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314 MRS BULLETIN • VOLUME 41 • APRIL 2016 • www.mrs.org/bulletin © 2016 Materials Research Society
Introduction
Materials such as Mg, Zr, and Ti with a hexagonal close-packed
(hcp) structure are used in automotive, nuclear, aeronautic, and
defense technologies, among others.
1 The basic plasticity mecha-
nisms associated with hcp structures are slip and twinning. The
easiest dislocation slip is along the
1120
close-packed direc-
tions on the (0001) basal plane or
{}
10 10
prismatic planes. 2 , 3
These dislocations, however, do not generate deformation along
the c -axis. The alternative mechanisms available for doing
so are
ca+
slip on
{}
10 11
pyramidal planes, tensile twins,
or compressive twins where the twin planes vary with the
material.
3 The activation of pyramidal slip requires a higher
critical resolved shear stress than that of the basal and pris-
matic slip. Thus,
{}
10 12 10 1 1
twinning, which has a critical
resolved shear stress close to the basal slip, is an important
mode for accommodating strain along the c -axis. 4 The local-
ized shear associated with twinning is partly the reason for the
poor ductility and low deformability of Mg alloys.
4 The cur-
rent emphasis for advancing applications of hexagonal materi-
als is to improve deformability while preserving a high fl ow
strength. The fundamental principle is to adjust the relative
activity among slip and twinning systems.
5 Therefore, an
in-depth understanding of mechanisms and mechanics of
deformation twinning in hexagonal materials is essential.
Twinning in hexagonal materials is directional with a unique
shear direction. Correspondingly, several specifi c characteristics
are associated with hexagonal materials: (1) Rolled hexagonal
metal plates exhibit a characteristic texture component with
the crystal c -axis (the basal pole) preferentially aligned along
the normal direction of the plates. (2) The fl ow-stress evolution
shows strong anisotropy between the in-plane and through-
thickness directions. (3) The in-plane fl ow stress is very dif-
ferent in tension from that in compression. Accompanying the
reorientation of most grains by twinning, the aggregate shows
an increase in hardening rate and continuous evolution of
grain microstructure with deformation.
Twin shear localizes in a defi ned domain of a grain. Twin
nucleation in hexagonal materials is driven by local stress
states and local atomistic confi gurations at grain boundaries
(GBs).
6 , 7 Twin growth, including propagation and thicken-
ing, is driven by long-range stress states across grains through
the motion of twin boundaries (TBs), either by the gliding of
twinning dislocations on the twin plane along the twinning
direction (propagation) or migration of TBs normal to the
twin plane (thickening) via nucleation and gliding of twin-
ning dislocations on the twin plane. This motivated the study
of structural characteristics of TBs and the pinning effect of
solute atoms on the migration of TBs.
8 Corresponding to the
Deformation twinning in hexagonal
materials
Xiaozhou Liao , Jian Wang , Jianfeng Nie , Yanyao Jiang , and
Peidong Wu
Due to the scarcity of “easy slip” systems in hexagonal materials with a hexagonal close-
packed structure (hcp), deformation twinning plays a crucial role in determining mechanical
properties and texture evolution. In this article, we highlight the current understanding of
mechanisms and mechanics of the twinning system
{}
1012 10 1 1
, which is commonly
activated in all hexagonal materials for nucleation and propagation of deformation twins,
twin–twin interactions, solute segregation at twin boundaries, and the development of
constitutive models that account for the fundamental mechanisms of twinning/detwinning.
Future directions such as characterizing the three-dimensional shapes of twins, the in uence
of solute atoms on twin propagation, and the in uence of twin–twin junctions on mechanical
properties of the hexagonal materials are discussed.
Xiaozhou Liao , School of Aerospace , Mechanical and Mechatronic Engineering , The University of Sydney , Australia ; xiaozhou.liao@sydney.edu.au
Jian Wang , Mechanical and Materials Engineering , University of Nebraska–Lincoln , USA ; jianwang@unl.edu
Jianfeng Nie , Department of Materials Science and Engineering , Monash University , Australia ; jianfeng.nie@monash.edu
Yanyao Jiang , Mechanical Engineering Department , University of Nevada , Reno , USA ; yjiang@unr.edu
Peidong Wu , Department of Mechanical Engineering , McMaster University , Canada ; peidong@mcmaster.ca
DOI: 10.1557/mrs.2016.64
DEFORMATION TWINNING IN HEXAGONAL MATERIALS
315
MRS BULLETIN • VOLUME 41 • APRIL 2016 • w w w . m r s . o r g / b u l l e t i n
crystallography of hexagonal structures, twin variants on dif-
ferent twin planes nucleate and grow during deformation.
These twin variants interact and react with each other, forming
twin–twin junctions that infl uence twin propagation and thick-
ening during loading, as well as detwinning and nucleation
of secondary twins during unloading.
9 For a comprehensive
understanding of nucleation and growth of twins, and twin–twin
interactions, atomic-level characterization of the structures of
TBs and twin–twin junctions and their infl uence on mechani-
cal properties at the micro- and mesoscales are essential.
In this article, we highlight the current understanding of
the mechanisms and mechanics associated with the twin-
ning system
{}
10 12 10 1 1
, which is commonly activated in
all hexagonal materials. Discussions are concentrated on the
nucleation and growth of deformation twins, twin–twin interac-
tions, solute segregation at TBs, and the development of con-
stitutive models that account for the fundamental mechanisms
of twinning/detwinning.
Nucleation and propagation of deformation
twins
Recent studies of twin nucleation in hexagonal
metals using topological analysis, molecular
static/dynamics, and density functional theory
(DFT) show that a twin nucleus must consist
of multiple atomic layers for it to be stable.
10
Twinning dislocations can only glide on pre-
existing TB planes and are always accompa-
nied by atomic-shuffl e accommodation. Two
important conclusions from these studies can
be reached: (1) The traditional pole mecha-
nism based on the gliding of a single twinning
dislocation is not feasible for twin nucleation
in hexagonal metals, because a single twinning
dislocation does not exist alone in a perfect
hcp structure; and (2) homogeneous nucle-
ation of twins inside a grain is energetically
and kinetically diffi cult, because it involves
a zonal dislocation with multiple atomic layers.
Extensive experimental electron backscatter
diffraction data support the notion that twins
always start at GBs.
11
These results motivated the investigation of
the relationship between twin nucleation and
GBs. Molecular dynamics simulations show
that low-angle symmetrical tilt GBs favor twin
nucleation when lattice dislocations approach
the GBs.
12 , 13 The Burgers vectors of GB dislo-
cations within symmetrical tilt GBs are larger
than that of the zonal twinning dislocation, and
can potentially react with incoming lattice dis-
locations or dissociate into partials to produce
the defects needed for a stable twin nucleus
formation ( Figure 1 a ). Most importantly, twin
nucleation was characterized as a pure-shuffl e
mechanism: a 90° rotation about the zone axis by atomic shuf-
fl ing or atoms in a prismatic plane in the matrix transforming
into a basal plane in the twin ( Figure 1b ).
14 , 15 Correspondingly,
the prism plane in the parent is nearly parallel to the basal plane
in the twin (the prism-basal boundary is called PB), or the basal
plane in the parent is nearly parallel to the prism plane in the
twin, in which case the basal-prism boundary (BP) results.
15 , 16
This mechanism deviates from the classic dislocation-based
nucleation mechanisms. Thus, a twin nucleus in hexagonal
materials is surrounded by the PB and BP interfaces instead
of conventional coherent TBs (CTBs). This crystallographic
feature was confi rmed in recent high-resolution transmission
electron microscopy (TEM) observations ( Figure 1c ).
17 , 18
The fi nding of PB and BP interfaces inspired researchers
to revisit twin growth. High-resolution TEM analysis of TBs
in hexagonal materials showed that TBs are serrated and com-
posed of both CTB, PB, and BP boundaries ( Figure 1d ).
16 , 19
Atomistic simulations further demonstrated that coherent PB
and BP boundaries are energetically stable, and their forma-
tion is associated with the pileup of twinning dislocations.
It has been concluded that the propagation and thickening of
Figure 1. (a) Atomistic structure of a twin nucleus nucleated at a symmetrical tilt grain
boundary (STGB) and outlined by coherent twin boundary (CTB) and prismatic-basal
boundaries (PBs).
16
(b) Dichromatic complex of twin (red symbols) and matrix (black
symbols) in Mg showing the pure-shuf e nucleation mechanism.
18
The green square
indicates the coincidence lattices of the twin and matrix crystals. The red and black
squares outline the real crystals. The green arrows show the displacements associated
with the pure-shuf e nucleation. (c) A transmission electron microscope (TEM) image of a
small twin showing that the twin is surrounded by PBs and basal-prism boundaries (BPs),
as magni ed at the top of (c). The red solid lines indicate PBs and BPs. Reprinted with
permission from Reference 17. © 2012 Macmillan Publishers Ltd. (d) A TEM image of
twin boundaries of a large twin consisting of CTBs (yellow lines) and PBs and BPs (red
lines).
18
The green arrows in (d) indicate stacking faults of basal planes.
DEFORMATION TWINNING IN HEXAGONAL MATERIALS
316 MRS BULLETIN • VOLUME 41 • APRIL 2016 • www.mrs.org/bulletin
twins involve the motion of twinning dislocations, PB, and BP
boundaries.
16 , 19 – 21 The motion of PB and BP boundaries can
be accomplished through either collective gliding of twinning
dislocations or transformation between basal and prism planes
that dictate the overall twin mobility.
16 Under some circum-
stances, the migration of BP and PB boundaries can dominate
twin growth,
22 , 23 resulting in signifi cant deviations of the TB
away from the
{}
10 12
plane. 17 , 22 , 23
Crystal plasticity-based modeling of twinning
Crystal plasticity-based approaches for modeling the consti-
tutive behavior of textured hexagonal alloys have proliferated
over the past decade or so. Early materials models consid-
ered slip as the major plastic deformation mechanism.
24
Simulation models, including twinning for hexagonal mate-
rials, have been developed to mainly describe the reorienta-
tion and hardening evolution associated with twinning under
monotonic loading conditions.
25 – 28 The crux of the problem
has involved correctly accounting for the behavior of twin-
ning and detwinning (TDT) mechanisms: twin nucleation and
twin growth.
Twin nucleation is empirically treated in these simulation
models by introducing a small twin volume when the resolved
shear stress on the twin plane exceeds a critical level. More
importantly, these models do not account for the statistical
nature of twin nucleation. Commonly used criteria for constitu-
tive models lead to signifi cant discrepancy between modeling
results and experimental observations.
29
To improve the predictive capability of the models, a prob-
ability model
30 for twin nucleation was recently developed
with inspiration from atomistic simulations of dislocation-GB
interactions.
13 , 14 In this nucleation model,
30 twins originate
from statistical distributions of GB dislocations that may vary
in spacing, Burgers vector, and line direction. A stochastic
Poisson process describes the number of GB dislocations, and
the rate of this process increases with both local stress and GB
area. As either factor increases, the rate of nucleation increases.
Nucleation occurs when the local resolved
shear stress on a given twin variant exceeds
the statistically assigned nucleation threshold
stress. In this way, for a bulk polycrystalline
hexagonal material under a prescribed loading
condition, the nucleation model dictates when
nucleation occurs, in which grains, with which
variant, and the number of twins.
30 Unlike
nucleation, subsequent growth of the twin vari-
ants is assumed to be deterministic and is treated
by a separate model, such as the visco-plastic
self-consistent model
26 or the elastic visco-
plastic self-consistent (EVPSC) model.
31
Recently, it was shown that the EVPSC
model, with the TDT description,
32 – 34 is able to
simulate TDT in hexagonal materials and cap-
ture key macroscopic features observed experi-
mentally in rolled plates,
35 extruded cylinders,
36
and extruded plates.
37 The TDT model assumes that a grain
has four potential operations associated with TDT ( Figure 2 ) :
twin nucleation, twin growth, twin shrinkage, and retwinning.
Twin nucleation and twin growth increase the twin volume
fraction, corresponding to twinning. Twin shrinkage decreases
the twin volume fraction, corresponding to detwinning.
Retwinning splits the twin band through detwinning or sec-
ondary twinning, decreasing the volume fraction of the origi-
nal twin variant while increasing the volume fraction of the
other twin variant.
It is important to point out that the EVPSC-TDT model
considers a twin as a new grain. The orientation of the
new grain is initially related to that of the parent through the
crystallographic–twin relationship, which reorients the c -axis
by 86.3° under extension twinning. However, it is worth men-
tioning that the twin only “interacts” with its parent during
subsequent straining steps. Furthermore, there is no special
enforcement equilibrium or compatibility between the twin
and the parent. Rather, the twin and the parent are forced to
satisfy equilibrium and compatibility with the homogeneous
equivalent medium that surrounds each of them.
More specifi cally, the TDT model is designed to enforce
a sort of pseudo-TB between the twin and its parent grain.
The crystallographic lattices for the parent grain and the
twin are mirrored across the TB. If an applied stress drives
the migration of the pseudo-TB into the parent via the glid-
ing of twinning dislocations, it increases the twin volume
fraction. Conversely, if the pseudo-TB moves into the twin
by the reverse gliding of the twinning dislocations, it decreases
the twin volume fraction.
33 Very recently, a new twin nucle-
ation, propagation, and growth (TNPG) model for hexagonal
materials has been developed.
38 This TNPG model explic-
itly takes into account the stress relaxation associated with
twin initiation and propagation. It has been rationalized that
the stress relaxation drives a just-nucleated twin to propa-
gate, while work hardening makes the twin grow after its
propagation.
Figure 2. Schematic representation of twinning and detwinning in a grain. (a) The twin-
free grain (matrix). (b) Twin nucleation. Solid green lines represent twin boundaries (TBs).
Lattices in the matrix and twin are represented by dotted blue lines and dotted red lines,
respectively. (c) Twin growth through the nucleation and glide of twinning dislocations
on the TBs in the matrix. (d) Twin shrinkage through the nucleation and glide of twinning
dislocations on the TBs within the twin. (e) Retwinning. Introduction of a twin variant in a
twinned grain.
33
The symbol “⊥” represents twinning dislocation.
DEFORMATION TWINNING IN HEXAGONAL MATERIALS
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Twin–twin junctions
When twin variants interact, twin–twin boundaries (TTBs)
form that subsequently affect TDT processes.
39 – 44 Twin–twin
interactions are classifi ed as Type I for two twin variants shar-
ing the same
1120
zone axis and as Type II for two twins
with different zone axes ( Figure 3 a ). 44
Three kinds of twin–twin structures have been identifi ed
in hcp materials:
44 a quilted-looking twin structure consist-
ing of twins arrested at other TBs ( Figure 3b ), an “apparent
crossing” twin structure that links twins impinging inde-
pendently on each side of twin lamella ( Figure 3c ), and a
double twin structure that results from secondary twinning
at twin–twin interfaces, such as T
62 from “apparent crossing”
T
6 and T 2
twin junctions ( Figure 3d ). For Type I twin–twin
interactions, one twin does not transmit across the TB and
into the other twin. For Type II twin–twin interactions, one
twin can transmit into the other under some special load-
ing conditions. In most cases, twin transmission does not
occur. Instead, TTBs form that contain boundary dislocations.
For Type I twin–twin interactions, the TTB is a low-angle tilt
boundary with the habit plane being either the basal or a pris-
matic plane.
43 For Type II twin–twin interactions, the TTB is a
high-index crystallographic plane.
44 TTB dislocations can be
inferred by the interaction of twinning dislocations associated
with the two twin variants. An “apparent crossing” twin struc-
ture is thus a consequence of TTB formation.
44
Once TTBs have formed, twinning dislocations associ-
ated with the incoming twin are blocked at the TB and form
boundary dislocations. Back stresses resulting from the pileup
of these boundary dislocations hinder the motion of twinning
dislocations toward the TTB, producing a strong repulsive
force near the TTB. Further growth and propagation of twins
requires a high stress, resulting in strain hardening during
twinning. Under reversed loading, detwinning may occur as a
reversal of the forming process.
For interacting twins, TTB dislocations can dissociate
into twinning dislocations that glide on the twinning plane,
resulting in a decrease in the twin thickness. However, the dis-
sociation is an energetically unfavorable process, therefore,
detwinning becomes more diffi cult with increasing loading
cycles because more TTBs form that hinder detwinning.
44 This
is consistent with experimental measurements.
9 More interest-
ingly, secondary twins can propagate from TTBs through two
mechanisms:
44 (1) secondary twins leading to “detwinning
from inside”; and (2) secondary twins where
the secondary twin plane intersects with the
primary twin plane along the same intersection
line, as observed in Figure 3d .
Solute segregation in fully CTBs and
annealing strengthening
Over the past decade, considerable efforts
have been made to impede the growth of
deformation twins by changing the orientation
and dimensions of Mg grains or by introduc-
ing secondary phase particles. Rare-earth ele-
ments are found to be effective in weakening
the basal texture of Mg alloys after extrusion
to make deformation twinning more diffi cult
to occur upon compression loading along the
extrusion direction.
A large number of studies have been con-
ducted to understand the interaction between
solute atoms and the motion of dislocations at
the atomic level.
45 , 46 In addition, the pinning
effect of solute atoms on TBs has recently
attracted considerable attention.
5 , 8
Two types of TBs have been recently rec-
ognized for
{}
10 12
twins: CTBs, and the BP
and PB boundaries.
15 , 16 It has been suggested
that the CTBs are responsible for twin propa-
gation and growth, which involve gliding of
twinning dislocations. BP and PB boundaries,
on the other hand, are involved in twin nucle-
ation via a pure-shuffl e nucleation mechanism
and in twin growth via the migration of the BP
and PB boundaries. These TBs have distinctive
Figure 3. (a) Six
{}
1012 1011
twin variants T
i (i = 1 to 6) in a hexagonal close-packed
structure can form three crystallographically different types of twin–twin interactions: Type
I twin–twin pair T
4 ←→T
1 with the intersection line along
1210
¯
¡°
¢±
, and Type II twin–twin
interaction T
2 ←→T
1 with the intersection along
2243
¯
¡°
¢±
and twin–twin interaction T
3 ←→T
1
with the intersection line along
0221
¯
¡°
¢±
. (b) Quilted-looking twin–twin junctions, (c) “apparent
crossing” twin–twin junctions T
6 ←→T
2 , and (d) formation of secondary twins T
62 from
“apparent crossing” T
6 and T
2 twin junctions.
44
Note: TTB, twin–twin boundary.
DEFORMATION TWINNING IN HEXAGONAL MATERIALS
318 MRS BULLETIN • VOLUME 41 • APRIL 2016 • www.mrs.org/bulletin
structures that may lead to different solubility of solute atoms.
The CTB shares atoms at regular intervals wherein A and B
sites have different excess volumes (negative in A site and
positive in B site),
5 as shown in Figure 4 a . In addition, due to
their crystallography, a BP or PB boundary experiences a nor-
mal stress (compression or tension) when a CTB is subjected
to a shear stress associated with twinning.
5 This difference
in stress state may further change solubility of solute atoms
among TBs and, in turn, change the distribution of solute
atoms at TBs.
5
Nie et al. discovered periodic segregation of solute
atoms at CTBs ( Figure 4b ) using scanning TEM (STEM).
8
DFT calculations provided further insights
into understanding solubility of 24 solute atoms
along CTB ( Figure 4c ).
5 The solute atoms with
the greater radius than Mg atom are preferred
at the B site, while solute atoms with the
smaller radius than Mg atom are preferred at
the A site, corresponding to the excess vol-
ume at A and B sites.
5 The distributed solute
atoms along TBs have been demonstrated
experimentally to suppress twin growth and
strengthen the materials.
8 These phenomena
are anomalous and intriguing, because it is
commonly accepted in the fi eld of physical
metallurgy that solute atoms do not segregate
to fully CTBs, and annealing makes alloys
softer. The segregation of solute atoms in TBs
provide vital clues to the development of Mg
extrusion alloys with further increased com-
pression yield strength by suppressing/retarding
twin growth.
Future directions
Twins are sheared domains in a matrix.
Naturally, they have a three-dimensional shape.
However, twins are generally viewed as two-
dimensional (2D) domains that propagate along
the twin shear direction and grow perpendic-
ular to the twin plane. Most of the substantial
work performed in recent decades on twins
have regarded twins as 2D entities, and have
concentrated on the motion and structure of
the twin profi le along the twinning direction
as if twins were straight infi nite entities in
the third dimension. Clearly, the mobility of
the lateral twin–parent interface has to play
a role in the lateral propagation of the twin,
and has to depend strongly on the confi gura-
tion of the interface.
Understanding the crystallographic charac-
ter of the lateral twin–parent interface of defor-
mation twins will advance our understanding of
physical mechanisms of twinning and promote
further studies on twin propagation/growth.
Regarding the pinning effect of solute atoms on TBs, STEM
images show periodic segregation of solute atoms in CTBs
in Mg alloys. The pinning effect of solute atoms on TBs
was demonstrated during mechanical loading. However, it is
not clear how solute atoms affect the motion of CTBs, PBs,
and BPs. For example, because the motion of CTBs is accom-
plished through the glide of twinning dislocations, the pin-
ning effect could be ascribed to the increase in the friction
force associated with the gliding of twinning dislocations,
or to the increase in the energy barrier to the nucleation of
twinning dislocations along the CTBs. In addition, twin–twin
junctions form when multiple twins interact with each other.
Figure 4. (a) Atomic structure of a coherent twin boundary (CTB) showing two atomic
sites, A and B. (b) High-angle annular dark- eld scanning transmission electron microscope
image showing periodic segregation of Gd atoms in
{}
1012
deformation twin boundaries
in a plastically deformed and annealed Mg-Gd alloy. Reprinted with permission from
Reference 8. © 2013 AAAS. (c) Density functional theory calculations showing the solubility
energy of solute atoms along a CTB.
5
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Solute atoms can segregate to these junctions, strengthening
the pinning effect on detwinning. However, atomic structures
of twin–twin junctions have not been characterized yet, and
the pinning strength of twin–twin junctions has not been
experimentally accessed.
Finally, crystal plasticity-based approaches have been
developed and demonstrated to be capable of modeling the
constitutive behavior of textured hexagonal alloys under mono-
tonic loading, strain path changes, or repeated loading for only
a few cycles. With increasing loading cycles, twin–twin junc-
tions form, and they have been shown to play a crucial role
in increasing strain hardening and controlling microstructural
evolution. A quantitative description of twin–twin interac-
tions and twin–twin junctions is still a challenge in developing
meso-/macroscale materials modeling tools.
Acknowledgments
X.L. and J.N. thank the Australian Research Council for their
support. J.W. would like to thank the US Department of
Energy, Offi ce of Science, Basic Energy Sciences, Materials
Sciences and Engineering Division. Y.J. acknowledges sup-
port from the National Science Foundation (CMMI-1462885).
P.W. thanks the Natural Sciences and Engineering Research
Council of Canada for their support.
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ww
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mrs
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org/spring 2016 mrc lecturew
The MRS Communications Lecture
recognizes excellence in the field
of materials research through work
published in MRS Communications.
It is intended to honor the authors of
an outstanding paper published in
the journal during the award year.
Molecular Design, Synthesis, and Characterization of
Conjugated Polymers for Interfacing Electronic Biomedical
Devices with Living Tissue
Congratulations to
David C. Martin, University of Delaware,
selected to present the inaugural
MRS Communications Lecture.
g
Inaugural MRS Communications Lecture
www.mrs.org/spring-2016-mrc-lecture
re
