Defect Engineering: A Path toward Exceeding Perfection

Abstract

Moving to nanoscale is a path to get perfect materials with superior properties. Yet defects, such as stacking faults (SFs), are still forming during the synthesis of nanomaterials and, according to common notion, degrade the properties. Here, we demonstrate the possibility of engineering defects to, surprisingly, achieve mechanical properties beyond those of the corresponding perfect structures. We show that introducing SFs with high density increases the Young’s Modulus and the critical stress under compressive loading of the nanowires above those of a perfect structure. The physics can be explained by the increase in intrinsic strain due to the presence of SFs and overlapping of the corresponding strain fields. We have used the molecular dynamics technique and considered ZnO as our model material due to its technological importance for a wide range of electromechanical applications. The results are consistent with recent experiments and propose a novel approach for the fabrication of stronger materials.

Full text

Defect Engineering: A Path toward Exceeding Perfection
Hamed Attariani,*
,†,‡
Kasra Momeni,
§
and Kyle Adkins
†
†
Department of Mechanical and Materials Engineering, Wright State University, Dayton, Ohio 45435, United States
‡
Engineering Program, Wright State University - Lake Campus, Celina, Ohio 45822, United States
§
Department of Mechanical Engineering, Louisiana Tech University, Ruston, Louisiana 71272, United States
*
SSupporting Information
ABSTRACT: Moving to nanoscale is a path to get perfect
materials with superior properties. Yet defects, such as stacking
faults (SFs), are still forming during the synthesis of
nanomaterials and, according to common notion, degrade
the properties. Here, we demonstrate the possibility of
engineering defects to, surprisingly, achieve mechanical
properties beyond those of the corresponding perfect
structures. We show that introducing SFs with high density
increases the Young’s Modulus and the critical stress under
compressive loading of the nanowires above those of a perfect
structure. The physics can be explained by the increase in
intrinsic strain due to the presence of SFs and overlapping of
the corresponding strain fields. We have used the molecular
dynamics technique and considered ZnO as our model material due to its technological importance for a wide range of
electromechanical applications. The results are consistent with recent experiments and propose a novel approach for the
fabrication of stronger materials.
1. INTRODUCTION
Nanomaterials have a number of high-energy partially
coordinated surface atoms that are comparable to the volume
of their low-energy fully coordinated atoms. This forms the
root of their size-dependent properties, such as enhancement of
mechanical and piezoelectric properties by reducing the size.
1−4
This size dependence provides an additional controlling
parameter for tailoring the characteristics of nanostructures.
Defect engineering on the nanoscale is another fascinating
possibility for building materials with various properties.
Defects such as stacking fault (SF), twinning, vacancies, and
interstitials are generally formed during the nanostructure
fabrication process, which can modify the mechanical,
5−7
electrical,
8
and optical properties.
9,10
Among different types of
nanostructures, one-dimensional nanostructures, for example,
nanowires (NWs), nanotubes (NTs), and nanobelts (NBs),
have been attracting significant attention from the research
community due to their wide range of applications, such as
composite reinforcement,
11,12
energy harvesting,
13,14
sen-
sors,
15,16
light-emitting diodes,
17,18
and hybrid energy storage
systems.
19,20
Therefore, tailoring and improving their proper-
ties, specifically, the mechanical properties, is key for their
effective utilization.
The common understanding is that (points and planar)
defects weaken the mechanical properties of nanostruc-
tures.
7,21−26
However, recent experiments on GaAs NWs
depicted that introducing a high density of SFs increases the
compressive critical stress and Young’s Modulus.
5,6
In this case,
interestingly, the Young’s Modulus of defected NWs is even
greater than that of the perfect wurtzite (WZ) structure. It is
worth mentioning that despite the experimental evidence
previous molecular dynamics simulations could not capture this
phenomenon.
5
Here, we explore the material design space using the two
aforementioned additional design parameters, that is, defect
concentration and size, and demonstrate tailoring the material
properties by engineering their coupled effect. We have
considered the ZnO NWs as the model material and have
shown that planar defects can strengthen NWs beyond that of
the ones with perfect structure. Our results indicate that the
Young’s Modulus of NWs, surprisingly, increases as the density
of the SFs increases in the NWs. Also, although the critical
stress increases by introducing more SFs for the compressive
loading, it has an inverse effect on the critical stress for tensile
loading. This unique behavior is explained by the localized
longitudinal (caxis) stress and strain at defect sites. The
interplay between SFs and free surfaces is the other cause of
this effect. At the bulk, SFs are typically embedded between
partial dislocations,
27
whereas at the nanoscale, they are
confined between free surfaces. In the latter case, the SF
creates a step at the surface, changing the local crystal structure,
Received: December 13, 2016
Accepted: February 10, 2017
Published: February 23, 2017
Article
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© 2017 American Chemical Society 663 DOI: 10.1021/acsomega.6b00500
ACS Omega 2017, 2, 663−669
This is an open access article published under an ACS AuthorChoice License, which permits
copying and redistribution of the article or any adaptations for non-commercial purposes.

which may alter the overall electromechanical properties of the
NWs.
2. NUMERICAL MODEL: DEVELOPMENT AND
VALIDATION
SFs, one of the most common types of planar defects in II−VI
and III−VI semiconductor nanostructures,
28−30
are categorized
into two types: (i) basal-plane and (ii) prismatic-plane SFs.
Here, we have developed a numerical model for the mechanics
of I1-SF in WZ ZnO, which has the lowest formation energy, 15
meV/unit-cell area,
31
among the different basal-plane SFs (I1,
I2, E) of WZ. The I1-SF Burger vector (
⎯→⎯⎯⎯
b
I1
) in ZnO is (1/3)
[011̅0] + (1/2) [0001],
28
which is generated by removing a
layer of c-plane atoms and moving the rest by
⎯→⎯⎯⎯
b
I1
. The perfect
WZ structure has a stacking sequence of ...AaBbAaBbAaB-
bAaBbAa..., where the uppercase and lowercase letters refer to
Zn and O atoms in two consecutive layers, respectively,
whereas I1-SF changes the stacking sequence to ...AaB-
bAaBbCcBbCcBbCc... (Figure 1a,b). Periodic boundary con-
ditions are applied along the caxis, to mimic a long NW, and
lateral directions are considered to be free. A Buckingham-type
interatomic potential is utilized with Binks’fitted parameters for
ZnO
32
(Table S1 in Supporting Information), which correctly
captures its mechanical and surface properties and has been
successfully used to study ZnO nanostructures. Also, the
developed atomistic model is verified as it reproduces the
reported experimental and numerical electromechanical proper-
ties of perfect ZnO NWs.
3,4,33−37
Numerical simulations of the defected structure are
performed by initially relaxing the NW for 100 ps at the
simulation temperature, T= 0.01 K, under microcanonical
ensemble (NVE). Then, the isothermal−isobaric ensemble
(NPT) with a Nosé
−Hoover thermostat is applied for another
100 ps to find the final relaxed configuration. In the last stage, a
constant strain rate of ±0.001 fs−1is applied along the caxis to
model the mechanical response of the NW under tension/
compression. Similar simulations are performed for a strain rate
of ±0.0001 fs−1to ensure that the results are independent of
strain rate. The Young’s Modulus is estimated by fitting a linear
expression on the early section of the stress−strain curve, ϵ<
0.01; this stands for the initial stage of loading. The numerical
model is implemented in the large-scale atomic/molecular
massively parallel simulator (LAMMPS) code,
38
and a time
step of 1 fs is chosen for all simulation steps.
One of the classical problems in atomistic simulations of
defects is the long-range interaction between the defects in a
simulation cell and their corresponding periodic images. To
overcome this issue and model a single SF, NWs of different
Figure 1. (a) Perfect WZ stacking sequence along the [0001] direction, where the uppercase and lowercase letters refer to O and Zn atoms in the
same layer, respectively. (b) The stacking sequence for I1-SF, where the arrows show the SF locations. (c) Longitudinal stress distribution along the c
axis for a perfect NW (dotted line) and a NW with a single defect (solid line). (d) Structure of a WZ NW with 13 SFs within 40 nm length.
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lengths are modeled and each relaxed longitudinal stress field
was compared to that of the similar perfect NW. Our
simulations indicate that the long-range interactions between
a SF and its image in a periodic cell are negligible for NWs of
length 40 nm and longer (Figure 1c). Here, to avoid
ambiguities in calculating the stress using atomistic simulations
due to unclear definition of the structure volume at such scales,
we have used a representative stress, σ*(= σzV/atom), to
illustrate the effect of SF on stress distribution within the
structure. High peaks appear at the defect, which rapidly decay
toward the periodic boundaries (Figure 1c); that is, at the
periodic boundaries, the stresses of the perfect and defective
NWs is almost the same. Thus, a length of 40 nm is chosen for
all simulated NWs here, whereas their diameters vary from 3 to
10 nm to study the effect of size. Furthermore, the effect of
defect density on mechanical behavior is investigated by
introducing numerous SFs, up to 13, in 40 nm length of a
perfect NW. Therefore, the distance between two adjacent SFs
varies from 20 to 3 nm for different defect densities. Figure 1d
shows the schematic of a defected NW with 13 SFs in 40 nm
length of the NW, which results in a distance of 3 nm between
two adjacent SFs.
3. RESULTS AND DISCUSSION
By applying periodic boundary conditions in all directions, we
have calculated the Young’s Modulus of bulk ZnO to be 146
GPa, which is in close agreement with the reported
experimental value, ≈140 GPa,
39−41
and verifies the developed
model. Also, the formation energy of I1-SF is calculated using
the Binks potential to ensure its capability for predicting the
properties of the faulted structure. The calculated I1-SF energy
is 14.1 meV/unit-cell area, which is in good agreement with
density functional theory calculations, 15 meV/unit-cell area
31
(see Supporting Information for detailed calculations). The
interaction between the defects and size scale on the structural
properties of NWs is studied by introducing a single I1-SF in
the middle of 40 nm long ZnO NWs of various diameters and
measuring their tension/compression response.
3.1. Mechanical Response and Size Dependence. The
stress gradually increases to reach a maximum, called critical
stress, where phase transformation occurs to release the
accumulated elastic energy that results in the stress drop (see
Figure S2). At the critical stress, the original WZ structure
transforms into a graphite-like (HX) phase under compression
and a body-centered tetragonal phase under tension.
4,34,36
However, in the presence of a SF, the NW breaks at the SF
under tensile loading without any phase transition because the
defect acts as an active site for crack initiation and the NW
cannot store enough elastic energy to initiate the phase
transition (Figure S2). In contrast, under compression, we still
observed the WZ →HX phase transition.
Variations of the Young’s Modulus and critical stress versus
diameter for perfect and defective (with a single I1-SF) NWs
are plotted in Figure 2a. Although the variation of Young’s
Modulus in the presence of a single SF is negligible (Figure 2a),
the critical stress generally reduces by introducing a SF (Figure
2b), and this effect is more pronounced for NWs with a
diameter smaller than 4 nm. The difference in the strength
(critical stresses) of defective and perfect NWs decreases by
increasing their diameters.
The overall size dependence of Young’s Modulus at a
nanoscale was frequently reported, using both experimental
2,35
and theoretical approaches,
4,33,42,43
and was associated with the
surface stress contribution. One well-known explanation is
based on the core−shell model,
44
where a shell (outer layers) is
under compressive stress due to surface stresses and the core
(inner layers) is under tension. The compressive stress at the
shell causes surface stiffening and increases the overall Young’s
Modulus of the NWs with smaller diameters. The gap between
critical stresses of defective and perfect NWs can be explained
by the intrinsic strain distribution along the longitudinal
direction, [0001], of the relaxed structure. The longitudinal
strain, ϵz, is calculated using OVITO
45−47
and is shown in
Figure 3. The SF induces intrinsic tensile strain at defect sites
and compressive strain at the defect surrounding, which causes
reduction in the critical stress. The size dependence of the
difference between the critical stresses of defective and perfect
NWs can be justified by the interplay between the surface and
SF energies. Generally, reducing the system size leads to an
increase in the total energy density because of the increase in
the surface energy. Therefore, introducing SFs into a NW of
smaller diameter requires more energy per atom in comparison
to that for a larger-diameter NW, which is the source for the
size dependence of the critical stress difference between perfect
and defective NWs. This has also been verified experimentally
Figure 2. Effect of I1-SF on the size-dependent mechanical response of
ZnO NWs. (a) Young’s Modulus of perfect and defective (single SF)
NWs under compression/tension vs diameter, which show negligible
effect of SF. (b) Variation of critical stress σcas a function of diameter
under compression/tension, which indicates larger reduction of σcfor
thinner NWs as SF is introduced into their structure. The superscripts
Ten and Comp stand for tensile and compression test, respectively.
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for III−V NWs,
48
for which the SF density depletes with
decreasing diameter and a perfect WZ NW can be produced by
reducing its diameter.
3.2. Defect Density. The possibility of tailoring the
mechanical properties of nanostructures through defect
engineering was investigated by introducing multiple SFs with
a constant separation distance into a ZnO NW of 10 nm
diameter. The spacing between SFs ranges from 3 to 20 nm for
different defect densities, that is, number of SFs in unit length
(ρSF). Variations of the Young’s Modulus and critical stress as a
function of the number of defects within 40 nm length (i.e.,
defect density, ρSF) are plotted in Figure 4 for both tensile and
compressive loadings. Our results show that increasing the ρSF
gradually increases the Young’s Modulus in tension and
compression. However, no drastic changes in the critical stress
were captured in tension and only a slight increase was
observed for compressive loading. Our simulations show that
introducing a high density of SFs, SF = 13, into a perfect
structure leads to a 6.23% increase in critical stress (the critical
stresses are summarized in Table S2). Surprisingly, the Young’s
Modulus of a highly defective NW (13 SFs in a 40 nm long
NW) is even higher than that of the perfect NWs, a result that
is nontrivial. This finding opens up a novel approach for
synthesizing nanostructures with a higher Young’s Modulus
through defect engineering. The stress−strain curves are
depicted in Figure S3 for more reference. It is worth
mentioning that this behavior was observed experimentally
for GaAs NWs under buckling; however, they could not capture
this physics using atomistic simulations.
5,6
The effect of strain
rate on the mechanical properties of NWs is a well-known
phenomenon.
49
Therefore, all simulations were repeated by
lowering the strain rate by 1 order of magnitude, 0.0001 fs−1,to
investigate the impact of this parameter on the ascending trend
of Young’s Modulus. Our results (Figure 4) show that despite
the lower strain rate Young’s Modulus still increases by
increasing the number of SFs.
The underlying physics is multifaceted, which may lie in
changes of the bond nature around defects, as proposed in refs
5and 6. The effect of SF on the atomistic structure of WZ NW
is shown in Figure 5, which reveals the formation of a step at
the defect site after relaxation. At the intersection of SF and free
surface, surface stresses cause a severe local deformation. At the
intersection of SF and the [011̅0] surface, the bond length of
Zn−O, located at the inner layer, represented by b1, decreases
from 1.978 Å in a perfect crystal to 1.884 Å in the deformed
structure. The out-of-plane Zn−O bond length, denoted b2,is
Figure 3. Longitudinal strain, ϵz, for NWs with different defect densities and a diameter of 10 nm. Results for (a) 1 SF, (b) 3 SFs, (c) 6 SFs, and (d)
13 SFs are presented, which indicate complexity and interference of strain field as the number of SFs increases.
Figure 4. Effect of SF density on the mechanical response of NWs. (a) Variation of tensile/compressive Young’s Modulus vs density of SFs,
indicating that a higher Young’s Modulus can be obtained by introducing higher defect densities in the NW. (b) Effect of SF density on the critical
stress, revealing degradation of this material property for the tensile loading, whereas it shows slight improvement under compressive loading and
small defect densities. All simulated NWs have the same diameter of 10 nm. The properties of a perfect NW are shown with dotted lines.
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2.141 Å, whereas the out-of-plane bond length in the perfect
structure is 2.005 Å. Also, the in-plane bond angle, θ1,is
123.112°in the highly deformed zone, whereas this value
decreases to 120.303°for a perfect WZ. Finally, the out-of-
plane angle, θ2, is 91.871°for the defective (single I1-SF) and
111.458°for a perfect structure. These variations in the bond
length/angle can be used to verify the change in mechanical
properties of the nanostructure, that is, E∝d−4, where dand E
are the bond length and Young’s Modulus, respectively.
50
Introducing more SFs results in a larger change in the bond
length and angle, which consequently alters the mechanical
response of the system. Another explanation for this
phenomenon can be given by considering the strain
distribution in the relaxed structure. The intrinsic longitudinal
strain in the presence of multiple SFs is depicted in Figure 3b−
d for different defect densities and indicates that the tensile
strain is induced at SF sites, whereas compressive strain appears
at the upper and lower regions of the SFs. As the density of SFs
increases, the tensile strain slightly decreases from 0.0116 to
0.0101, whereas the compressive strain increases from −0.0078
to −0.011. This change in the longitudinal strain is due to the
overlap between the strain fields of adjacent SFs. Referring to
the core−shell model, increasing the compressive strain at the
shell leads to a reduction in bond length and a higher Young’s
Modulus for the NWs.
To explore the effect of SF density on the critical stress, the
similar reasoning can be used. The sharp stress drop in the
stress−strain curve of ZnO NWs (Figures S2 and S3) can be
explained by the phase transition in ZnO NWs. During loading,
the NW stores energy in the form of elastic energy until a
critical value is reached. At this point, the stored energy will be
released by the phase transition mechanism. In compression, a
new HX phase nucleates from the surface and at some distance
from the SF (see Figure S2). This can be described by the
formation of highly localized deformed regions around SFs,
which change the bond type and crystal structure (Figure 5).
These domains are not the ideal sites for nucleation; hence, the
nucleation site will be shifted away from the SF locations.
Increasing the number of SFs increases the number of these
deformed zones and consequently limits the possibility of HX
phase nucleation. This leads to an increase in the energy
required for activating the phase transition mechanism and
subsequently an increase in the compressive critical stress.
4. CONCLUSIONS
In summary, we have investigated the possibility of applying
defect engineering to tailor the mechanical response of
nanostructures, using an atomistic modeling approach with
ZnO NWs as our model material. The simulations revealed that
introducing a higher density of I1-SFs will increase the Young’s
Modulus beyond that of the corresponding perfect structure
under both tensile and compressive loadings. Also, a highly
defective NW exhibits a higher strength under compression
test, whereas SFs reduce the tensile strength. The reason
behind this higher Young’s Modulus can be the change in the
bond length and overlapping of the SF strain fields. To study
the changes in the bond types and lengths, a detailed study
using ab initio techniques is required. Additionally, the
interaction between the surface energy and the SF intrinsic
stress predicts that adding the SFs in smaller NWs can have a
drastic impact on the mechanical properties of a material. The
results presented here suggest new routes for fabrication of
NWs with superior mechanical properties.
Considering the fact that intrinsic strain can mediate the
properties of nanostructures, additional detailed studies are
required to explore the effect of SFs on the electrical, optical,
and electromechanical response of NWs.
51,52
Also, there is a
feasibility to increase the NW activity by introducing SFs as
active sites for chemical reactions; thus, chemical activity of a
material can be tailored by introducing a proper distribution of
SFs. Furthermore, studying the effects of other types of SFs, I2
and E, point defects, and twin boundary on material response
would be another promising avenue for exploration.
53,54
Finally,
the possibility of strengthening a nanostructure via synthesizing
the WZ/zinc blende (ZB) polytype structures can be examined,
that is, the SFs are observed at the WZ/ZB interface.
■ASSOCIATED CONTENT
*
SSupporting Information
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acsomega.6b00500.
Strain−stress curves for NWs and their corresponding
phase transition in the presence of SFs and also the
Buckingham potential parameters and calculation of SF
formation energy (PDF)
■AUTHOR INFORMATION
Corresponding Author
*E-mail: hamed.attariani@wright.edu.
ORCID
Hamed Attariani: 0000-0002-4777-5116
Author Contributions
H.A. and K.M. performed the analysis and prepared the
manuscript. K.A. performed the molecular dynamic simulations.
Notes
The authors declare no competing financial interest.
■ACKNOWLEDGMENTS
The support of Wright State University and Louisiana Tech
University are gratefully acknowledged. This project is also
partly supported by Louisiana EPSCoR-OIA-1541079
Figure 5. Effect of SF on the atomic structure of a ZnO NW. (a)
Perfect WZ crystal structure in the absence of SF on the [011̅0]
surface. (b) The crystal structure at the intersection of SF and the
[011̅0] surface.
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(NSF(2017)-CIMMSeed-10). The authors would like to thank
Ohio Super Computing (OSC), Grant No. ECS- PWSU0463,
and Louisiana Optical Network Initiative (LONI) for providing
the computational resources. Also, we thank Drs. A. Soghrati
and B. Shiari for supporting this research in part through
computational resources by National Nanotechnology Infra-
structure Network Computation (NNIN/C) project at
University of Michigan, which is supported by the National
Science Foundation under Grant No. ECS-0335765.
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