Size dependence of Young's modulus in ZnO nanowires

Buckling and mechanical instability of ZnO nanorods grown on different substrates under uniaxial compression

Mechanical instability and buckling characterization of vertically aligned single-crystal ZnO nanorods grown on different substrates including Si, SiC and sapphire (α-Al(2)O(3)) was done quantitatively by the nanoindentation technique. The nanorods were grown on these substrates by the vapor-liquid-solid (VLS) method. The critical load for the ZnO nanorods grown on the Si, SiC and Al(2)O(3) substrates was found to be 188, 205 and 130 µN, respectively. These observed critical loads were for nanorods with 280 nm diameters and 900 nm length using Si as a substrate, while the corresponding values were 330 nm, 3300 nm, and 780 nm, 3000 nm in the case of SiC and Al(2)O(3) substrates, respectively. The corresponding buckling energies calculated from the force displacement curves were 8.46 × 10(-12), 1.158 × 10(-11) and 1.092 × 10(-11) J, respectively. Based on the Euler model for long nanorods and the J B Johnson model (which is an extension of the Euler model) for intermediate nanorods, the modulus of elasticity of a single rod was calculated for each sample. Finally, the critical buckling stress and strain were also calculated for all samples. We found that the buckling characteristic is strongly dependent on the quality, lattice mismatch and adhesion of the nanorods with the substrate.

The effects of surface and initial stresses on the bending stiffness of nanowires

A simple closed-form analytic solution has been obtained for the effect of initial residual stress on the bending stiffness and hence the natural frequency of a coaxial core-shell nanowire. The result obtained also applies for a pre-stressed macro core-shell structure or a simple nanowire. The relative effect of the initial residual stress is generally limited to the range of the material yield strain. The effect of the surface elasticity on the bending stiffness of a nanowire reduces with the increase in the diameter, but the initial surface stress effect can be retained for a nanowire or microwire at a constant level of up to the limit of elastic strain if it can be controlled, for example by the application of an electrical potential.

Structure-mechanical property of individual cobalt oxide nanowires

We present a comprehensive approach to address the correlation between mechanical properties of nanowires (NWs) with their characteristic size, microstructure, and chemical composition. Using this technique, the Young's modulus of Co3O4 NWs with different sizes was evaluated. Thermal annealing in inert atmosphere was found to induce chemical reduction of as-grown Co3O4 NWs into CoO NWs without modifying their geometrical shape. Both Co3O4 and CoO NWs exhibited a size-dependent variation in Young's modulus.

A study of the size-dependent elastic properties of ZnO nanowires and nanotubes

We present our calculations of the Young's modulus of ZnO nanowires and nanotubes by using the empirical Buckingham-type potential. Our results indicate that the Young's moduli of ZnO nanowires increase as the diameters decrease, and the Young's moduli of ZnO nanotubes increase as the thicknesses decrease. Furthermore, we find that such size-dependent elastic properties mainly arise from the lateral facets of the nanowires and nanotubes. In particular, for a ZnO nanotube with a thin wall, the Coulomb interaction between the ions of the outer and inner atomic layers plays an important role in the Young's moduli of the surface atomic layers.

Surface effect on the elastic behavior of static bending nanowires

The surface effect from surface stress and surface elasticity on the elastic behavior of nanowires in static bending is incorporated into Euler-Bernoulli beam theory via the Young-Laplace equation. Explicit solutions are presented to study the dependence of the surface effect on the overall Young's modulus of nanowires for three different boundary conditions: cantilever, simply supported, and fixed-fixed. The solutions indicate that the cantilever nanowires behave as softer materials when deflected while the other structures behave like stiffer materials as the nanowire cross-sectional size decreases for positive surface stresses. These solutions agree with size dependent nanowire overall Young's moduli observed from static bending tests by other researchers. This study also discusses possible reasons for variations of nanowire overall Young's moduli observed.

Atomistic study of structures and elastic properties of single crystalline ZnO nanotubes

The structural stability and Young's modulus of single crystalline ZnO nanotubes are investigated using atomistic simulations. Unlike the case for conventional layered nanotubes, the energetic stability of single crystalline ZnO nanotubes is related to the wall thickness. The potential energy of ZnO nanotubes with fixed outer and inner diameters decreases with increasing wall thickness, while the nanotubes with the same wall thickness are independent of the outer and inner diameters. The transformation of single crystalline ZnO nanotubes with a double layer from wurtzite phase to graphitic phase suggests the possibility of wall-typed ZnO nanotubes. The size-dependent Young's modulus of ZnO nanotubes is also investigated. The wall thickness plays a significant role in the Young's modulus of single crystalline ZnO nanotubes, whereas the variation of outer and inner diameters slightly affects the Young's modulus of nanotubes with same wall thickness.

Tunable electronic transport characteristics of surface-architecture-controlled ZnO nanowire field effect transistors

Surface-architecture-controlled ZnO nanowires were grown using a vapor transport method on various ZnO buffer film coated c-plane sapphire substrates with or without Au catalysts. The ZnO nanowires that were grown showed two different types of geometric properties: corrugated ZnO nanowires having a relatively smaller diameter and a strong deep-level emission photoluminescence (PL) peak and smooth ZnO nanowires having a relatively larger diameter and a weak deep-level emission PL peak. The surface morphology and size-dependent tunable electronic transport properties of the ZnO nanowires were characterized using a nanowire field effect transistor (FET) device structure. The FETs made from smooth ZnO nanowires with a larger diameter exhibited negative threshold voltages, indicating n-channel depletion-mode behavior, whereas those made from corrugated ZnO nanowires with a smaller diameter had positive threshold voltages, indicating n-channel enhancement-mode behavior.

Mechanical properties of microwave hydrothermally synthesized titanate nanowires

In this investigation titanate nanowires were synthesized by a microwave hydrothermal process and their nanomechanical characterization was carried out by a compression experiment via buckling instability using a nanomanipulator inside a scanning electron microscope. Nanowires of diameters 120-150 nm and length tens of microns can be synthesized by keeping a commercial nanoparticle inside a microwave oven at 350 W and 210 °C for 5 h. The nanowire was clamped between two cantilevered AFM tips attached to two opposing stages of the manipulator for nanomechanical characterization. The elasticity coefficients of the titanate nanowires were measured by applying a continuously increasing load and observing the buckling instability of the nanowires. The buckling behavior of a nanowire was analyzed from the series of SEM images of displacement of the cantilever attached to the nanowire due to application of load. The critical loads for different sized titanate nanowires were determined and their corresponding Young's modulus was computed with the Euler pinned-fixed end model. The Young's modulus of these microwave hydrothermal process synthesized titanate nanowires were determined to be approximately in the range 14-17 GPa. This investigation confirms the capability of the nanomanipulator via the buckling technique as a constructive device for measuring the mechanical properties of nanoscale materials.

Directed growth of horizontally aligned gallium nitride nanowires for nanoelectromechanical resonator arrays

We report the growth of horizontally aligned arrays and networks of GaN nanowires (NWs) as resonant components in nanoelectromechanical systems (NEMS). A combination of top-down selective area growth (SAG) and bottom-up vapor-liquid-solid (VLS) synthesis enables flexible fabrication of highly ordered nanowire arrays in situ with no postgrowth dispersion. Mechanical resonance of free-standing nanowires are measured, with quality factors (Q) ranging from 400 to 1000. We obtained a Young's modulus (E) of approximately 338 GPa from an array of NWs with varying diameters and lengths. The measurement allows detection of nanowire motion with a rotating frame and reveals dual fundamental resonant modes in two orthogonal planes. A universal ratio between the resonant frequencies of these two fundamental modes, irrespective of their dimensions, is observed and attributed to an isosceles cross section of GaN NWs.

Electrostatic potential in a bent piezoelectric nanowire. The fundamental theory of nanogenerator and nanopiezotronics

We have applied the perturbation theory for calculating the piezoelectric potential distribution in a nanowire (NW) as pushed by a lateral force at the tip. The analytical solution given under the first-order approximation produces a result that is within 6% from the full numerically calculated result using the finite element method. The calculation shows that the piezoelectric potential in the NW almost does not depend on the z-coordinate along the NW unless very close to the two ends, meaning that the NW can be approximately taken as a "parallel plated capacitor". This is entirely consistent to the model established for nanopiezotronics, in which the potential drop across the nanowire serves as the gate voltage for the piezoelectric field effect transistor. The maximum potential at the surface of the NW is directly proportional to the lateral displacement of the NW and inversely proportional to the cube of its length-to-diameter aspect ratio. The magnitude of piezoelectric potential for a NW of diameter 50 nm and length 600 nm is approximately 0.3 V. This voltage is much larger than the thermal voltage ( approximately 25 mV) and is high enough to drive the metal-semiconductor Schottky diode at the interface between atomic force microscope tip and the ZnO NW, as assumed in our original mechanism for the nanogenerators.

Aspect ratio dependence of the elastic properties of ZnO nanobelts

The Young's modulus of ZnO nanobelts was measured with an atomic force microscope by means of the modulated nanoindentation method. The elastic modulus was found to depend strongly on the width-to-thickness ratio of the nanobelt, decreasing from about 100 to 10 GPa, as the width-to-thickness ratio increases from 1.2 to 10.3. This surprising behavior is explained by a growth-direction-dependent aspect ratio and the presence of stacking faults in nanobelts growing along particular directions.

Mechanical elasticity of vapour-liquid-solid grown GaN nanowires

Mechanical elasticity of hexagonal wurtzite GaN nanowires with hexagonal cross sections grown through a vapour-liquid-solid (VLS) method was investigated using a three-point bending method with a digital-pulsed force mode (DPFM) atomic force microscope (AFM). In a diameter range of 57-135 nm, bending deflection and effective stiffness, or spring constant, profiles were recorded over the entire length of end-supported GaN nanowires and compared to the classic elastic beam models. Profiles reveal that the bending behaviour of the smallest nanowire (57.0 nm in diameter) is as a fixed beam, while larger nanowires (89.3-135.0 nm in diameter) all show simple-beam boundary conditions. Diameter dependence on the stiffness and elastic modulus are observed for these GaN nanowires. The GaN nanowire of 57.0 nm diameter displays the lowest stiffness (0.98 N m(-1)) and the highest elastic modulus (400 ± 15 GPa). But with increasing diameter, elastic modulus decreases, while stiffness increases. Elastic moduli for most tested nanowires range from 218 to 317 GPa, which approaches or meets the literature values for bulk single crystal and GaN nanowires with triangular cross sections from other investigators. The present results together with further tests on plastic and fracture processes will provide fundamental information for the development of GaN nanowire devices.

Determination of the natural frequency of a cantilevered ZnO nanowire resonantly excited by a sinusoidal electric field

The electric-field-induced mechanical resonance of an individual nanotube (NT) or nanowire (NW) has been utilized as a versatile technique for in situ measurement of the Young's modulus of the NT/NW in electron microscopes. The key step of this technique is to determine the fundamental natural frequency of the NT/NW. However, the emergence of super- and/or sub-harmonic resonances might make the determination uncertain. This paper investigates the resonance behaviour of ZnO NWs in a nanotip-nanowire system in order to clarify this obscurity. It is found that forced and parametric resonance are two basic modes of the observed multi-frequency resonances and that each mode exhibits a distinct characteristic. By controlling the driving force exerted on the NW to be either lateral or axial, the two otherwise entangled modes are clearly separated. Based on this resonance mode separation, a criterion for identifying the natural frequency of ZnO NWs is proposed.

Low-temperature in situ large strain plasticity of ceramic SiC nanowires and its atomic-scale mechanism

Large strain plasticity is phenomenologically defined as the ability of a material to exhibit an exceptionally large deformation rate during mechanical deformation. It is a property that is well established for metals and alloys but is rarely observed for ceramic materials especially at low temperature ( approximately 300 K). With the reduction in dimensionality, however, unusual mechanical properties are shown by ceramic nanomaterials. In this Letter, we demonstrated unusually large strain plasticity of ceramic SiC nanowires (NWs) at temperatures close to room temperature that was directly observed in situ by a novel high-resolution transmission electron microscopy technique. The continuous plasticity of the SiC NWs is accompanied by a process of increased dislocation density at an early stage, followed by an obvious lattice distortion, and finally reaches an entire structure amorphization at the most strained region of the NW. These unusual phenomena for the SiC NWs are fundamentally important for understanding the nanoscale fracture and strain-induced band structure variation for high-temperature semiconductors. Our result may also provide useful information for further studying of nanoscale elastic-plastic and brittle-ductile transitions of ceramic materials with superplasticity.

Applicability of isothermal unrealistic two-parameter equations of state for solids

The aim of the present study, an extension of a recent one (Bose Roy and Bose Roy 2005 J. Phys.: Condens. Matter 17 6193), is to assess and compare the curve-fitting utility of the isothermal unrealistic two-parameter equations of state for solids (EOS), proposed at different stages in the development of the EOS field, for the purposes of smoothing and interpolation of pressure-volume data, and extraction of accurate values of the isothermal bulk modulus and its pressure derivative. To this end, 21 such EOSs are considered, formulated by/labelled as Born-Mie (1920), Born-Mayer (1932), Bardeen (1938), Slater-Morse (1939), Birch-Murnaghan (1947), Pack-Evans-James (1948), Lagrangian (1951), Davydov (1956), Davis and Gordon (1967), Onat and Vaisnys (1967), Grover-Getting-Kennedy (1973), Brennan-Stacey (1979), Walzer-Ullmann-Pan'kov (1979), Rydberg (1981), Dodson (1987), Holzapfel (1991), Parsafar-Mason (1994), Shanker-Kushwah-Kumar (1997), Poirier-Tarantola (1998), Deng-Yan (2002) and Kun-Loa-Syassen (2003). Furthermore, all these EOSs are compared with our three-parameter EOS, as well as its two-parameter counterpart proposed in this work. We have applied all the EOS models, with no constraint on the parameters, to the accurate and model-independent isotherms of nine solids. The applicability has been assessed in terms of an unbiased composite test, comprising fitting accuracy, agreement of the fit parameters with experiment, stability of the fit parameters with variation in the compression/pressure ranges and on the basis of the number of wiggles of the data deviation curves about the fit parameters. Furthermore, a rigorous method is devised to scale the relative adequacy of the EOSs with respect to the test parameters. A number of remarkable findings emerge from the present study. Surprisingly, both the old EOSs, the Born-Mie and the Pack-Evans-James, are significantly better in their curve-fitting capability than the Birch-Murnaghan EOS which has been widely used and continues to be used for curve-fitting purposes as a standard EOS in the literature. The Born-Mayer as well as the Walzer-Ullmann-Pan'kov models also fit isotherms better than the Birch. The performance of the EOS based on the Rydberg potential-that has been rediscovered by Rose et al (1984 Phys. Rev. B 29 2963), and strongly promoted by Vinet et al (1989 J. Phys.: Condens. Matter 1 1941) as the so-called universal equation of state, and is currently used as a standard EOS along with that of the Birch-is very poor, on a comparative scale. Furthermore, the curve-fitting capability of our original three-parameter EOS, and more importantly its two-parameter counterpart, is superior to all the isothermal unrealistic two-parameter EOSs so far proposed in the literature.

Novel phase transformation in ZnO nanowires under tensile loading

We predict a previously unknown phase transformation from wurtzite to a graphitelike (P6(3)/mmc) hexagonal structure in [0110]-oriented ZnO nanowires under uniaxial tensile loading. Molecular dynamics simulations and first principles calculations show that this structure corresponds to a distinct minimum on the enthalpy surfaces of ZnO for such loading conditions. This transformation is reversible with a low level of hysteretic dissipation of 0.16 J/m3 and, along with elastic stretching, endows the nanowires with the ability to recover pseudoelastic strains up to 15%.