Effect of synthesis process on the Young's modulus of titanate nanowire

Phys. Status Solidi A 207, No. 2, 327–333 (2010) / DOI 10.1002/pssa.200925327 p s sa

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applications and materials science

Effect of synthesis process on the
Young’s modulus of titanate nanowire
Ming Chang*,1,2, Juti Rani Deka1, and Feng Cheng Chang1

1 Department of Mechanical Engineering, Chung Yuan Christian University, Chungli, Taiwan2 State Key Lab of Digital Manufacturing Equipment & Technology, Huazhong University of Science & Technology, Wuhan, China

Received 22 June 2009, revised 31 July 2009, accepted 20 August 2009

Published online 14 September 2009

PACS 62.20.dq, 62.20.mq, 62.23.Hj, 68.37.Hk, 81.16.Be

* Corresponding author: e-mail [email protected], Phone: þ88 63 2654303, Fax: þ88 63 2654399

Nanocrystalline materials have attracted a great deal of

attention because of their intriguing size-/shape-dependent

properties. Titanate nanowires have been synthesized from

titania (TiO2) nanoparticles using conventional hydrothermal

process. Young’s moduli of as-prepared titanate nanowires

have been determined in situ from the buckling instability of the

nanowires due to application of axial compressive load using a

nanomanipulator inside a scanning electron microscope. Based

on Euler’s buckling model, the Young’s moduli of the

nanowires are determined to be 32� 11 GPa. The obtained

Young’s moduli have been compared to that of the titanate

nanowires prepared with microwave hydrothermal process to

study the effect of synthesis process on the mechanical behavior

of nanomaterials. The prolonged holding time of a conventional

hydrothermal process helps in the significant enhancement of

the Young’s modulus of nanowire in comparison to that

prepared with microwave hydrothermal process.

� 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction One-dimensional (1D) nanostruc-tured materials have attracted considerable attention due totheir unusual electronic, optical, mechanical properties, andpotential nanodevice applications [1, 2]. The extremelysmall physical dimension of the nanostructure implies highsensitivity to external perturbation, which promises its use insensing and micro-/nano-electromechanical systems. Tita-nates are being extensively studied due to their potentialtechnological applications, such as photocatalysts, fuel-cellelectrolytes, and cation exchangers, for the treatment ofradioactive liquid waste [3–6], ceramic capacitors, asreinforcing agents of plastic, and as oxygen electrodes forpotentiometric gas sensors [7–9]. Many of these applicationsrequire high surface and interfacial areas therefore it isadvantageous to have titanate in the form of nanoparticles ornanowires. Stimulated by these interesting properties andwide application possibilities, researchers have made greatefforts in synthesizing 1D titania (TiO2)/titanate nano-structures utilizing a variety of techniques such as conven-tional and microwave hydrothermal treatment [10, 11],board mold [12], acoustic-chemical [13] and self-assemblymethods. Thermal treatment of TiO2 nanoparticles in NaOHproduces anatase TiO2 nanostructure with large surface area.The hydrothermal process is a powerful method forobtaining TiO2-based nanotubes or nanowires and can

produce large amounts of material in a single step at lowcost. In addition to crystalline anatase TiO2 nanostructures,some titanate structures are generally found to be theconstituents of the nanostructure. Titanate nanowires arewide-band semiconductor, which is a useful feature fornanodevice application. The morphology and microstructureof titanate nanostructures are highly dependent on thesynthesis conditions and the preparation method. Thesealkali-metal titanates have monoclinic structure with almostthe same lattice constant [14]. Titanates with a high alkali-metal contents are open-layered structures and those withlow contents are tunnel structures [15]. The ion-exchangecharacteristic is an important property of these layeredmaterials, which is very useful in Li-ion battery and otherclean energy areas [16]. Titanates with higher alkali-metalcontents can be used as cation exchangers and catalystsbecause of their distinctive intercalation ability and catalyticactivity. On the other hand, alkali-metal titanates with lowalkali-metal contents exhibit high insulating, mechanicaland chemical ability. In recent years, more interest has beengiven to the optical and electronic characterization of titanatenanowires [17, 18] because of their wide applicationpossibility, but only a little attention has been given to theirmechanical properties [19]. In order to integrate 1D titanatenanomaterials into functional nanodevices, it is essential to


328 M. Chang et al.: Effect of synthesis process on the Young’s modulus of titanate nanowirep

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Figure 1 XRD pattern of the hydrothermally synthesized titanatenanowires.

Figure 2 SEM image of titanate nanowires.

Figure 3 TEM image of a titanate nanowire.

measure the mechanical and electromechanical properties ofindividual nanostructures precisely.

Young’s moduli of conventional hydrothermally pre-pared titanate nanowires have been determined in thisinvestigation to fully utilize the basic and technologicaladvantages offered by its small dimensions. The determi-nation of Young’s modulus permits in-depth knowledge ofmaterial deformation in the nanostructure that helps in thedesign and fabrication of next-generation sensors andactuators, coupling of electrical and mechanical propertiesat the nanoscale and multiphysics modeling. The mechanicalcharacterization of the nanowire is challenging as themanipulation of this extremely small structure is verytedious. The measurement has been carried out inside ascanning electron microscope (SEM) using a home-mademanipulator of nanometer resolution. Young’s modulus isdetermined from the buckling instability of the nanowire dueto the application of axial compressive load.

2 Synthesis of titanate nanowires and morpho-logical and microstructural characterizations Thestarting materials are anatase TiO2 nanopowder (99.7%,Aldrich); NaOH (98.5%, Mallinckrodt Chemicals); and HCl(37%, Riedel-de Haen). In a typical preparation procedure,1 g anatase TiO2 white powders are placed into a Teflon-lined autoclave of 50 ml capacity. The autoclave is filled with10 M NaOH aqueous solution up to 80% of the total volume,sealed into a stainless steel tank and maintained at 200 8C for24 h without shaking or stirring during heating. After theautoclave naturally cools to room temperature, the producthas been sequentially washed with 1 M HCl solution for atleast 2 h followed by washing with distilled water andabsolute ethanol for several times until the washing watershowed its pH less than 7. Acid treatment can decrease theNa:H ratio in the titanates by exchanging Naþ atoms locatedbetween the layers with Hþ and remove the Na ions from theprecipitate [20]. During these ion-exchange processes, thebasic structural features of the layered materials remainunchanged. The samples are dried in an oven for 6 h at 70 8Cand white, soft fibrous powders are obtained. Due to thegrowth of particles on thermal treatment, very thick layeredstructures occur that naturally decompose into wires afterwashing with HCl, which could induce a structuralrearrangement.

The crystallographic structures of the final product arecharacterized by X-ray diffraction (XRD). Using a PAN-alytical X’Pert PRO X-ray powder diffractometer withCuKa radiation (u�2u) scans are performed. The morphol-ogies of the nanowires have been studied using SEM (JEOL-JSM 6300) and high-resolution transmission electron micro-scopy (HRTEM, JEOL 2010). TEM samples are prepared bydispersing the powder in ethanol by ultrasonic treatmentfollowed by dropping onto a porous carbon film supported ona copper grid and dried.

The XRD pattern of the finally extracted white powder isshown in Fig. 1. The pattern reveals the overall crystallinestructure and phase purity of the nanowires. All the relatively


sharp peaks positioned at 2u¼ 118, 258, 378, and 48.58 couldbe indexed as characteristic sodium titanate peaks.

Figure 2 shows the typical SEM image of as-preparedtitanate nanowires. It reveals that the morphology of theparticle changes to wire-like structure on hydrothermaltreatment. The nanowires are ample in quantity and quiteclean, with no contamination attached to their surfaces. Theparticles change from spherical to columnar shape, indicat-ing increase in aspect ratio of the particles on heating.

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Phys. Status Solidi A 207, No. 2 (2010) 329

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Figure 4 (online colour at: www.pss-a.com) SEM images of(a) rectangular, (b) rhombus, and (c) elliptical cross-sectionednanowires.

Figure 3 is a low-magnification TEM image of a typicalsample, synthesized by a hydrothermal process at 200 8C.The features of the nanowires range from 80 to 300 nm indiameters and from 500 nm up to several micrometers inlengths. The areas near the ends of the nanowires exhibitrectangular structure in general, but some irregular shapessuch as rhombus and elliptical are also observed. Figure 4a–cshows SEM images (FESEM, Hitachi 4100) of therectangular, rhombus, and elliptical cross-sections of thenanowires ends.

3 Buckling instability and determination ofYoung’s modulus In situ mechanical characterizationof nanomaterials is a critical task due to their extremely smallstructure. Well-controlled lateral and longitudinal motionsare necessary for manipulation of nanostructure in order to

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measure their mechanical properties precisely. Tensile,bend, resonance, and compression tests are usually per-formed inside atomic force microscope (AFM), TEM, andSEM for mechanical characterization of nanowires. Amongthese techniques, compression test is adopted in this researchas it is a simple way to get the Young’s modulus of ananostructure without damage. Two different modes forstructure collapse, yielding and buckling, are generallyobserved in a compression tests. Yielding mode dominatesthe structure collapse for the short column. At large length todiameter ratio, the failure of the nanowire changes to abuckling mode due to the instability of the structure. As thecolumn buckles, instead of remaining straight, the nanowirebecomes sharply curved. Young’s modulus is determinedfrom the buckling instability of the nanostructure due toapplication of an axial compressive load.

3.1 Experimental setup and manipulation ofnanowire Nanomanipulation system has been designedand fabricated for in situ mechanical characterization ofnanostructure by assembling stages and picomotors that fitthe vacuum cavity of the JEOL-JSM 6300 SEM of resolution3.5 nm at 30 kV. The manipulator is designed with small size,low cost, wide translation range, reasonable precision, andrapid assembly in mind. The in situ technique within theSEM permits continuous high-resolution imaging during thetest. The designed nanomanipulator has two independentstages (X,Y) and (Z, u), each capable of nanometer-resolutionlinear motion and single-axis 3608 rotational motion. Threelinear and one rotational sigma stage-driven picomotors(8301-V and 8341-V, New focus) that is placed on the top ofthe Z-stage provide the linear and rotational motions,respectively. Two AFM tips FPC10 AIST and BS-Tap300Alare fixed to the rotating picomotor and X–Y stage,respectively, to hold the nanostructure for mechanicalcharacterization. The co-efficients of elasticities of the tipsare measured using the mechanical resonance method [21–23] and determined to be approximately 0.066 and 40 N m�1,respectively. The details about the determination of theelasticity coefficient of tips, design, and fabrication of thenanomanipulator are given elsewhere [11]. A soft tip is usedto manipulate the nanostructure from the source and acted asa load sensor that plays the critical part in the determinationof Young’s modulus.

3.2 In situ Young’s modulus measurement Asingle titanate nanowire is manipulated from the source andits ends are clamped to rigid and soft cantilevers by anelectron-beam-induced deposition (EBID) method to meas-ure the Young’s modulus. The distance between the two endsof the nanowire is used to characterize the buckling behavior.Continuously increasing axial loads are applied to thenanowire until it buckles by moving the stage containing therigid cantilever gradually upward using the attachedpicomotor. A schematic representation of the compressiontest is given in Fig. 5. The stress distribution at the ends of thenanowire due to the axial applied load depends upon the way



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Figure 5 Schematic representation of compression test.

in which the axial load is actually applied. The long axis ofthe nanowire is aligned along the axis of compressiveloading to uniformly distribute the load over the ends. It isensured that the nanowire buckles perpendicular to thedirection of the electron beam in order to measure thedisplacement precisely so that there is no hidden displace-ment along the electron-beam direction that may alter theactual measurement results.

The axial load deflects the soft cantilever that is used assensor to measure the force–displacement response of asingle nanowire. The applied load (P) on the nanowire isdetermined by multiplying the soft cantilever deflection (d)with its coefficient of elasticity (k). The loading process isrecorded in a series of SEM images to determine the loadapplied on the nanowire as there is no equipment availablefor direct measurement. A series of SEM images of bucklingof a nanowire is given in Fig. 6. From the sequence of theimages, the soft cantilever’s deflection (d) is computed.Equivalent numbers of pixels in the scale observed in theSEM image are considered and from that, the thickness of


one pixel is determined. By observing the change in numberof pixels at each loading, the deflection (d) of the cantileverhas been determined.

Figure 7 shows a curve that presents the applied load, asmeasured from the deflection of the cantilever, versus thedisplacement (d) that is characterized by the distancebetween the two ends of the nanowire. The curve representsthe highly flexible behavior of the nanowire under the actionof an axial load. The high flexibility is attributed to the lowdimension of the nanostructure. Also, in slender columnsmembrane stiffness is much greater than the bendingstiffness and large membrane strain can be stored with smalldeformation. When buckling occurs, comparatively largebending deformation is required to absorb the releasedmembrane strain energies [24].

Critical load Pcr, defined as the applied load higher thanwhich a nonlinear deformation occurs is determined from thebuckling instability of the nanowire. It is well known that thenanowire buckles about the principal axis of the cross-section having least moment of inertia when the load appliedis more than critical load, i.e., a slight increase in the appliedload above the critical load can buckle the nanowire. Thebehavior of an ideal column compressed by an axial load Pmay be summarized as follows: if P<Pcr, the nanowire is instable equilibrium in the straight position as shown in Fig. 6a;if P¼Pcr, the nanowire is in a neutral equilibrium in eitherthe straight or a slightly bent position; if P>Pcr, thenanowire is in unstable equilibrium in the straight position,and hence is buckled as shown in Fig. 6d. Slenderness ratio(L/r), L, being length and r, radius of gyration, of the columnplays an important role in the adoption of a particular modelto calculate the Young’s modulus. It is a measure of the

Figure 6 (a–d) A series of SEM images show-ing buckling of a titanate nanowire.

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Figure 7 Applied load–displacement curve.

Figure 8 SEM image of a ring manipulated from a nanowire.

columns flexibility and serves to classify the columns aslong, intermediate, or short. The radius of gyration iscalculated from the following relation:

Tab

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r ¼ffiffiffiI

A

r, (1)

where I is the moment of inertia of the column’s cross-sectional area A. Buckling occurs about the axis where theslenderness ratio has its maximum value. Slenderness ratiosof the nanowires synthesized in this study belong to thelong-column category and stress in the column remainselastic. Euler’s equation for a straight column undercompression is adopted to determine the buckling load.Euler’s formula is expressed as [25]

Pcr ¼Cp2EI

L2, (2)

where E is the Young’s modulus, and C is the end-conditionconstant. Even though the two ends of the nanowire are fixedto the AFM tips by EBID during the test, the displacementand the rotation of the nanowire end toward the soft tipcannot be resisted like the rigid tip end. It is thereforeconsidered as a fixed-pinned model for which the end-condition constant is 2. The end-condition constant can beobtained either from the distance between two adjacentinflection points or the distance between adjacent peak and

le 1 Critical stresses, critical strains, and Young’s moduli of ti

wire width (nm) height (nm) critical stress, sc

647 259 3.05297 255 12.50211 192 7.28573 265 5.09573 265 15.83448 336 2.09

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valley of the buckling shape. The buckling occurred in thedirection of the least thickness as the end conditions are thesame in both width and height directions. Prior to thecompressive test the nanowire is imaged with a fieldemission SEM to measure its width and height. For all thetitanate nanowires, the compressive loads buckle thenanowire but cannot fracture it even under extremely largedeformation. The low dimension of a nanowire makes ithighly flexible and therefore can be manipulated intorequired shapes using the cantilevered tip. Figure 8 showsthe SEM image of a nanowire that is manipulated into a ring.

The critical buckling stress,scr, and the critical bucklingstrain, er, can be determined from the critical load of thenanowire. For a Euler buckling column, the critical bucklingstrain is given by er¼scr/E, and the critical buckling stressscr¼Pcr/A. Young’s moduli, buckling stresses, and bucklingstrains of several titanate nanowires measured from thebuckling instability are presented in Table 1. During thecompression test it is observed that a nanowire of diameter650 nm is unstable at a load of 0.5814mN, which is thecritical load of the nanowire, and its corresponding bucklingenergy is calculated to be 2.47� 10�13 J.

4 Results and discussion The average Young’smodulus of the conventional hydrothermally synthesizedtitanate nanowire is measured to be 32� 11 GPa and found tobe independent of its diameter. As the surface to volume ratioincreases in a nanostructure, the number of surface atomsincreases as well, resulting in more unbalanced surfaceatoms than those locked in the lattice. These atoms affect the

tanate nanowires.

r (MPa) critical strain, er (%) Young’s modulus (GPa)

21 14.2480 15.4423 30.4212 40.1633 47.825 42.05



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dislocation generation and motion in a different way from thelocked atoms inside the lattice, and influence the mechanicalbehavior of the nanowires. The small dimensions ofnanowires are almost defect-free, which facilitate in thedramatic increase in flexibility of the nanowire. The 33%variation in the measured Young’s modulus can be ascribedto the uncertainty in the measurements of loads, lengths,widths, and heights of the nanowires. Error in the measure-ment of Young’s modulus is given by

� 20

DE

E¼ DP

Pþ 2DL

Lþ Db

bþ 3

Dh

h: (3)

Equation (3) indicates that the major sources of errors inthe estimation of Young’s modulus are the load, displace-ment, length, and cross-section of the nanowire. The mostrelevant error may come from the measurements of thenanowires lengths and cross-sections. Because of the finitediameter of the SEM electron beam and the bright edges ofthe SEM images, the length and cross-sections of thenanowire might be measured as being too large. These couldresult in an underestimation of the Young’s modulus,especially since the nanowire length comes in squared andheight enters as the third power in the calculation of Young’smodulus. Error in the estimation of force is due to uncertaintyin the measurement of the cantilever’s deflection, which isalso limited by the pixel resolution of the SEM image. Thismeasurement must rely on SEM that provides a projected 2Dimage and therefore can monitor the misalignment in the x–yplane, but cannot detect slight height mismatch in the zdirection. Height mismatch between the two ends of ananowire attached to the AFM tip leads to lower load andhigher strain, which consequently affect the measuredYoung’s modulus of the nanowire. To minimize the errorin measured load and length, the deflection of the soft tip andthe distance between the two tips are determined verycarefully for each nanowire. The restrictions at the nanowireends, ratio of the length of the wire to its diameter, and thedeflection may collectively contribute to the deviation ofmeasured Young’s modulus. The geometric sizes and shapesof the nanowires may also affect the measured Young’smodulus. The different shapes of the cross-sections of thenanowires as shown in Fig. 4a–c affect the moment of inertia,which may change the Young’s modulus.

Young’s modulus of hydrothermally synthesized tita-nate nanowire is measured to be approximately 45% higherthan that of a microwave hydrothermally synthesizednanowire [11]. Employing the same measurement approach,the average Young’s modulus of titanate nanowire synthe-sized with the microwave hydrothermal method is computedto be approximately 16� 2 GPa. There may be severalpossible reasons for this enhancement of the Young’smodulus of the conventional hydrothermally preparednanowires over use of the microwave hydrothermal process.The obvious improvement in the Young’s modulus is mostlikely a result of relatively higher temperature and longerholding time to promote crystallization in the synthesis of the

10 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

nanowire with the conventional hydrothermal method. Theslow crystallization process allows growth of a nanowirewith minimal crystalline defects and more organizedmolecular stacking with extended growth along the nanowirelong axis. The prolonged holding time helps in the buildingup on seeds and that is not a spontaneously generatednucleation site.

Nanowire geometry, crystallographic orientation, andsynthesis process significantly affect the experimental result.The crystallization kinetics of the formation of titanatenanowire under conventional hydrothermal and microwavehydrothermal conditions is a function of reaction temper-ature, time, and reactants concentration. As the nanowire isformed more slowly in comparison to the microwavehydrothermal process, the crystals are larger, which in turnincreases the strength of the nanowire making it harder tobreak. Moreover, different material fabrication methods maylead to different atomic defect sizes and types.

Although microwave heating offers many advantagesover conventional autoclave heating, including rapid heatingto crystallization temperature, homogeneous nucleation, andfast supersaturation by the rapid dissolution of precipitatedhydroxides [11], which leads to lower crystallizationtemperatures and shorter crystallization times, but theYoung’s modulus of a nanowire prepared with a conven-tional hydrothermal method is measured to be higher.Because of its advantages such as simple procedure andlow cost, it would be desirable to use a conventionalhydrothermal process to synthesize titanate nanowire forapplication in nanomechanical devices.

5 Conclusions Fabrication and experimental obser-vations of uniaxial compression instabilities in titanatenanowire is reported in this investigation. Young’s modulusof individual titanate nanowire is determined from thebuckling of nanowire due to application of axial compressiveload. This in situ experiment inside an SEM ensures accuracyof the experimental procedures, which is challenging tosupervise at the nanoscale. Based on Euler’s buckling model,the Young’s moduli of the titanate nanowires prepared withthe conventional hydrothermal method are estimated to be32� 11 GPa and found to be 45% higher than that preparedwith a microwave hydrothermal method. The longer holdingtime increases the Young’s modulus of the titanate nanowiresignificantly, which is the advantage of using this methodcompared to the microwave hydrothermal method. It isobserved that the preparation technique has a significanteffect on the mechanical properties of the nanostructure. Thebuckling energies, critical stress and strain are alsodetermined from the buckling of the nanowire. The nano-wires of differing diameters studied here exhibit noobservable difference in crystal quality or surface chemistry,which may be the reason for the diameter-independentYoung’s modulus. Apart from in situ investigation ofmechanical property of nanostructure, the nanomanipulationsystem can manipulate these materials to fabricate variousnanodevices such as lines, nets, channels, rings, and gratings

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by controlling the suitable nanomaterials. It can beconcluded that the manipulator is particularly suitable formechanical property measurement of nanostructures andnanomachining due to its nanoscale spatial resolution,intrinsic long manipulating distance, no special requirementfor samples, and large working areas.

Acknowledgements The authors gratefully acknowledgethe support of Specific Research Fields in Chung Yuan ChristianUniversity project under grant CYCU-97-CR-ME and the NationalScience Council of Taiwan under project number 96-2221-E-033-042-MY3.

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Effect of synthesis process on the Young's modulus of titanate nanowire

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