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Research Papers

# Elastic Modulus Measurements on Large Diameter Nanowires Using a Nano-Assembled PlatformOPEN ACCESS

[+] Author and Article Information
Naveen K. R. Palapati

Department of Mechanical and
Nuclear Engineering,
Virginia Commonwealth University,
401 West Main Street,
Richmond, VA 23284
e-mail: palapatinkr@vcu.edu

Department of Mechanical
and Nuclear Engineering,
Virginia Commonwealth University,
401 West Main Street,
Richmond, VA 23284
e-mail: mutha@vcu.edu

Yujie Zhu

Department of Chemical and
Biomolecular Engineering,
University of Maryland,
College Park, MD 20742
e-mail: yzhu@umd.edu

Chunsheng Wang

Department of Chemical and
Biomolecular Engineering,
University of Maryland,
College Park, MD 20742
e-mail: cswang@umd.edu

Arunkumar Subramanian

Department of Mechanical and
Nuclear Engineering,
Virginia Commonwealth University,
401 West Main Street,
Richmond, VA 23284
e-mail: asubramanian@vcu.edu

1Corresponding author.

Manuscript received March 6, 2014; final manuscript received July 15, 2014; published online August 19, 2014. Assoc. Editor: Hsiao-Ying Shadow Huang.

J. Nanotechnol. Eng. Med 5(2), 021001 (Aug 19, 2014) (6 pages) Paper No: NANO-14-1020; doi: 10.1115/1.4028045 History: Received March 06, 2014; Revised July 15, 2014

## Abstract

This paper presents atomic force spectroscopy (AFM) results from large diameter nanowires (NWs), which range in radius from 150 nm to 300 nm, within a nano-assembled platform. The nanomechanical platform is constructed by assembling single NWs across pairs of gold nano-electrodes using dielectrophoresis and contains a short, suspended segment of the NW (in air) between the assembly electrodes. Atomic force microscope (AFM) force spectroscopy measurements are obtained by indenting the NW within this suspended segment and result in deformation of the NW involving a combination of both, bending and nano-indentation modes. This paper demonstrates the measurement technique using lithium iron phosphate NWs as a model system and presents a finite element model to extract the Young's modulus from nanomechanical data. The estimated Young's modulus of this material, which is an electrode material system of interest for next-generation lithium-ion batteries, was found to be diameter dependent and was observed to range in values between 100 MPa and 575 MPa.

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## Introduction

Characterization and optimization of mechanical properties of nanomaterials are critical to assess their suitability for a number of emerging application areas of nanotechnology such as nano-electromechanical systems, sensors, scanning probe microscopy tips, and lithium-ion batteries [1-4]. The extraction of mechanical properties of a material system, irrespective of its scale, involves two components: (1) the controlled and precise application of a force (in terms of its magnitude, direction, and location of impact) and (2) an accurate measurement of the material deformation/displacement, which is caused by the applied external force. In the case of materials and structures with nanoscopic dimensions, approaches that entail the in situ application of the force stimuli within electron or scanning probe microscopes have commonly been employed over the past decade to extract mechanical properties such as Young's modulus, hardness, and tensile strength [5-16]. In the case of electron microscopes, the force stimuli are typically applied using AFM cantilevers or nanorobotic manipulation systems, and the electron micrographs are employed to obtain the resulting material deformation/displacement. Examples of previous reports on this approach include the measurement of critical buckling loads in carbon nanotubes and the estimation of Young's modulus in nanomaterials [5-7].

Another widely used technique to characterize the mechanical behavior of nanomaterials involves force spectroscopy performed with an AFM in the contact mode [8-16]. In this method, a known force is exerted on the sample by pushing a precisely calibrated AFM tip (in terms of its mechanical stiffness) against it and the resulting material deflection/deformation is estimated from the associated movement of the piezosystem that controls the sample stage height. There are two sample configurations in which AFM-based force spectroscopy is commonly performed on low-dimensional nanosystems: (1) three-point bending mode [8-10] where the NW is suspended between mechanical anchors at its ends in order to form a doubly clamped beam and the AFM tip is pushed against the NW at its midlengths to deform it. This configuration is employed with high-aspect ratio, small-diameter (<100 nm) NWs, and (2) nano-indentation mode [11-16], in which the NW is placed firmly on top of a substrate and the AFM tip pushes the NW surface to induce radial deformation in it. This approach is more common with low-aspect ratio, large diameter NW systems (>100 nm). The nano-indentation mode entails two regions of mechanical contact—one between the AFM and the NW and the second between the NW and the substrate. The extraction of mechanical properties, such as Young's modulus, relies on precise modeling of the two contact interfaces and also introduces additional uncertainties due to the possibility of slippage between the NW/substrate, which has been observed in some of the previous reports [11].

In this paper, we will present a new device configuration for indentation-based atomic force spectroscopy of large diameter NWs in which the NW is suspended in air in the region between mechanical anchors. One consideration in this structure is the small aspect ratio of the suspended NW segment, which is a direct consequence of the large diameter of our NWs. In this method, the NW deformation will involve contributions from both, bending as well as probe-induced localized material deformation. Another attribute is that the impact of the NW/substrate contact interface and the resultant substrate deformations is minimized since it is not located directly below the point of contact with the indentation tip. Furthermore, this device is fabricated using dielectrophoretic (DEP) nano-assembly based integration of NWs on to the nanomechanical anchors and lends itself to obtain information from arrays of NW devices, which are constructed in parallel on a silicon chip.

We employ lithium iron phosphate NWs (LiFePO4 NWs) as a model system for this investigation [17]. LiFePO4 is a commonly used cathode material for lithium-ion batteries due to its low cost, nontoxicity, and intrinsic structural/chemical stability [18]. With recent interest in the use of nanomaterials in battery electrodes due to their potential for high storage capacity at exceptional charge/discharge rates, NWs of LiFePO4 are attracting a lot of attention [17]. Even though mechanical degradation of battery electrodes is one of the critical failure modes in Li-ion systems, there has been very little understanding so far on the mechanical properties of battery materials. Very recently, there was a computational estimation of the Young's modulus of bulk-scale LixMnO2 in the delithiated state and an experimental study of the mechanical properties of silicon NWs under electrochemical lithiation [19,20]. There has also been an estimation of elastic constants of olivine LiFePO4 from first principles calculations in a previous study [21]. In our paper, we will leverage AFM force spectroscopy plots and fit these data to computational models in order to extract the Young's modulus of LiFePO4 NWs from experimental measurements for the first time.

## Materials and Methods

###### Synthesis and Characterization of LiFePO4 NWs.

LiFePO4 wires were synthesized from a previously reported electrospinning method [17]. All chemicals were purchased from Sigma Aldrich and directly used in the experiments without any further treatment. Briefly, stoichiometric LiH2PO4 and Fe(NO3)3·9H2O were dissolved into 10 ml distilled water with a concentration of 0.2 mol/l. Then, 0.45 g poly(ethylene oxide) with molecular weight of 600,000 g/mol was added into the solution with vigorous stirring for 2 h. The obtained mixture was loaded into a plastic syringe connected to a stainless steel needle with an inner diameter of 0.008 in. (McMaster-Carr). The plastic syringe was then connected to a syringe pump, which controlled the flow rate of the solution to be 6 μl/min during the electrospinning process. A constant voltage of 15 kV was applied between the needle and the fiber collector, which was a grounded stainless steel plate, to initiate the process. The distance between the needle and the fiber collector was set to be 15 cm during the whole process. The as-collected fibers were carbonized in a tube furnace at 600 °C for 5 h under Ar atmosphere with a heating rate of 2 °C/min to obtain carbon-coated LiFePO4 fibers.

###### Device Fabrication.

The steps involved in the electrode nanofabrication process and assembly of LiFePO4 NWs are shown in Fig. 1. In this process, we work with silicon chips that have a thickness of 500 μm and measure 4 mm × 6 mm in lateral dimensions. The silicon chips contain a 500 nm layer of silicon nitride on top for electrical isolation. This is followed by the definition of 75 nm thick gold electrodes. The electrode design consists of an array of electrode pairs, which measure 5 μm in width and are separated by either a 400 nm or an 800 nm gap. The electrodes are defined by electron-beam lithography and lift-off. A 15 nm layer of chromium is used to improve the adhesion of gold to the oxide. Next, LiFePO4 NWs are deposited onto the electrodes by AC dielectrophoresis [22,23]. For this step, the LiFePO4 NWs are suspended and sonicated in ethanol to insure their homogeneity in solution (i.e., to achieve a uniform concentration of NWs in the ethanol suspension). The chip is then immersed in a reservoir containing this suspension and an AC electric field is applied with a high frequency function generator. After the deposition is complete, the chip is removed from the reservoir and rinsed in clean ethanol. Finally, it is blown dry with a nitrogen gun.

###### Atomic Force Spectroscopy.

We perform static force versus deformation measurements (using a VEECO Icon AFM) to extract the Young's modulus of individual LiFePO4 NWs. In this experiment, the NW is indented with the AFM tip at its midlengths within the suspended segment. This is accomplished by moving AFM sample stage against the cantilever tip and monitoring the tip deflection (ztip) as a function of stage piezo movement (zpiezo). The mechanical stiffness of the AFM cantilever (ktip) is precisely estimated from its geometry and AFM frequency tuning plots using Sader's method [24]. As a result, the force exerted by the AFM tip on the NW is computed as Display Formula

(1)$FNW=Ftip=ktip×ztip$

The deformation of the NW is given as Display Formula

(2)$ZNW=Zpiezo-Ztip$

From Eqs. (1) and (2), we plot the force versus deformation curve of the individual LiFePO4 NW.

## Results and Discussion

The crystal structure of the LiFePO4 NWs was characterized using powder X-ray diffraction (XRD) on a D8 Advanced with LynxEye and SolX (Bruker AXS, WI) using a CuKα radiation source operated at 40 kV and 40 mA. The morphology of the NWs was characterized using both Hitachi SU-70 analytical ultra-high resolution scanning electron microscopy (SEM) and JEOL 2100F field emission transmission electron microscopy (TEM). The results of these characterization techniques are summarized in Fig. 2. As shown by the SEM image in Fig. 2(a), the carbonized LiFePO4 has a long and fibrous morphology. Figures 2(b) and 2(c) show the TEM and high resolution TEM (HRTEM) images of one fiber, in which the fine lattice fringe of LiFePO4 and the surface-coated amorphous carbon can be clearly observed. XRD pattern in Fig. 2(d) shows that the LiFePO4 fibers are crystalline without any detectable impurity, consistent with the HRTEM image.

The NWs from the powder sample were then assembled on to gold nano-electrodes using dielectrophoresis, as explained in the Materials and Methods Section. By controlling deposition parameters, such as NW suspension concentration, applied AC bias voltage/frequency and deposition time, we were able to determine the conditions for realizing single NW assembly across nano-electrode pairs [22,23]. For this material system, the parameters employed are an AC voltage of 6 Vp-p at 1 kHz for a deposition time of 120 s. The results from this assembly process are shown in Fig. 3. Panels (a) and (b) show SEM images of representative NWs, while panels (c) and (d) show the corresponding tapping mode AFM images of these NWs. From the AFM images, it is clear that the NWs are flat and fully suspended in air in the region between the electrodes. Furthermore, the diameters of the NWs are determined from section plots, which were obtained from the tapping mode AFM images.

After a determination of NW diameters from AFM scans, we perform force spectroscopy measurements by indenting the NWs at the midlengths of their suspended segments using contact-mode AFM imaging. The force versus deformation plots for the NW samples are extracted from the raw AFM data using the method described in the Materials and Methods Section. A representative plot of the force versus deformation data is shown in Fig. 4(a). As can be seen from this measurement, the material exhibits a linear elastic behavior within its deformation regime. It is important to note that two types of deformations occur within the NW: (1) beamlike bending of the entire NW in the suspended region and (2) indentation-induced, localized deformation of the NW surface at the region of contact with the AFM tip. This is due to the large diameter NW being suspended across mechanical anchors (i.e., gold assembly electrodes) such that the aspect ratio of the suspended NW segment is small (<3:1). Thus, the measurement comprises a combination of NW deformations observed in both, the nano-indentation and three-point bending modes, which have previously been reported for NW force spectroscopy measurements [8-16].

In order to understand the contribution of each of these deformation modes to the overall NW deformation and to extract the Young's modulus of the LiFePO4 NWs, we have performed finite element simulations using Ansys software. In previous reports involving nano-indentation measurements with NWs, different computational methods have been employed to extract the modulus of elasticity and material hardness. These include the Oliver–Pharr method [9,13] and finite element modeling [8,16,25]. Of these techniques, the Oliver–Pharr method assumes a flat sample surface and overestimates the tip-surface contact area and the NW Young's modulus due to the rounded surface of NWs [8,14]. Hence, we have employed a finite element model in Ansys software to compute the Young's modulus of NWs. The NW was meshed using the SOLID285 element, which is a 3D, four-node tetrahedral element and the AFM tip force was exerted as a point load on the top surface of the NW (shown schematically in Fig. 4(b)). This assumption is justified by the use of sharp AFM tips, with a tip radius specification of 10 nm, which is much smaller as compared to the diameter of the NWs (>300 nm). In this finite element model, the deformation of the AFM tip at the point of contact was assumed to be negligible and the NW was assumed to be isotropic in its material properties. The side view of the deformed profile of the NW, as estimated by the finite element model, is shown in Fig. 4(b). This contour plot clearly shows the bending of the NW in the suspended region. Also, the 3D-view of the NW (Fig. 4(c)) clearly indicates the localized deformation induced on the surface of the NW at the point of contact with the AFM tip. This combined mode of bending and nano-indentation induced surface deformation in large diameter NWs, which are employed in our effort, is thus verified by our finite element models.

In addition, we extract the Young's modulus of the NWs from the finite element model in order to fit the experimentally observed force versus deformation plots with a linear fit. For example, for the NW discussed in Figs. 4(a)4(c), which had a radius of 168 nm and a suspended length of 400 nm, the estimated value of the Young's modulus was 113 MPa. The linear force versus deformation plot based on the estimated value of the Young's modulus is shown in Fig. 4(a) along with the experimental data (in black circles) and it can clearly be seen that this linear fit represents an accurate description of the force-deflection relationship of the NW beam in the elastic regime. This linear behavior also contrasts with the nonlinear behavior observed in smaller diameter NWs (<50 nm) due to the stress-stiffening effects at large deformations in these one-dimensional elements [10]. Another interesting aspect that emerges from our measurements is the dependence of Young's modulus on the diameter of the NWs. We find that the modulus of elasticity is on the order of ∼100–120 MPa for NWs with radii ranging from 168 to 182 nm. On the other hand, with larger NWs (that extend between 228 nm and 255 nm in radius), the Young's modulus was estimated to approximately be twice in magnitude, in the 220–255 MPa range (with one NW exhibiting a significantly higher modulus of 575 MPa). With previous measurements on the Young's modulus of different material systems, there have been observations of both dependence and independence of the elastic modulus on the NW diameter [12,26]. This indicates that this size dependence varies from one material system to another. In the case of LiFePO4 NWs, the diameter dependence of properties, such as ion diffusivity and phase transformation mechanisms, is well known [27-29], pointing to the influence of size on the material's other properties as well. The influence of NW's crystallinity (single versus polycrystalline and orientation) and its resultant impact on the Young's modulus of the material can also be not ruled out.

## Conclusions

We have presented a new device architecture based on DEP nano-assembly for performing atomic force spectroscopy on large diameter NWs. This assembled device has a large diameter NW bridging metallic nano-electrodes, which also serve as its mechanical anchors, such that the interelectrode NW segment is flat and fully suspended in air. The indentation of the NW at its suspended midlength region results in a combined deformation mode, which consists of two components: (1) a bending mode and (2) a surface deformation mode, which is induced by localized interactions of the NW surface with the AFM tip. This combined deformation mode has been modeled successfully using a finite element code written within Ansys. Based on a fit of the modeling results with experimentally observed mechanics data, we have determined the Young's modulus of the material system. This represents the first estimation of Young's modulus of LiFePO4 NWs, which is an important parameter that influences the long-term mechanical stability of this battery electrode material system. With the suitability of the DEP process to integrate diverse material systems within this construct, we believe that this nano-assembly enabled mechanical property measurement approach has the potential to provide valuable insights into the investigation of nanomaterial systems for next-generation lithium-ion batteries.

## Acknowledgements

This work was performed, in part, at the Center for Integrated Nanotechnologies (CINT), an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by Los Alamos National Laboratory (Contract No. DE-AC52-06NA25396) and Sandia National Laboratories (Contract No. DE-AC04-94AL85000). N.R.P. and A.S. acknowledge the support of Dr. Tom Harris and Dr. John Nogan for activities performed at CINT. We would like to acknowledge the assistance of Dr. Dmitry Pestov in the user training and operation of microscopy equipment at VCU's Nanomaterial Characterization Center. Y.Z. and C.W. acknowledge financial support by part of Nanostructures for Electrical Energy Storage (NEES), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award No. DESC0001160, and technical support from the X-ray Crystallographic Center and Nano Center at the University of Maryland College Park.

A part of the material presented within this paper, which relates to work performed at Virginia Commonwealth University, is based upon work supported by the National Science Foundation under Grant No. 1266438.

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## References

Burg, B. R., Helbling, T., Hierold, C., and Poulikakos, D., 2011, “Piezoresistive Pressure Sensors With Parallel Integration of Individual Single-Walled Carbon Nanotubes,” J. Appl. Phys., 109, p. 064310.
Jensen, K., Weldon, J., Garcia, H., and Zettl, A., 2007, “Nanotube Radio,” Nano Lett., 7, pp. 3508–3511. [PubMed]
Nakajima, M., Arai, F., Dong, L. X., and Fukuda, T., 2004, “Calibration of Carbon Nanotube Probes for Pico-Newton Order Force Measurement Inside a Scanning Electron Microscope,” J. Robot. Mechatronics, 16, pp. 155–162.
Huang, J. Y., Zhong, L., Wang, C. M., Sullivan, J. P., Xu, W., Zhang, L. Q., Mao, S. X., Hudak, N. S., Liu, X. H., Subramanian, A., Fan, H. Y., Qi, L., Kushima, A., and Li, J., 2010, “In-situ Observation of the Electrochemical Lithiation of a Single SnO2 Nanowire Electrode,” Science, 330, pp. 1515–1520. [PubMed]
Goldberg, D., Costa, P. M. F. J., Lourie, O., Mitome, M., Bai, X. D., Kurashima, K., Zhi, C. Y., Tang, C. C., and Bando, Y., 2007, “Direct Force Measurements and Kinking Under Elastic Deformation of Individual Multiwalled Boron Nitride Nanotubes,” Nano Lett., 7, pp. 2146–2151.
Yu, M. F., Lourie, O., Dyer, M. J., Moloni, K., Kelly, T. F., and Ruoff, R. S., 2000, “Strength and Breaking Mechanism of Multiwalled Carbon Nanotubes Under Tensile Load,” Science, 287(5453), pp. 637–640. [PubMed]
Dong, L. X., Arai, F., and Fukuda, T., 2004, “Destructive Constructions of Nanostructures With Carbon Nanotubes Through Nanorobotic Manipulation,” IEEE/ASME Trans. Mechatronics, 9(2), pp. 350–357.
Kim, Y.-J., Son, K., Choi, I.-C., Choi, I.-S., Park, W. I., and Jang, J.-I., 2011, “Exploring Nanomechanical Behavior of Silicon Nanowires: AFM Bending Versus Nanoindentation,” Adv. Funct. Mater., 21, pp. 279–286.
Zhang, H., Tang, J., Zhang, L., An, B., and Qin, L.-C., 2008, “Atomic Force Microscopy Measurement of the Young's Modulus and Hardness of Single LaB6 Nanowires,” Appl. Phys. Lett., 92, p. 173121.
Tombler, W. T., Zhou, C. W., Alexseyev, L., Kong, J., Dai, H. J., Lei, L., Jayanthi, C. S., Tang, M. J., and Wu, S. Y., 2000, “Reversible Electromechanical Characteristics of Carbon Nanotubes Under Local-Probe Manipulation,” Nature, 405, pp. 769–772. [PubMed]
Zheng, M., Ke, C., Bae, I.-T., Park, C., Smith, M. W., and Jordan, K., 2012, “Radial Elasticity of Multi-Walled Boron Nitride Nanotubes,” Nanotechnology, 23, p. 095703. [PubMed]
Sohn, Y.-S., Park, J., Yoon, G., Song, J., Jee, S.-W., Lee, J.-H., Na, S., Kwon, T., and Eom, K., 2010, “Mechanical Properties of Silicon Nanowires,” Nanoscale Res. Lett., 5, pp. 2011–2016.
Li, X., Gao, H., Murphy, C. J., and Caswell, K. K., 2003, “Nanoindentation of Silver Nanowires,” Nano Lett., 3(11), pp. 1485–1498.
Feng, G., Nix, W. D., Yoon, Y., and Lee, C. J., 2006, “A Study of the Mechanical Properties of Nanowires Using Nanoindentation,” J. Appl. Phys., 99, p. 074304.
Kumar, P., and Kiran, M. S. R. N., 2010, “Nanomechanical Characterization of Indium Nano/Microwires,” Nanoscale Res. Lett., 5, pp. 1085–1092. [PubMed]
Wang, Z., Mook, W. M., Niederberger, C., Ghisleni, R., Philippe, L., and Michler, J., 2012, “Compression of Nanowires Using a Flat Indenter: Diametrical Elasticity Measurement,” Nano Lett., 12, pp. 2289–2293. [PubMed]
Zhu, C. B., Yu, Y., Gu, L., Weichert, K., and Maier, J., 2011, “Electrospinning of Highly Electroactive Carbon-Coated Single-Crystalline LiFePO4 Nanowires,” Angew. Chem., Int. Ed., 50(28), pp. 6278–6282.
Yuan, L., Wang, Z., Zhang, W., Hu, X., Chen, J., Huang, Y., and Goodenough, J. B., 2011, “Development and Challenges of LiFePO4 Cathode Material for Lithium-Ion Batteries,” Energy Environ. Sci., 4, pp. 269–284.
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Lee, S., Park, J., Sastry, A. M., and Lu, W., 2013, “Molecular Dynamics Simulations of SOC-Dependent Elasticity of LixMn2O4 Spinels in Li-Ion Batteries,” J. Electrochem. Soc., 160(6), pp. A968–A972.
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## Figures

Fig. 1

Schematic of the DEP assembly process. (a) Growth of silicon nitride on a silicon substrate. (b) Definition of gold nano-electrodes. (c) Assembly of LiFePO4 NWs using AC dielectrophoresis. (d) Removal of chip from reservoir after assembly followed by a N2-gun blow-drying step.

Fig. 2

Lithium iron phosphate NWs (LiFePO4 NWs). (a) SEM image of carbonized NWs from the synthesized sample. (b) and (c) TEM images of the NWs. (d) Powder XRD pattern.

Fig. 3

(a)–(c) Representative SEM images of DEP assembled LiFePO4 NWs. (d) and (e) AFM images of NW devices, which clearly show that the NW is fully suspended in air in the region between the gold assembly electrodes. The gold electrodes also serve as mechanical anchors for the NW beam during AFM force spectroscopy measurements. (f) AFM section plot of a NW, indicating its diameter to be 571 nm.

Fig. 4

(a) Static force versus deformation plot of a representative LiFePO4 NW device, which was obtained from AFM force spectroscopy data. While the experimental data points are shown using hollow squares, the linear fit from Ansys finite element computational models is shown using a black line (the NW radius and suspended length were 168 nm and 400 nm, respectively). (b) Side-view of the deformation profile of a representative NW, as obtained from Ansys finite element models. This image clearly shows the bending induced in the NW in the suspended region. The contact point location with the AFM tip is illustrated in this panel. (c) A 3D-view of the NW deformation profile (same NW as in panel (b)) clearly showing the localized probe-induced deformation of the NW surface at the point of contact with the AFM tip. The contact region of the AFM tip is shown in the inset with a zoomed-in image and the point of indentation is highlighted with a red arrow. (d) The extracted value of Young's modulus plotted as a function of NW radius.

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