REVIEWS
Stabilizing nanostructures in metals
using grain and twin boundary
architectures
K. Lu1,2
Abstract | Forming alloys with impurity elements is a routine method for modifying the
properties of metals. An alternative approach involves the incorporation of interfaces into the
crystalline lattice to enhance the metal’s properties without changing its chemical composition.
The introduction of high-density interfaces in nanostructured materials results in greatly
improved strength and hardness; however, interfaces at the nanoscale show low stability. In this
Review, I discuss recent developments in the stabilization of nanostructured metals by modifying
the architectures of their interfaces. The amount, structure and distribution of several types of
interfaces, such as high- and low-angle grain boundaries and twin boundaries, are discussed.
I survey several examples of materials with nanotwinned and nanolaminated structures, as well
as with gradient nanostructures, describing the techniques used to produce such samples and
tracing their exceptional performances back to the nanoscale architectures of their interfaces.
Shenyang National
Laboratory for Materials
Science, Institute of Metal
Research, Chinese Academy
of Sciences, Shenyang
110016, China.
2
Herbert Gleiter Institute of
Nanoscience, Nanjing
University of Science and
Technology, Nanjing 210094,
China.
1
[email protected]
Article number: 16019
doi:10.1038/natrevmats.2016.19
Published online 31 Mar 2016
The traditional method for modifying the properties of
metals is to alloy them with impurity elements to change
their microstructure and/or their phase constitution.
For example, the addition of carbon and manganese
makes steels harder, and alloying steel with nickel and
chromium makes it more resistant to corrosion1.
The incorporation of structural defects into crystalline lattices provides an alternative approach to the
control of metal characteristics, with the additional
advantage of leaving the chemical compositions unaltered. When a piece of iron sheet is repeatedly bent back
and forth, it becomes progressively harder; this process
is known as work-hardening. The hardening occurs
because this treatment creates crystallographic defects
such as point defects, dislocations and grain boundaries;
these defects resist dislocation motion, making it more
difficult for the metal to deform further. Such a ‘defectbased approach’ (that is, ‘alloying’ with defects instead of
other chemical elements) offers the possibility to widely
tune the properties of a metal. With the progressive
exhaustion of natural resources, in particular of noble
and rare-earth elements2, the defect-based approach is
becoming increasingly important for material sustainability. Moreover, as it does not require alloying, this
method makes it easier to recycle and reuse materials.
Out of the various possible defects, interfaces (planar
defects) are the most studied in this methodology.
As the structural units (for example, grains or phase
domains) decrease in size towards the nanometre scale,
the number of interfaces increases and their effect is
amplified to the point that some material properties are
essentially determined by the nature of the interfaces,
rather than by the crystalline lattice3,4. The strength of
metals with nanometre-sized grains can be an order
of magnitude higher than that of their coarse-grained
counterparts, owing to the very high density of grain
boundaries4,5; thus, nanostructured aluminium can be
stronger than normal steels6.
However, metals with homogeneous nanometre-sized
grains become brittle and show almost no tensile ductility, even in the case of metals that are ductile in their
coarse-grained forms, such as copper and aluminium5,7.
In addition, the nanometre-sized grains are thermally
unstable and show an increased tendency to undergo
grain coarsening when compared with regular coarse
grains8. For nanograined pure copper, for example,
grain coarsening occurs even at room temperature9. The
limited mechanical and thermal stabilities become an
intrinsic ‘Achilles’ heel’ of nanograined metals, hindering
the processing and the technological applications of this
new material family.
The past decade has witnessed significant progress
in the stabilization of nanostructures in metals. Several
types of low-energy interfaces, such as twin boundaries10,11, low-angle grain boundaries12,13 and different
kinds of interphase boundaries (BOX 1) were found to be
effective in altering the characteristics of various metals
and, at the same time, in stabilizing the nanostructures. By
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Box 1 | Grain and interphase boundaries
Crystalline solids usually consist of a large number of grains separated by grain
boundaries. Grain boundaries are generally classified in terms of the misorientation
between two neighbouring grains (panel a) into high-angle grain boundaries, with
misorientation angles larger than 15°, and low-angle grain boundaries, with
misorientation angles below 15°. The structure of some low-angle grain boundaries
can be described as an array of dislocations, as seen in the centre image. The excess
energy of low-angle grain boundaries increases monotonically with the
misorientation angle. A twin boundary is a special type of boundary, in which the
arrangement of atoms on one side, the matrix, is the mirror reflection of the
arrangement on the other side, the twin; the two are separated by the twin
composition plane. The twin boundary energy is usually an order of magnitude
smaller than the energy of the conventional high-angle grain boundaries.
Interfaces separating two crystals differing in composition, lattice structure or both
are called interphase boundaries (panel b). They are usually divided into three classes
depending on the degree of atomic matching or coherence across the interface. In
incoherent interfaces, the atomic matching is sufficiently poor that there is no
correspondence of atom planes and lines across the interface, even locally; in
semi-coherent interfaces, the disregistry between the two crystal structures is
accommodated by periodic misfit dislocations in the interface; finally, in fully
coherent interfaces, there is continuity of atomic planes and lines across the interface
between the two phases. Interphase boundary energies of coherent interfaces are
the lowest (5–200 mJ m−2), followed by those of semi-coherent (200–800 mJ m−2)
and incoherent interfaces (800–2,500 mJ m−2)103.
a Grain boundary
High-angle grain boundary
Low-angle grain boundary
Twin boundary
A B
B C
Matrix
C B
A C
B
Twin
b Interphase boundary
Incoherent
Semi-coherent
Coherent
Nature Reviews | Materials
tailoring the structure and distribution of these interfaces
at the nanoscale, unprecedented properties and property
synergies can be obtained, opening new frontiers for the
development of stable nanomaterials.
In this Review, I discuss recent developments in
the stabilization of nanostructures in metals by means
of interfacial architecture. Several interfaces in nano­
structured metals are analysed to identify the effects of
their quantity, structure and distribution on the global
performance of the material.
Homogeneous nanograined structures
Strength and hardness. Homogeneous refinement of
polycrystalline grains with conventional grain boundaries generally leads to hardening in metals and alloys4,5.
For example, the hardness and strength of pure nickel in
the micrometre to submicrometre range (FIG. 1a) follow
the empirical Hall–Petch relation14,15; that is, the strength
increases with the inverse square root of the grain size, d.
For grain sizes below 100 nm, most hardness data sit
below the extrapolated Hall–Petch line. For even smaller
grains (below 15 nm for pure Ni (REFS 16–18)), a hardness plateau or even a softening appears, although the
experimental data are not fully consistent. The softening
behaviour has been verified by measuring the hardness
of electrodeposited fully dense Ni(W) solid solution with
grain sizes of a few nanometres, in which the solution
hardening of W is negligible19,20.
The Hall–Petch relation is a consequence of dislocation pile-ups in polycrystals. In grains with a diameter d < 100 nm, dislocation pile‑up hardly exists; thus,
this concept is no longer applicable for the description
of the plastic flow. Instead, new strengthening mechanisms may be active, such as deformation by means
of uncorrelated dislocations (an Orowan-type mechanism) or a whisker-type deformation behaviour with
a 1/d dependence21–23. This latter mechanism seems to
be consistent with the measured hardness in the range
d = 15–100 nm. Dislocation activity has been identified
from microscopic observations of nanometre-sized
grains24 and from measurements of strain-rate sensitivity
in a number of nanograined metals5,25.
The softening at extremely small grain sizes has been
attributed to grain-boundary mechanisms that dominate the plastic deformation26,27. Although experimental observations of grain-boundary sliding and grain
rotations are controversial, evidence of grain-boundary
migration has been reported for several materials28–33.
The mechanically driven grain-boundary migration
leads to grain coarsening and to softening at ambient
temperature under tension 28–30, compression 31 and
indentation32,33 tests. The grain-boundary migration
process can sustain very large strains (>100%) in nanograined structures before cracking 30. Experimental
observations and atomistic simulations suggest that in
nanograined materials the numerous grain boundaries
no longer only act as barriers to slip transmission, but
they also become the primary facilitators for plastic
deformation5.
Ductility. Grain refinement usually leads to an increased
ductility in polycrystalline metals with coarse grains
(above 1 μm), but tensile ductility drops sharply if grain
sizes are reduced to the submicrometre range. This
happens even for those metals that are very ductile
in their coarse-grained forms (FIG. 1b). Because strain
measurements are sensitive to experimental conditions,
such as strain rates and sample sizes, reported values of
tensile ductility show some variability. However, a general observation is that the tensile uniform elongation
before necking is very limited for d < 100 nm, usually to
below 5%. The tensile brittleness of nanograined metals
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a
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Ni (Hv)
Ni (3σy)
Ni (W) (Hv)
Hall–Petch relation
Hv, 3σy (GPa)
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Grain size (nm)
Figure 1 | Grain-size effects on strength, ductility and thermal stability. a | Measured
grain-size dependences of hardness (Hv) and yield strength (σy) in
pure nickel
processed
Nature
Reviews
| Materials
with different techniques13,77,78,104–109 and in NiW alloys formed by electrodeposition17,18. The
Hall–Petch plot from coarse-grained Ni was extrapolated in the refined scale (dashed line).
b | Measured grain-size dependence of tensile uniform elongation110–116, showing the
maximum limit before necking, for Ni, Cu, Fe and Al. c | Reduced temperature for grain
coarsening (T/Tm, where Tm is the bulk equilibrium melting point) for the same pure metals
as shown in panel b9,117–128.
is consistent with the observed decrease in the resistance to fatigue-crack growth under cyclic loading of
nano-grained samples, relative to their coarse-grained
counterparts34. However, an improved fatigue life, as
measured by the evolution of the stress (S) as a function
of the number of cycles to failure (N) — an S–N-type
plot — is obtained as a consequence of the high strength5
of the nanograined samples.
The tensile brittleness measured in homogeneous
nanograined metals implies that the detected dislocation
activity and grain-boundary migration are not effective in accommodating plastic strains under tension.
Some observations, however, indicate that nanograined
metals may not be intrinsically brittle. Large numbers
of dimples have been observed in fracture surfaces of
nanograined metals, which are a signature of substantial
plastic deformation before failure35. Large plastic strains
have been reported for other deformation modes such
as compression and rolling 36,37. Extensive investigations
suggest that the tensile brittleness originates from the
absence of work-hardening of nanometre-sized grains
and from strain localization under tension, which results
in early necking occurring immediately after yielding. If
some work-hardening were provided and strain localization were suppressed, tensile ductility could be obtained
in nanograined structures.
Thermal stability. A substantial driving force for grain
coarsening is provided by the large amount of enthalpy
that is stored in the high-density grain boundaries in
nanograined materials. Thus, nanograins can grow at
much lower temperatures than coarse grains8, and significant grain growth has been observed even at room
temperature for pure metals such as copper, aluminium
and magnesium9. The grain-coarsening temperature
decreases for smaller grains, in particular those below
100 nm (FIG. 1c). As the grain size approaches 10 nm, the
grain-coarsening temperature becomes as low as ~0.15Tm,
where Tm is the equilibrium bulk melting point. The
reduced thermal stability of nanograins not only limits
their technological applications but also makes them difficult to process: the low grain-coarsening temperature
complicates the processing of extremely fine-grained
metals (<10 nm), because the tiny grains are unstable at
ambient temperature.
Another consequence of the low stability of small
grains is that when metals are heavily deformed,
strain-induced grain refinement saturates at the submicrometre level if the strain exceeds a certain value
(typically 5–30)38. Additional straining does not further
reduce the grain size because of the intrinsic instability
of nano-sized (below 100 nm) and submicrometre-sized
(between 100 and 1,000 nm) grains. Thus, strain-induced
grain refinement ceases as a dynamic balance is reached
between structure refinement and coarsening (and
recovery) of the refined grains at ambient temperature.
Nanograined structures can be stabilized by proper
alloying with kinetic or thermodynamic strategies9.
In kinetic stabilization, grain boundaries are pinned
in various ways to decrease their mobility by using,
for example, second-phase drag, solute drag and
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Box 2 | Dislocation–twin boundary interactions in face-centred cubic metals
D
Twin boundary
Slip transfer
Matrix
Twinning
partial slip
b1
A
C
B
b3
Twin boundary
Confined layer slip
Twin
λ
b2
D
T
Twin boundary
Nature Reviews | Materials
In face-centred cubic metals, there are three possible types of interaction between
dislocations and twin boundaries, classified on the basis of extended dislocations into
12 {111}<110> slip systems45,46, as illustrated by the double Thompson tetrahedron in
the image.
•Slip transfer mode (hard mode I): both the slip plane and the Burgers vector, b, (the
vector required to form a closed loop, known as a Burgers circuit, if an atom‑to‑atom
path is taken in a crystal containing a dislocation) form an angle with the twin boundary.
Similar to grain-boundary strengthening, the slip resistance is large and depends on the
twin-boundary spacing, λ, as λ−1/2.
•Confined-layer slip mode (hard mode II): the slip plane forms an angle with the twin
boundary, but b is parallel to the twin boundary. The slip resistance is proportional to λ−1.
•Twinning partial slip mode (soft mode): both the slip plane and b are parallel to the twin
boundary. The slip resistance is low because of the reduced constraint from the
relatively large grain sizes.
chemical ordering. The effect of these modifications of
the grain-boundary mobility in nanograined materials
has been analysed with classical theories for different
systems9,39. Thermodynamic stabilization lowers the
specific grain-boundary energy by solute segregation
of the grain boundaries, because the driving force of
grain coarsening is proportional to the grain-boundary
energy. The effects of solute segregation at grain
boundaries on grain-boundary energy and on grainsize stability have been studied in detail40,41. For alloy
systems with a large heat of segregation, the nanograined alloys are in a metastable state for a particular
grain size, which decreases with increasing concentration of the solute element. A nanostructure stability
map has been developed, allowing the design of stable
nanostructured alloys42. Extremely stable nanograined
structures have been synthesized in several alloys42.
Nevertheless, stabilizing nanograined structures
by alloying to decrease the grain-boundary mobility or grain-boundary energy does not improve their
mechanical stability (ductility). To enhance ductility, it
is necessary to provide a mechanism of work-hardening
and strain delocalization in the nanostructure. To
improve thermal stability, more-stable boundaries need
to be formed. Twin boundaries with nanoscale spacing are effective for both purposes. Low-angle grain
boundaries and low-energy interphase boundaries are
also viable solutions for nanostructure stabilization. In
addition, gradient nanostructures have been demonstrated to enhance the ductility of materials that have
different types of boundaries. These nanostructures with
distinctive interface architectures are presented in the
following sections.
Nanotwinned structures
Twin boundaries with extremely low excess energy
effectively hinder dislocation motion and can thus
act as stable interfaces for strengthening metals. Early
experiments indicated that the twin-boundary effect
on hardness in copper alloys is quantitatively the
same as that of grain boundaries43. Measurements and
computer simulations verified that the twin-boundary strengthening can become dominant if the
twin-boundary spacing is reduced to the nanometre
range10,44. Superior properties have been demonstrated
in nanotwinned materials, including engineered alloys
and non-metallic systems.
Interaction of dislocations with twin boundaries.
Nanotwinned materials are structurally characterized
by relatively large grains (typically in the micrometre
range) containing twin boundaries with thicknesses
in the range of a few nanometres to a few tens of
nanometres10,11. The presence of the nanoscale twin
boundaries in the grains changes the dislocation glide
behaviour considerably, because interactions between
dislocations and TBs dominate the plastic deformation.
In face-centred cubic (fcc) metals, there are three possible types of dislocation–twin-boundary interaction:
slip transfer mode (hard mode I), confined-layer slip
mode (hard mode II) and twinning partial slip mode
(soft mode); they are classified on the basis of extended
dislocations (for example, the combination of partial
dislocations and stacking faults) into 12 {111}<110>
slip systems45,46 (BOX 2).
Different slip modes are usually associated with different dislocation sources, and the activation of any
of these three slip modes is controlled by the loading
conditions. In both hard modes, when dislocations (or
segments) are on opposite sides of the twin boundary,
the slip can interact with the twin boundary in different ways, depending on the nature of the material
and on the applied strain47–49. The dislocations can cut
across the twin boundary and transmit into the adjoining twin lamellae, be absorbed into the coherent TB,
dissociate into different partial dislocations that glide
into the twin and along the twin boundary, or form
dislocation locks at the twin boundary. In extremely
thin twins (a few nanometres thick), atomistic simulations have recently revealed another dislocation mechanism: this involves the collective motion of a type of
jogged dislocation that spans multiple twins50,51. Thus,
nanoscale twin boundaries seem not only to act as
effective barriers to dislocation slip, but also to provide room for dislocation accumulation and storage.
In this respect, they are fundamentally different from
conventional grain boundaries, which show an insufficient ability to accumulate dislocations, often leading
to plastic instability.
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1,000
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Nanotwinned (random)
Nanotwinned (parallel)
Nanograined
Nature Reviews | Materials
Figure 2 | Nanoscale twins and twin-boundary strengthening. a–d | Comparison between twin-boundary and
grain-boundary strengthening. Panel a shows the dependence of yield strength (σy) on twin thickness. Panel b shows
tensile elongation to failure. Panel c shows the work-hardening coefficient. Panel d shows the rate sensitivity. The
samples are randomly oriented nanotwinned Cu (REF. 53), parallel nanotwinned columnar Cu (REF. 57), and
homogeneous coarse-grained (CG; dashed line in panel c) and nanograined Cu (REFS 10,52,54,56). e,f | Typical
transmission electron microscopy images of randomly oriented equiaxed Cu grains containing edge‑on nano-twins54
(panel e) and Cu with columnar grains with nanotwins parallel to the deposition plane57 (panel f). λ, twin thickness; GD,
growth direction (directed perpendicular to the page for panel e). Panels a, c and e are adapted with permission from
REF. 54, American Association for the Advancement of Science. Panels b and d are adapted with permission from
REF. 10, American Association for the Advancement of Science. Panel f is adapted with permission from REF. 57, Elsevier.
Nanotwinned copper. In nanotwinned Cu, the twin
thickness influences the tensile properties. In ultra­finegrained Cu containing intra-grain, nanoscale, randomly
oriented edge‑on twins synthesized by pulsed electrodeposition, the tensile yield strength increases with
reducing twin thickness, λ, for λ > 15 nm. This is the
same dependence as that of nanograined Cu on grain
size; both samples follow the empirical Hall–Petch relationship10,52–54 (FIG. 2a). This means that nanoscale twin
boundaries, by blocking dislocation motion, provide as
much strengthening as conventional high-angle grain
boundaries. Further decreasing λ results in a drop in
strength, after a maximum strength is reached for 15 nm
(REF. 54). Experiments and molecular dynamics simulations suggest that this maximum strength originates
from a transition of the plastic deformation mechanism
from dislocation slip transfer (hard mode I) to nucleation and gliding of twinning partials (soft mode)54,55.
A pronounced increase in the tensile elongationto‑failure and work-hardening coefficients is observed
upon decreasing λ, in contrast to the reduction of
these quantities reported for smaller values of d in
nanograined metals11,54 (FIG. 2b,c). In particular, very
high work-hardening is observed as λ drops to a few
nanometres. The decrease in twin thickness promotes
dislocation–twin-boundary interactions and creates
more room for dislocation storage, leading to more
pronounced strain hardening. An increasing strain-rate
sensitivity was measured upon decreasing λ (REF. 56),
analogous to what was obtained by grain refinement in
Cu and Cu alloys52 (FIG. 2d).
The material properties can also be changed through
the nanotwin architecture. Strength and ductility of nanotwinned metals are influenced by the architecture of the
nanotwins, in particular by their structural anisotropy.
This was demonstrated in two types of nano-twinned Cu
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samples with randomly oriented equiaxed grains containing edge‑on nanotwins (FIG. 2e) and with columnar grains
with nanotwins parallel to the deposition plane (FIG. 2f). The
measured tensile yield strength increases with decreasing
λ for both samples but in different ways57 (FIG. 2a). For the
randomly oriented sample, the Hall–Petch type strength
increase indicates that the dominant mechanism is slip
transfer (hard mode I). For the columnar samples, strength
values are smaller and are proportional to λ−1; the threading dislocation slip inside the lamellar channels dominates
plastic deformation (hard model II). The work-hardening
capacity and the uniform tensile ductility decrease at
smaller grain sizes. The Cu samples with columnar grains
undergo inhomogeneous deformation during uniaxial tension, in which grain boundaries experience much larger
plastic strain than that sustained by grain interiors.
Stress-controlled high-cycle fatigue life and fatigue
limit (at the fatigue life of 107 cycles) of nanotwinned
Cu are higher than those of coarse-grained Cu (REF. 58).
Strain-controlled low-cycle fatigue life is also increased
by the nanotwinned structure, and the endurance limit
is higher than that of the coarse-grained and ultrafinegrained Cu (REF. 59). Owing to the threading dislocation
propagation inside nanotwin lamellar channels, the cyclic
stability is maintained after an initial cyclic-hardening
stage, in contrast to the continuous cyclic softening
observed in ultrafine-grained Cu. The saturation stress
increases with increasing strain amplitude and decreasing λ; nanotwinned structures were found to be stable
under high stress and different loading conditions (that
is, compression, torsion and tension)60.
Because of the extremely low enthalpy stored in coherent twin boundaries, the thermal stability of nanotwins is
superior to that of nanograined structures61. In type 330
stainless steel, twins with a thickness of 4–5 nm remained
unchanged after annealing at 0.5Tm for 1 hour 62. In a
magneto-sputtered nanotwinned Cu film, no significant
thickening of twin lamellae was detected after annealing
at 0.8Tm (REF. 63).
Electrical resistivity of coherent twin boundaries in Cu
at room temperature is at least one order of magnitude
smaller than that of grain boundaries; thus, an unprecedented combination of ultrahigh strength and high conductivity is obtained in nanotwinned Cu (REF. 11). The unique
effect of nanotwin boundaries on the strength–conductivity
synergy cannot be produced with other types of internal
boundaries. Other benefits of the nano­twinned structures
include a suppression of the electromigration-induced failure of Cu lines in integrated circuits, because the atomic
transport driven by electrical current at grain boundaries
is reduced by an order of magnitude by the presence of the
nanotwins within Cu grains64.
Nanotwinned steels. Twinning can be obtained in metals by plastic deformation under appropriate conditions.
Nanotwinned structures can be induced in a fraction of
grains in austenitic steels by means of dynamic (highrate) plastic deformation, followed by thermal annealing 65,66. The resulting single-phase duplex structure, with
nanotwinned grains embedded in micrometre-sized
recrystallized grains, has an enhanced strength–ductility
synergy and high work-hardening rates compared with
conventional austenitic and dual-phase steels. A combination of 1.0‑GPa tensile strength with a 27% elongation-to‑failure was achieved in nanotwinned 316L
stainless steel66. The superior characteristics originate
from the presence of the nanotwinned austenitic grains,
which possess a very high yield strength (about 2 GPa
with λ ≈ 28 nm) and, at the same time, considerable tensile ductility and work-hardening. At small tensile strains
(<5%), the nanotwinned grains deform homogeneously
with the surrounding recrystallized grains, without generating notable strain localization near their interfaces67,
unlike what happens in conventional dual-phase structures. Nanotwinned structures have been generated in
several austenitic steels (for example, FeMn, FeMnC and
austenitic stainless steels), which, in each case, resulted
in enhanced properties66,68,69. Optimization of the quantity and distribution of the nanotwinned grains, together
with other strengthening mechanisms, offers a promising
approach for the improvement of the global mechanical
performance of steels.
Nanotwinned superalloys. The main challenge for disc
superalloys used in aircraft engines and land-based gas
turbines, which mainly consist of γ-phase matrix and
γʹ precipitates (for example, Ni3Al-type with L12 structure), is the high temperature at which they must operate.
Recently, a new cast-and-wrought disc NiCo superalloy
system (TMW) based on nanotwin strengthening has
been developed70. On increasing the Co concentration,
the stacking fault energy of the Ni‑based alloy decreases
markedly, from 36 mJ m−2 (15% Co) to 20 mJ m−2 (25%
Co), resulting in the formation of numerous nanoscale
annealing twins (with thickness as small as 10 nm) after
heat treatment. Owing to the high thermal stability of
twin boundaries and to the temperature-insensitive
twinning stress, the nanotwin strengthening is effective
at elevated temperatures — up to 725 °C, about 0.5Tm. An
improvement of about 76 °C in the operating temperature was obtained in the TMW alloy relative to the commercial superalloy U720Li for creep testing at 630 MPa.
Remarkably, the nanotwin strengthening does not compromise other properties such as low-cycle fatigue life,
crack-growth rate and hot workability 71.
Nanotwins in cubic boron nitride and diamond.
Different methods for the preparation of nanograined
ceramics (such as boron nitride, BN) and diamond have
been explored for many years, with the aim of increasing their hardness. Nevertheless, the degree of grain-size
refinement is limited by the reduced thermal stability of
refined grains under the high pressure and temperatures
required during processing. For example, for cubic BN
(c‑BN), a minimum grain size of 14 nm with a hardness
of 85 GPa was obtained at pressures of ~20 GPa (REF. 72).
For well-sintered nanograined diamonds, grain sizes
are limited to 10–30 nm, and they have a low thermal
stability compared with that of natural diamonds73.
Structure refinement in superhard materials has been
finally achieved owing to the use of nanotwinned structures. Twins with thicknesses as small as 3.8 nm have
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been created in bulk c‑BN samples using BN precursor
nanoparticles possessing onion-like nested structures
with intrinsically puckered BN layers and numerous
stacking faults. A record-high hardness was reported74
in these nanotwinned c‑BN samples, exceeding 100 GPa,
which is comparable to the optimal hardness of synthetic diamond. More recently, nanotwinned diamond
has been synthesized by using a precursor of onion-like
carbon nanoparticles. High-density multiple twins,
with an average thickness of 5 nm, were formed in a diamond bulk sample synthesized at 20 GPa and 2,000 °C75
(FIG. 3a,b). A Vickers hardness of 200 GPa, even higher
than that of natural diamond, was reported for synthetic bulk nanotwinned diamond, with a high fracture
toughness of about 15 MPa m−1/2. The in‑air oxidation
temperature is more than 200 °C higher than that of natural diamond. The reported record-high hardness and
thermal stability were attributed to the presence of the
high-density nanotwins, although the dislocation–twin
boundary interaction does not dominate the plastic
deformation in superhard ceramics and diamond. These
unprecedented properties need to be verified by further
measurements, and the role of nanotwins still has to be
clarified through further experimental and analytical
investigations.
Nanolaminated structures
Nanolaminates with low-angle boundary. In metals
with high stacking fault energies, such as Ni and Al, twin
boundaries are difficult to form. Low-angle grain boundaries, which, similar to twin boundaries, can hinder dislocation motion, providing an alternative low-energy
interface for the stabilization of nanostructures. Lowangle grain boundaries are normally formed through
dislocation multiplication and interaction during
plastic straining.
Strain-induced dislocations are not randomly distributed but accumulate in dislocation boundaries
(either geometrically necessary or incidental dislocation boundaries) that separate regions with relatively low
a
b
GB
Interlocked
area
GB
GB
30 nm
5 nm
Nature Reviews
Figure 3 | Nanotwins in diamond. a | Transmission electron microscopy
image| Materials
of
nanotwinned structures in a diamond bulk sample synthesized at 20 GPa and 2,000 °C.
b | High-resolution transmission electron microscopy image of intersecting nanotwins
(outlined by the square in panel a) viewed along the [101] zone axis. Twin boundaries are
marked with arrows75. GB, grain boundary. Figure is from REF. 75, Nature Publishing Group.
dislocation densities76. The spacing and misorientations
of these boundaries depend on strain, strain rates and
strain gradient. The latter two parameters are crucial
for the formation of low-angle grain boundaries. With
increasing strain, the boundary spacing decreases and
misorientation angles increase following a power–law
relationship76,77. Increasing strain rates and/or lowering
deformation temperatures result in the formation of
more low-angle grain boundaries, because dislocation
annihilation kinetics, and recovery and relaxation, are
suppressed. For example, if Ni is compressed at a strain
rate of 102–103 s−1, very small boundary spacings with
a large fraction of low-angle grain boundaries (~70%)
are formed compared with what is obtained under lowrate deformation (~20% in cold rolling and torsion)78.
Increasing the strain gradient, which is proportional
to the density of stored geometrically necessary dislocations79, enhances dislocation storage and reduces
boundary spacing.
Using a surface mechanical grinding treatment on a
pure Ni rod, a very high rate of shear deformation (up
to 104 s−1) was imposed at the top surface layer (~80 μm
thick) with high strain gradients (0.4–0.1 μm−1)13; at a
certain strain level, laminated structures with an average thickness of 20 nm were formed13. The interfaces
between the adjoining lamellae were all low-angle grain
boundaries, with misorientation angles typically below
10° (FIG. 4a–c). This strongly textured nanolaminated
structure is distinct from that obtained from conventional heavy deformation (submicrometre-sized elongated grains with mostly high-angle grain boundaries).
With the same technique, similar nanolaminates were
generated in the surface layer of a body-centred cubic
(bcc) interstitial-free steel12.
Nanolaminated structures with low-angle grain
boundaries are extremely hard owing to their very
small thickness, and they are highly stable owing to
the low-energy boundary state. The Vickers hardness
of 20‑nm laminates in Ni is about 6.4 GPa, which is
higher than any value reported for Ni processed with
heavy plastic deformation13. The hardness follows a
Hall–Petch line if the lamellar thickness is taken as
equivalent to the grain size, indicating that the nanospaced low-angle grain boundaries are as effective in
resisting dislocation motion as conventional high-angle grain boundaries. The thermal stability of low-angle
grain boundaries is also good: the onset temperature for
the thickening of the nanolaminates (~506 °C) is higher
than the coarsening temperature of nanograins of comparable sizes (~443 °C). The combination of hardness
and stability of the nanolaminates with low-angle
grain boundaries stands out from the general trend for
refined structures13.
The formation of boundaries at low-energy states
(low-angle grain or twin boundaries) thus stabilizes
nanostructures and hence aids structural refinement.
Conventional plastic deformation refines grains of metals down to the submicrometre regime, with mostly
high-angle boundaries. The stable structural sizes
decrease to several tens of nanometres as most grain
boundaries become low-angle. Even smaller lamellar
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a
1
b
Sample
Tip
2
3
V2
20 nm
V1
4
c
3º
200 nm
d
Boundary energy
γ HAGB
γLAGB
γITB
γCTB
1
10
Material
Grains
100
1,000
Structural size (nm)
Laminates
Twins
Growth twins
Cu
Ni
Fe
Al
316L steel
Cu–Al
Cu–Zn
Fe–Mn
Diamond
c-BN
Figure 4 | Nanolaminated structures in nickel and boundary
energy
effect
on
Nature
Reviews
| Materials
minimum structural size. a | A bright-field cross-sectional and longitude-sectional
transmission electron microscopy (TEM) image of the nanolaminated structures in Ni
(REF. 13). The schematic drawing shows the processing set-up and the sample
orientation, in which V1 is the rotation velocity of the sample and V2 is the moving
velocity of the tip. b | A high-resolution TEM image of the nanolaminated structure
containing four lamellae (1, 2, 3 and 4)13. c | A Fourier-filtered image
_ corresponding to
the area in the rectangle in panel b, showing contiguity of the ( 111 ) atomic plane in
lamella 2 to the (111) in lamella 3, with a misorientation angle of 3° across the
boundary, indicated by the dashed line. d | Correlation between minimum structural
sizes reported in literature and the boundary energy for the elements and
single-phase materials listed in the table, processed by means of various plastic
deformation techniques and other methods12,13,54,66,74,75,121,129–139. The boundary energies
for high-angle grain boundary (γHAGB), low-angle grain boundary (γLAGB), incoherent
twin boundary (γITB) and coherent twin boundary (γCTB) are indicated. Note that γCTB
values are only a few per cent of those for γHAGB. Panels a, b and c are adapted with
permission from REF. 13, American Association for the Advancement of Science.
spacing is induced (around 10 nm) when incoherent
twin boundaries are generated by plastic deformation
in metals with low stacking-fault energies. The finest
laminated structures, with characteristic sizes of a few
nanometres, are formed with coherent twin boundaries that possess the lowest excess energy among these
interfaces, as in the case of electrodeposited copper 54
and diamond75. A clear, general trend is that the minimum achievable structural size in single-phase materials
decreases on reducing the boundary energy (FIG. 4d).
Nanolaminated composites. The formation of lowenergy interfaces is also crucial for the stabilization
of multiphase nanostructures. Low-energy interphase
boundaries are frequently formed during the precipitation of a second phase from a supersaturated solid
solution; the thermodynamic driving force is a decrease
in the volume free energy at the cost of an increase
in interfacial energy. Hence, low-energy interphase
boundaries are preferentially formed to minimize the
total free energy. For example, when particles of Pb
are precipitated from an Al(Pb) supersaturated solid
solution, the nanometre-sized Pb particles with truncated shapes bounded by {111} and {100} facets exhibit
a cube–cube relationship with the Al matrix, forming
semi-coherent Pb/Al interfaces80. Owing to the lowenergy, semi-coherent interphase boundaries between
particle and matrix, the nanostructure is significantly
stabilized: the melting temperature of the Pb nano­
particles is increased to 40 °C above the equilibrium
melting point of bulk Pb (REFS 81,82).
Low-energy interphase boundaries are also formed
under extreme mechanical straining of layered nanocomposites. Metalworking techniques can be used to
create composites of different metals in bulk quantities
for structural applications, but the resulting bimetal
interfaces typically lack crystallographic order and are
thus unstable. Using the technique of accumulative roll
bonding on stacked Pb and Al foils, nanometre-thick
multilayers can be fabricated with increasing strains.
Layers of Pb are thinned down to about 20 nm and
are sandwiched between Al nanolayers; semi-coherent
epitaxial Pb/Al interfaces form, with a cubic–cubic orientation relationship83. The semi-coherent Pb/Al interfaces result in an elevated melting temperature of the Pb
nanolayers.
Nanolayered materials made of alternating layers
of Cu and Nb have been fabricated in bulk form with
the accumulative roll bonding technique84. By applying
an increasing strain, the individual layer thickness was
reduced from 2 mm to 20 nm (FIG. 5a). High-resolution
transmission electron microscopy (TEM) micrographs
of the preferred interfaces show that they are regularly
ordered at the atomic level, as they were formed in
near-equilibrium thermodynamic processes. Two types
of regular zigzag atomic-scale facets were identified
(FIG. 5b,c): {111}Cu//{101}Nb and {001}Cu//{011}Nb.
This
_ is a consequence of the faceted topology of the
{3 38}Cu and {112}Nb, and {112}Cu and {112}Nb
crystallographic planes that are being joined85. Owing
to the lattice mismatch between Cu and Nb, misfit
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a
b
[110]Cu
_
(338)
c
_
1) (111
(00_ ) (1 _)
1 01)
(01
_
1) (1
(00_ ( 11_)
1) 101
)
(01
Cu
[110]Cu
_
(112)
Nb
50 nm
1 nm
[111]Nb
[111]Nb
1 nm
Nature Reviews | Materials
Figure 5 | Bimetal nanolaminates made of copper–niobium. a | Typical transmission electron microscopy (TEM) image
84,85
of the Cu–Nb bimetal nanolaminates after extreme straining
. b,c | High-resolution TEM micrographs
_ of preferred Cu/
_
Nb interfaces formed in the bimetal nano-laminates: { 338 }<443>Cu//{112}<110>Nb (panel b) and { 112 }<111> Cu//
{112}<110>Nb (panel c)85. Adapted with permission from REF. 85, Proceedings of the National Academy of Sciences.
dislocations are formed at the bimetal interfaces. The
formation of these interfaces is supported by atomistic
calculations, which show two energy minima, corresponding to the two types of observed interfaces.
Experimental measurements show that the largescale low-energy interfaces make the nanocomposite
extremely strong and, at the same time, very stable. The
samples maintain their integrity upon treatment with
further straining, elevated temperatures and light-ion
irradiation.
Another example of nanostructure stabilization
through the formation of low-energy interfaces is provided by severe drawing of a pearlitic steel wire86,87 (a
lamellar structure composed of alternating iron and
iron carbide layers). The carbide phase dissolves with
increasing strain, transforming the initial two-phase
pearlite structure into a carbon-supersaturated iron
phase in the form of nanoscale columnar structures.
Gibbs segregation of the supersaturated carbon from
the iron subgrain boundaries reduces their interface
energy, lowering the driving force for dynamic recovery and crystal coarsening. A stable cross-sectional
subgrain size smaller than 10 nm is thereby obtained,
leading to a record-high tensile strength of 7 GPa.
Gradient nanostructures
As discussed above, the observed tensile brittleness of
nanograined metals originates from the superposition of
strain localization and early necking, owing to the lack
of work-hardening. To provide work-hardening and to
delocalize strain in nanograined structures, a unique
architecture was designed: a layer of nanograined material adheres to a ductile coarse-grained substrate of the
same material; between them is positioned a transition
layer with graded grain size30,88 (FIG. 6a). This architecture with a graded spatial variation of grain sizes (or
grain-boundary density), which is elastically homogeneous but plastically exhibits a gradient, enables the
delocalization of strains and work-hardening from the
coarse-grained substrate. This principle applies to different grain morphologies (such as equiaxed, laminated
and columnar) with various types of boundaries, including twin boundaries88. It results in plastic deformation
behaviours that are fundamentally different from those
of the free-standing homogeneous nanograined and
coarse-grained samples.
The spatial variation of grain sizes can be generated by the controlled surface plastic deformation of
bulk coarse-grained metals, using a gradient variation
of strain and strain rate from the surface to the interior 30,89,90. Several gradient deformation approaches
(surface impact, surface grinding and surface rolling)
have been developed to produce gradient nanograined
(or nanotwinned or nanolaminated) structures in surface layers of bulk metals88. Nanometre-sized grains
are generated by very high strain rates (up to ~104 s−1)
and strain gradients (~0.5 μm−1) in the top surface
layer — a treatment different from the conventional
heavy plastic deformation of bulk metals with which
submicrometre-sized grains are normally obtained.
Alternatively, gradient nanostructures can be prepared
by means of deposition processes (physical and chemical vapour deposition, or electrodeposition) with controlled deposition kinetics, which enable the grading of
the spatial variation of microstructures and/or chemical
compositions.
Mechanical behaviour. Uniaxial tensile tests performed
on Cu ‘dog-bone’ shaped samples with a gauge diameter
of 6 mm showed that the generation of a gradient nanograined skin (the grain sizes in the top 60‑μm-thick
layer were below 100 nm) on top of a coarse-grained
core can double the yield strength of the sample owing
to the very strong surface layer 30. Interestingly, the
nanograined layer and the coarse-grained core were
elongated coherently with a strain of ~60% before failure. This elongation-to‑failure is comparable to that of
coarse-grained Cu. If removed from the substrate, the
free-standing nano-grained skin exhibits almost no
tensile elongation.
The gradient nanograined surface layer presents a
unique strain delocalization mechanism that is optimal
for enhancing fatigue properties of conventional materials under cyclic loading, as demonstrated in several
recent studies91–93. Fatigue-crack initiation is suppressed
by the hard and ductile nanograined skin, whereas the
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a
b
Surface
CG
GNG
Hardness
Ductility
Strain softening
Strain hardening
After straining
Before straining
Homogeneous
plastic deformation
Grain refinement
NG + CG
0
NG
Depth from surface
Yield strength
Figure 6 | Strength–ductility synergy and strain softening and hardening of gradient nanograined structures.
Nature Reviews
a | The blue curve shows how the yield strength increases at the expense of ductility for homogeneous
plastic | Materials
deformation of coarse-grained (CG) metals or for homogeneous refinement to nanometre-sized grains (NG). Similar
strength–ductility trade-offs appear for random mixtures of coarse grains and nanograins (NG + CG). By contrast, a
synergy between yield strength and ductility is achieved with gradient nanograined (GNG) structures (orange curve)98.
b | Schematic representation of a sample with a gradient nanograined skin and variation of the hardness profiles as a
function of the depth from the surface before and after straining100. Panel a is adapted with permission from REF. 98,
American Association for the Advancement of Science.
soft coarse-grained interior effectively arrests crack
propagation. The increase in the fatigue limit can be
larger than 100% for engineered alloys with a gradient
nanograined surface layer.
Superior strength–ductility combinations have been
reported for several gradient nanograined and gradient
nanotwinned materials94–96. In contrast to the traditional
‘banana curve’ for the trade-off between strength and
ductility, which is characteristic of homogeneously
deformed or homogeneous nanograined metals and of
random mixtures of nano and coarse grains, the overall
strength gain obtained using gradient nanostructuring
is much more pronounced than the ductility loss97,98
(FIG. 6a). Finer nanograins or thicker gradient skins may
push the strength–ductility line even further up99.
Plastic deformation mechanism. If a homogeneousgrained material is strained, plastic deformation sets
in almost simultaneously in different grains, producing stress–strain localization between adjacent grains
if they cannot deform in concert. When a material with
a grain-size gradient is strained, deformation in coarse
grains begins first and smaller grains deform at higher
loads. With an increasing load, plastic deformation
propagates from coarse-grained regions to finer and
finer grains progressively, until it reaches the topmost
nanograined layer. Intergranular stress between neighbouring grains of different sizes is effectively released
and strain localization is suppressed, enabling the
nanograined skin to undertake plastic deformation
concurrently with the other parts of the sample98.
The deformation of the nanograined layer is dominated by a mechanically driven grain-boundary migration, with concomitant grain coarsening and softening 30.
At the same time, deformed coarse grains are hardened
by dislocations, providing work-hardening for the
whole sample. Thus, strain hardening and grain-boundary migration-induced softening occur simultaneously
in the gradient structure 100 (FIG. 6b) . In submicrometre-sized regions, neither hardening nor softening is
induced, because the two mechanisms are balanced; this
corresponds to the strain-induced saturation structures
in which the density of dislocations and grain boundaries (grain size) reaches saturation38. The gradient
microstructures constitute a unique system in which
various plastic deformation mechanisms of largely different microstructures are concurrently activated; this
is a combination that does not exist in homogeneous
structures and in random mixtures of nano- and
coarse grains.
Other properties. During plastic deformation of metals under tension, buckling or drawing, obvious surface roughening (usually referred to as ‘orange peel’)
takes place owing to the inhomogeneous deformation
experienced by neighbouring grains with different
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crystallographic misorientations. Increased surface
roughness can enhance stress concentration or even
crack nucleation, which is detrimental to the processability of the metal. Owing to the extraordinary tensile
ductility of gradient nanostructured surface layers, the
inhomogeneous plastic deformation of neighbouring
nanometre-sized grains is suppressed, and surface
roughening or cracking is eliminated completely 30,88.
The surface roughness of pure Cu with a gradient
nanograined surface layer remains in the submicrometre regime after tension, whereas it increases to a
few micrometres in coarse-grained samples at the same
strain30.
Enhanced wear resistance has been reported in several metals and alloys with gradient nanostructured surface layers101, owing to the substantial surface hardening.
Gradient nanostructures are also used to improve the
cohesion between different materials and to promote the
bonding of hard films and metals. Bonding between 304
stainless steel and an ultrahard thin film (for example,
CrN, TiN or diamond-like carbon) is enhanced by
using gradient nanostructured surface layers on the
steel102. The wear resistance of the bonded films is also
enhanced102. The stronger bonding originates from
the elevated diffusivity in the gradient nanostructures,
which aids the formation of metallurgical bonding.
Conclusions and perspective
An interface is a unique lattice defect with a wide spectrum of possible structures and energy states. With
the increasing awareness of the effect of interfaces
on the performance of materials, traditional processing–structure–property relationships — the core of
materials science — will be upgraded with the addition of
the structure of interfaces, of which there are numerous
variants. Research in the formation, structure and properties of interfaces at the nanoscale provides new challenges and opportunities for experimental, analytical
and simulation studies.
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Acknowledgements
The author thanks the Ministry of Science and Technology of
China (Grant 2012CB932201), the National Natural Science
Foundation of China (Grants 51231006), the Danish-Chinese
Center for Nanometals (Grants 51261130091 and
DNRF86‑5) and the Key Research Program of Chinese
Academy of Sciences (Grant KGZD‑EW‑T06) for financial support, and X. C. Liu, X. Y. Li and L. Lu for discussions and
assistance.
Competing interests statement
The author declares no competing interests.
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