is not at odds with these

earlier high-resolution TEM studies. A close examination of Fig. 1c

suggests that the kink distributions are relatively non-uniform from

TB to TB but that their density is rather persistent; that is, kink

density per unit area increases with twin density. For the sample

shown in Fig. 1c, there exists an average of one kink per 10-nm-long

CTB (Supplementary Fig. S3). These findings strongly suggest that

as with conventional GBs, many CTBs have defective structures

(that is, kinks or incoherent components) that have not been

considered in previous studies. The formation mechanisms of these

kinks are not well understood; however, they seem to be the intrinsic

characteristics of growth twins. It is conceivable that these features

are related to processing or deposition conditions, and are expected

to impact mechanical properties.

Another IPFOM image shown in Fig. 1d reveals that GBs in

nt-Cu are more defective and full of partial-dislocation-like defects,

as manifested by abundant kinks along the GBs. Interestingly, the

statistical misorientation angle distribution maps obtained from

both cross-section (Supplementary Fig. S4) and plan-view indicate

an appreciable fraction of low-angle GBs (misorientation <15

◦

),

leading to a GB network distribution that is far away from a

MacKenzie distribution

22

—the characteristic GB distribution of

a well-annealed coarse-grained copper. Note that the curvy and

defective nature of CTBs remains visible in this image. The GB dis-

tributions observed here strongly suggest that the classical Voronoi

construction approach for GB networks in past modelling studies

may not be applicable to nanotwinned materials reported here.

To help reveal the strain-dependent deformation mechanisms

and the deformation anisotropy (copper has an anisotropic factor

(A) of 3.21; A = 2C

44

/(C

11

−C

12

), where C

11

,C

12

and C

44

are elastic

constants of copper)), we performed in situ synchrotron X-ray

diffraction (SXRD) experiments at two different temperatures to

track in real-time the elastic and plastic deformation of nt-Cu. In

addition to offering a better statistical approach for bulk materials

23

,

the in situ SXRD has the advantageous capability of resolving

anisotropic microstrains

24

. Six crystallographic indices (that is,

111, 200, 220, 311, 222, 400) were followed simultaneously in

these in situ SXRD experiments. To investigate the microplas-

ticity, we quantitatively calculate the lattice strain deviation as

1ε

hkl

= ε

hkl

− σ /E

hkl

, where ε

hkl

= (d

hkl

− d

hkl

o

)/d

hkl

o

(d

hkl

o

and d

hkl

are the inter-planar spacing before and during loading, respec-

tively), σ is the applied stress and E

hkl

is the measured average

elastic modulus for a specific plane hkl (see Supplementary Table

S1). Figure 2a,b shows the 1ε

hkl

behaviour parallel to the tensile

axis (that is, longitudinal direction) for four representative Miller

indices tested at room temperature and 180

◦

C (see Supplementary

Fig. S6 for the heating profile), respectively; the 1ε

hkl

behaviour

for the transverse direction can be seen in Supplementary Fig. S7.

For clarity, the corresponding tensile stress–strain curves are in-

cluded, which show softening behaviour at both temperatures.

In coarse-grained face-centred-cubic copper, the deformation is

governed by full dislocation slips of 1/2h110i{111} type, leading

to preferential yielding and negative 1ε of 220 reflection at the

onset of macroscopic plasticity, whereas 200 exhibits the largest

positive 1ε (ref. 25). Interestingly, the 1ε trend in nt-Cu shows a

rather different behaviour, where 200 shows a pronounced negative

1ε before 0.2% yield stress, and sharply curls back to the positive

territory on further loading. The 111 reflection exhibits similar

curling behaviour; but to a smaller degree. By comparison, the

1ε of 220 remains positive during the deformation. The initial

negative deviation of 1ε for both 200 and 111 reflections in

nt-Cu is an indication of preferable slip activations next to h001i

and h111i orientations, suggestive of 1/6h112i{111} partial related

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NATURE MATERIALS DOI: 10.1038/NMAT3646

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0

50

100

150

200

250

300

350

¬600

¬400

¬200

0

200

400

600

0.00 0.01 0.02 0.03 0.04

111

200

220

311

Engineering stress (MPa)

Engineering strain

0.2%

0

100

200

300

400

500

600

¬1,000

¬500

0

500

1,000

Lattice strain deviation (×10

6

)

Lattice strain deviation (×10

6

)

0.000 0.005 0.01 0.015 0.02 0.025 0.03 0.035

111

200

220

311

Engineering stress (MPa)

Engineering strain

0.2%

a

b

σ

Figure 2 | Lattice strain deviation behaviour in tension. a,b, Engineering

stress–engineering strain curves (black) and lattice strain deviation

behaviour (coloured) of nt-Cu along the longitudinal direction at room

temperature (a) and 180

◦

C (b). The 0.2% macroscopic yield stress is

marked as σ

0.2%

. The strain rate is 6× 10

−5

s

−1

for both temperatures. The

plots show zoomed-in regions of the stress–strain curves corresponding to

plastic strains of 0.027 and 0.033 for the samples deformed at room

temperature and 180

◦

C, respectively.

deformation mechanisms (see the inverse pole figure shown in

Fig. 1b, inset). The 1ε behaviour further indicates that the mi-

croplasticity initiates well before the macroscopic yielding occurs

in these materials, probably owing to some easy dislocation sources

(such as those observed from IPFOM). Moreover, we find that

the deformation of nt-Cu is sensitive to the temperature (Fig. 2b).

The yield stress drops by 43% at 180

◦

C, the plastic deformation

of which is clearly more isotropic as the difference of 1ε among

various crystallographic orientations becomes substantially smaller

compared with room temperature.

The room-temperature peak broadening at different strain levels

plotted according to the Williamson–Hall approach (Fig. 3) sug-

gests that there is a significant amount of dislocation accumu-

lation and the development of strong anisotropy during loading

and after fracture, as evidenced by the increased Williamson–Hall

slope and the continuously broadening of all peaks (for example,

311) vis-à-vis the as-deposited state

26

. A substantial portion of

peak broadening remains permanent after fracture, in contrast

to the reversible peak broadening and strong plastic recovery in

nanocrystalline materials

23,27

. This behaviour generally agrees with

the evolution of the inhomogeneous (root-mean-square) strain

of nt-Cu and the texture development (Supplementary Fig. S8).

The increased dislocation density during deformation and after

0.01

0.02

0.03

0.04

0.05

0.06

20 30 40 50 60 70 80

As-deposited

0.01 strain

0.02 strain

0.03 strain

Fractured

FWHM (nm

¬1

)

Q (nm

¬1

)

111

200

220

311

222

400

Increased strain

Figure 3 | Full-width at half-maximum (FWHM) as a function of the

scattering vector (Q) at various loading strains and after fracture (that is,

Williamson–Hall plots). The scattering vector Q = 4πsinθ /λ, where 2θ is

the angle between incident and diffracted beams, and λ is the wavelength

(nm). These data are extracted from the proﬁle ﬁtting of 300 synchrotron

spectra recorded during the entire tensile test at room temperature. The

strain labelled in the ﬁgure includes macroscopic elastic and plastic

components (except for the fractured sample).

fracture contrasts with the lack of strain hardening in this material,

which may suggest other softening mechanisms that counterbalance

the dislocation hardening. Post-mortem TEM examinations of

the room-temperature-deformed sample shown in Fig. 4a indicate

strong accumulations of dislocations between the TBs and inside

the grains. TEM also reveals the disappearance of some growth

twins (that is, detwinning) in certain regions at room temperature.

At 180

◦

C, most TBs are annihilated, concomitant with grain

coarsening (Fig. 4b). These TEM observations, together with in situ

SXRD tensile results, offer some clues that these defective TBs are

unstable against thermo-mechanical deformations.

Although the experimental observations reported above are

qualitatively self-consistent, we speculate that the real atomic pro-

cesses involved with these kinked TBs during deformation are quite

complex. Therefore, molecular dynamics simulations using models

built from kinked TBs and perfect TBs (Supplementary Fig. S9) are

performed to explore this question. Two types of GB, smooth or

defective, are also incorporated to tackle the effects of GB character-

istics on mechanical behaviour; that is, GBs with either high or low

yield stresses, respectively (Supplementary Fig. S10). Furthermore,

owing to the highly idealized models (for example, the tensile axis

is perfectly parallel to TBs when in tension and thus no critical

resolved shear stress), we simulate the deformation behaviour of

nt-Cu under both uniaxial tension and pure shear conditions, as the

most likely loading scenario in the experiments is the mix of both

due to the incline of TBs (Fig. 1a). From the simulations, we find

that the nt-Cu models with kinked TBs have rather rich deformation

processes that do not exist in the case of perfect TBs.

The stress–strain curves from different simulated microstruc-

tures deformed in tension are shown in Fig. 5a. The highest yield

point and ultimate strength are observed in the sample with smooth

GBs and perfect TBs, suggestive of difficult plastic deformation

processes in these near-perfect samples. Threading dislocations are

observed to emit from GBs and glide along slip directions parallel

to TBs (Supplementary Table S2 and Supplementary Movie S1).

Although this type of crystal slip has been considered as a hard mode

in nt-Cu, with potential slip resistance owing to the constraints of

small twin spacing on dislocation glide

28

, newly emitted threading

dislocations are found to transmit easily without blockage through

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NATURE MATERIALS DOI: 10.1038/NMAT3646

ab

0.5 µm 0.5 µm

Figure 4 | Microstructure of post-mortem tensile samples. a,b, Bright-ﬁeld TEM images of nt-Cu deformed at room temperature (a) and 180

◦

C (b). Note

the loss of some growth twin structure in a (the region marked with asterisks), and the strong coarsening and complete disappearance of growth twins in b.

0% 1.7% tension 5% tension

P

M

L

M

MM

M

CTB

GBGB

cde

a

b

Pure tension

0123

Strain (%)

450123

Strain (%)

45

Density of new

dislocations (10

15

m

¬2

)

¬5

0

5

0

1

2

3

Stress (GPa)

Smooth GB + perfect TB

Defective GB + perfect TB

Smooth GB + kinked TB

Defective GB + kinked TB

Smooth GB + perfect TB

Defective GB + perfect TB

Smooth GB + kinked TB

Defective GB + kinked TB

Figure 5 | Molecular dynamics simulations of deformation mechanisms in nt-Cu subjected to uniaxial tension with a twin spacing of 5 nm.

a, Stress–strain curves for four idealized models containing either smooth or defective GBs, and perfect TBs or kinked TBs. Each arrow shows the onset of

yielding. b, Density of new dislocations as a function of applied strain. c–e, Microstructure and deformation mechanisms in a columnar grain with both

defective GBs and kinked TBs at different stages of deformation. Vertical arrows indicate the positions of migrating kink imperfections. P, partial

dislocations emitted from GBs; M, kink migration; L, Lomer locks.

perfect TBs (ref. 29), and disappear in the opposite GB in the course

of deformation (Supplementary Fig. S11 and Supplementary Movie

S1). These mechanisms result in no increase, or even a decrease,

in dislocation density in all models with perfect TBs (Fig. 5b).

The inclusion of defective GBs (similar to those observed from

experiments) substantially decreases the initial yield stress with

no change in deformation mechanisms. The same effects of GB

structure dominate the yield point of nt-Cu containing kink defects

(Fig. 5a,c,d, Supplementary Table S2 and Supplementary Movie

S2a). Remarkably, the introduction of kinks results in significant

dislocation pinning giving rise to the formation of Lomer–Cottrell

locks at the intersection of threading dislocations and kinks

(Fig. 5c–e, Supplementary Discussion, Supplementary Fig. S12 and

Supplementary Movie S2b). This kink-dependent mechanism is

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NATURE MATERIALS DOI: 10.1038/NMAT3646

LETTERS

consistent with the net increase in dislocation density observed after

initial yielding in our molecular dynamics simulations (Fig. 5b) and

in situ SXRD experiments (Fig. 3). The simulations further indicate

that these Lomer–Cottrell locks are short-lived and can be destroyed

on further deformation. Furthermore, marked softening is observed

at the stress peak (Fig. 5a and Supplementary Table S2) due to

partial dislocations nucleated at kink–GB junctions, gliding along

kink lines (Supplementary Fig. S13 and Supplementary Discussion).

Concurrently, the pinning of threading dislocations decreases, as

evidenced by the maximum in dislocation density reached in nt-Cu

with kinked TBs (Fig. 5b) because of kink migration, which also

contributes to the softening behaviour. Motion of kinks closest to

GBs is observable at the yield point, but becomes more important

to the plastic flow at larger strains (Fig. 5e) because of the low

resolved shear stress on kink steps in pure tension. We propose

that the competition between Lomer–Cottrell lock formation at

the initial yield point and kink-dependent softening mechanisms

at higher stresses may have contributed to the change in 200

lattice strain deviation observed in in situ SXRD experiments

(Supplementary Discussion).

Under pure shear stresses, the deformation of nt-Cu becomes

exclusively dominated by kink motion and migration of TBs (Sup-

plementary Table S2, Supplementary Fig. S14 and Supplementary

Movie S3). Interestingly, dislocations no longer nucleate from GBs

but rather from kink ledges (Supplementary Fig. S14d and Supple-

mentary Movie S3). The kinks are absorbed by GBs after migration,

which leads to detwinning. The shear stress for kink migration is

significantly smaller than that required to emit twinning partial dis-

locations from GBs in models with perfect TBs (Supplementary Fig.

S14a,b and Supplementary Movie S4). These results demonstrate

that shear stresses, such as those in the case of high-pressure torsion

from the experiments

30

, favour kink migration and detwinning—a

notion that bears surprising similarity to GB migrations

11

. The easy

motion and migration of kinks under pure shear qualitatively agree

with the early microscopic yielding of these materials and some

detwinning seen in in situ SXRD and TEMs.

Despite the remaining open questions and nearly idealized

approach of modelling, the combination of experimental and

molecular dynamics results here requires that CTBs be treated

as defective entities, in contrast to the traditional perfect-TB

assumption. The migration of kinks is an emphatic sign that

CTBs have intrinsic instability, notwithstanding experimental

observations that they tend to be more stable than conventional

GBs (refs 20,30). The migration of CTBs caused by kink motions

suggests that CTBs close to GBs or longer CTBs with smaller spacing

are more vulnerable to detwinning. This scenario is different from

the detwinning process through partial dislocation glide proposed

by modelling or from the detwinning caused by ITB motions

observed in some experiments

17,31

. Nevertheless, the kink-motion

proposition has strong implications to the detwinning phenomena

observed so far experimentally (for example, detwinning remains

active even at low temperatures and often occurs in certain

regions)

7,14,15

, as well as a maximum strength seen in nt-Cu (ref. 3).

The detwinning near GBs is likely to help unlock triple junctions

between GBs and TBs, facilitating GB migration and contributing

further to the strain softening. For short CTBs of a few nanometres,

a regime that is dominated by molecular dynamics simulations,

the likelihood of generating kinks decreases, and CTBs can be

considered quasi-perfect. On the other hand, the CTBs in the

materials experimentally studied and reported on here are in the

submicrometre range and observed to have inherent imperfections.

The presence of such defective CTBs must be considered in both

scientific research and practical utilities. We, in addition, believe

that the attention being given to potential defects in CTBs resulting

from annealing, deformation and various synthesis conditions is

desirable to fully understand CTB-strengthened materials.

Methods

The nanotwinned copper samples were synthesized by a layer-by-layer magnetron

sputtering technique. The details of sample conditions, twin density and geometry

are given in the Supplementary Information. The intrinsic nanoscale structures

of the as-synthesized CTB were characterized using an IPFOM technique in a

TEM. The details of the IPFOM technique, resolution, potential pixellation effect,

kink defect density, and additional high- and low-resolution IPFOM images are

available in the Supplementary Information. The tensile properties of nanotwinned

copper were characterized using an in situ SXRD approach performed at the

Advanced Photon Source of Argonne National Laboratory (USA) at two different

temperatures. Multiple nanotwinned samples were measured, and the in situ

deformation information was extracted from the lattice strain deviations, peak

profile and texture analysis (see more in the Supplementary Information).

In addition, the post-mortem deformation microstructure was examined by

conventional TEM. Multi-million atom molecular dynamics simulations were

carried out using models built from experimental observations, where both

perfect and defective twin boundaries were used, and the simulation results are

compared with each other and to experimental findings. Further simulation

details, results and movies are available in the Supplementary Information,

together with a Supplementary Discussion on lattice strain deviation behaviour,

additional deformation mechanisms, and the relevance of defective structures to

the mechanical behaviour of nanotwinned copper.

Received 7 November 2012; accepted 2 April 2013;

published online 19 May 2013

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Defective twin boundaries in nanotwinned metals

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