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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

http://pubs.acs.org/journal/acsodf

© 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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