Research ArticleEstimating Youngrsquos Modulus of Single-Walled ZirconiaNanotubes Using Nonlinear Finite Element Modeling

Ibrahim Dauda Muhammad1 Mokhtar Awang1 Othman Mamat1 and Ku Zilati Ku Shaari2

1Department of Mechanical Engineering Universiti Teknologi PETRONAS 31750 Tronoh Perak Malaysia2Department of Chemical Engineering Universiti Teknologi PETRONAS 31750 Tronoh Perak Malaysia

Correspondence should be addressed to Ibrahim Dauda Muhammad ibrahimuhdyahoocom

Received 17 October 2014 Revised 13 December 2014 Accepted 15 December 2014

Academic Editor Shiren Wang

Copyright copy 2015 Ibrahim Dauda Muhammad et al This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

The single-walled zirconia nanotube is structurallymodeled and its Youngrsquos modulus is valued by using the finite element approachThe nanotube was assumed to be a frame-like structure with bonds between atoms regarded as beam elements The properties ofthe beam required for input into the finite element analysis were computed by connecting energy equivalence between molecularand continuum mechanics Simulation was conducted by applying axial tensile strain on one end of the nanotube while the otherend was fixed and the corresponding reaction force recorded to compute Youngrsquos modulus It was found out that Youngrsquos modulusof zirconia nanotubes is significantly affected by some geometrical parameters such as chirality diameter thickness and lengthTheobtained values of Youngrsquosmodulus for a certain range of diameters are in agreement withwhat was obtained in the few experimentsthat have been conducted so farThis study was conducted on the cubic phase of zirconia having armchair and zigzag configurationThe optimal diameter and thickness were obtained which will assist in designing and fabricating bulk nanostructured componentscontaining zirconia nanotubes for various applications

1 Introduction

Zirconia (ZrO2) is considered to be among the most impor-

tant ceramic materials owing to its exceptional mechanicalproperties together with its stability at high temperatures [1]It is used as a refractory in insulation for metal coating alsoas abrasives enamels and glazes and as support materialfor catalysts [2] and due to its ion conductivity it is usedin oxygen pumps for partial regulation [3] gas sensors [4]and high temperature fuel cells [5] Also ZrO

2is considered

as one of the most radiation-resistant ceramics thus havingspecific application in the nuclear industry [6]

At atmospheric pressure ZrO2has three phases or poly-

morphs At high temperatures (above 2350∘C) ZrO2exists

as cubic fluorite structure (fm3m) while at low temperatures(below 1150∘C) monoclinic baddeleyite (P211C) structuredominates A tetragonal phase exists at intermediate phasehaving P42nmc symmetry [7] Most applications of ZrO

2

are based on its cubic polymorph which can be stabilized by

doping with oxides such as CaO MgO CeO2 and Y

2O3[8]

Improved results are obtained by reducing the crystallite sizeto few nm with an average of about 15 nm [9] this results inZrO2nanomaterials in formof dots slabs sheets and tubes at

atomic scale level For instance ZrO2is presently being tested

as catalyst support for several reactions and displays a muchhigher activity than some other oxides [10] Thus for someyears now progress has been attained on the synthesis andstudy of various nanostructure materials containing zirconiaSignificant consideration has been given to ZrO

2nanotube

(ZNT) due to its existing and potential applications suchas components of oxygen sensors host matrix for opticalfunctional materials and electrolytes in solid-oxide fuel cells[11]

Studies have shown that nanotubes have mechanicalproperties far superior when compared to that of bulkmaterial [4] These novel nanotubes (NTs) are projected tohave high stiffness wear resistance strength lower thermalconductivity and high melting temperature [2] and are

Hindawi Publishing CorporationJournal of NanomaterialsVolume 2015 Article ID 157423 8 pageshttpdxdoiorg1011552015157423

2 Journal of Nanomaterials

still retaining high plasticity because of their nearly infinitelength-to-width ratio [12] These higher material propertiesrender such nanotubes suitable for a range of applications[11]

Progress in scanning probe methods especially atomicforce microscope (AFM) has assisted in providing novelsettings to estimate somemechanical properties of nanotubes[12] Calculations and interpretations of physical propertiesof ZNT and similar materials most often are conducted usingAFM or electron microscopes the scanning electron micro-scope (SEM)or the transmission electronmicroscope (TEM)Possibly the most common instrument in characterizationof these materials is AFM [14] which applies very smallforces (nN) and detects tiny displacements (nm) Severalexperimental investigations on the mechanical propertieshave been conducted for carbon nanotubes [15ndash17] andinorganic nanotubes [18] with Youngrsquos modulus of ZNTdetected experimentally to be between 30 and 52GPa usingnanoindentation setup [19]

However several difficulties and challenges have beenexperienced during the mechanical characterization of nan-otubes due to their tiny size and high cost of requiredequipment [14] In addition there are other problems relatedto specimen collection handling and setting and quantifyingsmall forces and small deformations Precise setting of theload application spot and analysis of the results furthercomplicate the procedure [15]

Owing to some problems encountered during experi-mental analysis theoretical modelling methods have beenused recently to evaluate mechanical properties of NTsAmongst the existing modelling techniques the moleculardynamics (MD) method has been used widely [20] andis focused on the force field and total potential energylinked to the interatomic potentials of nanotubes Based onthis approach the bonding and nonbonding potentials arerepresented in relation to the force constants and the distancechange amongst the atomic bonds and then elastic moduliare estimated by using different small-strain deformationmodes [21] But MD simulation is not effective for time-consuming or fixed problem(s) thus it has limitation in thestudy of the mechanical properties of nanotubes The othermethod is the continuum or finite element method [22]whereby nanotubes are made up of elements regarded asbeams or shells that are subjected to bending tension or tor-sional loadingThis facilitates the nanotube to bemodelled asa shell-like or frame structure and the mechanical behaviourrealized by finite element method or classical continuummechanics [23]

The magnitude of axial Youngrsquos modulus for carbonnanotubes (CNT) has been found out by simulation to bein the range of 10 TPa to 55 TPa [20 24] with that ofWS2 MoS

2 and TiO

2nanotubes to be 143GPa 230GPa

and 270GPa respectively [22 23] Much information isrequired on the mechanical behaviour of ZNT as sufficientstudy has not been done experimentally and numerically[25] Therefore the purpose of this paper is to simulate themechanical behaviour of ZNT when exposed to axial tensionin order to estimate Youngrsquos modulus using finite element(FE) approach

2 Modeling and Simulation

21 Molecular Mechanics Based on the concept of molecularmechanics the total potential energy (119880) is specified as sumof specific potential constituents as a result of interactions [2123 24]

119880 = 119880120588+ 119880120579+ 119880120596

+ 119880120591+ 119880vdw + 119880es (1)

where119880120588119880120579119880120591 and119880

120596are energies related to bond stretch-

ing bond-angle inversion and bond torsion and inversionrespectively and are based on bonding while 119880vdw and 119880esare van derWaals and electrostatics interactions respectivelyand are not based on bondingThe energy terms in (1) can beexpressed using different functions depending on the loadingcondition and type of material [26] For the ZrndashO bond inZNT the ionic bonding dominates thus the significant partsof the potential energy are 119880

120588and 119880es and are represented

by Buckingham and Coulomb expressions respectively ForZrO2 the potential energy is expressed as a sum of two-body

interactions of the form [21]

119880 = 119860 exp(

minus119903119894119895

120588) minus

119862

1199036

119894119895

+

119902119894119902119895

4120587120576119900119903119894119895

(2)

where 119860 120588 and 119862 are constants describing the contributionsof short-range interaction of each particular pair and 119903

119894119895is the

distance between Zr and O2atoms Also 119902

119894and 119902

119895represent

the charges on the pairs of ions and 120576119900is the permittivity of

free spaceThe concept of energy equivalence can be used to link

the force factors in molecular mechanics and the elementstiffness in structural mechanics [15 20 22ndash24 26] whichwill allow simulation of the mechanical behavior of ZNTBased on Timoshenkorsquos theory of elasticity for beams therelations between the beam strain energies and the harmonicpotentials are expressed as [27]

119864 =

4119870119894119895119903119894119895

1205871198892 119866 =

32119870119894119895119896119897

119903119894119895

1205871198892 (3)

where 119864 and 119866 represent Youngrsquos modulus and shear mod-ulus respectively for ZrndashO bond in form of beam with 119889

as diameter and 119903119894119895as length Also 119870

119894119895and 119870

119894119895119896119897denote the

stretching force and bending force constants respectivelyThe diameter which is equivalent to thickness and the

Poisson ratio for the ZrndashO structural bond element canbe determined using analytical mechanistic or numericalmodels [26]

22 Finite Element Modeling (FEM)

221 Structure Thegeometry of inorganic nanotubes is builton the similar models used for CNT where the tubes aresupposed to be made by rolling up of nanosheets (NNS) toform a hollow cylinder andmay be single- ormultiwalled ForCNT the basic structural unit is a single atomic layer knownas graphene [28] The nanotube is defined by the translationvector L = 119897

1a + 1198972b and the chiral vector R = 119899a1 + 119898a2

(1198971 1198972 119899 and 119898 are integers and a1 and a2 are translation

Journal of Nanomaterials 3

a2

a1

C = na1 + ma2

Armchair Zigzag Chiral

Figure 1 Schematic representation of the relation between nanosheet and nanotubes [13]

Table 1 Computed constants for interactions of pairs of atoms inZrO2 [21]

Pair 119894119895 119860119894119895 (eV) 120588119894119895 (A) 119862 (eVA6)ZrndashO 98587 03760 00OndashO 227643 01490 2789ZrndashO 00 00 00

vectors of the 2D lattice) as shown in Figure 1 The nanotubeof the chirality (119899119898) is achieved by folding the layer in amanner that the chiral vectorR becomes the circumference ofthe nanotube The orthogonality relations (RL) = 0 are usedto define the NT chirality (119899119898) harmonious with the initial2D lattice periodicity [25] By designation (119899 119899) is armchair(119899 0) is zigzag and (119899119898) is chiral [29]

From analysis conducted on other nanotubes [20 22ndash28]the circumference length (119871) of the chiral vector (119862

ℎ) and

diameter of the single-walled ZNT are expressed as

119871 =1003816100381610038161003816119862ℎ

1003816100381610038161003816 = 119886radic1198992 + 1198982 + 119899119898

119889 =119871

120587=

119886

120587

radic1198992 + 1198982 + 119899119898

(4)

where 119886 is the lattice constant of ZrO2and is related to the

ZrndashO bond length Using first-principles calculations 119886 andZrndashO bond length were found out to be 50755 and 21953 Arespectively [30]

222 Modelling Based on available geometrical parame-ters for ZNT [25 30] single-walled ZNT having differentdimensions was developed by means of Surface Builder inMaterial Studio software for armchair and zigzag types Eachof the structures was saved as PDB file and the atomiccoordinates and connectivity data in the produced file for thenanotube were obtained using a coding from Python WingIDE [31] Thereafter a macro was written to model the ZNTin ANSYS with the atoms and bonds regarded as the nodesand elements respectively

For the modelling of the ZNT bonds the 3D BEAM188element is used The BEAM188 element is appropriate forinvestigating thin to relatively thick beam assemblies Thiselement is founded on Timoshenko beam theory Sheardistortion influences are built-in BEAM188 may be regardedas a 2-mode linear beam element having six degrees offreedom at all nodes The degrees of freedom at all nodes

0 005 01 015 02Strain

0

5E + 09

1E + 10

15E + 10

2E + 10

25E + 10

3E + 10

35E + 10

Stre

ss (N

m2 )

Figure 2 Stress-strain curve for ZrndashO bond as element

consist of translations in 119909 119910 and 119911 orientations and cyclesor rotations about the 119909 119910 and 119911 orientations Distortionof the cross-sections is presumed to be unrestricted Thebeam elements are suitable for use where linear nonlinearsizeable rotation andor significant strain occurs [32] Thediameter and Poisson ratio for the element (ZrndashO bond)were determined to be 0018 nm and 01897 respectivelyusing CrystalMaker and CASTEP [30] By differentiating thepotential energy expression in (2) the effective force in thebond or element is obtained as

119865 = minus119860 exp(minus119903120588)

120588minus

6119862

1199037minus

119902119894119902119895

41205871205761199001199032

(5)

For zirconia 120576119900

= 055263614 times 10minus12 C2eVminus1Aminus1 119902

119894=

119902Zr = 4119890 and 119902119895

= 119902O = minus2119890 where 119890 is magnitude ofelectronic charge 1602times10

minus19 C and the parameters of pairsof interactions of atoms in ZrO

2are presented in Table 1 [21]

For ZrndashO bond the relationship between stress and strainis shown in Figure 2 taking elementrsquos cross-sectional areato be 2545 times 10

minus20m2 The ZrndashO bond displays nonlinearor rate-dependent stress-strain behaviour due to large strainduring deformation [26 27] The problem due to large strainis reduced by usingMultilinear Isotropic HardeningMaterialModel (MISO) for the element

From the curve in Figure 2 Youngrsquos modulus of the ZrndashO element was computed to be 501 times 10

11 Pa (501GPa)representing the slope in the linear region and the value issimilar to 491GPa that was obtained for bulk ZrO

2by first-

principle calculations using CASTEP [30]

4 Journal of Nanomaterials

(a) (b)

Figure 3 FE models with boundary conditions for (a) armchair (20 20) and (b) zigzag (35 times 0) SWZNT

(a) (b)

Figure 4 Front side and top views for (a) 15 times 15 CNT and (b) 11 times 11 ZNT

223 Boundary Conditions Two main types of SWZNTsarmchair and zigzag were considered A fixed displacementwas applied at one end and prescribed displacement wasapplied at the other end axially as depicted in Figure 3Due to the applied displacement resultant reaction force (119865)occurs and is obtained after nonlinear simulation of forcesin all the nodes The procedure is repeated by changingthe applied displacements for different nanotubes havingdifferent configurations

Youngrsquos modulus (119864) for each nanotube after simulationwas determined using classical elasticity theory [20]

119864 =120590

120576=

119865119860119905

Δ119871119905119871119905

=119865119871119905

120587119889119905Δ119871119905

(6)

where 119865 is the resultant force on nodes at the applied end119860119905= 120587119889119905 is the cross-sectional area of the nanotube having

119889 as the diameter and 119905 as thickness and 119871119905and Δ119871

119905are

the initial length and elongation respectively in the axialdirection

In order to improve the accuracy of the simulated resultsthe nanotubes having the maximum 119864 with minimum diam-eter were selected and mesh convergence study is conductedby increasing the division of each element from 1 to 2 3 5 7and 10

3 Results and Discussion

The geometrical parameters of ZNT in relation to diameterand length depend on chirality with chiral type havingthe highest size followed by the zigzag and then armchairThe difference between two similar nanotubes in relation tolength and diameter is 17 1 26 for armchair zigzag andchiral types respectively The variations are similar to that ofboron nitride nanotubes (BNNT) and CNT [33 34] but thevalues are less than that of ZNTwhich have longer and thickeratomic bond Details of the geometrical parameters of someZNTs are stated in Table 2

The symmetry of the SWZNT is not uniform compared toCNTThe orientation depends on the chirality with armchairhaving more uniform diameter across the tube and zigzag

Journal of Nanomaterials 5

Table 2 Geometrical parameters for modeled ZNTs

Chirality (119899 times 119898) Diameter (A) Length (A) Atomsnodes Bondselements Bond length (A)Minimum Maximum Mean

5 times 5 10461 10084 820 1220 195 2263 21189 times 0 10872 10284 768 1293 1932 2364 20938 times 8 16738 10084 1312 1952 2012 2295 213614 times 0 16911 10284 1344 1988 1972 2165 203210 times 10 20923 10084 1640 2440 1978 2143 199717 times 0 20535 10284 1728 2431 1949 2103 199614 times 14 29292 10084 2296 3416 1961 2157 197224 times 0 28991 10284 2304 3432 1881 2114 196416 times 16 33476 10084 2624 3904 195 2157 196228 times 0 33823 10284 2784 4147 1873 211 1958

Mean 1873 2263 20229

050

100150200250300350400450500

00 10 20 30 40 50 60 70

Youn

grsquos m

odul

us (G

Pa)

Nanotube diameter (nm)Armchair (n times n)Zigzag (n times 0)

Figure 5 Effect of diameter on Youngrsquos modulus of SWZNTs

having variations leading to depressions across the tubeand in some cases less diameter at the ends The ZNT isnot a cylindrical tube as in CNT but it is irregular andis referred to as polygonal tube similar to other inorganicnanotubes [35] The difference in geometrical orientation ofZNT compared to CNT is illustrated in Figure 4 both havingthe same number of bondselements and approximately thesame diameter

It has been established that some mechanical propertiesof CNTs are influenced by size and chirality [20 24] Similartrend occurs in relation to ZNTs as indicated in Figure 5showing changes of Youngrsquos modulus of armchair and zigzagnanotubes with diameter The curve indicates significanteffect of diameter on the value of 119864 especially in relationto small diameters The zigzag ZNTs have higher Youngrsquosmodulus in comparison with armchair ZNTs with similardiameters but the pattern of increase is the same for allnanotubes The increase in Youngrsquos modulus as the diameterincreases is attributed to the effect of nanotube curvature[26 36]

As the nanotube diameter increases the effect of curva-ture reduces and 119864 converges to a value For a variation ofdiameter from 105 to 618 nm for the armchair SWZNTs andfrom 109 to 613 nm for the zigzag SWZNTs the values of

0

100

200

300

400

500

0 1 2 3 4 5 6 7 8 9 10 11

Youn

grsquos m

odul

us (G

Pa)

Aspect ratio (Ld)ArmchairZigzag

Figure 6 Effect of aspect ratio (119871119889) on Youngrsquos modulus ofSWZNTs

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7 8 9 10 11

Youn

grsquos m

odul

us (G

Pa)

Number of divisions in elements

Figure 7 Curve obtained from convergence test for (35 times 0)SWZNT

119864 vary from 217 to 385GPa and from 309GPa to 431GParespectively The findings indicate that Youngrsquos moduli com-puted for both armchair and zigzag SWZNTs are constant fordiameters ranging from 38 to 613 nm and are approximately380 and 427GPa for armchair and zigzag respectively

6 Journal of Nanomaterials

0

50

100

150

200

250

300

350

0 5 10 15 20 25 30

Youn

grsquos m

odul

us (G

Pa)

Length (nm)

(a)

0

50

100

150

200

250

300

350

0 2 4 6 8

Youn

grsquos m

odul

us (G

Pa)

Aspect ratio (Ld)

(b)

Figure 8 Variation of Youngrsquos modulus of (35 0) SWZNT with (a) length and (b) aspect ratio

0

100

200

300

400

500

600

0 2 4 6 8 10 12

Youn

grsquos m

odul

us (G

Pa)

1wall thickness (1nm)

0

100

200

300

400

500

600

00 05 10 15 20

Youn

grsquos m

odul

us (G

Pa)

Thickness (nm)

Figure 9 Effect of thickness on Youngrsquos modulus of (35 0) SWZNT

In contrast Youngrsquos moduli of the SWZNTs decrease asthe aspect ratio (119871119889) increases (Figure 6)This indicates thatincreasing the aspect ratio will negatively affect the structuralstability of the nanotubes as in other inorganic nanotubes[26]Thus in relation to optimumYoungrsquosmodulus minimaldiameter is required

Based on minimal diameter the SWZNT with optimalYoungrsquosmodulus was found out to be the zigzag typewith (350) configuration as indicated in Figure 5 But Youngrsquos modu-lus of SWZNTs obtained is much higher than experimentaland simulated values for inorganic nanotubes [18 19 22 23]In order to obtain a more accurate solution convergencetest was conducted using h-method by creating finer meshuntil the solution converges or approaches a particular valueFrom Figure 7 convergence occurred at 5 divisions of theelement having Youngrsquos modulus as 14164GPa compared to29796GPawhen division of the elementswas 1which is about110 reduction Dividing the elements further up to 10 unitsgave a difference of 3 fromwhat was obtained for 5 divisionsof the elements The results obtained for the convergence testof (35 0) SWZNT are shown in Figure 7

With respect to length and aspect ratio a similar patternwas observed for (35 times 0) SWZNT as illustrated in Figure 8There was tremendous increase in Youngrsquos modulus initially

until the optimum value of 297GPa was attained at 10 nmlength and aspect ratio of 2 and thereafter convergenceoccurred

As illustrated in Figure 4 the ZNT is not a cylindricaltube but polygonal tube Thus the thickness of the tubeis not assumed to be equivalent to the thickness of thebondelement as in CNT but is defined as difference of radialspaces between the furthest and innermost (oxygen) atoms inthe optimized structures [25] The wall thickness of SWZNTmodelled from cubic nanosheet varies between 0194 and0680 nm depending on symmetry and chirality [25] As wasobtained in CNT [36] the wall thickness has substantialinfluence on the computed Youngrsquos modulus as shown inFigure 9

From the results obtained after simulation it was notedthat the greater the wall thickness of SWZNTs the lesser thevalue of 119864 computed For a variation of 119905 from 005 nm to02 nm the value of 119864 varied from 565 to 67GPa for the(35 times 0) nanotube and from 431 to 53GPa for the (20 20)nanotubeThus the result confirmswhatwas obtained duringnanoindentation of ZNTwhere thicker arrays were found outto be softer than their thinner equivalents [19]

It has been established that for any tube wall thickness 119905

and chirality (119899 times 119898) there occurs a diameter 119889 below which

Journal of Nanomaterials 7

the NTs develop instability and experience impulsive damageor destruction [25] In order to maintain uniformity in theparametric studies of ZNT the value of 0194 was adoptedfor 119905 which is equivalent to the thickness of cubic zirconiananosheet cleaved along (111) plane [27]

4 Conclusions

In this study the tensile behavior of cubic single-walled zirco-nia nanotubes was simulated using nonlinear finite elementanalysis in order to establish geometrical parameters andmagnitude of Youngrsquos modulus The model was developedbased on the assumption that ZNTswhen subjected to load inform of strain behave as a space frame-like structuremade upof elements connected by nodesThis allows linking the forceconstants in molecular mechanics and the elastic propertiesof the beam-like element member in structural mechan-ics through the energy equivalence theory Simulations onnanotubes with different configurations were conducted bymaking one end fixed and subjecting the other end to axialtensile strain The geometry of SWZNTs was found out to bepolygonal tube not as cylindrical tube in CNTThe optimumYoungrsquos modulus of about 142GPa was obtained from zigzagSWZNT having diameter of about 615 nm Based on theresults obtained it can be concluded that the method used isan effective tool for investigating the mechanical propertiesof ZNTs and other nanotubes at less computational cost

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are grateful for the support provided by Univer-siti Teknologi PETRONAS andMalaysianMinistry of HigherEducation (MOHE) through the Long Term Research GrantScheme (LRGS) for One Baja Research Programme (Project6)

References

[1] M C Munoz S Gallego J I Beltran and J Cerda ldquoAdhesionat metal-ZrO

2interfacesrdquo Surface Science Reports vol 61 no 7

pp 303ndash344 2006[2] E J Walter S P Lewis and A M Rappe ldquoFirst principles study

of carbonmonoxide adsorption on zirconia-supported copperrdquoSurface Science vol 495 no 1-2 pp 44ndash50 2001

[3] S Meriani and C Palmonari Zirconiarsquo88 Advances in ZirconiaScience and Technology Kluwer Academic 1989

[4] V R Choudhary S Banerjee and S G Pataskar ldquoCombustionof dilute propane over transition metal-doped ZrO

2(cubic)

catalystsrdquo Applied Catalysis A General vol 253 no 1 pp 65ndash74 2003

[5] F Rohr P Hagenmuller and W van Gool Solid ElectrolytesMaterial Science Series Academic Press New York NY USA1978

[6] A Meldrum L A Boatner and R C Ewing ldquoNanocrystallinezirconia can be amorphized by ion irradiationrdquo Physical ReviewLetters vol 88 no 2 Article ID 025503 2001

[7] M Wilson U Schonberger and M W Finnis ldquoTransferableatomistic model to describe the energetics of zirconiardquo PhysicalReview B vol 54 no 13 pp 9147ndash9152 1996

[8] M Gateshki V Petkov T Hyeon J Joo M Niederberger andY Ren ldquoInterplay between the local structural disorder and thelength of structural coherence in stabilizing the cubic phase innanocrystalline ZrO

2rdquo Solid State Communications vol 138 no

6 pp 279ndash284 2006[9] Y L Soo P J Chen S H Huang et al ldquoLocal structures

surrounding Zr in nanostructurally stabilized cubic zirconiastructural origin of phase stabilityrdquo Journal of Applied Physicsvol 104 no 11 Article ID 113535 2008

[10] T Yamaguchi M Tan-No and K Tanabe ldquoZrO2as a catalyst

and catalyst supportrdquo Journal of the Japan Petroleum Institutevol 36 no 4 pp 250ndash267 1993

[11] G CaoNanostructures andNanomaterials Synthesis Propertiesand Applications Imperial College Press London UK 2004

[12] RA Evarestov Y F Zhukovskii AV Bandura and S PiskunovldquoSymmetry and models of single-wall BN and TiO

2nanotubes

with hexagonal morphologyrdquo Journal of Physical Chemistry Cvol 114 no 49 pp 21061ndash21069 2010

[13] B Wen Xing Z Chang Chun and C Wan Zhao ldquoSimulationof Youngrsquos modulus of single-walled carbon nanotubes bymolecular dynamicsrdquo Physica B CondensedMatter vol 352 no1ndash4 pp 156ndash163 2004

[14] Y Zhu C Ke and H D Espinosa ldquoExperimental techniquesfor the mechanical characterization of one-dimensional nanos-tructuresrdquo ExperimentalMechanics vol 47 no 1 pp 7ndash24 2007

[15] E W Wong P E Sheehan and C M Lieber ldquoNanobeammechanics elasticity strength and toughness of nanorods andnanotubesrdquo Science vol 277 no 5334 pp 1971ndash1975 1997

[16] M-F Yu T Kowalewski and R S Ruoff ldquoInvestigation ofthe radial deformability of individual carbon nanotubes undercontrolled indentation forcerdquo Physical Review Letters vol 85no 7 pp 1456ndash1459 2000

[17] M-F Yu O Lourie M J Dyer K Moloni T F Kelly andR S Ruoff ldquoStrength and breaking mechanism of multiwalledcarbon nanotubes under tensile loadrdquo Science vol 287 no 5453pp 637ndash640 2000

[18] T Shokuhfar G K Arumugam P A Heiden R S Yassar andC Friedrich ldquoDirect compressive measurements of individualtitaniumdioxide nanotubesrdquoACSNano vol 3 no 10 pp 3098ndash3102 2009

[19] L-N Wang and J-L Luo ldquoFabrication and mechanical proper-ties of anodized zirconium dioxide nanotubular arraysrdquo Journalof Physics D Applied Physics vol 44 no 7 Article ID 0753012011

[20] C-W Fan J-H Huang C Hwu and Y-Y Liu ldquoMechanicalproperties of single-walled carbon nanotubesmdasha finite elementapproachrdquo Advanced Materials Research vol 33ndash37 pp 937ndash942 2008

[21] C WangMultiscale modeling and simulation of nanocrystallinezirconium oxide [PhD thesis] University of Nebraska 2009

[22] E Kalfon-Cohen O Goldbart R Schreiber et al ldquoRadialcompression studies of WS

2nanotubes in the elastic regimerdquo

Journal of Vacuum Science and Technology B Microelectronicsand Nanometer Structures vol 29 no 2 Article ID 021009 2011

8 Journal of Nanomaterials

[23] T Lorenz D Teich J-O Joswig and G Seifert ldquoTheoreticalstudy of the mechanical behavior of individual TiS

2and MoS

2

nanotubesrdquo Journal of Physical Chemistry C vol 116 no 21 pp11714ndash11721 2012

[24] X Chen and G Cao ldquoA structural mechanics study of single-walled carbon nanotubes generalized from atomistic simula-tionrdquo Nanotechnology vol 17 no 4 pp 1004ndash1008 2006

[25] AV Bandura andRA Evarestov ldquoAb initio structuremodelingof ZrO

2nanosheets and single-wall nanotubesrdquo Computational

Materials Science vol 65 pp 395ndash405 2012[26] R Ansari S Rouhi M Mirnezhad and F Sadeghiyeh ldquoStudy-

ing the buckling and vibration characteristics of single-walledzinc oxide nanotubes using a nanoscale finite element modelrdquoApplied Physics A Materials Science and Processing vol 112 no3 pp 767ndash774 2013

[27] L Boldrin F Scarpa R Chowdhury and S Adhikari ldquoEffectivemechanical properties of hexagonal boron nitride nanosheetsrdquoNanotechnology vol 22 no 50 Article ID 505702 2011

[28] L Guimaraes A N Enyashin G Seifert and H A DuarteldquoStructural electronic and mechanical properties of single-walled halloysite nanotube modelsrdquo Journal of Physical Chem-istry C vol 114 no 26 pp 11358ndash11363 2010

[29] Y Mitsunori and I T Yuko ldquoSynthesis and applications ofzirconia and ruthenium oxide nanotubesrdquo in Inorganic andMetallic Nanotubular Materials T Kijima Ed pp 117ndash133Springer Berlin Germany 2010

[30] I D Muhammad M Awang O Mamat and Z B ShaarildquoFirst-principles calculations of the structural mechanical andthermodynamics properties of cubic zirconiardquoWorld Journal ofNano Science and Engineering vol 4 no 2 pp 97ndash103 2014

[31] I D Muhammad and M Awang ldquoExtracting the atomic coor-dinates and connectivity of zirconia nanotubes from PDB filesfor modelling in ANSYSrdquo Advances in Nanoparticles vol 3 pp92ndash98 2014

[32] ldquo4188 BEAM188 3-D Linear Finite Strain Beamrdquo September2014 httpmostrealskhtmlelem 55chapter4ES4-188htm

[33] RA Evarestov Y F Zhukovskii AV Bandura and S PiskunovldquoSymmetry and models of single-wall BN and TiO

2nanotubes

with hexagonal morphologyrdquoThe Journal of Physical ChemistryC vol 114 no 49 pp 21061ndash21069 2010

[34] D Dass R Prasher and R Vaid ldquoAnalytical study of unit celland molecular structures of single walled carbon nanotubesrdquoInternational Journal of Computational Engineering Researchvol 2 pp 1447ndash1457 2012

[35] K Tibbetts R Doe and G Ceder ldquoPolygonal model for layeredinorganic nanotubesrdquo Physical Review BmdashCondensed Matterand Materials Physics vol 80 no 1 Article ID 014102 2009

[36] K I Tserpes and P Papanikos ldquoFinite element modeling ofsingle-walled carbon nanotubesrdquo Composites Part B Engineer-ing vol 36 no 5 pp 468ndash477 2005

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Journal of Nanomaterials 3

a2

a1

C = na1 + ma2

Armchair Zigzag Chiral

Figure 1 Schematic representation of the relation between nanosheet and nanotubes [13]

Table 1 Computed constants for interactions of pairs of atoms inZrO2 [21]

Pair 119894119895 119860119894119895 (eV) 120588119894119895 (A) 119862 (eVA6)ZrndashO 98587 03760 00OndashO 227643 01490 2789ZrndashO 00 00 00

vectors of the 2D lattice) as shown in Figure 1 The nanotubeof the chirality (119899119898) is achieved by folding the layer in amanner that the chiral vectorR becomes the circumference ofthe nanotube The orthogonality relations (RL) = 0 are usedto define the NT chirality (119899119898) harmonious with the initial2D lattice periodicity [25] By designation (119899 119899) is armchair(119899 0) is zigzag and (119899119898) is chiral [29]

From analysis conducted on other nanotubes [20 22ndash28]the circumference length (119871) of the chiral vector (119862

ℎ) and

diameter of the single-walled ZNT are expressed as

119871 =1003816100381610038161003816119862ℎ

1003816100381610038161003816 = 119886radic1198992 + 1198982 + 119899119898

119889 =119871

120587=

119886

120587

radic1198992 + 1198982 + 119899119898

(4)

where 119886 is the lattice constant of ZrO2and is related to the

ZrndashO bond length Using first-principles calculations 119886 andZrndashO bond length were found out to be 50755 and 21953 Arespectively [30]

222 Modelling Based on available geometrical parame-ters for ZNT [25 30] single-walled ZNT having differentdimensions was developed by means of Surface Builder inMaterial Studio software for armchair and zigzag types Eachof the structures was saved as PDB file and the atomiccoordinates and connectivity data in the produced file for thenanotube were obtained using a coding from Python WingIDE [31] Thereafter a macro was written to model the ZNTin ANSYS with the atoms and bonds regarded as the nodesand elements respectively

For the modelling of the ZNT bonds the 3D BEAM188element is used The BEAM188 element is appropriate forinvestigating thin to relatively thick beam assemblies Thiselement is founded on Timoshenko beam theory Sheardistortion influences are built-in BEAM188 may be regardedas a 2-mode linear beam element having six degrees offreedom at all nodes The degrees of freedom at all nodes

0 005 01 015 02Strain

0

5E + 09

1E + 10

15E + 10

2E + 10

25E + 10

3E + 10

35E + 10

Stre

ss (N

m2 )

Figure 2 Stress-strain curve for ZrndashO bond as element

consist of translations in 119909 119910 and 119911 orientations and cyclesor rotations about the 119909 119910 and 119911 orientations Distortionof the cross-sections is presumed to be unrestricted Thebeam elements are suitable for use where linear nonlinearsizeable rotation andor significant strain occurs [32] Thediameter and Poisson ratio for the element (ZrndashO bond)were determined to be 0018 nm and 01897 respectivelyusing CrystalMaker and CASTEP [30] By differentiating thepotential energy expression in (2) the effective force in thebond or element is obtained as

119865 = minus119860 exp(minus119903120588)

120588minus

6119862

1199037minus

119902119894119902119895

41205871205761199001199032

(5)

For zirconia 120576119900

= 055263614 times 10minus12 C2eVminus1Aminus1 119902

119894=

119902Zr = 4119890 and 119902119895

= 119902O = minus2119890 where 119890 is magnitude ofelectronic charge 1602times10

minus19 C and the parameters of pairsof interactions of atoms in ZrO

2are presented in Table 1 [21]

For ZrndashO bond the relationship between stress and strainis shown in Figure 2 taking elementrsquos cross-sectional areato be 2545 times 10

minus20m2 The ZrndashO bond displays nonlinearor rate-dependent stress-strain behaviour due to large strainduring deformation [26 27] The problem due to large strainis reduced by usingMultilinear Isotropic HardeningMaterialModel (MISO) for the element

From the curve in Figure 2 Youngrsquos modulus of the ZrndashO element was computed to be 501 times 10

11 Pa (501GPa)representing the slope in the linear region and the value issimilar to 491GPa that was obtained for bulk ZrO

2by first-

principle calculations using CASTEP [30]

4 Journal of Nanomaterials

(a) (b)

Figure 3 FE models with boundary conditions for (a) armchair (20 20) and (b) zigzag (35 times 0) SWZNT

(a) (b)

Figure 4 Front side and top views for (a) 15 times 15 CNT and (b) 11 times 11 ZNT

223 Boundary Conditions Two main types of SWZNTsarmchair and zigzag were considered A fixed displacementwas applied at one end and prescribed displacement wasapplied at the other end axially as depicted in Figure 3Due to the applied displacement resultant reaction force (119865)occurs and is obtained after nonlinear simulation of forcesin all the nodes The procedure is repeated by changingthe applied displacements for different nanotubes havingdifferent configurations

Youngrsquos modulus (119864) for each nanotube after simulationwas determined using classical elasticity theory [20]

119864 =120590

120576=

119865119860119905

Δ119871119905119871119905

=119865119871119905

120587119889119905Δ119871119905

(6)

where 119865 is the resultant force on nodes at the applied end119860119905= 120587119889119905 is the cross-sectional area of the nanotube having

119889 as the diameter and 119905 as thickness and 119871119905and Δ119871

119905are

the initial length and elongation respectively in the axialdirection

In order to improve the accuracy of the simulated resultsthe nanotubes having the maximum 119864 with minimum diam-eter were selected and mesh convergence study is conductedby increasing the division of each element from 1 to 2 3 5 7and 10

3 Results and Discussion

The geometrical parameters of ZNT in relation to diameterand length depend on chirality with chiral type havingthe highest size followed by the zigzag and then armchairThe difference between two similar nanotubes in relation tolength and diameter is 17 1 26 for armchair zigzag andchiral types respectively The variations are similar to that ofboron nitride nanotubes (BNNT) and CNT [33 34] but thevalues are less than that of ZNTwhich have longer and thickeratomic bond Details of the geometrical parameters of someZNTs are stated in Table 2

The symmetry of the SWZNT is not uniform compared toCNTThe orientation depends on the chirality with armchairhaving more uniform diameter across the tube and zigzag

Journal of Nanomaterials 5

Table 2 Geometrical parameters for modeled ZNTs

Chirality (119899 times 119898) Diameter (A) Length (A) Atomsnodes Bondselements Bond length (A)Minimum Maximum Mean

5 times 5 10461 10084 820 1220 195 2263 21189 times 0 10872 10284 768 1293 1932 2364 20938 times 8 16738 10084 1312 1952 2012 2295 213614 times 0 16911 10284 1344 1988 1972 2165 203210 times 10 20923 10084 1640 2440 1978 2143 199717 times 0 20535 10284 1728 2431 1949 2103 199614 times 14 29292 10084 2296 3416 1961 2157 197224 times 0 28991 10284 2304 3432 1881 2114 196416 times 16 33476 10084 2624 3904 195 2157 196228 times 0 33823 10284 2784 4147 1873 211 1958

Mean 1873 2263 20229

050

100150200250300350400450500

00 10 20 30 40 50 60 70

Youn

grsquos m

odul

us (G

Pa)

Nanotube diameter (nm)Armchair (n times n)Zigzag (n times 0)

Figure 5 Effect of diameter on Youngrsquos modulus of SWZNTs

having variations leading to depressions across the tubeand in some cases less diameter at the ends The ZNT isnot a cylindrical tube as in CNT but it is irregular andis referred to as polygonal tube similar to other inorganicnanotubes [35] The difference in geometrical orientation ofZNT compared to CNT is illustrated in Figure 4 both havingthe same number of bondselements and approximately thesame diameter

It has been established that some mechanical propertiesof CNTs are influenced by size and chirality [20 24] Similartrend occurs in relation to ZNTs as indicated in Figure 5showing changes of Youngrsquos modulus of armchair and zigzagnanotubes with diameter The curve indicates significanteffect of diameter on the value of 119864 especially in relationto small diameters The zigzag ZNTs have higher Youngrsquosmodulus in comparison with armchair ZNTs with similardiameters but the pattern of increase is the same for allnanotubes The increase in Youngrsquos modulus as the diameterincreases is attributed to the effect of nanotube curvature[26 36]

As the nanotube diameter increases the effect of curva-ture reduces and 119864 converges to a value For a variation ofdiameter from 105 to 618 nm for the armchair SWZNTs andfrom 109 to 613 nm for the zigzag SWZNTs the values of

0

100

200

300

400

500

0 1 2 3 4 5 6 7 8 9 10 11

Youn

grsquos m

odul

us (G

Pa)

Aspect ratio (Ld)ArmchairZigzag

Figure 6 Effect of aspect ratio (119871119889) on Youngrsquos modulus ofSWZNTs

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7 8 9 10 11

Youn

grsquos m

odul

us (G

Pa)

Number of divisions in elements

Figure 7 Curve obtained from convergence test for (35 times 0)SWZNT

119864 vary from 217 to 385GPa and from 309GPa to 431GParespectively The findings indicate that Youngrsquos moduli com-puted for both armchair and zigzag SWZNTs are constant fordiameters ranging from 38 to 613 nm and are approximately380 and 427GPa for armchair and zigzag respectively

6 Journal of Nanomaterials

0

50

100

150

200

250

300

350

0 5 10 15 20 25 30

Youn

grsquos m

odul

us (G

Pa)

Length (nm)

(a)

0

50

100

150

200

250

300

350

0 2 4 6 8

Youn

grsquos m

odul

us (G

Pa)

Aspect ratio (Ld)

(b)

Figure 8 Variation of Youngrsquos modulus of (35 0) SWZNT with (a) length and (b) aspect ratio

0

100

200

300

400

500

600

0 2 4 6 8 10 12

Youn

grsquos m

odul

us (G

Pa)

1wall thickness (1nm)

0

100

200

300

400

500

600

00 05 10 15 20

Youn

grsquos m

odul

us (G

Pa)

Thickness (nm)

Figure 9 Effect of thickness on Youngrsquos modulus of (35 0) SWZNT

In contrast Youngrsquos moduli of the SWZNTs decrease asthe aspect ratio (119871119889) increases (Figure 6)This indicates thatincreasing the aspect ratio will negatively affect the structuralstability of the nanotubes as in other inorganic nanotubes[26]Thus in relation to optimumYoungrsquosmodulus minimaldiameter is required

Based on minimal diameter the SWZNT with optimalYoungrsquosmodulus was found out to be the zigzag typewith (350) configuration as indicated in Figure 5 But Youngrsquos modu-lus of SWZNTs obtained is much higher than experimentaland simulated values for inorganic nanotubes [18 19 22 23]In order to obtain a more accurate solution convergencetest was conducted using h-method by creating finer meshuntil the solution converges or approaches a particular valueFrom Figure 7 convergence occurred at 5 divisions of theelement having Youngrsquos modulus as 14164GPa compared to29796GPawhen division of the elementswas 1which is about110 reduction Dividing the elements further up to 10 unitsgave a difference of 3 fromwhat was obtained for 5 divisionsof the elements The results obtained for the convergence testof (35 0) SWZNT are shown in Figure 7

With respect to length and aspect ratio a similar patternwas observed for (35 times 0) SWZNT as illustrated in Figure 8There was tremendous increase in Youngrsquos modulus initially

until the optimum value of 297GPa was attained at 10 nmlength and aspect ratio of 2 and thereafter convergenceoccurred

As illustrated in Figure 4 the ZNT is not a cylindricaltube but polygonal tube Thus the thickness of the tubeis not assumed to be equivalent to the thickness of thebondelement as in CNT but is defined as difference of radialspaces between the furthest and innermost (oxygen) atoms inthe optimized structures [25] The wall thickness of SWZNTmodelled from cubic nanosheet varies between 0194 and0680 nm depending on symmetry and chirality [25] As wasobtained in CNT [36] the wall thickness has substantialinfluence on the computed Youngrsquos modulus as shown inFigure 9

From the results obtained after simulation it was notedthat the greater the wall thickness of SWZNTs the lesser thevalue of 119864 computed For a variation of 119905 from 005 nm to02 nm the value of 119864 varied from 565 to 67GPa for the(35 times 0) nanotube and from 431 to 53GPa for the (20 20)nanotubeThus the result confirmswhatwas obtained duringnanoindentation of ZNTwhere thicker arrays were found outto be softer than their thinner equivalents [19]

It has been established that for any tube wall thickness 119905

and chirality (119899 times 119898) there occurs a diameter 119889 below which

Journal of Nanomaterials 7

the NTs develop instability and experience impulsive damageor destruction [25] In order to maintain uniformity in theparametric studies of ZNT the value of 0194 was adoptedfor 119905 which is equivalent to the thickness of cubic zirconiananosheet cleaved along (111) plane [27]

4 Conclusions

In this study the tensile behavior of cubic single-walled zirco-nia nanotubes was simulated using nonlinear finite elementanalysis in order to establish geometrical parameters andmagnitude of Youngrsquos modulus The model was developedbased on the assumption that ZNTswhen subjected to load inform of strain behave as a space frame-like structuremade upof elements connected by nodesThis allows linking the forceconstants in molecular mechanics and the elastic propertiesof the beam-like element member in structural mechan-ics through the energy equivalence theory Simulations onnanotubes with different configurations were conducted bymaking one end fixed and subjecting the other end to axialtensile strain The geometry of SWZNTs was found out to bepolygonal tube not as cylindrical tube in CNTThe optimumYoungrsquos modulus of about 142GPa was obtained from zigzagSWZNT having diameter of about 615 nm Based on theresults obtained it can be concluded that the method used isan effective tool for investigating the mechanical propertiesof ZNTs and other nanotubes at less computational cost

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are grateful for the support provided by Univer-siti Teknologi PETRONAS andMalaysianMinistry of HigherEducation (MOHE) through the Long Term Research GrantScheme (LRGS) for One Baja Research Programme (Project6)

References

[1] M C Munoz S Gallego J I Beltran and J Cerda ldquoAdhesionat metal-ZrO

2interfacesrdquo Surface Science Reports vol 61 no 7

pp 303ndash344 2006[2] E J Walter S P Lewis and A M Rappe ldquoFirst principles study

of carbonmonoxide adsorption on zirconia-supported copperrdquoSurface Science vol 495 no 1-2 pp 44ndash50 2001

[3] S Meriani and C Palmonari Zirconiarsquo88 Advances in ZirconiaScience and Technology Kluwer Academic 1989

[4] V R Choudhary S Banerjee and S G Pataskar ldquoCombustionof dilute propane over transition metal-doped ZrO

2(cubic)

catalystsrdquo Applied Catalysis A General vol 253 no 1 pp 65ndash74 2003

[5] F Rohr P Hagenmuller and W van Gool Solid ElectrolytesMaterial Science Series Academic Press New York NY USA1978

[6] A Meldrum L A Boatner and R C Ewing ldquoNanocrystallinezirconia can be amorphized by ion irradiationrdquo Physical ReviewLetters vol 88 no 2 Article ID 025503 2001

[7] M Wilson U Schonberger and M W Finnis ldquoTransferableatomistic model to describe the energetics of zirconiardquo PhysicalReview B vol 54 no 13 pp 9147ndash9152 1996

[8] M Gateshki V Petkov T Hyeon J Joo M Niederberger andY Ren ldquoInterplay between the local structural disorder and thelength of structural coherence in stabilizing the cubic phase innanocrystalline ZrO

2rdquo Solid State Communications vol 138 no

6 pp 279ndash284 2006[9] Y L Soo P J Chen S H Huang et al ldquoLocal structures

surrounding Zr in nanostructurally stabilized cubic zirconiastructural origin of phase stabilityrdquo Journal of Applied Physicsvol 104 no 11 Article ID 113535 2008

[10] T Yamaguchi M Tan-No and K Tanabe ldquoZrO2as a catalyst

and catalyst supportrdquo Journal of the Japan Petroleum Institutevol 36 no 4 pp 250ndash267 1993

[11] G CaoNanostructures andNanomaterials Synthesis Propertiesand Applications Imperial College Press London UK 2004

[12] RA Evarestov Y F Zhukovskii AV Bandura and S PiskunovldquoSymmetry and models of single-wall BN and TiO

2nanotubes

with hexagonal morphologyrdquo Journal of Physical Chemistry Cvol 114 no 49 pp 21061ndash21069 2010

[13] B Wen Xing Z Chang Chun and C Wan Zhao ldquoSimulationof Youngrsquos modulus of single-walled carbon nanotubes bymolecular dynamicsrdquo Physica B CondensedMatter vol 352 no1ndash4 pp 156ndash163 2004

[14] Y Zhu C Ke and H D Espinosa ldquoExperimental techniquesfor the mechanical characterization of one-dimensional nanos-tructuresrdquo ExperimentalMechanics vol 47 no 1 pp 7ndash24 2007

[15] E W Wong P E Sheehan and C M Lieber ldquoNanobeammechanics elasticity strength and toughness of nanorods andnanotubesrdquo Science vol 277 no 5334 pp 1971ndash1975 1997

[16] M-F Yu T Kowalewski and R S Ruoff ldquoInvestigation ofthe radial deformability of individual carbon nanotubes undercontrolled indentation forcerdquo Physical Review Letters vol 85no 7 pp 1456ndash1459 2000

[17] M-F Yu O Lourie M J Dyer K Moloni T F Kelly andR S Ruoff ldquoStrength and breaking mechanism of multiwalledcarbon nanotubes under tensile loadrdquo Science vol 287 no 5453pp 637ndash640 2000

[18] T Shokuhfar G K Arumugam P A Heiden R S Yassar andC Friedrich ldquoDirect compressive measurements of individualtitaniumdioxide nanotubesrdquoACSNano vol 3 no 10 pp 3098ndash3102 2009

[19] L-N Wang and J-L Luo ldquoFabrication and mechanical proper-ties of anodized zirconium dioxide nanotubular arraysrdquo Journalof Physics D Applied Physics vol 44 no 7 Article ID 0753012011

[20] C-W Fan J-H Huang C Hwu and Y-Y Liu ldquoMechanicalproperties of single-walled carbon nanotubesmdasha finite elementapproachrdquo Advanced Materials Research vol 33ndash37 pp 937ndash942 2008

[21] C WangMultiscale modeling and simulation of nanocrystallinezirconium oxide [PhD thesis] University of Nebraska 2009

[22] E Kalfon-Cohen O Goldbart R Schreiber et al ldquoRadialcompression studies of WS

2nanotubes in the elastic regimerdquo

Journal of Vacuum Science and Technology B Microelectronicsand Nanometer Structures vol 29 no 2 Article ID 021009 2011

8 Journal of Nanomaterials

[23] T Lorenz D Teich J-O Joswig and G Seifert ldquoTheoreticalstudy of the mechanical behavior of individual TiS

2and MoS

2

nanotubesrdquo Journal of Physical Chemistry C vol 116 no 21 pp11714ndash11721 2012

[24] X Chen and G Cao ldquoA structural mechanics study of single-walled carbon nanotubes generalized from atomistic simula-tionrdquo Nanotechnology vol 17 no 4 pp 1004ndash1008 2006

[25] AV Bandura andRA Evarestov ldquoAb initio structuremodelingof ZrO

2nanosheets and single-wall nanotubesrdquo Computational

Materials Science vol 65 pp 395ndash405 2012[26] R Ansari S Rouhi M Mirnezhad and F Sadeghiyeh ldquoStudy-

ing the buckling and vibration characteristics of single-walledzinc oxide nanotubes using a nanoscale finite element modelrdquoApplied Physics A Materials Science and Processing vol 112 no3 pp 767ndash774 2013

[27] L Boldrin F Scarpa R Chowdhury and S Adhikari ldquoEffectivemechanical properties of hexagonal boron nitride nanosheetsrdquoNanotechnology vol 22 no 50 Article ID 505702 2011

[28] L Guimaraes A N Enyashin G Seifert and H A DuarteldquoStructural electronic and mechanical properties of single-walled halloysite nanotube modelsrdquo Journal of Physical Chem-istry C vol 114 no 26 pp 11358ndash11363 2010

[29] Y Mitsunori and I T Yuko ldquoSynthesis and applications ofzirconia and ruthenium oxide nanotubesrdquo in Inorganic andMetallic Nanotubular Materials T Kijima Ed pp 117ndash133Springer Berlin Germany 2010

[30] I D Muhammad M Awang O Mamat and Z B ShaarildquoFirst-principles calculations of the structural mechanical andthermodynamics properties of cubic zirconiardquoWorld Journal ofNano Science and Engineering vol 4 no 2 pp 97ndash103 2014

[31] I D Muhammad and M Awang ldquoExtracting the atomic coor-dinates and connectivity of zirconia nanotubes from PDB filesfor modelling in ANSYSrdquo Advances in Nanoparticles vol 3 pp92ndash98 2014

[32] ldquo4188 BEAM188 3-D Linear Finite Strain Beamrdquo September2014 httpmostrealskhtmlelem 55chapter4ES4-188htm

[33] RA Evarestov Y F Zhukovskii AV Bandura and S PiskunovldquoSymmetry and models of single-wall BN and TiO

2nanotubes

with hexagonal morphologyrdquoThe Journal of Physical ChemistryC vol 114 no 49 pp 21061ndash21069 2010

[34] D Dass R Prasher and R Vaid ldquoAnalytical study of unit celland molecular structures of single walled carbon nanotubesrdquoInternational Journal of Computational Engineering Researchvol 2 pp 1447ndash1457 2012

[35] K Tibbetts R Doe and G Ceder ldquoPolygonal model for layeredinorganic nanotubesrdquo Physical Review BmdashCondensed Matterand Materials Physics vol 80 no 1 Article ID 014102 2009

[36] K I Tserpes and P Papanikos ldquoFinite element modeling ofsingle-walled carbon nanotubesrdquo Composites Part B Engineer-ing vol 36 no 5 pp 468ndash477 2005

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

4 Journal of Nanomaterials

(a) (b)

Figure 3 FE models with boundary conditions for (a) armchair (20 20) and (b) zigzag (35 times 0) SWZNT

(a) (b)

Figure 4 Front side and top views for (a) 15 times 15 CNT and (b) 11 times 11 ZNT

223 Boundary Conditions Two main types of SWZNTsarmchair and zigzag were considered A fixed displacementwas applied at one end and prescribed displacement wasapplied at the other end axially as depicted in Figure 3Due to the applied displacement resultant reaction force (119865)occurs and is obtained after nonlinear simulation of forcesin all the nodes The procedure is repeated by changingthe applied displacements for different nanotubes havingdifferent configurations

Youngrsquos modulus (119864) for each nanotube after simulationwas determined using classical elasticity theory [20]

119864 =120590

120576=

119865119860119905

Δ119871119905119871119905

=119865119871119905

120587119889119905Δ119871119905

(6)

where 119865 is the resultant force on nodes at the applied end119860119905= 120587119889119905 is the cross-sectional area of the nanotube having

119889 as the diameter and 119905 as thickness and 119871119905and Δ119871

119905are

the initial length and elongation respectively in the axialdirection

In order to improve the accuracy of the simulated resultsthe nanotubes having the maximum 119864 with minimum diam-eter were selected and mesh convergence study is conductedby increasing the division of each element from 1 to 2 3 5 7and 10

3 Results and Discussion

The geometrical parameters of ZNT in relation to diameterand length depend on chirality with chiral type havingthe highest size followed by the zigzag and then armchairThe difference between two similar nanotubes in relation tolength and diameter is 17 1 26 for armchair zigzag andchiral types respectively The variations are similar to that ofboron nitride nanotubes (BNNT) and CNT [33 34] but thevalues are less than that of ZNTwhich have longer and thickeratomic bond Details of the geometrical parameters of someZNTs are stated in Table 2

The symmetry of the SWZNT is not uniform compared toCNTThe orientation depends on the chirality with armchairhaving more uniform diameter across the tube and zigzag

Journal of Nanomaterials 5

Table 2 Geometrical parameters for modeled ZNTs

Chirality (119899 times 119898) Diameter (A) Length (A) Atomsnodes Bondselements Bond length (A)Minimum Maximum Mean

5 times 5 10461 10084 820 1220 195 2263 21189 times 0 10872 10284 768 1293 1932 2364 20938 times 8 16738 10084 1312 1952 2012 2295 213614 times 0 16911 10284 1344 1988 1972 2165 203210 times 10 20923 10084 1640 2440 1978 2143 199717 times 0 20535 10284 1728 2431 1949 2103 199614 times 14 29292 10084 2296 3416 1961 2157 197224 times 0 28991 10284 2304 3432 1881 2114 196416 times 16 33476 10084 2624 3904 195 2157 196228 times 0 33823 10284 2784 4147 1873 211 1958

Mean 1873 2263 20229

050

100150200250300350400450500

00 10 20 30 40 50 60 70

Youn

grsquos m

odul

us (G

Pa)

Nanotube diameter (nm)Armchair (n times n)Zigzag (n times 0)

Figure 5 Effect of diameter on Youngrsquos modulus of SWZNTs

having variations leading to depressions across the tubeand in some cases less diameter at the ends The ZNT isnot a cylindrical tube as in CNT but it is irregular andis referred to as polygonal tube similar to other inorganicnanotubes [35] The difference in geometrical orientation ofZNT compared to CNT is illustrated in Figure 4 both havingthe same number of bondselements and approximately thesame diameter

It has been established that some mechanical propertiesof CNTs are influenced by size and chirality [20 24] Similartrend occurs in relation to ZNTs as indicated in Figure 5showing changes of Youngrsquos modulus of armchair and zigzagnanotubes with diameter The curve indicates significanteffect of diameter on the value of 119864 especially in relationto small diameters The zigzag ZNTs have higher Youngrsquosmodulus in comparison with armchair ZNTs with similardiameters but the pattern of increase is the same for allnanotubes The increase in Youngrsquos modulus as the diameterincreases is attributed to the effect of nanotube curvature[26 36]

As the nanotube diameter increases the effect of curva-ture reduces and 119864 converges to a value For a variation ofdiameter from 105 to 618 nm for the armchair SWZNTs andfrom 109 to 613 nm for the zigzag SWZNTs the values of

0

100

200

300

400

500

0 1 2 3 4 5 6 7 8 9 10 11

Youn

grsquos m

odul

us (G

Pa)

Aspect ratio (Ld)ArmchairZigzag

Figure 6 Effect of aspect ratio (119871119889) on Youngrsquos modulus ofSWZNTs

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7 8 9 10 11

Youn

grsquos m

odul

us (G

Pa)

Number of divisions in elements

Figure 7 Curve obtained from convergence test for (35 times 0)SWZNT

119864 vary from 217 to 385GPa and from 309GPa to 431GParespectively The findings indicate that Youngrsquos moduli com-puted for both armchair and zigzag SWZNTs are constant fordiameters ranging from 38 to 613 nm and are approximately380 and 427GPa for armchair and zigzag respectively

6 Journal of Nanomaterials

0

50

100

150

200

250

300

350

0 5 10 15 20 25 30

Youn

grsquos m

odul

us (G

Pa)

Length (nm)

(a)

0

50

100

150

200

250

300

350

0 2 4 6 8

Youn

grsquos m

odul

us (G

Pa)

Aspect ratio (Ld)

(b)

Figure 8 Variation of Youngrsquos modulus of (35 0) SWZNT with (a) length and (b) aspect ratio

0

100

200

300

400

500

600

0 2 4 6 8 10 12

Youn

grsquos m

odul

us (G

Pa)

1wall thickness (1nm)

0

100

200

300

400

500

600

00 05 10 15 20

Youn

grsquos m

odul

us (G

Pa)

Thickness (nm)

Figure 9 Effect of thickness on Youngrsquos modulus of (35 0) SWZNT

In contrast Youngrsquos moduli of the SWZNTs decrease asthe aspect ratio (119871119889) increases (Figure 6)This indicates thatincreasing the aspect ratio will negatively affect the structuralstability of the nanotubes as in other inorganic nanotubes[26]Thus in relation to optimumYoungrsquosmodulus minimaldiameter is required

Based on minimal diameter the SWZNT with optimalYoungrsquosmodulus was found out to be the zigzag typewith (350) configuration as indicated in Figure 5 But Youngrsquos modu-lus of SWZNTs obtained is much higher than experimentaland simulated values for inorganic nanotubes [18 19 22 23]In order to obtain a more accurate solution convergencetest was conducted using h-method by creating finer meshuntil the solution converges or approaches a particular valueFrom Figure 7 convergence occurred at 5 divisions of theelement having Youngrsquos modulus as 14164GPa compared to29796GPawhen division of the elementswas 1which is about110 reduction Dividing the elements further up to 10 unitsgave a difference of 3 fromwhat was obtained for 5 divisionsof the elements The results obtained for the convergence testof (35 0) SWZNT are shown in Figure 7

With respect to length and aspect ratio a similar patternwas observed for (35 times 0) SWZNT as illustrated in Figure 8There was tremendous increase in Youngrsquos modulus initially

until the optimum value of 297GPa was attained at 10 nmlength and aspect ratio of 2 and thereafter convergenceoccurred

As illustrated in Figure 4 the ZNT is not a cylindricaltube but polygonal tube Thus the thickness of the tubeis not assumed to be equivalent to the thickness of thebondelement as in CNT but is defined as difference of radialspaces between the furthest and innermost (oxygen) atoms inthe optimized structures [25] The wall thickness of SWZNTmodelled from cubic nanosheet varies between 0194 and0680 nm depending on symmetry and chirality [25] As wasobtained in CNT [36] the wall thickness has substantialinfluence on the computed Youngrsquos modulus as shown inFigure 9

From the results obtained after simulation it was notedthat the greater the wall thickness of SWZNTs the lesser thevalue of 119864 computed For a variation of 119905 from 005 nm to02 nm the value of 119864 varied from 565 to 67GPa for the(35 times 0) nanotube and from 431 to 53GPa for the (20 20)nanotubeThus the result confirmswhatwas obtained duringnanoindentation of ZNTwhere thicker arrays were found outto be softer than their thinner equivalents [19]

It has been established that for any tube wall thickness 119905

and chirality (119899 times 119898) there occurs a diameter 119889 below which

Journal of Nanomaterials 7

the NTs develop instability and experience impulsive damageor destruction [25] In order to maintain uniformity in theparametric studies of ZNT the value of 0194 was adoptedfor 119905 which is equivalent to the thickness of cubic zirconiananosheet cleaved along (111) plane [27]

4 Conclusions

In this study the tensile behavior of cubic single-walled zirco-nia nanotubes was simulated using nonlinear finite elementanalysis in order to establish geometrical parameters andmagnitude of Youngrsquos modulus The model was developedbased on the assumption that ZNTswhen subjected to load inform of strain behave as a space frame-like structuremade upof elements connected by nodesThis allows linking the forceconstants in molecular mechanics and the elastic propertiesof the beam-like element member in structural mechan-ics through the energy equivalence theory Simulations onnanotubes with different configurations were conducted bymaking one end fixed and subjecting the other end to axialtensile strain The geometry of SWZNTs was found out to bepolygonal tube not as cylindrical tube in CNTThe optimumYoungrsquos modulus of about 142GPa was obtained from zigzagSWZNT having diameter of about 615 nm Based on theresults obtained it can be concluded that the method used isan effective tool for investigating the mechanical propertiesof ZNTs and other nanotubes at less computational cost

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are grateful for the support provided by Univer-siti Teknologi PETRONAS andMalaysianMinistry of HigherEducation (MOHE) through the Long Term Research GrantScheme (LRGS) for One Baja Research Programme (Project6)

References

[1] M C Munoz S Gallego J I Beltran and J Cerda ldquoAdhesionat metal-ZrO

2interfacesrdquo Surface Science Reports vol 61 no 7

pp 303ndash344 2006[2] E J Walter S P Lewis and A M Rappe ldquoFirst principles study

of carbonmonoxide adsorption on zirconia-supported copperrdquoSurface Science vol 495 no 1-2 pp 44ndash50 2001

[3] S Meriani and C Palmonari Zirconiarsquo88 Advances in ZirconiaScience and Technology Kluwer Academic 1989

[4] V R Choudhary S Banerjee and S G Pataskar ldquoCombustionof dilute propane over transition metal-doped ZrO

2(cubic)

catalystsrdquo Applied Catalysis A General vol 253 no 1 pp 65ndash74 2003

[5] F Rohr P Hagenmuller and W van Gool Solid ElectrolytesMaterial Science Series Academic Press New York NY USA1978

[6] A Meldrum L A Boatner and R C Ewing ldquoNanocrystallinezirconia can be amorphized by ion irradiationrdquo Physical ReviewLetters vol 88 no 2 Article ID 025503 2001

[7] M Wilson U Schonberger and M W Finnis ldquoTransferableatomistic model to describe the energetics of zirconiardquo PhysicalReview B vol 54 no 13 pp 9147ndash9152 1996

[8] M Gateshki V Petkov T Hyeon J Joo M Niederberger andY Ren ldquoInterplay between the local structural disorder and thelength of structural coherence in stabilizing the cubic phase innanocrystalline ZrO

2rdquo Solid State Communications vol 138 no

6 pp 279ndash284 2006[9] Y L Soo P J Chen S H Huang et al ldquoLocal structures

surrounding Zr in nanostructurally stabilized cubic zirconiastructural origin of phase stabilityrdquo Journal of Applied Physicsvol 104 no 11 Article ID 113535 2008

[10] T Yamaguchi M Tan-No and K Tanabe ldquoZrO2as a catalyst

and catalyst supportrdquo Journal of the Japan Petroleum Institutevol 36 no 4 pp 250ndash267 1993

[11] G CaoNanostructures andNanomaterials Synthesis Propertiesand Applications Imperial College Press London UK 2004

[12] RA Evarestov Y F Zhukovskii AV Bandura and S PiskunovldquoSymmetry and models of single-wall BN and TiO

2nanotubes

with hexagonal morphologyrdquo Journal of Physical Chemistry Cvol 114 no 49 pp 21061ndash21069 2010

[13] B Wen Xing Z Chang Chun and C Wan Zhao ldquoSimulationof Youngrsquos modulus of single-walled carbon nanotubes bymolecular dynamicsrdquo Physica B CondensedMatter vol 352 no1ndash4 pp 156ndash163 2004

[14] Y Zhu C Ke and H D Espinosa ldquoExperimental techniquesfor the mechanical characterization of one-dimensional nanos-tructuresrdquo ExperimentalMechanics vol 47 no 1 pp 7ndash24 2007

[15] E W Wong P E Sheehan and C M Lieber ldquoNanobeammechanics elasticity strength and toughness of nanorods andnanotubesrdquo Science vol 277 no 5334 pp 1971ndash1975 1997

[16] M-F Yu T Kowalewski and R S Ruoff ldquoInvestigation ofthe radial deformability of individual carbon nanotubes undercontrolled indentation forcerdquo Physical Review Letters vol 85no 7 pp 1456ndash1459 2000

[17] M-F Yu O Lourie M J Dyer K Moloni T F Kelly andR S Ruoff ldquoStrength and breaking mechanism of multiwalledcarbon nanotubes under tensile loadrdquo Science vol 287 no 5453pp 637ndash640 2000

[18] T Shokuhfar G K Arumugam P A Heiden R S Yassar andC Friedrich ldquoDirect compressive measurements of individualtitaniumdioxide nanotubesrdquoACSNano vol 3 no 10 pp 3098ndash3102 2009

[19] L-N Wang and J-L Luo ldquoFabrication and mechanical proper-ties of anodized zirconium dioxide nanotubular arraysrdquo Journalof Physics D Applied Physics vol 44 no 7 Article ID 0753012011

[20] C-W Fan J-H Huang C Hwu and Y-Y Liu ldquoMechanicalproperties of single-walled carbon nanotubesmdasha finite elementapproachrdquo Advanced Materials Research vol 33ndash37 pp 937ndash942 2008

[21] C WangMultiscale modeling and simulation of nanocrystallinezirconium oxide [PhD thesis] University of Nebraska 2009

[22] E Kalfon-Cohen O Goldbart R Schreiber et al ldquoRadialcompression studies of WS

2nanotubes in the elastic regimerdquo

Journal of Vacuum Science and Technology B Microelectronicsand Nanometer Structures vol 29 no 2 Article ID 021009 2011

8 Journal of Nanomaterials

[23] T Lorenz D Teich J-O Joswig and G Seifert ldquoTheoreticalstudy of the mechanical behavior of individual TiS

2and MoS

2

nanotubesrdquo Journal of Physical Chemistry C vol 116 no 21 pp11714ndash11721 2012

[24] X Chen and G Cao ldquoA structural mechanics study of single-walled carbon nanotubes generalized from atomistic simula-tionrdquo Nanotechnology vol 17 no 4 pp 1004ndash1008 2006

[25] AV Bandura andRA Evarestov ldquoAb initio structuremodelingof ZrO

2nanosheets and single-wall nanotubesrdquo Computational

Materials Science vol 65 pp 395ndash405 2012[26] R Ansari S Rouhi M Mirnezhad and F Sadeghiyeh ldquoStudy-

ing the buckling and vibration characteristics of single-walledzinc oxide nanotubes using a nanoscale finite element modelrdquoApplied Physics A Materials Science and Processing vol 112 no3 pp 767ndash774 2013

[27] L Boldrin F Scarpa R Chowdhury and S Adhikari ldquoEffectivemechanical properties of hexagonal boron nitride nanosheetsrdquoNanotechnology vol 22 no 50 Article ID 505702 2011

[28] L Guimaraes A N Enyashin G Seifert and H A DuarteldquoStructural electronic and mechanical properties of single-walled halloysite nanotube modelsrdquo Journal of Physical Chem-istry C vol 114 no 26 pp 11358ndash11363 2010

[29] Y Mitsunori and I T Yuko ldquoSynthesis and applications ofzirconia and ruthenium oxide nanotubesrdquo in Inorganic andMetallic Nanotubular Materials T Kijima Ed pp 117ndash133Springer Berlin Germany 2010

[30] I D Muhammad M Awang O Mamat and Z B ShaarildquoFirst-principles calculations of the structural mechanical andthermodynamics properties of cubic zirconiardquoWorld Journal ofNano Science and Engineering vol 4 no 2 pp 97ndash103 2014

[31] I D Muhammad and M Awang ldquoExtracting the atomic coor-dinates and connectivity of zirconia nanotubes from PDB filesfor modelling in ANSYSrdquo Advances in Nanoparticles vol 3 pp92ndash98 2014

[32] ldquo4188 BEAM188 3-D Linear Finite Strain Beamrdquo September2014 httpmostrealskhtmlelem 55chapter4ES4-188htm

[33] RA Evarestov Y F Zhukovskii AV Bandura and S PiskunovldquoSymmetry and models of single-wall BN and TiO

2nanotubes

with hexagonal morphologyrdquoThe Journal of Physical ChemistryC vol 114 no 49 pp 21061ndash21069 2010

[34] D Dass R Prasher and R Vaid ldquoAnalytical study of unit celland molecular structures of single walled carbon nanotubesrdquoInternational Journal of Computational Engineering Researchvol 2 pp 1447ndash1457 2012

[35] K Tibbetts R Doe and G Ceder ldquoPolygonal model for layeredinorganic nanotubesrdquo Physical Review BmdashCondensed Matterand Materials Physics vol 80 no 1 Article ID 014102 2009

[36] K I Tserpes and P Papanikos ldquoFinite element modeling ofsingle-walled carbon nanotubesrdquo Composites Part B Engineer-ing vol 36 no 5 pp 468ndash477 2005

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Journal of Nanomaterials 5

Table 2 Geometrical parameters for modeled ZNTs

Chirality (119899 times 119898) Diameter (A) Length (A) Atomsnodes Bondselements Bond length (A)Minimum Maximum Mean

5 times 5 10461 10084 820 1220 195 2263 21189 times 0 10872 10284 768 1293 1932 2364 20938 times 8 16738 10084 1312 1952 2012 2295 213614 times 0 16911 10284 1344 1988 1972 2165 203210 times 10 20923 10084 1640 2440 1978 2143 199717 times 0 20535 10284 1728 2431 1949 2103 199614 times 14 29292 10084 2296 3416 1961 2157 197224 times 0 28991 10284 2304 3432 1881 2114 196416 times 16 33476 10084 2624 3904 195 2157 196228 times 0 33823 10284 2784 4147 1873 211 1958

Mean 1873 2263 20229

050

100150200250300350400450500

00 10 20 30 40 50 60 70

Youn

grsquos m

odul

us (G

Pa)

Nanotube diameter (nm)Armchair (n times n)Zigzag (n times 0)

Figure 5 Effect of diameter on Youngrsquos modulus of SWZNTs

having variations leading to depressions across the tubeand in some cases less diameter at the ends The ZNT isnot a cylindrical tube as in CNT but it is irregular andis referred to as polygonal tube similar to other inorganicnanotubes [35] The difference in geometrical orientation ofZNT compared to CNT is illustrated in Figure 4 both havingthe same number of bondselements and approximately thesame diameter

It has been established that some mechanical propertiesof CNTs are influenced by size and chirality [20 24] Similartrend occurs in relation to ZNTs as indicated in Figure 5showing changes of Youngrsquos modulus of armchair and zigzagnanotubes with diameter The curve indicates significanteffect of diameter on the value of 119864 especially in relationto small diameters The zigzag ZNTs have higher Youngrsquosmodulus in comparison with armchair ZNTs with similardiameters but the pattern of increase is the same for allnanotubes The increase in Youngrsquos modulus as the diameterincreases is attributed to the effect of nanotube curvature[26 36]

As the nanotube diameter increases the effect of curva-ture reduces and 119864 converges to a value For a variation ofdiameter from 105 to 618 nm for the armchair SWZNTs andfrom 109 to 613 nm for the zigzag SWZNTs the values of

0

100

200

300

400

500

0 1 2 3 4 5 6 7 8 9 10 11

Youn

grsquos m

odul

us (G

Pa)

Aspect ratio (Ld)ArmchairZigzag

Figure 6 Effect of aspect ratio (119871119889) on Youngrsquos modulus ofSWZNTs

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7 8 9 10 11

Youn

grsquos m

odul

us (G

Pa)

Number of divisions in elements

Figure 7 Curve obtained from convergence test for (35 times 0)SWZNT

119864 vary from 217 to 385GPa and from 309GPa to 431GParespectively The findings indicate that Youngrsquos moduli com-puted for both armchair and zigzag SWZNTs are constant fordiameters ranging from 38 to 613 nm and are approximately380 and 427GPa for armchair and zigzag respectively

6 Journal of Nanomaterials

0

50

100

150

200

250

300

350

0 5 10 15 20 25 30

Youn

grsquos m

odul

us (G

Pa)

Length (nm)

(a)

0

50

100

150

200

250

300

350

0 2 4 6 8

Youn

grsquos m

odul

us (G

Pa)

Aspect ratio (Ld)

(b)

Figure 8 Variation of Youngrsquos modulus of (35 0) SWZNT with (a) length and (b) aspect ratio

0

100

200

300

400

500

600

0 2 4 6 8 10 12

Youn

grsquos m

odul

us (G

Pa)

1wall thickness (1nm)

0

100

200

300

400

500

600

00 05 10 15 20

Youn

grsquos m

odul

us (G

Pa)

Thickness (nm)

Figure 9 Effect of thickness on Youngrsquos modulus of (35 0) SWZNT

In contrast Youngrsquos moduli of the SWZNTs decrease asthe aspect ratio (119871119889) increases (Figure 6)This indicates thatincreasing the aspect ratio will negatively affect the structuralstability of the nanotubes as in other inorganic nanotubes[26]Thus in relation to optimumYoungrsquosmodulus minimaldiameter is required

Based on minimal diameter the SWZNT with optimalYoungrsquosmodulus was found out to be the zigzag typewith (350) configuration as indicated in Figure 5 But Youngrsquos modu-lus of SWZNTs obtained is much higher than experimentaland simulated values for inorganic nanotubes [18 19 22 23]In order to obtain a more accurate solution convergencetest was conducted using h-method by creating finer meshuntil the solution converges or approaches a particular valueFrom Figure 7 convergence occurred at 5 divisions of theelement having Youngrsquos modulus as 14164GPa compared to29796GPawhen division of the elementswas 1which is about110 reduction Dividing the elements further up to 10 unitsgave a difference of 3 fromwhat was obtained for 5 divisionsof the elements The results obtained for the convergence testof (35 0) SWZNT are shown in Figure 7

With respect to length and aspect ratio a similar patternwas observed for (35 times 0) SWZNT as illustrated in Figure 8There was tremendous increase in Youngrsquos modulus initially

until the optimum value of 297GPa was attained at 10 nmlength and aspect ratio of 2 and thereafter convergenceoccurred

As illustrated in Figure 4 the ZNT is not a cylindricaltube but polygonal tube Thus the thickness of the tubeis not assumed to be equivalent to the thickness of thebondelement as in CNT but is defined as difference of radialspaces between the furthest and innermost (oxygen) atoms inthe optimized structures [25] The wall thickness of SWZNTmodelled from cubic nanosheet varies between 0194 and0680 nm depending on symmetry and chirality [25] As wasobtained in CNT [36] the wall thickness has substantialinfluence on the computed Youngrsquos modulus as shown inFigure 9

From the results obtained after simulation it was notedthat the greater the wall thickness of SWZNTs the lesser thevalue of 119864 computed For a variation of 119905 from 005 nm to02 nm the value of 119864 varied from 565 to 67GPa for the(35 times 0) nanotube and from 431 to 53GPa for the (20 20)nanotubeThus the result confirmswhatwas obtained duringnanoindentation of ZNTwhere thicker arrays were found outto be softer than their thinner equivalents [19]

It has been established that for any tube wall thickness 119905

and chirality (119899 times 119898) there occurs a diameter 119889 below which

Journal of Nanomaterials 7

the NTs develop instability and experience impulsive damageor destruction [25] In order to maintain uniformity in theparametric studies of ZNT the value of 0194 was adoptedfor 119905 which is equivalent to the thickness of cubic zirconiananosheet cleaved along (111) plane [27]

4 Conclusions

In this study the tensile behavior of cubic single-walled zirco-nia nanotubes was simulated using nonlinear finite elementanalysis in order to establish geometrical parameters andmagnitude of Youngrsquos modulus The model was developedbased on the assumption that ZNTswhen subjected to load inform of strain behave as a space frame-like structuremade upof elements connected by nodesThis allows linking the forceconstants in molecular mechanics and the elastic propertiesof the beam-like element member in structural mechan-ics through the energy equivalence theory Simulations onnanotubes with different configurations were conducted bymaking one end fixed and subjecting the other end to axialtensile strain The geometry of SWZNTs was found out to bepolygonal tube not as cylindrical tube in CNTThe optimumYoungrsquos modulus of about 142GPa was obtained from zigzagSWZNT having diameter of about 615 nm Based on theresults obtained it can be concluded that the method used isan effective tool for investigating the mechanical propertiesof ZNTs and other nanotubes at less computational cost

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are grateful for the support provided by Univer-siti Teknologi PETRONAS andMalaysianMinistry of HigherEducation (MOHE) through the Long Term Research GrantScheme (LRGS) for One Baja Research Programme (Project6)

References

[1] M C Munoz S Gallego J I Beltran and J Cerda ldquoAdhesionat metal-ZrO

2interfacesrdquo Surface Science Reports vol 61 no 7

pp 303ndash344 2006[2] E J Walter S P Lewis and A M Rappe ldquoFirst principles study

of carbonmonoxide adsorption on zirconia-supported copperrdquoSurface Science vol 495 no 1-2 pp 44ndash50 2001

[3] S Meriani and C Palmonari Zirconiarsquo88 Advances in ZirconiaScience and Technology Kluwer Academic 1989

[4] V R Choudhary S Banerjee and S G Pataskar ldquoCombustionof dilute propane over transition metal-doped ZrO

2(cubic)

catalystsrdquo Applied Catalysis A General vol 253 no 1 pp 65ndash74 2003

[5] F Rohr P Hagenmuller and W van Gool Solid ElectrolytesMaterial Science Series Academic Press New York NY USA1978

[6] A Meldrum L A Boatner and R C Ewing ldquoNanocrystallinezirconia can be amorphized by ion irradiationrdquo Physical ReviewLetters vol 88 no 2 Article ID 025503 2001

[7] M Wilson U Schonberger and M W Finnis ldquoTransferableatomistic model to describe the energetics of zirconiardquo PhysicalReview B vol 54 no 13 pp 9147ndash9152 1996

[8] M Gateshki V Petkov T Hyeon J Joo M Niederberger andY Ren ldquoInterplay between the local structural disorder and thelength of structural coherence in stabilizing the cubic phase innanocrystalline ZrO

2rdquo Solid State Communications vol 138 no

6 pp 279ndash284 2006[9] Y L Soo P J Chen S H Huang et al ldquoLocal structures

surrounding Zr in nanostructurally stabilized cubic zirconiastructural origin of phase stabilityrdquo Journal of Applied Physicsvol 104 no 11 Article ID 113535 2008

[10] T Yamaguchi M Tan-No and K Tanabe ldquoZrO2as a catalyst

and catalyst supportrdquo Journal of the Japan Petroleum Institutevol 36 no 4 pp 250ndash267 1993

[11] G CaoNanostructures andNanomaterials Synthesis Propertiesand Applications Imperial College Press London UK 2004

[12] RA Evarestov Y F Zhukovskii AV Bandura and S PiskunovldquoSymmetry and models of single-wall BN and TiO

2nanotubes

with hexagonal morphologyrdquo Journal of Physical Chemistry Cvol 114 no 49 pp 21061ndash21069 2010

[13] B Wen Xing Z Chang Chun and C Wan Zhao ldquoSimulationof Youngrsquos modulus of single-walled carbon nanotubes bymolecular dynamicsrdquo Physica B CondensedMatter vol 352 no1ndash4 pp 156ndash163 2004

[14] Y Zhu C Ke and H D Espinosa ldquoExperimental techniquesfor the mechanical characterization of one-dimensional nanos-tructuresrdquo ExperimentalMechanics vol 47 no 1 pp 7ndash24 2007

[15] E W Wong P E Sheehan and C M Lieber ldquoNanobeammechanics elasticity strength and toughness of nanorods andnanotubesrdquo Science vol 277 no 5334 pp 1971ndash1975 1997

[16] M-F Yu T Kowalewski and R S Ruoff ldquoInvestigation ofthe radial deformability of individual carbon nanotubes undercontrolled indentation forcerdquo Physical Review Letters vol 85no 7 pp 1456ndash1459 2000

[17] M-F Yu O Lourie M J Dyer K Moloni T F Kelly andR S Ruoff ldquoStrength and breaking mechanism of multiwalledcarbon nanotubes under tensile loadrdquo Science vol 287 no 5453pp 637ndash640 2000

[18] T Shokuhfar G K Arumugam P A Heiden R S Yassar andC Friedrich ldquoDirect compressive measurements of individualtitaniumdioxide nanotubesrdquoACSNano vol 3 no 10 pp 3098ndash3102 2009

[19] L-N Wang and J-L Luo ldquoFabrication and mechanical proper-ties of anodized zirconium dioxide nanotubular arraysrdquo Journalof Physics D Applied Physics vol 44 no 7 Article ID 0753012011

[20] C-W Fan J-H Huang C Hwu and Y-Y Liu ldquoMechanicalproperties of single-walled carbon nanotubesmdasha finite elementapproachrdquo Advanced Materials Research vol 33ndash37 pp 937ndash942 2008

[21] C WangMultiscale modeling and simulation of nanocrystallinezirconium oxide [PhD thesis] University of Nebraska 2009

[22] E Kalfon-Cohen O Goldbart R Schreiber et al ldquoRadialcompression studies of WS

2nanotubes in the elastic regimerdquo

Journal of Vacuum Science and Technology B Microelectronicsand Nanometer Structures vol 29 no 2 Article ID 021009 2011

8 Journal of Nanomaterials

[23] T Lorenz D Teich J-O Joswig and G Seifert ldquoTheoreticalstudy of the mechanical behavior of individual TiS

2and MoS

2

nanotubesrdquo Journal of Physical Chemistry C vol 116 no 21 pp11714ndash11721 2012

[24] X Chen and G Cao ldquoA structural mechanics study of single-walled carbon nanotubes generalized from atomistic simula-tionrdquo Nanotechnology vol 17 no 4 pp 1004ndash1008 2006

[25] AV Bandura andRA Evarestov ldquoAb initio structuremodelingof ZrO

2nanosheets and single-wall nanotubesrdquo Computational

Materials Science vol 65 pp 395ndash405 2012[26] R Ansari S Rouhi M Mirnezhad and F Sadeghiyeh ldquoStudy-

ing the buckling and vibration characteristics of single-walledzinc oxide nanotubes using a nanoscale finite element modelrdquoApplied Physics A Materials Science and Processing vol 112 no3 pp 767ndash774 2013

[27] L Boldrin F Scarpa R Chowdhury and S Adhikari ldquoEffectivemechanical properties of hexagonal boron nitride nanosheetsrdquoNanotechnology vol 22 no 50 Article ID 505702 2011

[28] L Guimaraes A N Enyashin G Seifert and H A DuarteldquoStructural electronic and mechanical properties of single-walled halloysite nanotube modelsrdquo Journal of Physical Chem-istry C vol 114 no 26 pp 11358ndash11363 2010

[29] Y Mitsunori and I T Yuko ldquoSynthesis and applications ofzirconia and ruthenium oxide nanotubesrdquo in Inorganic andMetallic Nanotubular Materials T Kijima Ed pp 117ndash133Springer Berlin Germany 2010

[30] I D Muhammad M Awang O Mamat and Z B ShaarildquoFirst-principles calculations of the structural mechanical andthermodynamics properties of cubic zirconiardquoWorld Journal ofNano Science and Engineering vol 4 no 2 pp 97ndash103 2014

[31] I D Muhammad and M Awang ldquoExtracting the atomic coor-dinates and connectivity of zirconia nanotubes from PDB filesfor modelling in ANSYSrdquo Advances in Nanoparticles vol 3 pp92ndash98 2014

[32] ldquo4188 BEAM188 3-D Linear Finite Strain Beamrdquo September2014 httpmostrealskhtmlelem 55chapter4ES4-188htm

[33] RA Evarestov Y F Zhukovskii AV Bandura and S PiskunovldquoSymmetry and models of single-wall BN and TiO

2nanotubes

with hexagonal morphologyrdquoThe Journal of Physical ChemistryC vol 114 no 49 pp 21061ndash21069 2010

[34] D Dass R Prasher and R Vaid ldquoAnalytical study of unit celland molecular structures of single walled carbon nanotubesrdquoInternational Journal of Computational Engineering Researchvol 2 pp 1447ndash1457 2012

[35] K Tibbetts R Doe and G Ceder ldquoPolygonal model for layeredinorganic nanotubesrdquo Physical Review BmdashCondensed Matterand Materials Physics vol 80 no 1 Article ID 014102 2009

[36] K I Tserpes and P Papanikos ldquoFinite element modeling ofsingle-walled carbon nanotubesrdquo Composites Part B Engineer-ing vol 36 no 5 pp 468ndash477 2005

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

6 Journal of Nanomaterials

0

50

100

150

200

250

300

350

0 5 10 15 20 25 30

Youn

grsquos m

odul

us (G

Pa)

Length (nm)

(a)

0

50

100

150

200

250

300

350

0 2 4 6 8

Youn

grsquos m

odul

us (G

Pa)

Aspect ratio (Ld)

(b)

Figure 8 Variation of Youngrsquos modulus of (35 0) SWZNT with (a) length and (b) aspect ratio

0

100

200

300

400

500

600

0 2 4 6 8 10 12

Youn

grsquos m

odul

us (G

Pa)

1wall thickness (1nm)

0

100

200

300

400

500

600

00 05 10 15 20

Youn

grsquos m

odul

us (G

Pa)

Thickness (nm)

Figure 9 Effect of thickness on Youngrsquos modulus of (35 0) SWZNT

In contrast Youngrsquos moduli of the SWZNTs decrease asthe aspect ratio (119871119889) increases (Figure 6)This indicates thatincreasing the aspect ratio will negatively affect the structuralstability of the nanotubes as in other inorganic nanotubes[26]Thus in relation to optimumYoungrsquosmodulus minimaldiameter is required

Based on minimal diameter the SWZNT with optimalYoungrsquosmodulus was found out to be the zigzag typewith (350) configuration as indicated in Figure 5 But Youngrsquos modu-lus of SWZNTs obtained is much higher than experimentaland simulated values for inorganic nanotubes [18 19 22 23]In order to obtain a more accurate solution convergencetest was conducted using h-method by creating finer meshuntil the solution converges or approaches a particular valueFrom Figure 7 convergence occurred at 5 divisions of theelement having Youngrsquos modulus as 14164GPa compared to29796GPawhen division of the elementswas 1which is about110 reduction Dividing the elements further up to 10 unitsgave a difference of 3 fromwhat was obtained for 5 divisionsof the elements The results obtained for the convergence testof (35 0) SWZNT are shown in Figure 7

With respect to length and aspect ratio a similar patternwas observed for (35 times 0) SWZNT as illustrated in Figure 8There was tremendous increase in Youngrsquos modulus initially

until the optimum value of 297GPa was attained at 10 nmlength and aspect ratio of 2 and thereafter convergenceoccurred

As illustrated in Figure 4 the ZNT is not a cylindricaltube but polygonal tube Thus the thickness of the tubeis not assumed to be equivalent to the thickness of thebondelement as in CNT but is defined as difference of radialspaces between the furthest and innermost (oxygen) atoms inthe optimized structures [25] The wall thickness of SWZNTmodelled from cubic nanosheet varies between 0194 and0680 nm depending on symmetry and chirality [25] As wasobtained in CNT [36] the wall thickness has substantialinfluence on the computed Youngrsquos modulus as shown inFigure 9

From the results obtained after simulation it was notedthat the greater the wall thickness of SWZNTs the lesser thevalue of 119864 computed For a variation of 119905 from 005 nm to02 nm the value of 119864 varied from 565 to 67GPa for the(35 times 0) nanotube and from 431 to 53GPa for the (20 20)nanotubeThus the result confirmswhatwas obtained duringnanoindentation of ZNTwhere thicker arrays were found outto be softer than their thinner equivalents [19]

It has been established that for any tube wall thickness 119905

and chirality (119899 times 119898) there occurs a diameter 119889 below which

Journal of Nanomaterials 7

the NTs develop instability and experience impulsive damageor destruction [25] In order to maintain uniformity in theparametric studies of ZNT the value of 0194 was adoptedfor 119905 which is equivalent to the thickness of cubic zirconiananosheet cleaved along (111) plane [27]

4 Conclusions

In this study the tensile behavior of cubic single-walled zirco-nia nanotubes was simulated using nonlinear finite elementanalysis in order to establish geometrical parameters andmagnitude of Youngrsquos modulus The model was developedbased on the assumption that ZNTswhen subjected to load inform of strain behave as a space frame-like structuremade upof elements connected by nodesThis allows linking the forceconstants in molecular mechanics and the elastic propertiesof the beam-like element member in structural mechan-ics through the energy equivalence theory Simulations onnanotubes with different configurations were conducted bymaking one end fixed and subjecting the other end to axialtensile strain The geometry of SWZNTs was found out to bepolygonal tube not as cylindrical tube in CNTThe optimumYoungrsquos modulus of about 142GPa was obtained from zigzagSWZNT having diameter of about 615 nm Based on theresults obtained it can be concluded that the method used isan effective tool for investigating the mechanical propertiesof ZNTs and other nanotubes at less computational cost

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are grateful for the support provided by Univer-siti Teknologi PETRONAS andMalaysianMinistry of HigherEducation (MOHE) through the Long Term Research GrantScheme (LRGS) for One Baja Research Programme (Project6)

References

[1] M C Munoz S Gallego J I Beltran and J Cerda ldquoAdhesionat metal-ZrO

2interfacesrdquo Surface Science Reports vol 61 no 7

pp 303ndash344 2006[2] E J Walter S P Lewis and A M Rappe ldquoFirst principles study

of carbonmonoxide adsorption on zirconia-supported copperrdquoSurface Science vol 495 no 1-2 pp 44ndash50 2001

[3] S Meriani and C Palmonari Zirconiarsquo88 Advances in ZirconiaScience and Technology Kluwer Academic 1989

[4] V R Choudhary S Banerjee and S G Pataskar ldquoCombustionof dilute propane over transition metal-doped ZrO

2(cubic)

catalystsrdquo Applied Catalysis A General vol 253 no 1 pp 65ndash74 2003

[5] F Rohr P Hagenmuller and W van Gool Solid ElectrolytesMaterial Science Series Academic Press New York NY USA1978

[6] A Meldrum L A Boatner and R C Ewing ldquoNanocrystallinezirconia can be amorphized by ion irradiationrdquo Physical ReviewLetters vol 88 no 2 Article ID 025503 2001

[7] M Wilson U Schonberger and M W Finnis ldquoTransferableatomistic model to describe the energetics of zirconiardquo PhysicalReview B vol 54 no 13 pp 9147ndash9152 1996

[8] M Gateshki V Petkov T Hyeon J Joo M Niederberger andY Ren ldquoInterplay between the local structural disorder and thelength of structural coherence in stabilizing the cubic phase innanocrystalline ZrO

2rdquo Solid State Communications vol 138 no

6 pp 279ndash284 2006[9] Y L Soo P J Chen S H Huang et al ldquoLocal structures

surrounding Zr in nanostructurally stabilized cubic zirconiastructural origin of phase stabilityrdquo Journal of Applied Physicsvol 104 no 11 Article ID 113535 2008

[10] T Yamaguchi M Tan-No and K Tanabe ldquoZrO2as a catalyst

and catalyst supportrdquo Journal of the Japan Petroleum Institutevol 36 no 4 pp 250ndash267 1993

[11] G CaoNanostructures andNanomaterials Synthesis Propertiesand Applications Imperial College Press London UK 2004

[12] RA Evarestov Y F Zhukovskii AV Bandura and S PiskunovldquoSymmetry and models of single-wall BN and TiO

2nanotubes

with hexagonal morphologyrdquo Journal of Physical Chemistry Cvol 114 no 49 pp 21061ndash21069 2010

[13] B Wen Xing Z Chang Chun and C Wan Zhao ldquoSimulationof Youngrsquos modulus of single-walled carbon nanotubes bymolecular dynamicsrdquo Physica B CondensedMatter vol 352 no1ndash4 pp 156ndash163 2004

[14] Y Zhu C Ke and H D Espinosa ldquoExperimental techniquesfor the mechanical characterization of one-dimensional nanos-tructuresrdquo ExperimentalMechanics vol 47 no 1 pp 7ndash24 2007

[15] E W Wong P E Sheehan and C M Lieber ldquoNanobeammechanics elasticity strength and toughness of nanorods andnanotubesrdquo Science vol 277 no 5334 pp 1971ndash1975 1997

[16] M-F Yu T Kowalewski and R S Ruoff ldquoInvestigation ofthe radial deformability of individual carbon nanotubes undercontrolled indentation forcerdquo Physical Review Letters vol 85no 7 pp 1456ndash1459 2000

[17] M-F Yu O Lourie M J Dyer K Moloni T F Kelly andR S Ruoff ldquoStrength and breaking mechanism of multiwalledcarbon nanotubes under tensile loadrdquo Science vol 287 no 5453pp 637ndash640 2000

[18] T Shokuhfar G K Arumugam P A Heiden R S Yassar andC Friedrich ldquoDirect compressive measurements of individualtitaniumdioxide nanotubesrdquoACSNano vol 3 no 10 pp 3098ndash3102 2009

[19] L-N Wang and J-L Luo ldquoFabrication and mechanical proper-ties of anodized zirconium dioxide nanotubular arraysrdquo Journalof Physics D Applied Physics vol 44 no 7 Article ID 0753012011

[20] C-W Fan J-H Huang C Hwu and Y-Y Liu ldquoMechanicalproperties of single-walled carbon nanotubesmdasha finite elementapproachrdquo Advanced Materials Research vol 33ndash37 pp 937ndash942 2008

[21] C WangMultiscale modeling and simulation of nanocrystallinezirconium oxide [PhD thesis] University of Nebraska 2009

[22] E Kalfon-Cohen O Goldbart R Schreiber et al ldquoRadialcompression studies of WS

2nanotubes in the elastic regimerdquo

Journal of Vacuum Science and Technology B Microelectronicsand Nanometer Structures vol 29 no 2 Article ID 021009 2011

8 Journal of Nanomaterials

[23] T Lorenz D Teich J-O Joswig and G Seifert ldquoTheoreticalstudy of the mechanical behavior of individual TiS

2and MoS

2

nanotubesrdquo Journal of Physical Chemistry C vol 116 no 21 pp11714ndash11721 2012

[24] X Chen and G Cao ldquoA structural mechanics study of single-walled carbon nanotubes generalized from atomistic simula-tionrdquo Nanotechnology vol 17 no 4 pp 1004ndash1008 2006

[25] AV Bandura andRA Evarestov ldquoAb initio structuremodelingof ZrO

2nanosheets and single-wall nanotubesrdquo Computational

Materials Science vol 65 pp 395ndash405 2012[26] R Ansari S Rouhi M Mirnezhad and F Sadeghiyeh ldquoStudy-

ing the buckling and vibration characteristics of single-walledzinc oxide nanotubes using a nanoscale finite element modelrdquoApplied Physics A Materials Science and Processing vol 112 no3 pp 767ndash774 2013

[27] L Boldrin F Scarpa R Chowdhury and S Adhikari ldquoEffectivemechanical properties of hexagonal boron nitride nanosheetsrdquoNanotechnology vol 22 no 50 Article ID 505702 2011

[28] L Guimaraes A N Enyashin G Seifert and H A DuarteldquoStructural electronic and mechanical properties of single-walled halloysite nanotube modelsrdquo Journal of Physical Chem-istry C vol 114 no 26 pp 11358ndash11363 2010

[29] Y Mitsunori and I T Yuko ldquoSynthesis and applications ofzirconia and ruthenium oxide nanotubesrdquo in Inorganic andMetallic Nanotubular Materials T Kijima Ed pp 117ndash133Springer Berlin Germany 2010

[30] I D Muhammad M Awang O Mamat and Z B ShaarildquoFirst-principles calculations of the structural mechanical andthermodynamics properties of cubic zirconiardquoWorld Journal ofNano Science and Engineering vol 4 no 2 pp 97ndash103 2014

[31] I D Muhammad and M Awang ldquoExtracting the atomic coor-dinates and connectivity of zirconia nanotubes from PDB filesfor modelling in ANSYSrdquo Advances in Nanoparticles vol 3 pp92ndash98 2014

[32] ldquo4188 BEAM188 3-D Linear Finite Strain Beamrdquo September2014 httpmostrealskhtmlelem 55chapter4ES4-188htm

[33] RA Evarestov Y F Zhukovskii AV Bandura and S PiskunovldquoSymmetry and models of single-wall BN and TiO

2nanotubes

with hexagonal morphologyrdquoThe Journal of Physical ChemistryC vol 114 no 49 pp 21061ndash21069 2010

[34] D Dass R Prasher and R Vaid ldquoAnalytical study of unit celland molecular structures of single walled carbon nanotubesrdquoInternational Journal of Computational Engineering Researchvol 2 pp 1447ndash1457 2012

[35] K Tibbetts R Doe and G Ceder ldquoPolygonal model for layeredinorganic nanotubesrdquo Physical Review BmdashCondensed Matterand Materials Physics vol 80 no 1 Article ID 014102 2009

[36] K I Tserpes and P Papanikos ldquoFinite element modeling ofsingle-walled carbon nanotubesrdquo Composites Part B Engineer-ing vol 36 no 5 pp 468ndash477 2005

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Journal of Nanomaterials 7

the NTs develop instability and experience impulsive damageor destruction [25] In order to maintain uniformity in theparametric studies of ZNT the value of 0194 was adoptedfor 119905 which is equivalent to the thickness of cubic zirconiananosheet cleaved along (111) plane [27]

4 Conclusions

In this study the tensile behavior of cubic single-walled zirco-nia nanotubes was simulated using nonlinear finite elementanalysis in order to establish geometrical parameters andmagnitude of Youngrsquos modulus The model was developedbased on the assumption that ZNTswhen subjected to load inform of strain behave as a space frame-like structuremade upof elements connected by nodesThis allows linking the forceconstants in molecular mechanics and the elastic propertiesof the beam-like element member in structural mechan-ics through the energy equivalence theory Simulations onnanotubes with different configurations were conducted bymaking one end fixed and subjecting the other end to axialtensile strain The geometry of SWZNTs was found out to bepolygonal tube not as cylindrical tube in CNTThe optimumYoungrsquos modulus of about 142GPa was obtained from zigzagSWZNT having diameter of about 615 nm Based on theresults obtained it can be concluded that the method used isan effective tool for investigating the mechanical propertiesof ZNTs and other nanotubes at less computational cost

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are grateful for the support provided by Univer-siti Teknologi PETRONAS andMalaysianMinistry of HigherEducation (MOHE) through the Long Term Research GrantScheme (LRGS) for One Baja Research Programme (Project6)

References

[1] M C Munoz S Gallego J I Beltran and J Cerda ldquoAdhesionat metal-ZrO

2interfacesrdquo Surface Science Reports vol 61 no 7

pp 303ndash344 2006[2] E J Walter S P Lewis and A M Rappe ldquoFirst principles study

of carbonmonoxide adsorption on zirconia-supported copperrdquoSurface Science vol 495 no 1-2 pp 44ndash50 2001

[3] S Meriani and C Palmonari Zirconiarsquo88 Advances in ZirconiaScience and Technology Kluwer Academic 1989

[4] V R Choudhary S Banerjee and S G Pataskar ldquoCombustionof dilute propane over transition metal-doped ZrO

2(cubic)

catalystsrdquo Applied Catalysis A General vol 253 no 1 pp 65ndash74 2003

[5] F Rohr P Hagenmuller and W van Gool Solid ElectrolytesMaterial Science Series Academic Press New York NY USA1978

[6] A Meldrum L A Boatner and R C Ewing ldquoNanocrystallinezirconia can be amorphized by ion irradiationrdquo Physical ReviewLetters vol 88 no 2 Article ID 025503 2001

[7] M Wilson U Schonberger and M W Finnis ldquoTransferableatomistic model to describe the energetics of zirconiardquo PhysicalReview B vol 54 no 13 pp 9147ndash9152 1996

[8] M Gateshki V Petkov T Hyeon J Joo M Niederberger andY Ren ldquoInterplay between the local structural disorder and thelength of structural coherence in stabilizing the cubic phase innanocrystalline ZrO

2rdquo Solid State Communications vol 138 no

6 pp 279ndash284 2006[9] Y L Soo P J Chen S H Huang et al ldquoLocal structures

surrounding Zr in nanostructurally stabilized cubic zirconiastructural origin of phase stabilityrdquo Journal of Applied Physicsvol 104 no 11 Article ID 113535 2008

[10] T Yamaguchi M Tan-No and K Tanabe ldquoZrO2as a catalyst

and catalyst supportrdquo Journal of the Japan Petroleum Institutevol 36 no 4 pp 250ndash267 1993

[11] G CaoNanostructures andNanomaterials Synthesis Propertiesand Applications Imperial College Press London UK 2004

[12] RA Evarestov Y F Zhukovskii AV Bandura and S PiskunovldquoSymmetry and models of single-wall BN and TiO

2nanotubes

with hexagonal morphologyrdquo Journal of Physical Chemistry Cvol 114 no 49 pp 21061ndash21069 2010

[13] B Wen Xing Z Chang Chun and C Wan Zhao ldquoSimulationof Youngrsquos modulus of single-walled carbon nanotubes bymolecular dynamicsrdquo Physica B CondensedMatter vol 352 no1ndash4 pp 156ndash163 2004

[14] Y Zhu C Ke and H D Espinosa ldquoExperimental techniquesfor the mechanical characterization of one-dimensional nanos-tructuresrdquo ExperimentalMechanics vol 47 no 1 pp 7ndash24 2007

[15] E W Wong P E Sheehan and C M Lieber ldquoNanobeammechanics elasticity strength and toughness of nanorods andnanotubesrdquo Science vol 277 no 5334 pp 1971ndash1975 1997

[16] M-F Yu T Kowalewski and R S Ruoff ldquoInvestigation ofthe radial deformability of individual carbon nanotubes undercontrolled indentation forcerdquo Physical Review Letters vol 85no 7 pp 1456ndash1459 2000

[17] M-F Yu O Lourie M J Dyer K Moloni T F Kelly andR S Ruoff ldquoStrength and breaking mechanism of multiwalledcarbon nanotubes under tensile loadrdquo Science vol 287 no 5453pp 637ndash640 2000

[18] T Shokuhfar G K Arumugam P A Heiden R S Yassar andC Friedrich ldquoDirect compressive measurements of individualtitaniumdioxide nanotubesrdquoACSNano vol 3 no 10 pp 3098ndash3102 2009

[19] L-N Wang and J-L Luo ldquoFabrication and mechanical proper-ties of anodized zirconium dioxide nanotubular arraysrdquo Journalof Physics D Applied Physics vol 44 no 7 Article ID 0753012011

[20] C-W Fan J-H Huang C Hwu and Y-Y Liu ldquoMechanicalproperties of single-walled carbon nanotubesmdasha finite elementapproachrdquo Advanced Materials Research vol 33ndash37 pp 937ndash942 2008

[21] C WangMultiscale modeling and simulation of nanocrystallinezirconium oxide [PhD thesis] University of Nebraska 2009

[22] E Kalfon-Cohen O Goldbart R Schreiber et al ldquoRadialcompression studies of WS

2nanotubes in the elastic regimerdquo

Journal of Vacuum Science and Technology B Microelectronicsand Nanometer Structures vol 29 no 2 Article ID 021009 2011

8 Journal of Nanomaterials

[23] T Lorenz D Teich J-O Joswig and G Seifert ldquoTheoreticalstudy of the mechanical behavior of individual TiS

2and MoS

2

nanotubesrdquo Journal of Physical Chemistry C vol 116 no 21 pp11714ndash11721 2012

[24] X Chen and G Cao ldquoA structural mechanics study of single-walled carbon nanotubes generalized from atomistic simula-tionrdquo Nanotechnology vol 17 no 4 pp 1004ndash1008 2006

[25] AV Bandura andRA Evarestov ldquoAb initio structuremodelingof ZrO

2nanosheets and single-wall nanotubesrdquo Computational

Materials Science vol 65 pp 395ndash405 2012[26] R Ansari S Rouhi M Mirnezhad and F Sadeghiyeh ldquoStudy-

ing the buckling and vibration characteristics of single-walledzinc oxide nanotubes using a nanoscale finite element modelrdquoApplied Physics A Materials Science and Processing vol 112 no3 pp 767ndash774 2013

[27] L Boldrin F Scarpa R Chowdhury and S Adhikari ldquoEffectivemechanical properties of hexagonal boron nitride nanosheetsrdquoNanotechnology vol 22 no 50 Article ID 505702 2011

[28] L Guimaraes A N Enyashin G Seifert and H A DuarteldquoStructural electronic and mechanical properties of single-walled halloysite nanotube modelsrdquo Journal of Physical Chem-istry C vol 114 no 26 pp 11358ndash11363 2010

[29] Y Mitsunori and I T Yuko ldquoSynthesis and applications ofzirconia and ruthenium oxide nanotubesrdquo in Inorganic andMetallic Nanotubular Materials T Kijima Ed pp 117ndash133Springer Berlin Germany 2010

[30] I D Muhammad M Awang O Mamat and Z B ShaarildquoFirst-principles calculations of the structural mechanical andthermodynamics properties of cubic zirconiardquoWorld Journal ofNano Science and Engineering vol 4 no 2 pp 97ndash103 2014

[31] I D Muhammad and M Awang ldquoExtracting the atomic coor-dinates and connectivity of zirconia nanotubes from PDB filesfor modelling in ANSYSrdquo Advances in Nanoparticles vol 3 pp92ndash98 2014

[32] ldquo4188 BEAM188 3-D Linear Finite Strain Beamrdquo September2014 httpmostrealskhtmlelem 55chapter4ES4-188htm

[33] RA Evarestov Y F Zhukovskii AV Bandura and S PiskunovldquoSymmetry and models of single-wall BN and TiO

2nanotubes

with hexagonal morphologyrdquoThe Journal of Physical ChemistryC vol 114 no 49 pp 21061ndash21069 2010

[34] D Dass R Prasher and R Vaid ldquoAnalytical study of unit celland molecular structures of single walled carbon nanotubesrdquoInternational Journal of Computational Engineering Researchvol 2 pp 1447ndash1457 2012

[35] K Tibbetts R Doe and G Ceder ldquoPolygonal model for layeredinorganic nanotubesrdquo Physical Review BmdashCondensed Matterand Materials Physics vol 80 no 1 Article ID 014102 2009

[36] K I Tserpes and P Papanikos ldquoFinite element modeling ofsingle-walled carbon nanotubesrdquo Composites Part B Engineer-ing vol 36 no 5 pp 468ndash477 2005

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

8 Journal of Nanomaterials

[23] T Lorenz D Teich J-O Joswig and G Seifert ldquoTheoreticalstudy of the mechanical behavior of individual TiS

2and MoS

2

nanotubesrdquo Journal of Physical Chemistry C vol 116 no 21 pp11714ndash11721 2012

[24] X Chen and G Cao ldquoA structural mechanics study of single-walled carbon nanotubes generalized from atomistic simula-tionrdquo Nanotechnology vol 17 no 4 pp 1004ndash1008 2006

[25] AV Bandura andRA Evarestov ldquoAb initio structuremodelingof ZrO

2nanosheets and single-wall nanotubesrdquo Computational

Materials Science vol 65 pp 395ndash405 2012[26] R Ansari S Rouhi M Mirnezhad and F Sadeghiyeh ldquoStudy-

ing the buckling and vibration characteristics of single-walledzinc oxide nanotubes using a nanoscale finite element modelrdquoApplied Physics A Materials Science and Processing vol 112 no3 pp 767ndash774 2013

[27] L Boldrin F Scarpa R Chowdhury and S Adhikari ldquoEffectivemechanical properties of hexagonal boron nitride nanosheetsrdquoNanotechnology vol 22 no 50 Article ID 505702 2011

[28] L Guimaraes A N Enyashin G Seifert and H A DuarteldquoStructural electronic and mechanical properties of single-walled halloysite nanotube modelsrdquo Journal of Physical Chem-istry C vol 114 no 26 pp 11358ndash11363 2010

[29] Y Mitsunori and I T Yuko ldquoSynthesis and applications ofzirconia and ruthenium oxide nanotubesrdquo in Inorganic andMetallic Nanotubular Materials T Kijima Ed pp 117ndash133Springer Berlin Germany 2010

[30] I D Muhammad M Awang O Mamat and Z B ShaarildquoFirst-principles calculations of the structural mechanical andthermodynamics properties of cubic zirconiardquoWorld Journal ofNano Science and Engineering vol 4 no 2 pp 97ndash103 2014

[31] I D Muhammad and M Awang ldquoExtracting the atomic coor-dinates and connectivity of zirconia nanotubes from PDB filesfor modelling in ANSYSrdquo Advances in Nanoparticles vol 3 pp92ndash98 2014

[32] ldquo4188 BEAM188 3-D Linear Finite Strain Beamrdquo September2014 httpmostrealskhtmlelem 55chapter4ES4-188htm

[33] RA Evarestov Y F Zhukovskii AV Bandura and S PiskunovldquoSymmetry and models of single-wall BN and TiO

2nanotubes

with hexagonal morphologyrdquoThe Journal of Physical ChemistryC vol 114 no 49 pp 21061ndash21069 2010

[34] D Dass R Prasher and R Vaid ldquoAnalytical study of unit celland molecular structures of single walled carbon nanotubesrdquoInternational Journal of Computational Engineering Researchvol 2 pp 1447ndash1457 2012

[35] K Tibbetts R Doe and G Ceder ldquoPolygonal model for layeredinorganic nanotubesrdquo Physical Review BmdashCondensed Matterand Materials Physics vol 80 no 1 Article ID 014102 2009

[36] K I Tserpes and P Papanikos ldquoFinite element modeling ofsingle-walled carbon nanotubesrdquo Composites Part B Engineer-ing vol 36 no 5 pp 468ndash477 2005

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CorrosionInternational Journal of

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Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials