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RESEARCH ARTICLE
www.advtheorysimul.com
Heterophase Interface Dominated Deformation and
Mechanical Properties in Al-Cu-Li Alloys
Shuo Wang, Chi Zhang, Xin Li, and Junsheng Wang*
As a common phenomenon in multiphase systems, interfacial deformation
has a significant impact on the mechanical properties of materials. By
utilizing the brittle cleavage and plastic slip modes, the deformation
mechanism is tracked and mechanical properties of precipitate/matrix and
precipitate/precipitate heterophase interfaces are induced in third-generation
Al-Li alloys, including??????’(Al
3
Li)/??????-Al,??????’(Al
2
Cu)/??????-Al, and??????’(Al
3
Li)/??????’(Al
2
Cu)
(depending on the ultrafine??????’/??????’/??????’ composite precipitate). Based on bond
energy and ideal stress calculations under tensile and shear deformations, it
is noted that the universal interface separating the two phases is not the
weakest link in these systems. In??????’/??????’/??????’, specifically, the defined coherent
interface I closing to the??????’ may become a weak cracking point under tensile
loading. Whereas, the semi-coherent interface II on the edge of the??????’/??????’/??????’
tends to undergo interplanar slip along the [001] direction at relatively low
shear stress. By releasing a partial dislocation under shear deformation, the
local stable stacking fault can occur in this semi-coherent interface. And the
interface-mediated plasticity within the ultrafine??????’/??????’/??????’composite
precipitate could be expected to solve the origin of the strength-ductility
conflict in modern Al-Li alloys. Besides, the electronic structures and atomic
bonding are performed to reveal the mechanism behind the improved
interface strength.
1. Introduction
Third- and fourth-generation Al-Li alloys have gained increasing
attention in aircraft, aerospace, and military applications than
conventional Al alloys, due to their superior properties such as
high specific strength, modulus, and good fatigue crack growth
resistance and fracture toughness.
[ 1,2 ]
Yet, the ductility and frac-
ture toughness of the previous two generations are poor, in which
shearable??????’-Al
3Li precipitates are mainly formed with the high
S. Wang, C. Zhang, X. Li
School of Materials Science and Engineering
Beijing Institute of Technology
Beijing 100081, China
Prof. J. Wang
School of Materials Science and Engineering, and Advanced Research
Institute of Multidisciplinary Science
Beijing Institute of Technology
Beijing 100081, China
E-mail: [email protected]
The ORCID identification number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/adts.202100059
DOI: 10.1002/adts.202100059
content of Li. In this case, dislocations can
shear these??????’ precipitates under planar slip
deformation, causing local stress to concen-
trate on grain boundaries, grain boundary
(GB) triple junctions, and precipitation-free
zones, which promote the nucleation and
growth of micro-cracks. Eventually, the ma-
terial fractures prematurely. Optimizing the
alloy compositions by reducing Li and si-
multaneously adding Mg, Ag, Zr, and Cu el-
ements to create non-shearable strengthen-
ing phases, such as T
1(Al
2CuLi),??????′(Al
2Cu),
S′(Al
2CuMg),??????′(Al
3Zr), and Al
2LiMg, has
become a superior microalloying approach
to tailor precipitates and improve the frac-
ture ductility response of modern Al-Li
alloys.
[ 3–9 ]
A high density of nanoscale precipitates
as obstacles to dislocation glide, often cause
high-stress concentrations around these
particles. As a result, precipitate/matrix
or precipitate/precipitate heterophase
interfaces become vulnerable sites that
tend to suffer cleavage fracture or plastic
instability.
[ 10–16 ]
At elevated temperatures
particularly, the lattice expansion of dif-
ferent precipitates induced deformation
incompatibilities, and a progressive strain
localization at the interfaces could trigger interfacial decohesion
early. Revealed by in situ transmission electron microscopy ten-
sile tests, for example, the interfacial decohesion occurs at the
??????/??????′interface under tensile deformation. When the??????′grows to
the critical size, interfacial voids nucleate at the interface and then
propagate into cracks.
[16]
Similarly, in powder metallurgy Ti alloys
utilizing in situ scanning electron microscopy, microcracks nu-
cleate at both??????″-precipitate/matrix interfaces and grain bound-
aries, in which severe microcracks coalescence and propagation
cause the sudden brittle fracture of the samples.
[11]
On the other hand, the heterophase interface-mediated defor-
mation can also achieve a superb strength-ductility combination
in multiple-phase alloys.
[ 17–21 ]
In one respect, heterophase inter-
faces can serve as the carriers of plastic flow to super-harden
composites with supra-nanostructure, in which defects and the
relative dislocation activity are usually absent. At sufficiently high
external stress, they can serve as dislocation sources and obsta-
cles due to the lattice misfit with matrix, which facilitates nucle-
ation and propagation of dislocations near these non-shearable
precipitates. As these mobile dislocations release high-stress con-
centrations, the propagation of microcrack is mitigated, thus en-
hancing the ductility and strength of materials.
Adv. Theory Simul.2021,4, 2100059 © 2021 Wiley-VCH GmbH2100059 (1 of 11)
www.advtheorysimul.com
Heterophase Interface Dominated Deformation and
Mechanical Properties in Al-Cu-Li Alloys
Shuo Wang, Chi Zhang, Xin Li, and Junsheng Wang*
As a common phenomenon in multiphase systems, interfacial deformation
has a significant impact on the mechanical properties of materials. By
utilizing the brittle cleavage and plastic slip modes, the deformation
mechanism is tracked and mechanical properties of precipitate/matrix and
precipitate/precipitate heterophase interfaces are induced in third-generation
Al-Li alloys, including??????’(Al
3
Li)/??????-Al,??????’(Al
2
Cu)/??????-Al, and??????’(Al
3
Li)/??????’(Al
2
Cu)
(depending on the ultrafine??????’/??????’/??????’ composite precipitate). Based on bond
energy and ideal stress calculations under tensile and shear deformations, it
is noted that the universal interface separating the two phases is not the
weakest link in these systems. In??????’/??????’/??????’, specifically, the defined coherent
interface I closing to the??????’ may become a weak cracking point under tensile
loading. Whereas, the semi-coherent interface II on the edge of the??????’/??????’/??????’
tends to undergo interplanar slip along the [001] direction at relatively low
shear stress. By releasing a partial dislocation under shear deformation, the
local stable stacking fault can occur in this semi-coherent interface. And the
interface-mediated plasticity within the ultrafine??????’/??????’/??????’composite
precipitate could be expected to solve the origin of the strength-ductility
conflict in modern Al-Li alloys. Besides, the electronic structures and atomic
bonding are performed to reveal the mechanism behind the improved
interface strength.
1. Introduction
Third- and fourth-generation Al-Li alloys have gained increasing
attention in aircraft, aerospace, and military applications than
conventional Al alloys, due to their superior properties such as
high specific strength, modulus, and good fatigue crack growth
resistance and fracture toughness.
[ 1,2 ]
Yet, the ductility and frac-
ture toughness of the previous two generations are poor, in which
shearable??????’-Al
3Li precipitates are mainly formed with the high
S. Wang, C. Zhang, X. Li
School of Materials Science and Engineering
Beijing Institute of Technology
Beijing 100081, China
Prof. J. Wang
School of Materials Science and Engineering, and Advanced Research
Institute of Multidisciplinary Science
Beijing Institute of Technology
Beijing 100081, China
E-mail: [email protected]
The ORCID identification number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/adts.202100059
DOI: 10.1002/adts.202100059
content of Li. In this case, dislocations can
shear these??????’ precipitates under planar slip
deformation, causing local stress to concen-
trate on grain boundaries, grain boundary
(GB) triple junctions, and precipitation-free
zones, which promote the nucleation and
growth of micro-cracks. Eventually, the ma-
terial fractures prematurely. Optimizing the
alloy compositions by reducing Li and si-
multaneously adding Mg, Ag, Zr, and Cu el-
ements to create non-shearable strengthen-
ing phases, such as T
1(Al
2CuLi),??????′(Al
2Cu),
S′(Al
2CuMg),??????′(Al
3Zr), and Al
2LiMg, has
become a superior microalloying approach
to tailor precipitates and improve the frac-
ture ductility response of modern Al-Li
alloys.
[ 3–9 ]
A high density of nanoscale precipitates
as obstacles to dislocation glide, often cause
high-stress concentrations around these
particles. As a result, precipitate/matrix
or precipitate/precipitate heterophase
interfaces become vulnerable sites that
tend to suffer cleavage fracture or plastic
instability.
[ 10–16 ]
At elevated temperatures
particularly, the lattice expansion of dif-
ferent precipitates induced deformation
incompatibilities, and a progressive strain
localization at the interfaces could trigger interfacial decohesion
early. Revealed by in situ transmission electron microscopy ten-
sile tests, for example, the interfacial decohesion occurs at the
??????/??????′interface under tensile deformation. When the??????′grows to
the critical size, interfacial voids nucleate at the interface and then
propagate into cracks.
[16]
Similarly, in powder metallurgy Ti alloys
utilizing in situ scanning electron microscopy, microcracks nu-
cleate at both??????″-precipitate/matrix interfaces and grain bound-
aries, in which severe microcracks coalescence and propagation
cause the sudden brittle fracture of the samples.
[11]
On the other hand, the heterophase interface-mediated defor-
mation can also achieve a superb strength-ductility combination
in multiple-phase alloys.
[ 17–21 ]
In one respect, heterophase inter-
faces can serve as the carriers of plastic flow to super-harden
composites with supra-nanostructure, in which defects and the
relative dislocation activity are usually absent. At sufficiently high
external stress, they can serve as dislocation sources and obsta-
cles due to the lattice misfit with matrix, which facilitates nucle-
ation and propagation of dislocations near these non-shearable
precipitates. As these mobile dislocations release high-stress con-
centrations, the propagation of microcrack is mitigated, thus en-
hancing the ductility and strength of materials.
Adv. Theory Simul.2021,4, 2100059 © 2021 Wiley-VCH GmbH2100059 (1 of 11)
www.advancedsciencenews.com www.advtheorysimul.com
Recently, a novel??????’/??????’/??????’ composite precipitate in Al-Cu-
Li alloys with supra-nanostructure characteristics in thick-
ness has been proposed in experiments and our theoreti-
cal calculations.
[ 22–24 ]
The aging temperature-dependent sponta-
neous nucleation of the??????’ upon the pre-precipitated??????’inacoher-
ent relationship could restrict the coarsening of the??????’ in thick-
ness. Consequently, there will be a low-level elastic distortion
between the metastable??????’ and the matrix lattice, especially for
the semi-coherent interface at the??????’/matrix edge (for example,
a favored interfacial configuration 2c
??????’:3a
Alwith misfit strain is
−4.56%
[25]
). The effects of the sandwich??????’ on the formation of
??????’ particles are generally similar to that triggered by interfacial
segregation of alloying elements. Elements such as Si, Sc, and
Ag segregated to the??????’/??????-Al interfaces can reduce the interfacial
energy and thus limit the coarsening of??????’ precipitates.
[26]
These
ultrafine precipitates uniformly distributed in the matrix can mit-
igate lattice strain and local stress concentration in compari-
son to thick ones. However, the underlying deformation mech-
anisms and relative mechanical performances induced by these
heterophase interfaces in modern Al-Cu-Li alloys are still not
known.
The main objective of this study is to identify the potential
deformation behaviors and associated brittle-tough properties of
precipitate/matrix and precipitate/precipitate heterophase inter-
faces containing coherent and semi-coherent interfacial config-
urations for??????’/??????,??????’/??????,and??????’/??????’ interfacial structures in the Al-
Cu-Li alloys. A tiltΣ5 (210)[001] GB of the Al matrix is preferred
as a benchmark to compare. Based on a density functional the-
ory (DFT) approach, brittle cleavage and plastic slip deformations
at these interfaces have been performed using alias deformation
added to the rigid-grain-shift (RGS) methodology.
[27]
By extract-
ing energy-displacement data, the ideal cleavage stress in tension
and the ideal slides stress in shear are obtained. We then deter-
mine the energetically favorable deformation mode. It should be
mentioned that the weakest link determining the cohesion of the
interfacial structures is not always the usual interface but the
next closest neighbor, so the nearby interfaces are also consid-
ered. Besides, the enhanced stability and strength of the inter-
faces have been revealed based on electronic structures and the
crystal orbital Hamilton population (COHP) theory.
[28]
The cur-
rent heterophase-interface-engineering exploration can not only
provide some instructive suggestions toward high strength and
high ductility Al-Li alloys based on the multi-phase interfaces in-
duced brittle and plastic deformations but serve as a reference
for micro-alloying induced precipitation mechanism to overcome
the contradiction between strength and ductility in light alloys.
2. Experimental Section
2.1. First-Principle Calculations
In this work, the bulk and interfacial structure relative calcula-
tions, including structural relaxations, electronic self-consistent
iterations, and the related derivatives were performed using the
Vienna ab initio simulation package.
[29]
The generalized gradi-
ent approximation parametrized by Perdew–Burke–Ernzerhof
[30]
had been employed to describe the electronic exchange and cor-
relations. Using the Monkhorst–Packset scheme, the Brillouin
zone integrals
[31]
were done over ak-point grid of the density
Figure 1.The schematics of the cleavage and slide processes of the
A/B(C)‒precipitate/matrix(precipitate) heterophase interfaces in a spe-
cific crystallographic position employing alias deformation. a) Tensile de-
formation; b) shear deformation. Note that a vacuum layer of 12Ånormal
to interfaces was introduced to avoid periodic interaction.
at 0.03 and 0.04 (in the unit of 2??????Å
–1
), for bulk and interfa-
cial samples, respectively. Pseudoatomic calculations were per-
formed for Al 3s
2
3p
1
,Cu3d
10
4p
1
, and Li_sv 1s
1
2s
1
2p
1
.Anen-
ergy cutoff of 600 eV was enough for setting up the plane-wave
basis of all atoms. The self-convergence accuracy of the itera-
tive was set at less than 1×10
–5
eV atom
–1
and 0.02 eV Å
–1
for forces.
2.2. Ideal Cleavage and Slide Stresses by Alias Deformation
To clarify the most common form of deformation for these het-
erophase interfaces, the cleavage under tensile and the slip un-
der shear were employed to characterize their brittle and plas-
tic natures, respectively. The alias deformation was applied here
instead of the affine deformation since the fracture characteris-
tics of the preset object can be captured directly by the former.
[32]
As shown inFigure 1a, two neighboring crystallographic planes
were separated into two distinct parts through a gradually in-
creasing separation distancednormal to the interface. Based on
Rose’s binding-energy-distance relation,
[33]
the universal bind-
ing energyE
bfor this cleaving system can be expressed as
Equation (1),
E
b
(d)=G
c
[
1−
(
1+
d
d
ic
)
exp
(
−
d
d
ic
)]
(1)
whereG
cis defined as the cleavage energy that equals the work of
separationW
ad. At the critical spacingd
ic, the stress reached the
maximum through the??????(d)=??????Eb∕??????d, namely the ideal cleav-
age stress??????
ic.TheG
ccan be used to assess the interfacial fracture
toughness and thermodynamic stability of various interfaces, ac-
cording to Chen’s model,
[34]
because of the equal projections of
Young’s modulus along the direction perpendicular to interfaces.
In the case of plasticity, the slide can be achieved by shear defor-
mation (Figure 1b), the upper part of the interfacial structure was
rigidly sliding to the lower along a slip vectorxoryon a given
position. The ideal slide stress??????
iscan be obtained from the first
Adv. Theory Simul.2021,4, 2100059 © 2021 Wiley-VCH GmbH2100059 (2 of 11)
Recently, a novel??????’/??????’/??????’ composite precipitate in Al-Cu-
Li alloys with supra-nanostructure characteristics in thick-
ness has been proposed in experiments and our theoreti-
cal calculations.
[ 22–24 ]
The aging temperature-dependent sponta-
neous nucleation of the??????’ upon the pre-precipitated??????’inacoher-
ent relationship could restrict the coarsening of the??????’ in thick-
ness. Consequently, there will be a low-level elastic distortion
between the metastable??????’ and the matrix lattice, especially for
the semi-coherent interface at the??????’/matrix edge (for example,
a favored interfacial configuration 2c
??????’:3a
Alwith misfit strain is
−4.56%
[25]
). The effects of the sandwich??????’ on the formation of
??????’ particles are generally similar to that triggered by interfacial
segregation of alloying elements. Elements such as Si, Sc, and
Ag segregated to the??????’/??????-Al interfaces can reduce the interfacial
energy and thus limit the coarsening of??????’ precipitates.
[26]
These
ultrafine precipitates uniformly distributed in the matrix can mit-
igate lattice strain and local stress concentration in compari-
son to thick ones. However, the underlying deformation mech-
anisms and relative mechanical performances induced by these
heterophase interfaces in modern Al-Cu-Li alloys are still not
known.
The main objective of this study is to identify the potential
deformation behaviors and associated brittle-tough properties of
precipitate/matrix and precipitate/precipitate heterophase inter-
faces containing coherent and semi-coherent interfacial config-
urations for??????’/??????,??????’/??????,and??????’/??????’ interfacial structures in the Al-
Cu-Li alloys. A tiltΣ5 (210)[001] GB of the Al matrix is preferred
as a benchmark to compare. Based on a density functional the-
ory (DFT) approach, brittle cleavage and plastic slip deformations
at these interfaces have been performed using alias deformation
added to the rigid-grain-shift (RGS) methodology.
[27]
By extract-
ing energy-displacement data, the ideal cleavage stress in tension
and the ideal slides stress in shear are obtained. We then deter-
mine the energetically favorable deformation mode. It should be
mentioned that the weakest link determining the cohesion of the
interfacial structures is not always the usual interface but the
next closest neighbor, so the nearby interfaces are also consid-
ered. Besides, the enhanced stability and strength of the inter-
faces have been revealed based on electronic structures and the
crystal orbital Hamilton population (COHP) theory.
[28]
The cur-
rent heterophase-interface-engineering exploration can not only
provide some instructive suggestions toward high strength and
high ductility Al-Li alloys based on the multi-phase interfaces in-
duced brittle and plastic deformations but serve as a reference
for micro-alloying induced precipitation mechanism to overcome
the contradiction between strength and ductility in light alloys.
2. Experimental Section
2.1. First-Principle Calculations
In this work, the bulk and interfacial structure relative calcula-
tions, including structural relaxations, electronic self-consistent
iterations, and the related derivatives were performed using the
Vienna ab initio simulation package.
[29]
The generalized gradi-
ent approximation parametrized by Perdew–Burke–Ernzerhof
[30]
had been employed to describe the electronic exchange and cor-
relations. Using the Monkhorst–Packset scheme, the Brillouin
zone integrals
[31]
were done over ak-point grid of the density
Figure 1.The schematics of the cleavage and slide processes of the
A/B(C)‒precipitate/matrix(precipitate) heterophase interfaces in a spe-
cific crystallographic position employing alias deformation. a) Tensile de-
formation; b) shear deformation. Note that a vacuum layer of 12Ånormal
to interfaces was introduced to avoid periodic interaction.
at 0.03 and 0.04 (in the unit of 2??????Å
–1
), for bulk and interfa-
cial samples, respectively. Pseudoatomic calculations were per-
formed for Al 3s
2
3p
1
,Cu3d
10
4p
1
, and Li_sv 1s
1
2s
1
2p
1
.Anen-
ergy cutoff of 600 eV was enough for setting up the plane-wave
basis of all atoms. The self-convergence accuracy of the itera-
tive was set at less than 1×10
–5
eV atom
–1
and 0.02 eV Å
–1
for forces.
2.2. Ideal Cleavage and Slide Stresses by Alias Deformation
To clarify the most common form of deformation for these het-
erophase interfaces, the cleavage under tensile and the slip un-
der shear were employed to characterize their brittle and plas-
tic natures, respectively. The alias deformation was applied here
instead of the affine deformation since the fracture characteris-
tics of the preset object can be captured directly by the former.
[32]
As shown inFigure 1a, two neighboring crystallographic planes
were separated into two distinct parts through a gradually in-
creasing separation distancednormal to the interface. Based on
Rose’s binding-energy-distance relation,
[33]
the universal bind-
ing energyE
bfor this cleaving system can be expressed as
Equation (1),
E
b
(d)=G
c
[
1−
(
1+
d
d
ic
)
exp
(
−
d
d
ic
)]
(1)
whereG
cis defined as the cleavage energy that equals the work of
separationW
ad. At the critical spacingd
ic, the stress reached the
maximum through the??????(d)=??????Eb∕??????d, namely the ideal cleav-
age stress??????
ic.TheG
ccan be used to assess the interfacial fracture
toughness and thermodynamic stability of various interfaces, ac-
cording to Chen’s model,
[34]
because of the equal projections of
Young’s modulus along the direction perpendicular to interfaces.
In the case of plasticity, the slide can be achieved by shear defor-
mation (Figure 1b), the upper part of the interfacial structure was
rigidly sliding to the lower along a slip vectorxoryon a given
position. The ideal slide stress??????
iscan be obtained from the first
Adv. Theory Simul.2021,4, 2100059 © 2021 Wiley-VCH GmbH2100059 (2 of 11)
www.advancedsciencenews.com www.advtheorysimul.com
inflexion point relying on the generalized stacking fault energy
(GSFE)??????as Equations (2) and (3),
[35]
??????
is
(d)=−????????????∕??????d (2)
??????(d)=
E
SF
(d)−E
0
A
(3)
whereE
SFandE
0are the energy of slipped and perfect struc-
tures, respectively.Ais the area of the slip plane. As a measure of
the energy cost between two adjacent plane motions, the??????repre-
sents the nature of slip which was related to the stable, unstable,
and twin fault energies. In previous research, the energy-derived
properties of the??????were used to reveal and forecast the phenom-
ena related to dislocations, partial dislocations, kinetic movement
(such as climb and cross-slip), and phase transition.
[36]
The plas-
tic deformation was also closely related to the??????since it represents
lattice resistance to the emission of a dislocation near the crack
tip.
[37]
For the sake of computational efficiency, however, only a
pair of mutually perpendicular slip vectors in-plane, namelyx
andyas shown in Figure 1b, were used for the calculation of
the??????.
2.3. RGS Methodology
The cohesion and tensile strength calculations of an interfacial
structure were closely related to the deformation methodology
employed, which usually referred to the RGS and the RGS+
"atomic coordinates relaxation" (with the Poisson contraction
that was perpendicular to the interface) methodologies. In gen-
eral, the RGS always overestimated the ideal cleavage stress. In
contrast, the latter tended to yield a series of lower ideal cleavage
stresses, since the internal stress was released with the relaxation
of atomic positions. It should be noted, however, that when the
same methodology was used to assess these indicators across dif-
ferent systems, the relative values did not differ much.
[ 38,39 ]
Ac-
cordingly, the lower computational resource cost RGS methodol-
ogy was adopted for the large-scale search of possible interface
deformations in complex multiphase alloys.
3. Results and Discussion
3.1. Interface Modes
To construct the mentioned heterophase interfaces, the interfa-
cial orientation relationship (OR), termination, and interfacial
strain must all be taken into account. It is well-know that the
??????’ phase is completely coherent with the??????matrix, having the
well-recognized OR of {010}
??????’<001>
??????’//{010}
??????<001>
??????. For the
??????’ within the matrix, two different crystallographic interfacial
orientations exist between the plate-shaped??????’ and the matrix.
One is a coherent interface (001)
??????′<100>
??????′//(001)
??????<100>
??????on
the broad faces of the??????’, and the other is a semi-coherent in-
terface with (010)
??????′<100>
??????′//(010)
??????<100>
??????around the rim of
the??????’. Based on the past experimentally characterizations and
our theoretical calculations,
[ 22,24,40 ]
the??????’/??????’/??????’ composite precip-
itate adopts a coherent OR (001)
??????′<100>
??????′//(001)
??????’<100>
??????’on the
broad faces of the??????’ while retaining the semi-coherent OR (010)
??????′
<100>
??????′//(010)
??????<100>
??????at other edges.
To approximate the real deformation situations, the lattice pa-
rameters of all phases adopted their experimental values at am-
bient temperature,
[ 41,42 ]
namely, the body-centered tetragonal??????’
with lattice constants ofa=4.04 Å, andc=5.80 Å, the L1
2??????’
with lattice constants ofa=3.972 Å, and the face-centered cubic
??????with lattice constants ofa=4.01 Å. The elastic moduli of these
phases are in the order of??????’>??????’>??????based on the experimen-
tal and simulation results. Especially, the elastic modulus of the
??????’ and the??????’are≈125.7%
[43]
and 39.0%
[42]
higher than that of
the??????matrix, respectively. Therefore, the??????lattice is expanded to
match the unstrained??????’(??????’) in??????’/??????(??????’/??????) interfacial structures
due to their lower resistance to volume and shape change. The
same strain strategy is also used in the??????’/??????’ interfacial structure.
For the interface-instability-induced fracture, it is noted that
the weakest link that determines the cohesion of the interfacial
structure is not always the usual interface but maybe the neigh-
bor that possesses a wide interplanar distance and weak atomic
bonds. Indeed, in the previous case, such fracture response was
proposed in the??????’/??????’/??????’.
[22]
To avoid choosing an incorrect cleav-
age interface, we construct three kinds of interfacial candidates
in the vicinity of the normal one. Such a detailed process has been
employed in ref. [44].Figure 2. shows the crystallographic struc-
tures studied in this work, in each one except theΣ5 (210)[001]
GB, three kinds of interfacial candidates are considered.
3.2. Binding Energy and Ideal Cleavage Stress
Figure 3shows the binding energy and derived cleavage stress
of all heterophase interfaces. All binding energy-displacement
curves fit Rose’s relation well. As the vacuum displacementdin-
creases to 4Å, binding energies converge to specific values and
simultaneously their first derivatives approach zero, that is, the
cleavage stress is zero. Since the binding energy of a vacuum-
interfacial structure is equal to the energy required to separate
an interfacial structure into two free surfaces, the present binding
energy is called the cleavage energyG
c. According to the relation-
ship between theG
cand fracture toughness mentioned above,
by comparing theG
cof all considered interfaces from I to III
as listed inTable 1, we can find that in??????’ composited interfacial
structures, the closer to the??????’ phase, the worse the toughness of
the interface. Conversely, the worst toughness appears in the??????
matrix for the??????’/??????regardless of coherent or semi-coherent lat-
tice relationships. This may be due to the generation of strong
covalent bonding between Al and Cu atoms which response to
enhanced stabilities of the interfacial combination. The details
will be described below.
Derived from the bonding energy, the ideal cleavage stress can
intuitively exhibit the strength of these interfaces against cleav-
age. The results given by ideal cleavage stress??????
icare in line with
the results based on theG
cfor each specified interface posi-
tion, suggesting that theG
ccan also be a measure of interface
strength. For each specific interface within??????’/??????,bothG
cand??????
ic
are relatively lower than those in??????’/??????(both coherent and semi-
coherent configurations) and??????’/??????’. From the interface cohesion
and strength calculations, although we know that the??????’/??????is sus-
ceptible to fracture at the interface III, no evidence has been
Adv. Theory Simul.2021,4, 2100059 © 2021 Wiley-VCH GmbH2100059 (3 of 11)
inflexion point relying on the generalized stacking fault energy
(GSFE)??????as Equations (2) and (3),
[35]
??????
is
(d)=−????????????∕??????d (2)
??????(d)=
E
SF
(d)−E
0
A
(3)
whereE
SFandE
0are the energy of slipped and perfect struc-
tures, respectively.Ais the area of the slip plane. As a measure of
the energy cost between two adjacent plane motions, the??????repre-
sents the nature of slip which was related to the stable, unstable,
and twin fault energies. In previous research, the energy-derived
properties of the??????were used to reveal and forecast the phenom-
ena related to dislocations, partial dislocations, kinetic movement
(such as climb and cross-slip), and phase transition.
[36]
The plas-
tic deformation was also closely related to the??????since it represents
lattice resistance to the emission of a dislocation near the crack
tip.
[37]
For the sake of computational efficiency, however, only a
pair of mutually perpendicular slip vectors in-plane, namelyx
andyas shown in Figure 1b, were used for the calculation of
the??????.
2.3. RGS Methodology
The cohesion and tensile strength calculations of an interfacial
structure were closely related to the deformation methodology
employed, which usually referred to the RGS and the RGS+
"atomic coordinates relaxation" (with the Poisson contraction
that was perpendicular to the interface) methodologies. In gen-
eral, the RGS always overestimated the ideal cleavage stress. In
contrast, the latter tended to yield a series of lower ideal cleavage
stresses, since the internal stress was released with the relaxation
of atomic positions. It should be noted, however, that when the
same methodology was used to assess these indicators across dif-
ferent systems, the relative values did not differ much.
[ 38,39 ]
Ac-
cordingly, the lower computational resource cost RGS methodol-
ogy was adopted for the large-scale search of possible interface
deformations in complex multiphase alloys.
3. Results and Discussion
3.1. Interface Modes
To construct the mentioned heterophase interfaces, the interfa-
cial orientation relationship (OR), termination, and interfacial
strain must all be taken into account. It is well-know that the
??????’ phase is completely coherent with the??????matrix, having the
well-recognized OR of {010}
??????’<001>
??????’//{010}
??????<001>
??????. For the
??????’ within the matrix, two different crystallographic interfacial
orientations exist between the plate-shaped??????’ and the matrix.
One is a coherent interface (001)
??????′<100>
??????′//(001)
??????<100>
??????on
the broad faces of the??????’, and the other is a semi-coherent in-
terface with (010)
??????′<100>
??????′//(010)
??????<100>
??????around the rim of
the??????’. Based on the past experimentally characterizations and
our theoretical calculations,
[ 22,24,40 ]
the??????’/??????’/??????’ composite precip-
itate adopts a coherent OR (001)
??????′<100>
??????′//(001)
??????’<100>
??????’on the
broad faces of the??????’ while retaining the semi-coherent OR (010)
??????′
<100>
??????′//(010)
??????<100>
??????at other edges.
To approximate the real deformation situations, the lattice pa-
rameters of all phases adopted their experimental values at am-
bient temperature,
[ 41,42 ]
namely, the body-centered tetragonal??????’
with lattice constants ofa=4.04 Å, andc=5.80 Å, the L1
2??????’
with lattice constants ofa=3.972 Å, and the face-centered cubic
??????with lattice constants ofa=4.01 Å. The elastic moduli of these
phases are in the order of??????’>??????’>??????based on the experimen-
tal and simulation results. Especially, the elastic modulus of the
??????’ and the??????’are≈125.7%
[43]
and 39.0%
[42]
higher than that of
the??????matrix, respectively. Therefore, the??????lattice is expanded to
match the unstrained??????’(??????’) in??????’/??????(??????’/??????) interfacial structures
due to their lower resistance to volume and shape change. The
same strain strategy is also used in the??????’/??????’ interfacial structure.
For the interface-instability-induced fracture, it is noted that
the weakest link that determines the cohesion of the interfacial
structure is not always the usual interface but maybe the neigh-
bor that possesses a wide interplanar distance and weak atomic
bonds. Indeed, in the previous case, such fracture response was
proposed in the??????’/??????’/??????’.
[22]
To avoid choosing an incorrect cleav-
age interface, we construct three kinds of interfacial candidates
in the vicinity of the normal one. Such a detailed process has been
employed in ref. [44].Figure 2. shows the crystallographic struc-
tures studied in this work, in each one except theΣ5 (210)[001]
GB, three kinds of interfacial candidates are considered.
3.2. Binding Energy and Ideal Cleavage Stress
Figure 3shows the binding energy and derived cleavage stress
of all heterophase interfaces. All binding energy-displacement
curves fit Rose’s relation well. As the vacuum displacementdin-
creases to 4Å, binding energies converge to specific values and
simultaneously their first derivatives approach zero, that is, the
cleavage stress is zero. Since the binding energy of a vacuum-
interfacial structure is equal to the energy required to separate
an interfacial structure into two free surfaces, the present binding
energy is called the cleavage energyG
c. According to the relation-
ship between theG
cand fracture toughness mentioned above,
by comparing theG
cof all considered interfaces from I to III
as listed inTable 1, we can find that in??????’ composited interfacial
structures, the closer to the??????’ phase, the worse the toughness of
the interface. Conversely, the worst toughness appears in the??????
matrix for the??????’/??????regardless of coherent or semi-coherent lat-
tice relationships. This may be due to the generation of strong
covalent bonding between Al and Cu atoms which response to
enhanced stabilities of the interfacial combination. The details
will be described below.
Derived from the bonding energy, the ideal cleavage stress can
intuitively exhibit the strength of these interfaces against cleav-
age. The results given by ideal cleavage stress??????
icare in line with
the results based on theG
cfor each specified interface posi-
tion, suggesting that theG
ccan also be a measure of interface
strength. For each specific interface within??????’/??????,bothG
cand??????
ic
are relatively lower than those in??????’/??????(both coherent and semi-
coherent configurations) and??????’/??????’. From the interface cohesion
and strength calculations, although we know that the??????’/??????is sus-
ceptible to fracture at the interface III, no evidence has been
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Figure 2.Schematic illustration of crystallographic structures and deformation interfaces before relaxation for??????’/??????,??????’/??????,and??????’/??????’, as well as theΣ5
(210) GB in Al-Cu-Li alloys. The semi-coherent lattice arrangement in??????’/??????adopts 2c
??????’
:3a
Al
with a misfit of−4.56%, as shown in (d). Relative positions
of three interfaces are indicated by the red dashed lines labeled by I, II, and III. For the side view of each model, the solid balls indicate the atoms of the
upper-layer right above the interface (annotated as 1), and the open balls are the opposite (annotated as 0.5). A vacuum of 12 Å is used perpendicular
to the layer to avoid the slab’s interaction with their periodic images.
found in experiments. This may be since for these shearable par-
ticles, the critical resolved shear stress in the close-packed plane
along the close-packed direction is very low (Figures S1 and S2,
Supporting Information), thus they are more prone to shear dur-
ing plastic deformation. Conversely, the inability of dislocations
to cut through these non-shearable??????’ precipitates often leads to
significant stress concentrations around them, which causes in-
terface cleavage to become the major failure in the??????’/??????interface
structure. Comparing theG
cand??????
icof all interfaces furtherly,
it can be seen that the toughness and strength of the??????’/??????semi-
coherent interface I are lowest overall, indicating that cleavage
fracture is more likely to occur hereunder tensile. Apparently, this
result is consistent with the experimental observations of Chen
et al.,
[16]
while our results further give the location of the fracture
and its causes.
What stands out in Table 1 is that the interface I in??????’/??????’has
a very low ideal cleavage stress of 11.24 GPa, which is slightly
higher than that of a perfectΣ5 (210) GB. For these nanoscale
??????’/??????’/??????’ composite precipitates, only≈2–3 nm of??????’phasesare
coherently arranged at both ends of the??????’. These very thin
nanocrystals are generally free of defects and the misfit dislo-
cation activity is absent here.
[21]
For the??????’ embedded between
the matrix and the??????’, on the one hand, they will be subjected
to high tensile stress from the internal??????’ due to the large elas-
tic modulus of the??????’. On the other hand, there will be an ex-
panded lattice misfit between the matrix and these transitional
??????’ phases. Thus, we believe that these??????’ are also non-shearable
and can deform only elastically. When dislocations migrate along
with the close-packed directions within the close-packed planes,
large backstresses normal to the interface can be induced due
to the non-shearability of this composite precipitate. These back-
stresses will effectively resist the dislocation motion. With the
concentration of backstress near the interface, the interface I in
??????’/??????’ may turn into a vulnerable fracture site in response to back-
stress loadings, leading to premature brittle fracture of Al-Li al-
loys.
In addition, we note that the same atomic configurations exist
for interface I in??????’/??????and interface III in??????’/??????’, but the interface
toughness and ideal cleavage strength are different. This may be
due to the different phases to which they are attached, resulting
in the different atomic bonding (both Al─Al and Al─Li bonds).
The electronic origin of these differences will be elaborated on in
the following paragraphs.
3.3. GSFE and Ideal Slide Stress
The GSFE??????and interplanar slide stress??????along principal axes of
considered interfaces (displayed in Figure 2) from calculations
are shown inFigure 4. According to the relationship of the??????
Adv. Theory Simul.2021,4, 2100059 © 2021 Wiley-VCH GmbH2100059 (4 of 11)
Figure 2.Schematic illustration of crystallographic structures and deformation interfaces before relaxation for??????’/??????,??????’/??????,and??????’/??????’, as well as theΣ5
(210) GB in Al-Cu-Li alloys. The semi-coherent lattice arrangement in??????’/??????adopts 2c
??????’
:3a
Al
with a misfit of−4.56%, as shown in (d). Relative positions
of three interfaces are indicated by the red dashed lines labeled by I, II, and III. For the side view of each model, the solid balls indicate the atoms of the
upper-layer right above the interface (annotated as 1), and the open balls are the opposite (annotated as 0.5). A vacuum of 12 Å is used perpendicular
to the layer to avoid the slab’s interaction with their periodic images.
found in experiments. This may be since for these shearable par-
ticles, the critical resolved shear stress in the close-packed plane
along the close-packed direction is very low (Figures S1 and S2,
Supporting Information), thus they are more prone to shear dur-
ing plastic deformation. Conversely, the inability of dislocations
to cut through these non-shearable??????’ precipitates often leads to
significant stress concentrations around them, which causes in-
terface cleavage to become the major failure in the??????’/??????interface
structure. Comparing theG
cand??????
icof all interfaces furtherly,
it can be seen that the toughness and strength of the??????’/??????semi-
coherent interface I are lowest overall, indicating that cleavage
fracture is more likely to occur hereunder tensile. Apparently, this
result is consistent with the experimental observations of Chen
et al.,
[16]
while our results further give the location of the fracture
and its causes.
What stands out in Table 1 is that the interface I in??????’/??????’has
a very low ideal cleavage stress of 11.24 GPa, which is slightly
higher than that of a perfectΣ5 (210) GB. For these nanoscale
??????’/??????’/??????’ composite precipitates, only≈2–3 nm of??????’phasesare
coherently arranged at both ends of the??????’. These very thin
nanocrystals are generally free of defects and the misfit dislo-
cation activity is absent here.
[21]
For the??????’ embedded between
the matrix and the??????’, on the one hand, they will be subjected
to high tensile stress from the internal??????’ due to the large elas-
tic modulus of the??????’. On the other hand, there will be an ex-
panded lattice misfit between the matrix and these transitional
??????’ phases. Thus, we believe that these??????’ are also non-shearable
and can deform only elastically. When dislocations migrate along
with the close-packed directions within the close-packed planes,
large backstresses normal to the interface can be induced due
to the non-shearability of this composite precipitate. These back-
stresses will effectively resist the dislocation motion. With the
concentration of backstress near the interface, the interface I in
??????’/??????’ may turn into a vulnerable fracture site in response to back-
stress loadings, leading to premature brittle fracture of Al-Li al-
loys.
In addition, we note that the same atomic configurations exist
for interface I in??????’/??????and interface III in??????’/??????’, but the interface
toughness and ideal cleavage strength are different. This may be
due to the different phases to which they are attached, resulting
in the different atomic bonding (both Al─Al and Al─Li bonds).
The electronic origin of these differences will be elaborated on in
the following paragraphs.
3.3. GSFE and Ideal Slide Stress
The GSFE??????and interplanar slide stress??????along principal axes of
considered interfaces (displayed in Figure 2) from calculations
are shown inFigure 4. According to the relationship of the??????
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Figure 3.Binding energy and cleavage stress as a function of the separation distance for various interfaces within??????’/??????,??????’/??????,and??????’/??????’ interfacial
structures, as well as in theΣ5 (210) GB. The binding energy versus displacement curves evaluated via RGS+alias tensile deformation and fitted by
Rose’s binding-energy-distance relation.
Adv. Theory Simul.2021,4, 2100059 © 2021 Wiley-VCH GmbH2100059 (5 of 11)
Figure 3.Binding energy and cleavage stress as a function of the separation distance for various interfaces within??????’/??????,??????’/??????,and??????’/??????’ interfacial
structures, as well as in theΣ5 (210) GB. The binding energy versus displacement curves evaluated via RGS+alias tensile deformation and fitted by
Rose’s binding-energy-distance relation.
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Figure 4.The generalized stacking fault energy (GSFE)??????and slide stress as a function of the slide displacement for various interfaces. For simplicity,
the discussion of the slide stress in response to slide displacement here will be restricted to minimum sliding displacement. Namely, 3.97 Å for??????’/??????,
4.04 Å for coherent??????’/??????and??????’/??????’, and 5.8 for semi-coherent??????’/??????interfacial structures.
Adv. Theory Simul.2021,4, 2100059 © 2021 Wiley-VCH GmbH2100059 (6 of 11)
Figure 4.The generalized stacking fault energy (GSFE)??????and slide stress as a function of the slide displacement for various interfaces. For simplicity,
the discussion of the slide stress in response to slide displacement here will be restricted to minimum sliding displacement. Namely, 3.97 Å for??????’/??????,
4.04 Å for coherent??????’/??????and??????’/??????’, and 5.8 for semi-coherent??????’/??????interfacial structures.
Adv. Theory Simul.2021,4, 2100059 © 2021 Wiley-VCH GmbH2100059 (6 of 11)
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Ta b l e 1 .The cleavage energyG
c
, critical spacingd
ic
, and the ideal cleav-
age stress??????
icfor all interfaces evaluated by the RGS model under tensile
deformation.
System Interface G
c
,Jm
–2
d
ic
,Å ??????
ic
,GPa??????’/?????? I 2.048 0.558 13.483
II 1.774 0.562 11.595
III 1.735 0.576 11.066
??????’/??????(coherent) I 2.942 0.628 17.201
II 2.556 0.601 15.596
III 2.251 0.581 14.236
??????’/??????(semi-coherent) I 1.856 0.564 12.090
II 1.842 0.541 12.514
III 2.311 0.528 16.075
??????’/??????’ I 1.796 0.615 11.240
II 2.117 0.626 12.409
III 2.771 0.623 16.365
??????-Σ5 (210)[001] – 1.772 0.583 11.170
– – 0.596
a)
10.860
a)
a)
Ref. [45].
with respect to the normalized displacement, we can find that
these curves repeat themselves periodically in dimensions rela-
tive to the supercell interfacial structures, namely, the 2×1along
[010] and [100] directions of the unit cell, respectively. Among
these interfaces, from interface I to III in??????’/??????, coherent-??????’/??????,
and??????’/??????’ as well as the interface I in semi-coherent-??????’/??????, there
is only one peak which corresponds to an unstable stacking fault
energy, but no local minimum over the entire energy range. This
demonstrates that these interfaces have difficulty emitting in-
dividual partial dislocations, but only perfect dislocations along
these principal axes within sliding planes, resulting in stacking
faults.
The unstable GSFE??????
USand ideal slide stress??????
ishave been
summarized inTable 2. In the??????’/??????, for most of the interfaces
sliding along bothxandydirections, the ideal slide stress is al-
most twice the ideal cleavage stress except the interface I along
thex-direction, at which slightly lower ideal slide stress demon-
strates the possibility of this case being subjected to shear if the
dislocation is absent. While in the coherent??????’/??????interfacial struc-
ture, these ideal slide stresses are much higher than their ideal
cleavage stresses, no matter interfaces sliding alongxorydirec-
tion, showing strong resistance to shear deformation by this co-
herent atomic alignment. In the semi-coherent??????’/??????interfacial
structure, similar results can be obtained for the interface I slid-
ing along both directions and the interface III sliding along the
y-direction. However, for interfaces II and III sliding along the
[001] direction, they exhibit significant differences. As seen in
Figure 4h1,i1, apart from the maximum, the local minimal stack-
ing fault energies imply the possibility of stable stacking faults,
that is, their capabilities of emission of partial dislocations.
The details of the??????concerning the normalized displacement
at half of the sliding period are shown inFigure 5(the essential
snapshot sequence of crystal structures during sliding are dis-
played in Figures S3 and S4, Supporting Information, for inter-
face II and III, respectively). For interface II, its maximum??????
US
is 1.78 J m
–2
namely the energy barrier that this interplanar slid-
ing has to overcome to release a leading partial dislocation. In
this process, a stable stacking fault emerges at pointcwith sta-
ble stacking fault energy??????
ISof 0.34 J m
–2
. Simultaneously, the
ideal sliding stress??????
isassociated with the emission of this par-
tial dislocation is 11.56 GPa. For interface III, there are two local
minimums atcandeshowing stable stacking faults. As these
stacking faults motions overcoming the barriers of??????
a
US
(equal to
1.45 J m
–2
)and??????
b
US
(equal to 2.08 J m
–2
), the required critical??????
is
needs to reach 15.31 GPa and 17.80 GPa, respectively, to release
two different partial dislocations. Clearly, they are greater than
that of the stable stacking fault in interface II. More importantly,
the??????
isof interface II sliding alongy-direction is the lowest (ex-
cept the interface I in??????’/??????’ under tensile stress normal to the in-
terface, 11.24 GPa) among all??????’ constituted interfaces under var-
ious deformation modes. It seems to demonstrate that a stacking
fault structure is likely to create at this semi-coherent interface,
furthermore which will promote the??????’/??????’ plastically deform un-
der shear stress. Based on prior knowledge, we have known that
larger semi-coherent precipitates formed at high temperatures
are prone to introduce local stress concentrations, which in turn
promote crack initiation, like those in maraging steels.
[ 46,47 ]
Con-
trary to what presenting in maraging steels, these metastable??????’
precipitates discussed here could be restricted to several nanome-
ters in thickness, demonstrating that there will be a very low lat-
tice misfit as well as a minimized elastic strain between this semi-
coherent interface and the matrix. This fine and homogeneous
distribution state of the metastable??????’ in the matrix will continue
into the stable??????with aging, suppressing crack initiation at coarse
??????/Al-matrix interfaces. Furtherly, a direction-dependent stacking
fault can be activated with a high concentration of stresses at this
semi-coherent interface. This enhanced stacking fault migration
becomes a significant step to release local stresses. Therefore,
we can conclude that due to the heterophase nucleation of the??????’
upon on the broad faces of the pre-precipitated??????’, it not only pre-
vents the nucleation of microcracks at this semi-coherent lattice
interface but also enhances the toughness of the material through
the local plastic flow. This nanoscale??????’/??????’/??????’ composite precipi-
tate would not only increase the stiffness but also the toughness
of Al-Cu-Li alloys.
3.4. Charge Density and Bonding Analyses
DFT electronic-structure calculations provide fundamental in-
sights for the interatomic bonding mechanisms which determine
the stability of the interfacial structures. Generally, charge ac-
cumulation is associated with the strengthening of interatomic
bonds and vice versa, which ultimately lead interfacial structures
to exhibit different stability and strength. As shown inFigure 6a1,
b1, according to the valence charge density distributions in??????’/??????
and??????’/??????’ interfacial structures, strong bonds form between in-
ter atoms Al and Al as well as inter atoms Al and Li. In??????’/??????’,
one can find a more pronounced charge aggregation between Cu
and inter Al atoms, indicating strong atomic bonding between
these atoms, in comparison to inter Al─Li bonds. Is it possible
that the strong bonds between Al and Cu will make Al lean to-
ward the inner Cu and move away from the interface? To an-
swer this question, we have measured the major atomic bond
Adv. Theory Simul.2021,4, 2100059 © 2021 Wiley-VCH GmbH2100059 (7 of 11)
Ta b l e 1 .The cleavage energyG
c
, critical spacingd
ic
, and the ideal cleav-
age stress??????
icfor all interfaces evaluated by the RGS model under tensile
deformation.
System Interface G
c
,Jm
–2
d
ic
,Å ??????
ic
,GPa??????’/?????? I 2.048 0.558 13.483
II 1.774 0.562 11.595
III 1.735 0.576 11.066
??????’/??????(coherent) I 2.942 0.628 17.201
II 2.556 0.601 15.596
III 2.251 0.581 14.236
??????’/??????(semi-coherent) I 1.856 0.564 12.090
II 1.842 0.541 12.514
III 2.311 0.528 16.075
??????’/??????’ I 1.796 0.615 11.240
II 2.117 0.626 12.409
III 2.771 0.623 16.365
??????-Σ5 (210)[001] – 1.772 0.583 11.170
– – 0.596
a)
10.860
a)
a)
Ref. [45].
with respect to the normalized displacement, we can find that
these curves repeat themselves periodically in dimensions rela-
tive to the supercell interfacial structures, namely, the 2×1along
[010] and [100] directions of the unit cell, respectively. Among
these interfaces, from interface I to III in??????’/??????, coherent-??????’/??????,
and??????’/??????’ as well as the interface I in semi-coherent-??????’/??????, there
is only one peak which corresponds to an unstable stacking fault
energy, but no local minimum over the entire energy range. This
demonstrates that these interfaces have difficulty emitting in-
dividual partial dislocations, but only perfect dislocations along
these principal axes within sliding planes, resulting in stacking
faults.
The unstable GSFE??????
USand ideal slide stress??????
ishave been
summarized inTable 2. In the??????’/??????, for most of the interfaces
sliding along bothxandydirections, the ideal slide stress is al-
most twice the ideal cleavage stress except the interface I along
thex-direction, at which slightly lower ideal slide stress demon-
strates the possibility of this case being subjected to shear if the
dislocation is absent. While in the coherent??????’/??????interfacial struc-
ture, these ideal slide stresses are much higher than their ideal
cleavage stresses, no matter interfaces sliding alongxorydirec-
tion, showing strong resistance to shear deformation by this co-
herent atomic alignment. In the semi-coherent??????’/??????interfacial
structure, similar results can be obtained for the interface I slid-
ing along both directions and the interface III sliding along the
y-direction. However, for interfaces II and III sliding along the
[001] direction, they exhibit significant differences. As seen in
Figure 4h1,i1, apart from the maximum, the local minimal stack-
ing fault energies imply the possibility of stable stacking faults,
that is, their capabilities of emission of partial dislocations.
The details of the??????concerning the normalized displacement
at half of the sliding period are shown inFigure 5(the essential
snapshot sequence of crystal structures during sliding are dis-
played in Figures S3 and S4, Supporting Information, for inter-
face II and III, respectively). For interface II, its maximum??????
US
is 1.78 J m
–2
namely the energy barrier that this interplanar slid-
ing has to overcome to release a leading partial dislocation. In
this process, a stable stacking fault emerges at pointcwith sta-
ble stacking fault energy??????
ISof 0.34 J m
–2
. Simultaneously, the
ideal sliding stress??????
isassociated with the emission of this par-
tial dislocation is 11.56 GPa. For interface III, there are two local
minimums atcandeshowing stable stacking faults. As these
stacking faults motions overcoming the barriers of??????
a
US
(equal to
1.45 J m
–2
)and??????
b
US
(equal to 2.08 J m
–2
), the required critical??????
is
needs to reach 15.31 GPa and 17.80 GPa, respectively, to release
two different partial dislocations. Clearly, they are greater than
that of the stable stacking fault in interface II. More importantly,
the??????
isof interface II sliding alongy-direction is the lowest (ex-
cept the interface I in??????’/??????’ under tensile stress normal to the in-
terface, 11.24 GPa) among all??????’ constituted interfaces under var-
ious deformation modes. It seems to demonstrate that a stacking
fault structure is likely to create at this semi-coherent interface,
furthermore which will promote the??????’/??????’ plastically deform un-
der shear stress. Based on prior knowledge, we have known that
larger semi-coherent precipitates formed at high temperatures
are prone to introduce local stress concentrations, which in turn
promote crack initiation, like those in maraging steels.
[ 46,47 ]
Con-
trary to what presenting in maraging steels, these metastable??????’
precipitates discussed here could be restricted to several nanome-
ters in thickness, demonstrating that there will be a very low lat-
tice misfit as well as a minimized elastic strain between this semi-
coherent interface and the matrix. This fine and homogeneous
distribution state of the metastable??????’ in the matrix will continue
into the stable??????with aging, suppressing crack initiation at coarse
??????/Al-matrix interfaces. Furtherly, a direction-dependent stacking
fault can be activated with a high concentration of stresses at this
semi-coherent interface. This enhanced stacking fault migration
becomes a significant step to release local stresses. Therefore,
we can conclude that due to the heterophase nucleation of the??????’
upon on the broad faces of the pre-precipitated??????’, it not only pre-
vents the nucleation of microcracks at this semi-coherent lattice
interface but also enhances the toughness of the material through
the local plastic flow. This nanoscale??????’/??????’/??????’ composite precipi-
tate would not only increase the stiffness but also the toughness
of Al-Cu-Li alloys.
3.4. Charge Density and Bonding Analyses
DFT electronic-structure calculations provide fundamental in-
sights for the interatomic bonding mechanisms which determine
the stability of the interfacial structures. Generally, charge ac-
cumulation is associated with the strengthening of interatomic
bonds and vice versa, which ultimately lead interfacial structures
to exhibit different stability and strength. As shown inFigure 6a1,
b1, according to the valence charge density distributions in??????’/??????
and??????’/??????’ interfacial structures, strong bonds form between in-
ter atoms Al and Al as well as inter atoms Al and Li. In??????’/??????’,
one can find a more pronounced charge aggregation between Cu
and inter Al atoms, indicating strong atomic bonding between
these atoms, in comparison to inter Al─Li bonds. Is it possible
that the strong bonds between Al and Cu will make Al lean to-
ward the inner Cu and move away from the interface? To an-
swer this question, we have measured the major atomic bond
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Ta b l e 2 .The unstable generalized stacking fault energy??????
usand ideal slide stress??????
isof all interfacial structures, which were performed alias shear
deformation along withxandyslip directions in defined deformation interfaces. Note that the plane (210) of??????-Σ5 sliding along the [001] direction
is difficult due to large??????
is
. In contrast, the close-packed plane (111) of the??????matrix has the lowest??????
is
sliding along the close-packed direction [11
„
2],
indicating its unique advantage in plastic deformation.
System Interface ??????
us
(x), J m
–2
??????
is
(x), GPa ??????
us
(y), J m
–2
??????
is
(y), GPa??????’/?????? I 3.596 12.810 3.596 24.313
II 2.917 25.001 2.915 23.806
III 2.960 25.147 2.960 23.971
??????’/??????(coherent) I 9.388 85.088 9.388 80.570
II 8.387 76.250 8.390 72.279
III 3.768 33.902 3.768 32.164
??????’/??????(semi-coherent) I 4.503 36.580 4.169 37.268
II 1.757 12.767 – –
III 1.978 16.491 – –
??????’/??????’ I 3.128 31.412 3.141 24.895
II 4.494 44.765 4.476 36.300
III 10.826 38.273 10.725 89.799
??????-Σ5 (210)[001] – 1.467 18.034 – –
– 0.169 1.722 – –
??????(111)[11
„
2] – 0.177
a)
–––
– 0.171
b)
–––
a)
Ref. [48];
b)
Ref. [49].
Figure 5.Generalized planar fault energy (GPFE) curves and derived ideal sliding stress??????
isfor interfaces II and III sliding along [001] direction in the
semi-coherent??????’/??????.
lengthdfor connecting the interfaces. As seen in Figure 6a2,b2,
taking into account the atomic symmetry properties at inter-
faces, there are three typical Al─Al bonds, including Al
1
─Al
2
,
Al
1
─Al
3
,andAl
1
─Al
4
as well as two typical Al─Li bonds, includ-
ing Li
5
─Al
3
and Li
5
─Al
4
. All these Al─Al and Al─Li bonds have
shorter bond length values in??????’/??????’ than in??????’/??????, as summarized
in Figure 6a3,b3. It is demonstrated that despite the existence of
strong bonding between inter Al atoms and the second nearest
neighbor Cu layers, these Al atoms do not move away from the
interfacial Al and Li atoms. On the contrary, they are closer to
each other.
To get a better understanding of the electron orbital mech-
anisms, the COHP and relevant integrated values (integrating
from the lowest energy considered up to Fermi level, ICOHP)
are performed to measure the covalent bond strength of these
inter Al─Al and Al─Li bonds. For convenience, we use negative
ICOHP (-ICOHP) values to express its monotonicity with cova-
lent bond strength, that is, a bigger value of -ICOHP corresponds
to higher covalent bond strength. According to the -ICOHP val-
ues summarized in Figure 6a3,b3, the covalent bond strength of
inter Al-Al is the major contributor that is responsible for stabi-
lizing and strengthening these heterophase interfaces. However,
the contribution from inter Al─Li bonds is insignificant, more
specifically, the -ICOPH of the inter Al-Li is only 12% of the inter
Al-Al. In fact, this disparity was also confirmed in previous theo-
retical calculations.
[22]
Comparing the -ICOHP values for each of
Adv. Theory Simul.2021,4, 2100059 © 2021 Wiley-VCH GmbH2100059 (8 of 11)
Ta b l e 2 .The unstable generalized stacking fault energy??????
usand ideal slide stress??????
isof all interfacial structures, which were performed alias shear
deformation along withxandyslip directions in defined deformation interfaces. Note that the plane (210) of??????-Σ5 sliding along the [001] direction
is difficult due to large??????
is
. In contrast, the close-packed plane (111) of the??????matrix has the lowest??????
is
sliding along the close-packed direction [11
„
2],
indicating its unique advantage in plastic deformation.
System Interface ??????
us
(x), J m
–2
??????
is
(x), GPa ??????
us
(y), J m
–2
??????
is
(y), GPa??????’/?????? I 3.596 12.810 3.596 24.313
II 2.917 25.001 2.915 23.806
III 2.960 25.147 2.960 23.971
??????’/??????(coherent) I 9.388 85.088 9.388 80.570
II 8.387 76.250 8.390 72.279
III 3.768 33.902 3.768 32.164
??????’/??????(semi-coherent) I 4.503 36.580 4.169 37.268
II 1.757 12.767 – –
III 1.978 16.491 – –
??????’/??????’ I 3.128 31.412 3.141 24.895
II 4.494 44.765 4.476 36.300
III 10.826 38.273 10.725 89.799
??????-Σ5 (210)[001] – 1.467 18.034 – –
– 0.169 1.722 – –
??????(111)[11
„
2] – 0.177
a)
–––
– 0.171
b)
–––
a)
Ref. [48];
b)
Ref. [49].
Figure 5.Generalized planar fault energy (GPFE) curves and derived ideal sliding stress??????
isfor interfaces II and III sliding along [001] direction in the
semi-coherent??????’/??????.
lengthdfor connecting the interfaces. As seen in Figure 6a2,b2,
taking into account the atomic symmetry properties at inter-
faces, there are three typical Al─Al bonds, including Al
1
─Al
2
,
Al
1
─Al
3
,andAl
1
─Al
4
as well as two typical Al─Li bonds, includ-
ing Li
5
─Al
3
and Li
5
─Al
4
. All these Al─Al and Al─Li bonds have
shorter bond length values in??????’/??????’ than in??????’/??????, as summarized
in Figure 6a3,b3. It is demonstrated that despite the existence of
strong bonding between inter Al atoms and the second nearest
neighbor Cu layers, these Al atoms do not move away from the
interfacial Al and Li atoms. On the contrary, they are closer to
each other.
To get a better understanding of the electron orbital mech-
anisms, the COHP and relevant integrated values (integrating
from the lowest energy considered up to Fermi level, ICOHP)
are performed to measure the covalent bond strength of these
inter Al─Al and Al─Li bonds. For convenience, we use negative
ICOHP (-ICOHP) values to express its monotonicity with cova-
lent bond strength, that is, a bigger value of -ICOHP corresponds
to higher covalent bond strength. According to the -ICOHP val-
ues summarized in Figure 6a3,b3, the covalent bond strength of
inter Al-Al is the major contributor that is responsible for stabi-
lizing and strengthening these heterophase interfaces. However,
the contribution from inter Al─Li bonds is insignificant, more
specifically, the -ICOPH of the inter Al-Li is only 12% of the inter
Al-Al. In fact, this disparity was also confirmed in previous theo-
retical calculations.
[22]
Comparing the -ICOHP values for each of
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Figure 6.The valence charge density distribution and crystal orbital Hamilton population (COHP) analysis for inter Al─Al and inter Al─Li bonding
interactions in a) the interface I of??????’/??????and b) the interface III of??????’/??????’. a1,b1) The valence electrons density distribution with main values 0.02 and 0.03
(the unit is in e bohr
−3
) for two kinds of interfacial structures. a2,b2) Schematic illustration of inter Al-Al and Al-Li atomic interactions. Here, including
three typical Al─Al bonds, that is, Al
1
─Al
2
,Al
1
─Al
3
,andAl
1
─Al
4
.TwoAl─Li bonds, that is, Li
5
─Al
3
and Li
5
─Al
4
at interfaces. a3,b3) Summary of the
atomic bond lengthdas well as the -ICOHP. As seen, the difference of interatomic bonds, affecting the interfacial strength and stability, arises from
Al─Al bonds rather than Al─Li bonds. a4,b4) Major orbital-pair contributions to the Al
1
─Al
2
bond (colored).
Adv. Theory Simul.2021,4, 2100059 © 2021 Wiley-VCH GmbH2100059 (9 of 11)
Figure 6.The valence charge density distribution and crystal orbital Hamilton population (COHP) analysis for inter Al─Al and inter Al─Li bonding
interactions in a) the interface I of??????’/??????and b) the interface III of??????’/??????’. a1,b1) The valence electrons density distribution with main values 0.02 and 0.03
(the unit is in e bohr
−3
) for two kinds of interfacial structures. a2,b2) Schematic illustration of inter Al-Al and Al-Li atomic interactions. Here, including
three typical Al─Al bonds, that is, Al
1
─Al
2
,Al
1
─Al
3
,andAl
1
─Al
4
.TwoAl─Li bonds, that is, Li
5
─Al
3
and Li
5
─Al
4
at interfaces. a3,b3) Summary of the
atomic bond lengthdas well as the -ICOHP. As seen, the difference of interatomic bonds, affecting the interfacial strength and stability, arises from
Al─Al bonds rather than Al─Li bonds. a4,b4) Major orbital-pair contributions to the Al
1
─Al
2
bond (colored).
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these categories, remarkably, the inter Al-Al in??????’/??????’ always has
≈0.3 eV more than that in??????’/??????, which could become the main
reason for the difference in binding strength between two inter-
facial structures.
Taking Al
1
-Al
2
as an example, we further extracted the pro-
jected COHP (pCOHP) to describe this strong bond by decom-
posing the total Al
1
-Al
2
interaction into different orbital-pair
contributions, stemming from Al
1
3s-Al
2
3s, Al
1
3s-Al
2
3p, Al
1
3p-
Al
2
3s, and Al
1
3p-Al
2
3p. As shown in Figure 6a4,b4, we can find
that the difference in Al
1
─Al
2
bonding strength between these
two interfaces is primarily owing to their 3p-3p orbitals, which
account for 50% of the total difference. This is followed by the
Al
1
3p-Al
2
3s, accounting for≈30% of the difference. Further-
more, we find that the orbital-dependent contributions of two
types of Al
1
─Al
2
bonds share several similar characteristics. In
short, the Al
1
3p-Al
2
3p interaction contributes 50% to bonding
states of the whole interval of energy below the Fermi energy
level. No antibonding state near the Fermi level further confirms
the critical rule of the Al
1
3p-Al
2
3p orbital interaction on stabiliz-
ing these interface structures. Then, the sub-major bonding con-
tributions from the Al
1
3s-Al
2
3p and the Al
1
3p-Al
2
3s are close to
25% of the total, and simultaneously their bonding states are es-
sentially local in the relatively deep energy region (their binding
states are farther away from the Fermi energy level) compared to
Al
1
3p-Al
2
3p. However, the presence of a small magnitude of anti-
bonding states near the Fermi energy level indicates a weakening
influence of these orbital interactions on interface stability. In ad-
dition, we believe that the -ICOHP of Al
1
3a-Al
2
3s is too small to
affect the stability of the interface.
4. Conclusion
In summary, we have investigated the deformation modes and
relative mechanical performances introduced by various het-
erophase interfaces within??????’/??????,??????’/??????,and??????’/??????’ interfacial struc-
tures in Al-Cu-Li alloys. In the framework of density functional
theory, the brittle cleavage and plastic slip modes via alias de-
formation methodology have been performed. Then, utilizing
the tensile deformation-driven binding energy and ideal cleav-
age stress, as well as shear deformation-driven unstable GSFE
and ideal slides stress, we have obtained the location and mode
of interface deformation that is most likely to occur within in-
terfacial structures. Finally, electronic structure calculations re-
veal the mechanism behind the differences in the stability and
strength of these heterophase interfaces. The main conclusions
are summarized as follow:
1) The interface cleavage under tensile stress reveals a phase-
dependent fracture pattern. That is, in the??????’ constituted in-
terfacial structures, the failure tends to occur close to the??????’.
On the contrary, the failure tends to occur in the??????matrix
for the??????’/??????, regardless of coherent or semi-coherent inter-
facial relationships. This is due to the forming of different
atomic bonds. The valence charge density distribution indi-
cates strong Al─Al and Al─Cu bonds forming in the??????’/??????and
??????’/??????, respectively. The projective COHP calculations demon-
strate that despite similar atomic arrangements for interface
I and interface III in??????’/??????and??????’/??????’, respectively, the covalent
bonding strength of the inter Al-Al in??????’/??????’ is stronger than
that in??????’/??????, with bonding states 0.3 eV or higher. In more
details, its 3p-3p orbital interaction is the largest contributor
accounting for 50%, responsible for stabilizing and strength-
ening these heterophase interfaces.
2) According to binding energy and ideal cleavage stress results,
although the??????’/??????is most susceptible to fracture at inter-
face III, its critical resolved shear stress in the slip system
(111)[11
„
2] is very low, thus they are more prone to shear defor-
mation in plastic mode. Yet, for all that, we argue that due to
the absence of mismatch dislocations and the concentration
of back stress at these non-shearable interfaces, the interface
Iin??????’/??????’ could become a vulnerable site and hence cause an
early rupture, especially in response to tensile stress normal
to this coherent interface.
3) When the shear stress reaches a critical level in??????’/??????semi-
coherent interface, also as the semi-coherent interface of the
ultrafine??????’/??????’/??????’, a stacking fault namely the interface II slid-
ing along y-direction may be triggered by releasing a partial
dislocation, which requires a relatively lower ideal slide stress
11.56 GPa. This localized plastic slip could release concen-
trated stresses, resulting in an improved toughness of Al-Cu-
Li alloys. It should be noted that a semi-coherent??????’/??????inter-
face adopting 2c
??????’:3a
Alis used here, which will require studies
accounting for more semi-coherent interfaces in the future.
Supporting Information
Supporting Information is available from the Wiley Online Library or from
the author.
Acknowledgements
The authors would like to thank the helps from all lab mates at the Inte-
grated Computational Materials Engineering (ICME) lab, Beijing Institute
of Technology, China. The research work is supported by Supported by Na-
tional Natural Science Foundation of China (Project number: 52073030)
and the Key Laboratory Funding at Beijing Institute of Technology (Project
number: 6142902180305 and 61409220124).
Conflict of Interest
The authors declare no conflict of interest.
Data Availability Statement
Data available on request from the authors.
Keywords
Al-Li alloys, cleavage fracture, first-principle calculations, interface defor-
mation, plastic deformation, precipitate
Received: February 22, 2021
Revised: April 16, 2021
Published online: April 29, 2021
Adv. Theory Simul.2021,4, 2100059 © 2021 Wiley-VCH GmbH2100059 (10 of 11)
these categories, remarkably, the inter Al-Al in??????’/??????’ always has
≈0.3 eV more than that in??????’/??????, which could become the main
reason for the difference in binding strength between two inter-
facial structures.
Taking Al
1
-Al
2
as an example, we further extracted the pro-
jected COHP (pCOHP) to describe this strong bond by decom-
posing the total Al
1
-Al
2
interaction into different orbital-pair
contributions, stemming from Al
1
3s-Al
2
3s, Al
1
3s-Al
2
3p, Al
1
3p-
Al
2
3s, and Al
1
3p-Al
2
3p. As shown in Figure 6a4,b4, we can find
that the difference in Al
1
─Al
2
bonding strength between these
two interfaces is primarily owing to their 3p-3p orbitals, which
account for 50% of the total difference. This is followed by the
Al
1
3p-Al
2
3s, accounting for≈30% of the difference. Further-
more, we find that the orbital-dependent contributions of two
types of Al
1
─Al
2
bonds share several similar characteristics. In
short, the Al
1
3p-Al
2
3p interaction contributes 50% to bonding
states of the whole interval of energy below the Fermi energy
level. No antibonding state near the Fermi level further confirms
the critical rule of the Al
1
3p-Al
2
3p orbital interaction on stabiliz-
ing these interface structures. Then, the sub-major bonding con-
tributions from the Al
1
3s-Al
2
3p and the Al
1
3p-Al
2
3s are close to
25% of the total, and simultaneously their bonding states are es-
sentially local in the relatively deep energy region (their binding
states are farther away from the Fermi energy level) compared to
Al
1
3p-Al
2
3p. However, the presence of a small magnitude of anti-
bonding states near the Fermi energy level indicates a weakening
influence of these orbital interactions on interface stability. In ad-
dition, we believe that the -ICOHP of Al
1
3a-Al
2
3s is too small to
affect the stability of the interface.
4. Conclusion
In summary, we have investigated the deformation modes and
relative mechanical performances introduced by various het-
erophase interfaces within??????’/??????,??????’/??????,and??????’/??????’ interfacial struc-
tures in Al-Cu-Li alloys. In the framework of density functional
theory, the brittle cleavage and plastic slip modes via alias de-
formation methodology have been performed. Then, utilizing
the tensile deformation-driven binding energy and ideal cleav-
age stress, as well as shear deformation-driven unstable GSFE
and ideal slides stress, we have obtained the location and mode
of interface deformation that is most likely to occur within in-
terfacial structures. Finally, electronic structure calculations re-
veal the mechanism behind the differences in the stability and
strength of these heterophase interfaces. The main conclusions
are summarized as follow:
1) The interface cleavage under tensile stress reveals a phase-
dependent fracture pattern. That is, in the??????’ constituted in-
terfacial structures, the failure tends to occur close to the??????’.
On the contrary, the failure tends to occur in the??????matrix
for the??????’/??????, regardless of coherent or semi-coherent inter-
facial relationships. This is due to the forming of different
atomic bonds. The valence charge density distribution indi-
cates strong Al─Al and Al─Cu bonds forming in the??????’/??????and
??????’/??????, respectively. The projective COHP calculations demon-
strate that despite similar atomic arrangements for interface
I and interface III in??????’/??????and??????’/??????’, respectively, the covalent
bonding strength of the inter Al-Al in??????’/??????’ is stronger than
that in??????’/??????, with bonding states 0.3 eV or higher. In more
details, its 3p-3p orbital interaction is the largest contributor
accounting for 50%, responsible for stabilizing and strength-
ening these heterophase interfaces.
2) According to binding energy and ideal cleavage stress results,
although the??????’/??????is most susceptible to fracture at inter-
face III, its critical resolved shear stress in the slip system
(111)[11
„
2] is very low, thus they are more prone to shear defor-
mation in plastic mode. Yet, for all that, we argue that due to
the absence of mismatch dislocations and the concentration
of back stress at these non-shearable interfaces, the interface
Iin??????’/??????’ could become a vulnerable site and hence cause an
early rupture, especially in response to tensile stress normal
to this coherent interface.
3) When the shear stress reaches a critical level in??????’/??????semi-
coherent interface, also as the semi-coherent interface of the
ultrafine??????’/??????’/??????’, a stacking fault namely the interface II slid-
ing along y-direction may be triggered by releasing a partial
dislocation, which requires a relatively lower ideal slide stress
11.56 GPa. This localized plastic slip could release concen-
trated stresses, resulting in an improved toughness of Al-Cu-
Li alloys. It should be noted that a semi-coherent??????’/??????inter-
face adopting 2c
??????’:3a
Alis used here, which will require studies
accounting for more semi-coherent interfaces in the future.
Supporting Information
Supporting Information is available from the Wiley Online Library or from
the author.
Acknowledgements
The authors would like to thank the helps from all lab mates at the Inte-
grated Computational Materials Engineering (ICME) lab, Beijing Institute
of Technology, China. The research work is supported by Supported by Na-
tional Natural Science Foundation of China (Project number: 52073030)
and the Key Laboratory Funding at Beijing Institute of Technology (Project
number: 6142902180305 and 61409220124).
Conflict of Interest
The authors declare no conflict of interest.
Data Availability Statement
Data available on request from the authors.
Keywords
Al-Li alloys, cleavage fracture, first-principle calculations, interface defor-
mation, plastic deformation, precipitate
Received: February 22, 2021
Revised: April 16, 2021
Published online: April 29, 2021
Adv. Theory Simul.2021,4, 2100059 © 2021 Wiley-VCH GmbH2100059 (10 of 11)
www.advancedsciencenews.com www.advtheorysimul.com
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Adv. Theory Simul.2021,4, 2100059 © 2021 Wiley-VCH GmbH2100059 (11 of 11)
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