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Computational Materials Science

journal homepage: www.elsevier.com/locate/commatsci

Defect engineering, a path to make ultra-high strength low-dimensionalnanostructures

Hamed Attariania,⁎, S. Emad Rezaeia, Kasra Momenib,c,⁎

a Department of Mechanical and Materials Engineering, Wright State University, Dayton, OH 45431, USAbMaterials Research Institute, Pennsylvania State University, University Park, PA 16802, USAc Department of Mechanical Engineering, Louisiana Tech University, Ruston, LA 71272, USA

A R T I C L E I N F O

Keywords:Defect engineeringNanowiresStress relaxationUltra-high strengthZinc oxideStacking faultAtomistic simulation

A B S T R A C T

A current understanding is that materials with perfect structures have better mechanical properties. Thus,lowering the defect concentration, particularly by reducing the size of synthesized materials such as nanowires(NWs), is one of the key goals in the fabrication of new materials. In contrast, here we demonstrate the possi-bility of enhancing the mechanical properties of the low-dimensional nanostructures by engineering defectsusing the classical molecular dynamics technique. Our results show that NWs with high-density of I1 stackingfaults (I1-SFs) have higher Young’s Module (up to 14% in compression) and critical stress (about 37% undercompression) in comparison to the perfect structure over a wide range of temperatures. This enhancement is inagreement with the in-situ experimental measurements of highly defective NWs and is explained by the interplaybetween surface stresses and the stress field of immobile SFs. The overlap of SF-induced stresses in regionsconfined by SFs partially relaxes with increasing temperature, while it remains the main reason for this non-trivial strengthening. Furthermore, a unique stress relaxation mechanism, twin boundary formation, is revealedfor highly defective NWs. The twin boundary formation postpones the phase transition and increases the resi-lience of the nanostructure over a wide range of temperatures, which results in a stress plateau in a highlydefective NW and an increase in ductility. Defect engineering is demonstrated as a new route for synthesizingadvanced materials with superior mechanical properties, and increasing their stiffness, strength, and ductility forapplications under extreme environments.

1. Introduction

One-dimensional nanomaterials, nanotubes (NT), nanowires (NWs),nanorods (NRs), and nanobelts (NBs), are promising candidates forsensors [1], lasers [2], optoelectronics [3], and photocatalysts [4]. Theresponse of these one-dimensional (1D) materials highly depends on thesize, defect concentration, and structure. Therefore, to achieve the de-sired characteristics (e.g., electrical, mechanical, and optical), thegrowth condition should be controlled. There is a long-standing notionamong researchers that the perfect structure is the ideal form of ma-terial in terms of mechanical properties, and intrinsic defects (e.g.,point and planar defects) degrade the mechanical properties. So, defectshave been treated as unwanted constituents that should be removedfrom the material or have their concentration reduced, e.g., by precisecontrolling of the growth process [5,6]. Here, our main goal is to un-derstand the correlation between defect structure and properties in low-dimensional materials and seek a way to enhance mechanical

performance of this class of materials by engineering inherent structuraldefects. This will open up a new avenue for design materials withtunable properties and subsequently expand the design space.

The tuning of material properties by modifying defect concentrationhas recently attracted a great deal of attention in the research com-munity. This topic is of great importance when one deals with nanos-tructured materials, because their response highly depends on the de-fect size, type, and concentration, e.g., doping the nanostructures withspecific elements can change their electrical properties [7]. Further-more, experimental [8] and numerical studies [9] show that the ra-diation tolerance of nanocrystalline SiC (nc-SiC) with a high density ofSFs can be enhanced by an order of magnitude. A few experimentalstudies show that systematically introducing nano-twin boundaries inCu [10] or stacking faults (SFs) [11,12] in GaAs NWs enhances themechanical properties that can be achieved by precise control over thesynthesizing process [13]. Also, introducing twins in Ag [14] and Ni[15] NW alters the deformation mechanism -i.e. plasticity and

https://doi.org/10.1016/j.commatsci.2018.05.005Received 11 January 2018; Received in revised form 20 April 2018; Accepted 4 May 2018

⁎ Corresponding authors at: Department of Mechanical and Materials Engineering, Wright State University, Dayton, OH 45431, USA (H. Attariani), Materials Research Institute,Pennsylvania State University, University Park, PA 16802, USA (K. Momeni).

E-mail addresses: hamed.attariani@wright.edu (H. Attariani), kmomeni@latech.edu (K. Momeni).

Computational Materials Science 151 (2018) 307–316

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dislocation nucleation. Additionally, MD simulations confirmed thisstrengthening mechanism in SiC [16] and ZnO NWs [17] at T=0 K andrelatively low density of the SFs. These studies predicted the strength-ening mechanism, although the stress relaxation mechanism is stillunchanged; the stress drops due to the phase transition or fracture. Thiscareful engineering of internal defects creates barriers for dislocationmotion or phase transition and subsequently alters the physical prop-erties of nanostructures. Despite the fact that manipulating internaldefects, e.g., adding precipitates or grain refinement to enhance theyield strength, is a common method at the macroscale level, it has notbeen well-studied at the nanoscale level. It is worth mentioning that thestrengthening methods in macroscale have their own setbacks, like areduction in ductility [18] that can be overcome in nanoscale. How-ever, on the other side of the spectrum, there is a long-standing notionthat these defects are the root cause of structural weakening [19–24];consequently, there is not a consensus on the exact effects of the defectson mechanical properties. Therefore, understanding the underlyingphysics opens a new avenue through which to predict, design, andfabricate a new class of one-dimensional materials with superiorproperties. Here, we showed that this enhancement in mechanicalproperties can be achieved over a wide temperature range,T= 100–500 K. Also, a new stress relaxation mechanism for ZnO NWs,twin formation, was predicted for high density of SFs, which is un-precedented.

2. Computational model

In order to study the potential strengthening mechanism in defect-engineered low-dimensional materials, ZnO NWs are chosen as themodel material due to their technological importance [25–28]. Thestable structure for ZnO NWs is Wurtzite (WZ) that consists of stackingABABABAB; each letter corresponds to a layer including zinc andoxygen atom. The I1-SF is the most common planar defect in ZnO NWs[29], which changes the stacking sequence to ABAB|CBCB so that thefault is placed between layer B and C. This planar defect was frequentlyobserved in synthesized NWs due to their low formation energy [30].The I1-SF burger vector = +R (1/3)[0110] (1/2)[0001] [29] can begenerated by removing a layer from the perfect crystal and moving theother portion of NW by R. The schematic for faulted NW is shown inFig. 1a.

Initially, the NW was relaxed for 500 ps at various simulationtemperatures, T=100–500 K, under NVE ensemble to equilibrate theenergy. The relaxation time was chosen via an iterative process, en-suring that the stress fields of SFs are relaxed. A maximum temperatureof 500 K is chosen that is smaller than Tm/3≈ 750 K to avoid the

emergence of time-dependent behaviors such as creep. Then, the NPTensemble with a Nose–Hoover thermostat was used for another 500 psto find the relaxed configuration. In the next stage, a constant strainrate of± 0.1 1/ps, to avoid strain-rate dependent responses, was ap-plied along the c-axis, [0 0 0 1], (Fig. 1a) to model the mechanical re-sponse of NW under tension/compression. The time step for all simu-lation cases was 1 fs. All of the simulated NWs have a diameter of 10 nmand are 40 nm in length. The Large-scale Atomic/Molecular MassivelyParallel Simulator (LAMMPS) code [31] was employed for MD simu-lations. Various defect density was introduced in NW; the number ofstacking faults varies between 2 and 26 that are separated with equaldistances. In the bulk structure, SF is constrained between two partialdislocations and can glide over these partial dislocations [32], but dueto the high surface-to-volume ratio of NWs, these planar defects arepinned at the external surfaces and are immobile. The radial distribu-tion function test was performed on the WZ NW to find the latticeparameters; see Fig. 1b. The calculated c/a ratio is 1.55, which is closeto the previous DFT calculations (c/a=1.6) [33], MD simulations (c/a= 1.57) [33], and experimental measurements (c/a=1.606) [34].The difference between the obtained ratios is due to the size effect.

To ensure the validity of our simulations, the formation energy of I1-SF and the bulk Young's of WZ structure was calculated. At roomtemperature, Young’s Modulus is 146 GPa, which is in agreement withexperimental studies, ≈140 GPa [35]. Also, the formation energy is14.1 meV/unit-cell area, which is close to the density functional theorycalculations 15meV/ (unit-cell area) [30]; the detailed calculation canbe found in Refs. [17,36] .

3. Results and discussion

The stress-strain curve for the perfect 1D-nanostructures follows asawtooth pattern. The stress increases with increasing strain, and elasticenergy gradually accumulates in the material until it reaches a criticalvalue, i.e. critical stress [36–39]. At this point, the structure releases theelastic energy via a stress relaxation mechanism, e.g., dislocation nu-cleation/phase transition, which can be designated as a critical strain.The simulated stress-strain curves for a perfect and defective NWs with2, 13, and 26 SFs are plotted in Figs. 2–5 for T=300 K. Fig. 2 shows theresponse of a perfect NW under tensile/compression loading and theassociated phase transition as a common stress relaxation mechanism inperfect ZnO NWs [33,36,39,40]. In compression, nucleation of hex-agonal (HX) polymorph leads to a drop in stress (point PC2), and nu-cleation of a body center tetragonal polymorph (BCT) (point PT2) re-leases the stress in tension. The coordination analysis was performed tovisualize the nucleation and propagation of new polymorphs (HX and

Fig. 1. (a) The I1-SF crystal structure. The dashedline shows the SF location along [0 0 0 1] direc-tion, uppercase letter refers to Zn atoms, and lowercase letter stands for O atoms. (b) Radial dis-tribution function for the perfect NW at T= 300 K.The WZ lattice parameters, a and c, were identifiedon the graph. The WZ unit cell and lattice para-meters were shown in the graph inset.

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BCT) during loading; see Fig. 2b–c. In a perfect NW, the nucleus of thenew phase appears at the free surface due to the atoms at the surfacehaving larger energy and being more prone to phase transition. Incompression, the new HX nucleus appear in two regions on the freesurfaces; the HX phase is shown by the red in Fig. 2a, and will propa-gate with increasing strain (PC3). A similar phenomenon is observed fortension; nucleation of BCT at the free surfaces (Fig. 2c, point PT2),however, in this case, the NW is completely transformed to BCT poly-morph at the large strains (Fig. 2c, point PT3).

In the next step, different densities of SFs are introduced in the NW,and a tensile/compression test was performed to investigate the effectof SFs on deformation, stress relaxation, and phase transition. Thestress-strain curves for three representative NWs with different SFdensities are plotted in Figs. 3–5. It is worth noting that the PT (WZ→HX and WZ→ BCT) was observed for various SFs density; however, the

nucleation sites and kinetics of PT were affected by SFs density (seeFigs. 3–5). Fig. 3 shows the compressive and tensile stress-strain curvefor a NW with two SFs ( =ρ SF μm5 /SF ). In the defected NW, the HXphase nucleates between the SFs; three HX regions are observed at SFC2

in Fig. 3b. The shift in nucleation sites can be explained by forminghighly deformed zones at the intersection of SF and free surface (dashedbox in Fig. 3b, point SFC,T1) which arrests the phase transition. Intensile loading, the nucleation is less homogenous, Fig. 3c, and it startsfrom one side (point SFT2) and gradually propagates along the surface(point SFT3). Any further increase in the load leads to propagation of thenew phase (BCT) toward the center of NW till the phase transformation(point SFT4) completes. By increasing the density of SFs, more nuclea-tion sites are observed between SFs in compressive loading (see Fig. 4,point SFC2). The increase in the number of nucleation sites is associatedwith local SF-induced stress distribution. However, SFs serve as barriers

Fig. 2. Perfect NW. (a) Stress-strain curve. The WZto HX phase transition is observed in compression(b), and WZ to BCT is occurred in tension (c). Thecoordination number analysis was performed todetect the new phases; the coordination number ofHX and BCT is five (red), and WZ has a co-ordination number of four (green). The snapshotsof the crystal structure associated with the vitalpoints, e.g., critical stress, on the stress-straingraph are depicted to illustrate the deformationand phase transition. Superscript “T” representsthe stress-strain state on tensile curve, and super-script “C” denotes the compression. (For inter-pretation of the references to colour in this figurelegend, the reader is referred to the web version ofthis article.)

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to growth and propagation of the new phase. Therefore, one shouldexpect that the required energy for nucleation should be lower thanperfect structure due to the inhomogeneity in stress distribution alongthe NW, while the necessary energy for complete phase transition isexpected to be higher than the perfect counterpart. The nucleationenergy for various temperatures and SF density under compression aresummarized in Table 1. The initial reduction in nucleation energy withrespect to the perfect NW and its continuous growth by increasingnumber of SFs verifies the hypothesis mentioned above.

Increasing the SF density to =ρ SF625 /μmSF (#SFs= 26) results in

a different mechanical response and unique stress relaxation and phasetransition mechanism; see Fig. 5. The SF-induced stress causes phasetransition (appearance of BCT phase) at the intersection of SF and freesurface in the absence of external loads (dashed box in Fig. 5b, pointSFT1,C1). A similar WZ to BCT reconstruction has been observed ex-perimentally for nano-islands at surfaces, [41] which proves the feasi-bility of this transition. A decrease in SF spacing results in an increase inlocal SF-induced stress due to overlapping stress fields of neighboringSFs, which subsequently facilitates the local transforming of WZ to BCTat the SF/free surface intersection. The stable polymorph under tensile

Fig. 3. NW with SF density of 5 SF/μm (#SF=2). (a) Stress-strain curve. More nucleation sites are observed for compression (b) and nucleation is more hetero-geneous in tension (c). The coordination number analysis was performed to detect the new phases; the coordination number of HX and BCT is five (red), and WZ has acoordination number of four (green). The snapshots of the crystal structure associated with the vital points, e.g., critical stress, on the stress-strain graph are depictedto illustrate the deformation and phase transition. Superscript “T” represents the stress-strain state on tensile curve and superscript “C” denotes the compression.

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loading is BCT; therefore one can predict that the appearance of BCTpolymorph can lead to an increase in nucleation energy of HX poly-morph under compression; note that HX polymorph is stable undercompressive loading. The correctness of this postulation can be verifiedby comparing the nucleation energy of highly defective NW, SF=26,with its perfect counterpart (see Table 1).see Table 1see Table 1 Also, inthis case, the NW fractures at the SF without exhibiting the phasetransition; NWs with low SF density are transformed completely to BCTpolymorph under tension (see Fig. 2c, Fig. 3c, Fig. 4c). Therefore, thedensity of SF can change deformation and failure mode of NWs.

Furthermore, we found a plateau in the compressive stress-straincurve (between SFC2 – SFC3), indicating significant enhancement in theload-carrying capacity of defective NWs. The underlying physics can bedescribed by arresting the phase transition at SFs and subsequentlyincreasing the required load for nucleation and growth of the high-pressure polymorph within the initial phase. This increase in critical

phase transformation load activates a secondary stress relaxation me-chanism, i.e. twin boundary formation (Fig. 5b, point SFC4). Here, weobserved the formation of (2112) twin, which is one of the possible ZnOtwin planes [42]. Formation of the twin boundary lowers the stress,resulting in the reverse phase transition, i.e., HX to WZ. This new me-chanism paves the way to making ultra-high strength, low-dimensionalnanostructures via engineering defects.

The total longitudinal strain distribution, εz, for different strains in aNW with high density of defects ( =ρ SF μm625 /SF ) is shown in Fig. 6.The strain sign will change (tensile to compressive) at the twinboundary. Also, Fig. 6b depicts the formation of the twin and itsstructure in more detail, where an initial slice was selected and frozenat equilibrium stage in order to study the deformation. This slice ishighlighted in red, and its deformation at the instant of twin formationis illustrated in Fig. 6b.

The stress-strain curve for the highly defective NW

Fig. 4. NW with the SF density of 325 SF/μm(#SF=13). (a) Stress-strain curve. The HX phaseappears at multiple sites between SFs. The co-ordination number analysis was performed forcompression (b) and tension (c) to detect the newphases; the coordination number of HX and BCT isfive (red), and WZ has a coordination number offour (green). The snapshots of the crystal structureassociated with the vital points, e.g., critical stress,on the stress-strain graph are depicted to illustratethe deformation and phase transition. Superscript“T” represents the stress-strain state on tensilecurve and superscript “C” denotes the compres-sion. (For interpretation of the references to colourin this figure legend, the reader is referred to theweb version of this article.)

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( =ρ SF μm625 /SF ) under compressive loading and different tempera-ture is shown in Fig. 7. A stress plateau was identified for a wide rangeof temperatures, T=100–500 K (point a to b in Fig. 7). With increasingtemperature, the critical stress is almost constant (the maximum var-iation in critical stress is less than 4% despite the fact that the tem-perature varies from 100 to 500 K), whereas the critical strain (i.e., thestrain associated with large drop in stress), increases up to εz = 0.082.This behavior is related to the effect of temperature on bond strength(i.e., bond softening). It can be seen that this unique mechanical re-sponse makes the highly defective ZnO NWs potential candidate ma-terials for applications at elevated temperatures.

In order to study the effect of SFs on mechanical properties, Young’sModulus and critical stress of NWs with various defect densities,

Fig. 5. NW with the SF density of 625 SF/μm (#SF=26). (a) Stress-strain curve. The HX phase appears at multiple sites between SFs under compression (b) andtension (c), and the brittle fracture is observed from the SF location. The coordination number analysis was performed to detect the new phases; the coordinationnumber of HX and BCT is five (red), and WZ has a coordination number of four (green). The snapshots of the crystal structure associated with the vital points, e.g.,critical stress, on the stress-strain graph are depicted to illustrate the deformation and phase transition. Superscript “T” represents the stress-strain state on tensilecurve and superscript “C” denotes the compression. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of thisarticle.)

Table 1The HX nucleation energy (ev) for different SF density and temperature undercompressive loading.

Temperature (K)

#SF 100 K 200 K 300 K 400 K 500 K

Perfect 0.261 0.244 0.239 0.224 0.2072 0.185 0.1683 0.163 0.159 0.1503 0.181 0.179 0.153 0.158 0.134 0.228 0.217 0.207 0.192 0.1866 0.237 0.222 0.211 0.202 0.18313 0.242 0.223 0.207 0.207 0.20326 0.326 0.293 0.287 0.283 0.285

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temperature, and loading type (compression/tension) were calculatedand are shown in Figs. 8 and 9. Fig. 8 shows an increase in Young’sModulus in tension/compression with increasing density of SFs in allsimulated temperatures in comparison to the perfect counterpart. Anincrease in temperature results in relaxation of SF-induced stress andconsequently weakens the strengthening effect; however, a high densityof SF (#SF=13, 26) can still strengthen the material, even at hightemperatures. The highly defective NW (#SF=26) increases thecompressive Young’s Modulus about 14.6–14.84% and an increase of5.22–8.32% is seen in tensile Young’s Modulus in the simulated tem-perature range. The physics behind this increase in Young’s Moduluscan be explained by the change in bond nature [11,12,17] and intrinsicSF-induced stress [17]. Due to an overlap between SF-induced stressand surface stress, the atoms at the intersection of SF/free surface un-dergo a local deformation, as seen in Fig. 3b, and subsequently changethe bond characteristics [17]. Also, the SFs disturb the local stressaround them and generate a heterogeneous stress distribution. To il-lustrate the inhomogeneity, the longitudinal strain, εz, distribution forthe relaxed structure is plotted in Fig. 10 for T=300 K. The straindistribution changes around the SFs, and adding more defect to thesystem causes overlapping among the intrinsic stress. This consequentlyaffects the bond length, which leads to variation of Young’s Modulus;bond length is proportional to −d 4. In low temperature, i.e., 0 K, thisoverlapping causes an increase in compressive strain and a decrease intensile strain, leading to strengthening (see [17]). However, with in-creasing temperature, the SF-induced strain can be relaxed by thethermal fluctuations, and more defects are needed to exceed the perfectstructure. This phenomenon can be seen in Fig. 10 that illustrates thedistribution of the longitudinal strain, ∊z, for NWs with various defectdensities at T=300 K. Longitudinal strain does not show a specificpattern (e.g., ascending/descending) until #SF 6 and, subsequently, adrastic enhancement in Young’s Modulus cannot be observed (seeFig. 8c). However, a considerable increase in Young’s Modulus wasobserved when the number of SFs was increased to 13 (see Fig. 8c). Thiscorresponds to a reduction in tensile strain and an increase in

Fig. 6. Total longitudinal strain distribution, εz, and twin formation in highly defected NW. (a) equilibrium stage. The strain is localized at the intersection of SF/surface. (b) An intermediate loading stage. (c) Relaxed structure due to twin formation. (d) The red strip is selected at the unloaded NW to study the deformation. (e)Some atoms on the initial red strip are displaced to form the twin boundary. (f) The close-view of the deformed initial strip and twin plane.

Fig. 7. Stress-strain curves for highly defected NW under compression at dif-ferent temperatures. The stress plateau was observed for a wide range of tem-peratures and was marked by an arrow on the figure. The deformed structurecorresponding to critical stress (point a) and critical strain (point b) was illu-strated. These deformed NWs were color-coded by longitudinal strain dis-tribution. A large increase in temperature, 100–500 K, leads to about 10.8% inthe compressive critical stress of the perfect structure. However, this increase intemperature causes only 4% improvement in the compressive critical stress ofthe highly defective NW. Also, the increase in temperature yields to a rise in thecritical strain.

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compressive strain; see Fig. 10d and e. This shows the direct effect ofstrain distribution on fluctuation in Young’s Modulus. It is worthmentioning that this reasoning is not applicable to highly defective NW,given that in this case, overlapping SF-induced stress becomes largeenough to locally transform the WZ to BCT at the SF/free surface in-tersection zones and make a heterogeneous NW with two polymorphs(WZ and BCT). Fig. 9 depicts the variation of critical stress vs. SFdensity at different temperatures. Tensile critical stress is smaller in thedefective NWs in comparison to the perfect structure, whereas, despitethe initial reduction in compressive critical stress, it gradually increasesby raising the SF density and ultimately shows higher strength than theperfect NW; #SF=26 in all temperatures. Comparing the compressivecritical stress of the highly defective to the perfect NW shows a26.08–34.05% increase in critical stress, which is a considerablestrengthening. The compressive critical stress of low SF density is lowerthan the perfect structure in all temperatures. In NW with high SFdensity, the BCT polymorph appears at the intersection of SF/freesurface, despite the fact that HX is the stable polymorph in compres-sion; BCT is stable under tensile loading. Therefore, one requires moreenergy to transform this heterogeneous structure (WZ/BCT) to HX. Thenucleation energy of high SF density in Table 1 verifies this hypothesis.In the tensile loading, the SFs shows an opposite trend: reduction incritical tensile stress for all SF density and temperatures. This is due tothe fact that the intersection of SFs and the free surface can serve as anactive site for crack nucleation.

4. Conclusions

In summary, this study covers the mechanical response of defectiveNWs under various defect density, temperature, and loading conditions.The results demonstrate that decorating an NW with equal-spaced SFs

leads to a decrease in critical tensile stress in comparison to the perfectcounterpart over a wide temperature range (100–500 K). However, itenhances the tensile Young's Modulus: a 7% enhancement with respectto the perfect structure. Modeling the same defected NW under com-pression results in about a 14% increase in compressive Young’sModulus and about 30% improvement in compressive critical stress.This non-trivial result defies the prevailing notion that defects alwaysplay a dominant role in deteriorating the mechanical properties of thenanostructures. These findings potentially open a new route for thefabrication of durable and novel nano-energy generators assemblies.The physics behind this enhancement are multifaceted and can be ex-plained by the change in bond strength, overlapping the intrinsic SF-induced stress fields and the interplay between SF and surface stress.Introducing the SFs along the c-axis produces a bamboo-like structurethat shifts the nucleation site toward the middle of each segment andforms a barrier for the propagation of the new PT. These results suggestthe possibility of arresting PT at the immobile SFs, which subsequentlyimproves the compressive load carrying capacity of the highly defectedNWs. Moreover, a novel stress relaxation and deformation mechanismwas observed for these NWs. An increase in the density of SFs is ac-companied by an increase in the mechanical energy storage capacity ofthe NW and results in activating the new mechanism to release thestored energy; the PT was arrested at the SFs, and the NWs relaxed itsenergy by forming a twin boundary. This unique stress relaxation hasnot been observed for the NWs, and it verifies the ability of defectengineering in altering the mechanical response of materials underdifferent loading types. All these findings suggest a new route for thefabrication of high-strength, low-dimensional nanostructures.Additionally, the impact of defects on material properties is not onlylimited to the mechanical properties, and its imprint can be explored onother aspects of properties (e.g., catalytic, electric), which broadens

Fig. 8. Variation of Young's Modulus vs. numberof SFs for different temperature under tension/compression. The dashed lines are the Young'sModulus of the perfect structures and are plottedfor comparison at different temperatures. An as-cending trend in Young's Modulus with increasingSF density is observed for the simulation tem-perature range. However, increasing temperatureinduces fluctuations in Young's Modulus for lowSF's density.

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material design space and stretches the designer's flexibility in tuningthe desired properties. More in-depth studies with ab initio or densityfunctional theory (DFT) are required to shed light on the change inenergy landscape as well as in bond strength. Developing a model fornucleation and phase propagation is desirable to illustrate the interac-tion between PT and SFs.

Acknowledgments

The support of Wright State University and Louisiana TechUniversity, under Grant EPSCoR-OIA-1541079 (NSF(2017)-CIMMSeed-10), are gratefully acknowledged. Also, the authors would like to thankOhio Super Computing (OSC), Grant No. ECS-PWSU0463, andLouisiana Optical Network Initiative (LONI) for providing the compu-tational resources.

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