Thijsse_2014.

Thijsse_2014.
OPEN
SUBJECT AREAS:
COMPOSITES
STRUCTURAL PROPERTIES
SURFACES, INTERFACES AND
THIN FILMS
ATOMISTIC MODELS
Revisiting the Al/Al2O3 Interface:
Coherent Interfaces and Misfit
Accommodation
Ghanshyam Pilania1, Barend J. Thijsse2, Richard G. Hoagland1, Ivan Lazić2, Steven M. Valone1
& Xiang-Yang Liu1
1
Received
14 February 2014
Accepted
7 March 2014
Published
27 March 2014
Correspondence and
requests for materials
should be addressed to
X.-Y.L. ([email protected])
2
Materials Science and Technology Devision, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA and,
Department of Materials Science and Engineering, Delft University of Technology, Mekelweg 2, 2628 Delft, The Netherlands.
We study the coherent and semi-coherent Al/a-Al2O3 interfaces using molecular dynamics simulations with
a mixed, metallic-ionic atomistic model. For the coherent interfaces, both Al-terminated and O-terminated
nonstoichiometric interfaces have been studied and their relative stability has been established. To
understand the misfit accommodation at the semi-coherent interface, a 1-dimensional (1D) misfit
dislocation model and a 2-dimensional (2D) dislocation network model have been studied. For the latter
case, our analysis reveals an interface dislocation structure with a network of three sets of parallel
dislocations, each with pure-edge character, giving rise to a pattern of coherent and stacking-fault-like
regions at the interface. Structural relaxation at elevated temperatures leads to a further change of the
dislocation pattern, which can be understood in terms of a competition between the stacking fault energy
and the dislocation interaction energy at the interface. Our results are expected to serve as an input for the
subsequent dislocation dynamics models to understand and predict the macroscopic mechanical behavior of
Al/a-Al2O3 composite heterostructures.
A
luminum is one of the world’s most widely used metals, in large part due to its superior strength-to-weight
ratio, while alumina (Al2O3) is one of the most strongly bonded compounds in existence (with enthalpy of
formation of 1674.4 kJ/mol)1,2 and is widely used as a catalyst support, for structural ceramics, and as a
substrate for film growth3–6 Among the various polymorphs of alumina, corundum (a-Al2O3) is the most stable
phase at the ambient conditions and has been extensively studied7 The Al/a-Al2O3 interface is of enormous
scientific and technological significance due to the crucial role it plays in a range of important applications such as
metal-ceramic composites, protective coating for Al, casting and smelting processes, microelectronics, corrosion/
wear protection and catalysis8–11 As a consequence, large amount of experimental8,12–22 and theoretical23–33
research work has been devoted to this interface.
Based on high-resolution transmission electron microscopy, the primary orientational relationship at the Al/aAl2O3 interface has been observed to be one that matches the close-packed planes and directions in the two
phases17 In this orientation the Al(111) plane is parallel to the Al2O3(0001) basal plane and the following
directions are parallel to each other:
h101iAl kh0110iAl2 O3
ð1Þ
h121iAl kh2110iAl2 O3
ð2Þ
As is the case for other similar metal/Al2O3 interfaces2,34,35, the stoichiometry of clean Al/a-Al2O3 interface is a
function of the oxygen partial pressure. Previous first principles based analysis25 has suggested that the clean Al/
Al2O3 interface can be stoichiometric, oxygen terminated, or aluminum terminated, depending on the ambient
oxygen partial pressure. For the relatively low oxygen partial pressures36, usually associated with sessile drop
experiments, the interface is predicted to be stoichiometric. However, for relatively high oxygen partial pressures,
prevalent during fracture experiments, the interface has been suggested to be oxygen terminated25. Recent
experimental37 and theoretical31 studies reporting atomically abrupt Al(liquid)/a-Al2O3(solid) interface stabilized
by self-regulated interfacial Al vacancies have suggested an aluminum terminated interface.
SCIENTIFIC REPORTS | 4 : 4485 | DOI: 10.1038/srep04485
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Electronic structure and work of adhesion have been obtained
from first principles based quantum mechanical computations by
Batyrev and Kleinman26 and Siegel et al.28,29 assuming a coherent
interface. Streitz and Mintmire32,33,38 employed a force field accounting for the electrostatic interaction associated with charge transfer in
their MD simulations to study the solid Al/Al2O3 interface. However,
unlike the experimentally-observed abrupt interface17, the force field
predicted that O atoms should rapidly diffuse into the Al lattice,
resulting in a highly disordered region at the interface33. Zhang
et al.30 have studied the adhesion and nonwetting to wetting transition in the Al/a-Al2O3 interface using a reactive force field (ReaxFF)
approach39. They find that the evaporation of Al atoms and diffusion
of O atoms in a-Al2O3 primarily lead to the wetting of liquid Al on
the oxide surface.
Nanolayered laminated composites of aluminum and aluminum
oxide with interlayer spacing ranging from 50 to 500 nm have been
prepared in the past40 and found to exhibit interesting deformation
mechanism with extensive ductility. However, an atomistic understanding of the observed mechanical behavior is presently lacking.
Although available dislocation dynamics models are capable of
exploring evolution of interface dislocation networks and can predict
the microscopic properties of the nanolayered composites during
mechanical deformations at large length scales, such models depend
upon atomistic input to define interfacial properties and dislocation
reaction rules. A deeper understanding of the interface structure can
be crucial for understanding the macroscopic mechanical behavior of
the nanolayered composite heterostructures.
However, despite the significance of interfacial structure, studies
addressing them have remained quite scarce in the literature. The
reason for this scarcity is two fold. On the one hand, accurate ab initio
simulation techniques are not efficient enough to practically deal
with such large systems with several thousand systems41. On the
other hand, sophisticated atomistic potentials required for molecular
dynamics (MD) simulations, that can treat both metal and ceramic
systems on equal footing and adequately describe charge transfer
effects at the interface, were unavailable until recently. As a first step
towards this direction, the goal of the present study is to elucidate the
coherent and semi-coherent interface structures at the Al(111)/aAl2O3(0001) interface. This work is expected to provide novel
information on dislocation patterns that can form at the interface
to accommodate misfit strain as well as on the factors that govern the
formation of these patterns. The resulting knowledge from the present study is expected to serve as an input for the subsequent dislocation dynamics models42,43 to understand and predict the
macroscopic mechanical behavior of Al/a-Al2O3 composite
heterostructures.
Results
Coherent Interfaces. Employing the aforementioned experimentally
observed orientational relationship17, the Al/a-Al2O3 interface was
modeled in a slab geometry periodically repeating in the plane of
the interface. Further details of the aomistic model used and
the computational methodology employed can be found in the
Methods section presented towards the end of the manuscript. To
start with, both the O-terminated and the Al-terminated interfaces
were considered in our atomistic simulations. Since our computed
lattice constant for the fcc-Al (aAl 5 4.05 Å) and the a-alumina
0
0
(aAl2 O3 ~4:762 A and cAl2 O3 ~12:99 A) are in excellent agreement
with the corresponding experimentally measured17 values, we
recover the correct magnitude of the measured misfit strain
pffiffiffiffiffiffiffi
3=2aAl {aAl2 O3
~0:041:
ð3Þ
d~2 pffiffiffiffiffiffiffi
3=2aAl zaAl2 O3
The crystal geometry in the 2D interface is as follows. The periodic
.pffiffiffi
lengths in the parallel directions ½101Al and ½0110Al O are aAl
2
2
3
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pffiffiffi
and 2aAl2 O3 in the aluminum and alumina crystals, respectively. On
the other hand, the periodic lengths in the directions ½121Al and
rffiffiffi
3
½2110Al2 O3 are
aAl and aAl2 O3 in the aluminum and alumina
2
crystals, respectively. For a coherent interface three periods in
aluminum match one period in alumina along the direction
½101Al k½0110Al2 O3 , while one period in aluminum matches one
period in alumina along the normal direction (i.e.,
½121Al k½2110Al2 O3 ). As shown in Eq. (3), this produces a
compressive strain of 0.041 in both the directions on the aluminum.
Figure 1(a) shows our fully relaxed interfacial geometry between
the Al (111) and the O-terminated a-Al2O3 (0001) at 0 K. We find
that the computed interface geometry agrees well with the one
obtained using first principles density functional theory based calculations27 carried out using generalized gradient approximation of
Perdew et al.44 We further note that the atomic arrangement in the
vicinity of the interface plane is strongly influenced by the a-Al2O3
structure and leads to a splitting of the Al metal layer closest to the
interface into three distinct sub-layers (namely, layers A1, A2 and A3,
as marked in Fig. 1(a)) after relaxation. The Al atoms in the first two
sublayers (i.e., the layers A1 and A2) occupy the sites that are dictated
by a natural continuation of the a-Al2O3 lattice. That is, the Al metal
atoms in the first two sub-layers are pulled toward the O-terminated
alumina surface, occupying the sites that Al would occupy in
Figure 1 | Coherent interface models. Schematic of Front (left) and side
(right) views of the relaxed structure of (a) O-terminated and (b) Alterminated coherent Al/a-Al2O3 interfaces. For clarity Al atoms on the
metal side of the interface have been distinguished (colored differently)
than that of the Al2O3 side.
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bulk alumina. By relaxing in this way, all the dangling bonds on the
oxygen ions at the interface are saturated. The Al atoms in the third
sub-layer (i.e., the layer A3), are not directly bonded to the interfacial
O atoms and occupy a hollow site in a slightly distorted hexagonal
lattice formed by the first two Al metal sub-layers.
The relaxed interface geometry between the Al (111) and the Alterminated a-Al2O3 (0001) interface is presented in Fig. 1(b). In their
first principles investigation, Zhang et al.25 have found this surface
configuration as the most stable after considering a number of interface configurations of Al atoms in the metal layer adjacent to the
interface with respect to the alumina surface, reached by effectively
sliding the metal layer along the alumina surface. It is interesting to
note here that the Al-terminated interface shown in Fig. 1(b) can be
formed by removing the third sub-layer A3 (highlighted in Fig. 1(a))
of the Al metal atoms in the O-terminated interface. Therefore, the
chemical potential of the Al atoms in the layer A3 can be used to
evaluate the relative stability of the two interfaces. We find that the
transfer of the Al atoms in the the layer A3 of the O-terminated
interface to a bulk Al metal reservoir is indeed thermodynamically
favorable, resulting in the lower-energy Al-terminated interface.
This indicates the superior stability of the Al-terminated interface
in a low oxygen chemical potential regime. According to our
CTIP1RFMEAM potential calculations the Al-terminated interface
is more stable by 1.98 J/m2, while parallel DFT-PBE calculations
also show a qualitative agreement favoring the Al-termination by
0.90 J/m2 over the O-termination.
Based on interface adhesion energy analysis, previous DFT calculations have also predicted the Al-termination for the Al(111)/
a-Al2O3 solid-solid interfaces28. We also note that Al(liquid)/
a-Al2O3(solid) interface has also recently been found to be atomistically sharp with Al termination in both in situ high-resolution transmission electron microscopy experiments37 as well as through firstprinciples MD simulations31. Therefore, we chose the Al-terminated
interface to study the structure of misfit dislocations at this interface.
However, we do not expect the pattern of misfit dislocations formed
at the O-terminated interface to be drastically different than that of
the Al-terminated interface, since the two interfaces are related to
one another through addition or removal of an extra sub-layer of Al
atoms in the vicinity of the interface plane. Such mass transport
should be easily achievable by a suitable mechanism such as dislocation glide or diffusion of Al atoms on the metal side of the interface,
especially at elevated temperatures.
1D Misfit Dislocations. Since the lattice parameters in the Al and the
a-Al2O3 phases are not identical, a long range elastic stress field
accompanies a perfectly coherent interface. The coherency field
can be relieved through formation of a 2D misfit dislocation
network at the interface. However, before going to the case of a 2D
network, we first investigate the case of misfit dislocation arrays only
along the ½101Al k½0110Al2 O3 direction, while assuming a perfectly
coherent interface along the ½121Al k½2110Al2 O3 direction. For this
1D misfit model, the interface supercell dimensions along the
directions ½101Al k½0110Al2 O3 and ½121Al k½2110Al2 O3 were 65.96 Å
and 4.76 Å, respectively. In this case, to minimize overall strain in the
½101Al direction, twenty-three aluminum periods were made to
match eight alumina periods, instead of the 351 ratio that
produces a coherent interface. This reduces the overall strain in
this direction from 0.041 to 1.7831023. In the other direction the
period ratio was kept at 151, leaving the strain unaltered at 0.041, as
mentioned above for a perfectly coherent interface.
To quantify the misfit dislocation structure, we measured disregistry across the interface plane after relaxation. For the disregistry
measurement the two Al layers nearest to the relaxed interface plane
(one on Al2O3 side and one on the Al metal side) were taken into
account (c.f. Fig. 2(a)). To carryout this measurement a reference
state must be chosen, in which the two adjoining crystals are
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coherent. To construct the coherent dichromatic pattern (CDP) reference state45, we compressed and stretched the Al layers on the Almetal side and on the Al2O3 side, respectively, by equal amounts
along the direction ½101Al k½0110Al2 O3 . The top and side views of
the reference state are depicted in Fig. 2(b). After constructing the
reference state, a correspondence list between nearest neighbor Al
atoms in the metal layer and the ceramic layer is compiled in this
configuration. Disregistry vectors D~
r are finally computed as
rijR ,
D~
r~~
rijD {~
ð4Þ
where~
rijR is the relative position between the ith atom and the jth atom
that form a pair in the reference and ~
rijD is the relative position
Figure 2 | 1D misfit dislocation model. (a) Relaxed and (b) coherent
dichromatic pattern (CDP) reference structures containing two Al layers
nearest to the interface that were used for the disregistry analysis of the 1D
misfit dislocation model. Al atoms on the ceramic and metal sides of the
interface have been shown in purple and lavender colors, respectively. (c)
Disregistry vectors D~
r computed as the difference between the positions of
the selected pair of Al atoms in the relaxed and reference configurations.
(d) Screw and edge components of the disregistry vectors.
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between the same pair of atoms at the interface46,47. The disregistry
between the two Al atomic planes on either side of the interface is
thus a position dependent vector field. Furthermore, since the
Burgers vectors of the misfit dislocation arrays are expected to lie
within the interface plane, we restrict our attention to disregistry
components along the directions ½101Al and ½121Al only. We find
that the resulting disregistry pattern is mainly dominated by the
homogeneous deformation used in constructing the strained reference configuration. As a further analysis, in Fig. 2(d) we plot the
^ of the disregistry vectors along directions
components D~
r:^j and D~
r :n
^j and n
^, parallel and normal to the set of misfit dislocation lines
(laying along the direction ½121Al ), respectively. We find that the
screw component along the direction ^
j remains close to zero
throughout and exhibits some small deviations owing to a slight
buckling of the Al metal layer adjacent to the interface plane after
relaxation. On the other hand, the edge component along the dir^ simply shows a straight line with a constant slope. The shape
ection n
of this pattern is indicative of the presence of a purely Vernier-type
misfit dislocation with wide overlapping dislocation cores.
2D Misfit Dislocation Network. For the 2D misfit dislocation model,
the dimension of the supercell along the directions ½101Al k
½0110Al2 O3 and ½121Al k½2110Al2 O3 were 65.96 Å and 114.29 Å,
respectively. Here, twenty-three aluminum periods were made to
match eight alumina periods in the ½101Al direction and twentythree aluminum periods were made to match twenty-four alumina
periods in the ½121Al direction. The dimensions of the simulation cell
were chosen so as to minimize the strain required for maintaining the
periodic boundary conditions along the two orthogonal sets of
directions in the interface plane while maintaining a minimal
system size.
After relaxation, the interface structure was analyzed by measuring the disregistry across the interface plane, as described above
for the 1D misfit dislocation model. Disregistry vectors D~
r computed
as the difference between the positions of the corresponding pair of
Al atoms (in the adjacent layers above and below the interface plane)
in the relaxed and reference configurations are shown in Fig. 3(a).
^ of the disregistry vectors along the
The edge component D~
r:n
½1210Al2 O3 direction is plotted in Fig. 3(b), while the screw component remains zero throughout and is not shown in the figure. Similar
pattern for the disregistry component was also obtained for the
½2110Al2 O3 and ½1120Al2 O3 directions, indicating that there exist
three sets of edge dislocations at an angle of 120u from each other.
A closer look at the Fig. 3(b) reveals steps-like flat periodic regions
which are the result of the tendency of the interface deformation to
localize into compact coherent regions, while the steepest slope
correspond to the dislocation cores. Several parameters characterizing the dislocation network can be read from the Fig. 3(b).
Difference between successive horizontal flat regions of the disreg^ is the magnitude of the net edge component be
istry component D~
r :n
5 2.48 Å of the Burgers vectors of the dislocations. On the other
hand, the spacing s 5 57.1 Å between the parallel sets of dislocations
along the ½1210Al2 O3 direction is the distance between the successive
horizontal regions along the abscissa.
The 2D dislocation network for the relaxed Al/a-Al2O3 interface
as predicted from our disregistry analysis is presented in Fig. 3(c).
The interface structure reported is also found to be consistent with
the Frank–Bilby equation45,48–50, details of which are provided in
the Method section of the present manuscript. For clarity, only three
Al-layers (i.e., layer A, consisting both the sub-layers A1 and A2,
layer B and layer C as depicted in the inset of the Fig. 3(c)) at the
interface are included in the figure with atoms in each of the three
layers colored according to their charges. The positions and line
directions for the identified three sets of edge dislocations are presented as solid black lines and black arrows in the figure, while the
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Burgers vectors are depicted as blue arrows. The dislocation network
clearly reveals coherent (fcc-like) and stacking fault (hcp-like)
regions, separated by the dislocations lines. Some of the coherent
(hexagonal) and stacking fault (triangular) regions are highlighted
in green and blue, respectively. Here note that, unlike layers B and C,
the layer A (i.e., the first Al-layer at the interface on the ceramic side)
is not a closed pack layer of Al atoms and has a hexagonal lattice
instead. Therefore, the terms fcc-like and hcp-like are used here only
in a qualitative and local sense with their scope limited to the interface region alone.
Figure 4(a) shows the charge distribution of the Al and O atoms
across the interface along the ½111Al k½0001Al2 O3 direction. It can be
seen that after a couple of atomic layers away from the interface, on
both the metal and the ceramic sides, bulk-like behavior in the charge
distribution is recovered. On the metal side the Al atoms remain
charge neutral throughout. Surface effects at the free surface on the
Al2O3 side lead to a deviation in the charges from their respective
bulk values. The in-plane charge distribution in the first three Al
metal layers closest to the interface is presented in Figures 4b-d.
Interestingly, the charges in the first layer B show a charge distribution pattern in close correlation with the coherent regions of the
predicted interface structure. This correlation can be attributed to the
slight variations in the local coordination of Al atoms influenced by
the interface dislocation structure. As we go deeper in the metal side
away from the interface, charges quickly diminish in the magnitude
and the correlated pattern gradually fades. For instance, the layer C
shown in Fig. 4c has an average charge that is about one order of
magnitude lower than that of the layer B, nonetheless still shows a
pattern in the charge distribution. However, the third metal layer
(i.e., the layer D) further away form the interface (c.f. Fig. 4(d))
reveals charges that are already negligible as compared to the other
two layers and do not carry any correlation with the interface
structure.
We note that the interface dislocation structure presented in
Fig. 3(c) was obtained at 0 K. In the molecular dynamics run, we
started the simulation at 100 K, and systematically removed the
kinetic energy of the system in each step during the dynamics.
Convergence was reached when the temperature was dropped to
0 K and all the force components on the atoms were lower than
0.01 eV/Å. However, owing to sluggish kinetics at such low temperatures one may not have converged to the thermodynamically most
stable state of the system under investigation. To further confirm the
anticipated structural change in the interface structure at elevated
temperatures, we carried out annealing of the 0 K relaxed structure at
500 K for 200 ps, followed by a ramping down to 0 K over a 100-ps
interval and finally relaxation at 0 K for another 200 ps.
The final interface structure is presented in Fig. 5(a) with the three
sets of dislocation lines and their Burgers vectors depicted in the
figure and is found to be 0.18 J/m2 lower in energy than the one
obtained at 0 K. The structure reveals that the annealing treatment
only has an effect of rigidly shifting the relative positions of any
of the two parallel sets of dislocations with respect to the third
set without changing the relative distance within a given set of
dislocations. This leads to an expansion of the alternate triangular
hcp-like regions (highlighted in blue) around a coherent hexagonal
region shown in Fig. 3(c), while the other three regions shrink to
form nodes as can be seen highlighted in green in Fig. 5(a). In other
words, the hcp-like regions transform from equal-area pairs into
pairs consisting of a large area triangle and a small area triangular
node. Furthermore, the coherent fcc-like regions transform into
almost triangular shape regions after the annealing treatment. It
can also be easily seen that in this interface structure each node is
surrounded by alternating fcc-like and hcp-like regions and has a
three-fold symmetry in the interface plane. We note that such interface structures have recently been predicted for interfaces formed
between various fcc metals51.
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Figure 3 | 2D misfit dislocation network. (a) Disregistry vectors in the interface plane computed with respected to a CDP reference structure. (b) Net
edge component of the disregistry vectors along the ½2110Al2 O3 direction. (c) The 2D misfit dislocation network for the relaxed Al/a-Al2O3 interface
predicted at 0K. Only three Al-layers (namely layers A, B and C as shown in the inset) are included in the figure with atoms in each of the three layers
colored according to their charges.
Discussion
To gain a deeper insight into the computed dislocation patterns, next
we investigate various factors that might play a role in controlling the
predicted interface structure. The energy difference per unit area
between the fcc-like coherent regions and the hcp-like stacking fault
regions is one of the crucial factors that has a strong influence on the
observed dislocation pattern. In one extreme limit, when the relative
energy of the stacking fault regions is much higher than that of the
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coherent regions, a hexagonal Wigner-Seitz mesh-like network of
misfit dislocations around the points of the best matching (indicated
as .) in the coherent region is expected52, as depicted in the top panel
of Fig. 6(a).
The other extreme situation arises when the energy difference
between the two regions is relatively small, as is the case in the present
study. We calculate the difference per unit area between the hcp-like
stacking fault regions and the fcc-like coherent regions to be
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Figure 4 | Charge distributions. (a) The charge distribution profile of the Al and O atoms normal to the interface plane along the ½111Al jj½0001Al2 O3
direction for the 2D misfit dislocation network relaxed at 0K. The in-plane charge distribution in the (b) first, (c) second and (d) third Al layers closest to
the interface on the metal side.
0.03 J/m2 (compared to our DFT computed value of 0.08 J/m2). In
this case, the alternate nodes in the hexagonal Wigner-Seitz meshlike network of misfit dislocations (shown as › in the top panel of
Fig. 6(a)) grow at the expense of the coherent regions until the ratio of
their interfacial areas approaches unity. As a result, a triangular mesh
of Shockley partial dislocations, as shown in the bottom panel of
Fig. 6(a), is observed. Note that going from one extreme case of the
hexagonal mesh to the other extreme case of the triangular mesh, the
Figure 5 | 2D misfit dislocation network after annealing. The 2D misfit dislocation network for the relaxed Al/a-Al2O3 interface after annealing at 500 K.
For clarity, only three Al-layers depicted in Fig. 3(c) are shown with atoms in each of the three layers colored according to their charges.
SCIENTIFIC REPORTS | 4 : 4485 | DOI: 10.1038/srep04485
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the charge transfer effects at the interface. The simulation results
predict an interface dislocation structure with a network consisting
of three sets of parallel dislocations, each with a pure edge character,
surrounding hexagonal coherent regions and triangular stacking
fault regions at the interface. The pattern formation can be rationalized in terms of a competition between the stacking fault energy and
the dislocation interaction energy and has implications for dislocation dynamics models aimed at understanding the macroscopic
mechanical behavior of the Al/a-Al2O3 composite heterostructures.
Methods
Figure 6 | Dislocation network patterns at the Al-Al2O3 interface. (a)
Schematic illustration depicting the effect of the relative energy difference
per unit area between the fcc-like coherent regions and the hcp-like stacking
fault regions at the interface. A high stacking fault energy favors a
hexagonal network of dislocations, while a low stacking fault energy leads
to a triangular dislocation mesh. (b) and (c) represent the schematics of the
dislocation patterns obtained in the present study at 0 K and after
annealing at 500 K, respectively. The dislocation line directions and
Burgers vectors are shown by black and blue arrows, respectively. See text
for further details.
area ratio of the stacking fault regions to the coherent regions varies
from zero to one. The two interface dislocation patterns, reported in
Fig. 3(c) and Fig. 5, that we have predicted here represent two intermediate situations between the two possible extreme cases with the
1
ratio of the two regions being and slightly lower than 1 and are
3
depicted schematically in Fig. 6(b) and Fig. 6(c), respectively.
Dislocation interaction is the second important factor that controls the observed dislocation pattern at the interface. To further
elucidate this factor, in Fig. 6(b) we have schematically captured
the dislocation pattern obtained through structural relaxation near
the absolute temperature. The dislocation lines and Burgers vector
directions are shown by black and blue arrows, respectively. The
center of the coherent region is marked by symbol . , while the symbols # and › mark the centers of the alternate triangular stacking
fault regions. It is interesting to note that the dislocation interactions
are attractive and repulsive in the alternate triangular regions colored
in green and yellow, respectively, in Fig. 6(b). Therefore, owing to the
attractive interactions, a high temperature relaxation leads the green
triangular regions to shrink and collapse in a node. On the other
hand, the yellow triangles belonging to the second set of the stacking
fault regions, shown in Fig 6(b), grow larger upon relaxation to push
the dislocations further apart in order to minimize their repulsive
interactions. This leads to the dislocation pattern shown in Fig. 6(c)
(obtained after annealing of the 0 K relaxed structure at 500 K for
200 ps), while the total dislocation length per unit interfacial area
does not change.
In summary, we have studied the coherent and semi-coherent Al/
a-Al2O3 interfaces with experimentally known orientation relationship ½110ð111ÞA1 k½1010ð0001ÞAl2 O3 . Our atomistic simulations
employed a ‘‘reference free’’ version of the modified embedded atom
method (RF-MEAM) potential that is capable of adequately describe
SCIENTIFIC REPORTS | 4 : 4485 | DOI: 10.1038/srep04485
For our atomistic simulations, we employed a recently developed potential for the Al–
O system53, generated following a two-step construction method that is generally
applicable to ionic systems. As non-electrostatic part of the potential we use a reference free version of the modified embedded atom method (RF-MEAM) potential
that includes angular forces. For the electrostatic part we use the charge transfer ionic
potential (CTIP) model proposed by Zhou et al. (here after referred to as ZWFN)54.
The modified potential has been shown to achieve essential improvements over the
ZWFN potential, derived by the incorporation of angular dependent forces and
angular screening, as well as by the systematic fitting of the potential to a large energy
database of different AlxOy crystals, over a range of lattice constants and elastic
deformations. The current potential yields more realistic atomic charges, crystal
energies, lattice constants and correct ordering of phase stabilities for a range of Al–O
systems. Moreover, O–O interactions as well as O interactions with a pure Al (111)
and Al-terminated a-Al2O3 surfaces are realistically captured within this formulation.
For the coherent interfaces, aforementioned experimentally observed orientational
relationship17 with the Al-terminated interface was employed. The Al/a-Al2O3
interface was modeled in a slab geometry periodically repeating in the plane of the
interface. The Al2O3 part of the interface contained six oxygen atomic layers and
fourteen Al layers, and the metal part contains seven layers. A vacuum region of more
than 35 Å was used between the periodically repeating slabs in the direction normal to
the interface plane. The final interface structures are determined by relaxing all the
internal coordinates until all the force components on the atoms were lower than
0.01 eV/Å. For the relaxation of the interface structures we have used an anneal-andquench molecular dynamics (MD) formalism as described in the text, as opposed to
the molecular statics.
To compare with the results of atomistic simulations obtained using our
CTIP1RF–MEAM potential, the density functional theory (DFT)55,56 computations
for the coherent interface structures were performed using the Vienna ab initio
simulation package (VASP)57. VASP uses a plane-wave basis set for the expansion of
the single-particle Kohn-Sham wave functions. The projector-augmented wave
(PAW) frozen-core potentials58,59 were used to describe the electron-ion core interaction, and the quantum mechanical part of the electron-electron interactions was
approximated using the Perdew-Burke-Ernzerhof (PBE) exchange-correlation
functional44. Sampling of the irreducible wedge of the Brillouin zone is performed
with a regular Monkhorst-Pack grid of special k-points60. To facilitate the numerical
convergence associated with integrating the 0-K Fermi-Dirac distribution stepfunction, partial occupancies of the single-particle wave functions are introduced61,62.
The electronic wave functions are expanded in plane waves up to a cut-off energy of
500 eV. A vacuum region of 15 Å was used to prevent any spurious unphysical
interactions between the periodically repeating slabs in the direction normal to the
interface plane. The final interface structures are determined by relaxing all the
internal coordinates using the conjugate gradient method63 until all the HellmannFeynman forces64,65 were less than 0.01 V/Å.
The Frank-Bilby equation45,48–50 used in our analysis is given as follows:
X~
bl sincl
l
Ll
~Drc ^p:
ð5Þ
Here, index l runs over all the unique sets of dislocation lines present at the interface,
each with Burgers vector ~
bl and separation length Ll between the parallel lines within a
given set. cl denotes the angle between a dislocation line direction jl and the probe unit
vector ^p, measured in the anti-clockwise direction. Drc represents a deformation
matrix that maps a unit vector in the coherent reference configuration onto the
interface structure containing dislocations.
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Acknowledgments
This work was supported by the Los Alamos National Laboratory (LANL) Directed
Research and Development Program (20120053ER) and the US Department of Energy,
Office of Science, Office of Basic Energy Sciences. LANL is operated by Los Alamos
National Security, LLC, for the National Nuclear Security Administration of the U.S.
Department of Energy under Contract No. DE-AC52-06NA25396. Helpful discussions
with Terry Mitchell and Shuai Shao are gratefully acknowledged.
Author contributions
The project was conceived by X.Y.L. and R.G.H. The theoretical computations were
performed by G.P.; B.J.T. and I.L. provided the CTIP-RMEAM potential used to carryout
the simulations. All the authors participated in writing the manuscript and S.M.V. reviewed
the manuscript.
Additional information
Competing financial interests: The authors declare no competing financial interests.
8
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How to cite this article: Pilania, G. et al. Revisiting the Al/Al2O3 Interface: Coherent
Interfaces and Misfit Accommodation. Sci. Rep. 4, 4485; DOI:10.1038/srep04485 (2014).
SCIENTIFIC REPORTS | 4 : 4485 | DOI: 10.1038/srep04485
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