Size dependence of Young's modulus in ZnO nanowires

Piezoelectric effects and electromechanical theories at the nanoscale

Considerable effort has been made to study the piezoelectric effect on the nanoscale, which serves as a physical basis for a wide range of smart nanodevices and nanoelectronics. This paper reviews recent progress in the research on the piezoelectric properties and electromechanical effects of piezoelectric nanomaterials (PNs). The review begins with an introduction to existing PNs which exhibit a diverse range of atomic structures and configurations. The nanoscale measurement of their effective piezoelectric coefficients (EPCs) is summarised with an emphasis on the major factors determining the piezoelectric properties of PNs. The paper concludes with a review of the electromechanical theories that are able to capture the small-scale effects on PNs, which include the surface piezoelectricity, flexoelectricity and Eringen's nonlocal theory. In contrast to the classical theories, two types of EPCs are defined, which were found to be size-dependent and loading condition-selective.

Atomistic simulations of electric field effects on the Young's modulus of metal nanowires

We present a computational, atomistic study of electric field effects on the Young's modulus of metal nanowires. The simulations are electromechanically coupled, where the mechanical forces on the atoms are obtained from realistic embedded atom method potentials, and where the electrostatic forces on the atoms are obtained using a point dipole electrostatic model that is modified to account for the different polarizability and bonding environment of surface atoms. By considering three different nanowire axial orientations (left angle bracket 100 right angle bracket, left angle bracket 110 right angle bracket and right angle bracket 111 right angle bracket) of varying cross sectional sizes and aspect ratios, we find that the Young's modulus of the nanowires differs from that predicted for the purely mechanical case due to the elimination of nonlinear elastic stiffening or softening effects due to the electric field-induced positive relaxation strain relative to the relaxed mechanical configuration. We further find that left angle bracket 100 right angle bracket nanowires are most sensitive to the applied electric field, with Young's moduli that can be increased more than 20% with increasing aspect ratio. Finally, while the orientation of the transverse surfaces does impact the Young's modulus of the nanowires under applied electric field, the key factor controlling the magnitude of the stiffness change of the nanowires is the distance between atomic planes along the axial direction of the nanowire bulk.

Bundling of GaAs nanowires: a case of adhesion-induced self-assembly of nanowires

The origin of deflections of semiconductor nanowires (NWs) induced by an electron beam in scanning electron microscopy has been subject to different interpretations. Similarly, the subsequent clumping together of NWs into bundles is frequently observed, but no interpretation has yet been advanced. Here we present results on the bundling of NWs following the intentional bending by an electron beam. Furthermore, we extend the concept of lateral collapse, usually applied to fibrillar architectures mimicking the adhesiveness of natural surfaces (the so-called Gecko effect), to analyze the mechanism of the NW bundle formation. We demonstrate how the geometry of the NW arrays and the mechanical properties of the composing materials govern bundling and how these parameters should be taken into account in the design of NW arrays both for avoiding vertical misalignment when detrimental and for achieving patterning of NW arrays into nanoarchitectures.

Scanning force microscope for in situ nanofocused X-ray diffraction studies

A compact scanning force microscope has been developed for in situ combination with nanofocused X-ray diffraction techniques at third-generation synchrotron beamlines. Its capabilities are demonstrated on Au nano-islands grown on a sapphire substrate. The new in situ device allows for in situ imaging the sample topography and the crystallinity by recording simultaneously an atomic force microscope (AFM) image and a scanning X-ray diffraction map of the same area. Moreover, a selected Au island can be mechanically deformed using the AFM tip while monitoring the deformation of the atomic lattice by nanofocused X-ray diffraction. This in situ approach gives access to the mechanical behavior of nanomaterials.

Exohedral physisorption of ambient moisture scales non-monotonically with fiber proximity in aligned carbon nanotube arrays

Here we present a study on the presence of physisorbed water on the surface of aligned carbon nanotubes (CNTs) in ambient conditions, where the wet CNT array mass can be more than 200% larger than that of dry CNTs, and modeling indicates that a water layer >5 nm thick can be present on the outer CNT surface. The experimentally observed nonlinear and non-monotonic dependence of the mass of adsorbed water on the CNT packing (volume fraction) originates from two competing modes. Physisorbed water cannot be neglected in the design and fabrication of materials and devices using nanowires/nanofibers, especially CNTs, and further experimental and ab initio studies on the influence of defects on the surface energies of CNTs, and nanowires/nanofibers in general, are necessary to understand the underlying physics and chemistry that govern this system.

Bandgap engineering and manipulating electronic and optical properties of ZnO nanowires by uniaxial strain

Bandgap engineering is a common practice for tuning semiconductors for desired physical properties. Although possible strain effects in semiconductors have been investigated for over a half-century, a profound understanding of their influence on energy bands, especially for large elastic strain remains unclear. In this study, a systematic investigation of the transport properties of n-type [0001] ZnO nanowires was performed at room temperature using the in situ scanning tunnelling microscope-transmission electron microscope technique which shows that the transport properties vary with the applied external uniaxial strain. It has been found that the resistance of ZnO nanowires decreases continuously with increasing compressive strain, but increases under increased tensile strain, suggesting piezo-resistive characteristics. A series of near-band-edge emissions were measured and the corresponding variations of bandgaps were obtained during the application of tensile strain of individual ZnO nanowires via cathodoluminescence spectroscopy. From this, a relationship between the changes of energy bandgap and the transport properties, both induced by uniaxial strain, is built.

Poisson's Ratio and Young's Modulus of Lipid Bilayers in Different Phases

A general computational method is introduced to estimate the Poisson's ratio for membranes with small thickness. In this method, the Poisson's ratio is calculated by utilizing a rescaling of inter-particle distances in one lateral direction under periodic boundary conditions. As an example for the coarse grained lipid model introduced by Lenz and Schmid, we calculate the Poisson's ratio in the gel, fluid, and interdigitated phases. Having the Poisson's ratio, enable us to obtain the Young's modulus for the membranes in different phases. The approach may be applied to other membranes such as graphene and tethered membranes in order to predict the temperature dependence of its Poisson's ratio and Young's modulus.

Electrodeposition and behavior of single metal nanowire probes

This paper describes the fabrication of scanning probes with single metal nanowires (NWs) at the probe tip. The porous-template technique can produce NWs of various kinds of metals, with diameters down to 10-20 nm, which compete with multiwall carbon nanotube diameters. Metal NWs are grown by electrodeposition on the scanning probe tip. One NW can be selected to remain by focused ion beam technique. A variety of metals can be chosen as the tip material. Electric potentials of NWs at the probe tip can be measured. Single NW probes can measure surface topographies, electrode potentials, and their mechanical bending properties.

Investigation on the mechanism of nanodamage and nanofailure for single ZnO nanowires under an electric field

The electrical service behavior of ZnO nanowires (NWs) with various diameters was investigated by a nanomanipulation technique. The nanodamage and nanofailure phenomena of the ZnO NWs were observed when external voltages were applied. The threshold voltages of the ZnO NWs increased linearly from 15 to 60 V with increasing diameter. The critical current densities were distributed from 19.50 × 10(6) to 56.90 × 10(6) A m(-2), and the reciprocal of the critical current density increased linearly with increasing diameter as well. The thermal core-shell model was proposed to explain the nanodamage and nanofailure mechanism of ZnO NWs under an electric field. It can be expected that the investigation on the nanodamage and nanofailure of nanomaterials would have a profound influence on practical applications of photoelectric, electromechanical, and piezoelectric nanodevices.

Variation of exciton emissions of ZnO whiskers reversibly tuned by axial tensile strain

Applying strain on semiconductors is a powerful method to modulate its electronic structures and optical properties. In this study, the behavior of liquid-nitrogen exciton emissions and the longitudinal optical phonon-exciton interactions of tensile strained [0001]-orientated ZnO whiskers were investigated using in situ cathodoluminescence spectroscopy. It has been found that, under the axial tensile strain, various exciton emissions shift to the long wavelength and their shifts have a linear relationship with the applied strain. This linear relationship and reversible shift suggest that the strain plays a dominating role in manipulating light emissions of axially strained ZnO whiskers.

Time-resolved X-ray diffraction investigation of the modified phonon dispersion in InSb nanowires

The modified phonon dispersion is of importance for understanding the origin of the reduced heat conductivity in nanowires. We have measured the phonon dispersion for 50 nm diameter InSb (111) nanowires using time-resolved X-ray diffraction. By comparing the sound speed of the bulk (3880 m/s) and that of a classical thin rod (3600 m/s) to our measurement (2880 m/s), we conclude that the origin of the reduced sound speed and thereby to the reduced heat conductivity is that the C44 elastic constant is reduced by 35% compared to the bulk material.

Spectral and luminescent properties of ZnO–SiO2 core–shell nanoparticles with size-selected ZnO cores

Deposition of a SiO₂ shell on luminescent ZnO nanoparticles in dimethylsulfoxide precisely tunes the nanoparticle size from 3 to 6 nm.

The dynamic effect on mechanical contacts between nanoparticles

The rich behaviors of high-speed mechanical contacts at the nanoscale have been studied. The seldom observed elastic-plastic transition governed by Hertz and Thornton models has been clearly unveiled, the origins of the hardening effect and the deformation mechanism of nanoscale plasticity have been discussed in terms of structural changes after compression and a series of physical quantities are measured including contact forces, contact radius, contact stress, coefficient of restitution and total impact time. Our simulation results closely resemble experiments and/or theoretical predictions: (i) when impact speed v is higher than Y/ρc0, the elastic-plastic deformation transition occurs, (ii) the yielded apparent elastic modulus and hardness are larger than those of the bulk, (iii) the initiating yield stress Y and hardness P0 still satisfy P0 ≈ 1.6Y, (iv) particle's volume decreases during compression, (v) contact radius a follows a [proportionality] v(2/5), (vi) at v ≥ 2000 m s(-1), the coefficient of restitution follows e [proportionality] v(-1/4) and (vii) the total time of impact follows Tc [proportionality] v(-1/5). However, there also exist many quantitative differences. The contact radius and final contact radius are underestimated by the continuum predictions while the total impact time is overestimated, but all of them reasonably agree with theoretical predictions with an increase of contact area and impact speed. The theoretical equation is adapted to predict the final contact radius during normal impact, in which the contact radius at zero load is also formulated.

Anisotropic surface strain in single crystalline cobalt nanowires and its impact on the diameter-dependent Young's modulus

Understanding and measuring the size-dependent surface strain of nanowires are essential to their applications in various emerging devices. Here, we report on the diameter-dependent surface strain and Young's modulus of single-crystalline Co nanowires investigated by in situ X-ray diffraction measurements. Diameter-dependent initial longitudinal elongation of the nanowires is observed and ascribed to the anisotropic surface stress due to the Poisson effect, which serves as the basis for mechanical measurements. As the nanowire diameter decreases, a transition from the "smaller is softer" regime to the "smaller is tougher" regime is observed in the Young's modulus of the nanowires, which is attributed to the competition between the elongation softening and the surface stiffening effects. Our work demonstrates a new nondestructive method capable of measuring the initial surface strain and estimating the Young's modulus of single crystalline nanowires, and provides new insights on the size effect.

Individual boron nanowire has ultra-high specific Young's modulus and fracture strength as revealed by in situ transmission electron microscopy

Boron nanowires (BNWs) may have potential applications as reinforcing materials because B fibers are widely known for their excellent mechanical performance. However until now, there have been only few reports on the mechanical properties of individual BNW, and in situ transmission electron microscopy (TEM) investigations shining a light on their fracture mechanism have not been performed. In this paper, we applied in situ high-resolution TEM (HRTEM) technique to study the mechanical properties of individual BNWs using three loading schemes. The mean fracture strength and the maximum strain of individual BNWs were measured to be 10.4 GPa and 4.1%, respectively, during the tensile tests. And the averaged Young's modulus was calculated to be 308.2 GPa under tensile and compression tests. Bending experiments for the first time performed on individual BNWs revealed that their maximum bending strain could reach 9.9% and their ultimate bending stress arrived at 36.2 GPa. These figures are much higher than those of Si and ZnO nanowires known for their high bending strength. Moreover, the BNWs exhibited very high specific fracture strength (3.9 (GPa·cm(3))/g) and specific elastic modulus (130.6 (GPa·cm(3))/g), which are several dozens of times larger compared to many nanostructures known for their superb mechanical behaviors. At last, the effect of surface oxide layer on the Young's modulus, fracture strength and maximum bending strength of individual BNWs was elucidated to extract their intrinsic mechanical parameters using calculated corrections. All experimental results suggest that the present BNW are a bright promise as lightweight reinforcing fillers.

Polar surface effects on the thermal conductivity of ZnO nanowires: a shell-like surface reconstruction-induced preserving mechanism

We perform molecular dynamics (MD) simulations to investigate the effect of polar surfaces on the thermal transport in zinc oxide (ZnO) nanowires. We find that the thermal conductivity of nanowires with free polar (0001) surfaces is much higher than that of nanowires that have been stabilized with reduced charges on the polar (0001) surfaces, and also hexagonal nanowires without any transverse polar surface, where the reduced charge model has been proposed as a promising stabilization mechanism for the (0001) polar surfaces of ZnO nanowires. From normal mode analysis, we show that the higher thermal conductivity is due to the shell-like reconstruction that occurs for the free polar surfaces. This shell-like reconstruction suppresses twisting motion in the nanowires such that the bending phonon modes are not scattered by the other phonon modes, and this leads to substantially higher thermal conductivity of the ZnO nanowires with free polar surfaces. Furthermore, the auto-correlation function of the normal mode coordinate is utilized to extract the phonon lifetime, which leads to a concise explanation for the higher thermal conductivity of ZnO nanowires with free polar surfaces. Our work demonstrates that ZnO nanowires without polar surfaces, which exhibit low thermal conductivity, are more promising candidates for thermoelectric applications than nanowires with polar surfaces (and also high thermal conductivity).

Size-dependent correlations between strain and phonon frequency in individual ZnO nanowires

The effect of uniaxial tensile strain on individual ZnO nanowires with diameters ranging from 500 nm to 2.7 μm and the effect of pure bending strain on ZnO microwires are systematically investigated by Raman spectroscopy. It is found for the first time that the tensile and compressive strains result in a linear downshift and upshift of the phonon frequencies of the E2L, E2H, E1TO, and second-order modes compared with the strain-free state, respectively, while the A1TO mode is not influenced by the strain. Furthermore, the strain modulation on phonons depends strongly on the nanowire diameter. The E2H phonon deformation potential is ~3 cm(-1)/% for the 500 nm nanowire, while 1% tensile strain results only in ~1 cm(-1) downward frequency shift for the 2.7 μm ZnO wire. The results provide a versatile "local-self-calibration" and nondestructive method to measure and monitor the local strains in ZnO micro/nanostructures.

Preserving the Q-factors of ZnO nanoresonators via polar surface reconstruction

We perform molecular dynamics simulations to investigate the effect of polar surfaces on the quality (Q)-factors of zinc oxide (ZnO) nanowire-based nanoresonators. We find that the Q-factors in ZnO nanoresonators with free polar (0001) surfaces are about one order of magnitude higher than in nanoresonators that have been stabilized with reduced charges on the polar (0001) surfaces. From normal mode analysis, we show that the higher Q-factor is due to a shell-like reconstruction that occurs for the free polar surfaces. This shell-like reconstruction suppresses twisting motion in the nanowires such that the mixing of other modes with the resonant mode of oscillation is minimized, and leads to substantially higher Q-factors in ZnO nanoresonators with free polar surfaces.

Fundamental analysis of piezocatalysis process on the surfaces of strained piezoelectric materials

Recently, the strain state of a piezoelectric electrode has been found to impact the electrochemical activity taking place between the piezoelectric material and its solution environment. This effect, dubbed piezocatalysis, is prominent in piezoelectric materials because the strain state and electronic state of these materials are strongly coupled. Herein we develop a general theoretical analysis of the piezocatalysis process utilizing well-established piezoelectric, semiconductor, molecular orbital and electrochemistry frameworks. The analysis shows good agreement with experimental results, reproducing the time-dependent voltage drop and H₂ production behaviors of an oscillating piezoelectric Pb(Mg_1/3Nb_2/3)O₃-32PbTiO₃ (PMN-PT) cantilever in deionized water environment. This study provides general guidance for future experiments utilizing different piezoelectric materials, such as ZnO, BaTiO₃, PbTiO₃, and PMN-PT. Our analysis indicates a high piezoelectric coupling coefficient and a low electrical conductivity are desired for enabling high electrochemical activity; whereas electrical permittivity must be optimized to balance piezoelectric and capacitive effects.

Inorganic nanostructures with sizes down to 1 nm: a macromolecule analogue

Ultrathin nanostructures exhibit many interesting properties which are absent or less-pronounced in traditional nanomaterials of larger sizes. In this work, we report the synthesis of ultrathin nanowires and nanoribbons of rare earth hydroxides and demonstrate some new phenomena caused by their atomic-level lateral size (1 nm), including ligand-induced gelation, self-assembly framework, and conformational diversity. These features are typically, although not exclusively, found in polymer solutions. The properties of the inorganic backbone and the emerging polymeric characteristics combined prove to be very promising in the design of new hybrid materials.

Mapping the local elastic properties of nanostructured germanium surfaces: from nanoporous sponges to self-organized nanodots

Due to their reduced dimensions, the mechanical properties of nanostructures may differ substantially from those of bulk materials. Quantifying and understanding the nanomechanical properties of individual nanostructures is thus of tremendous importance both from a fundamental and a technological point of view. Here we employ a recently introduced atomic force microscopy mode, i.e., peak-force quantitative nanomechanical imaging, to map the local elastic properties of nanostructured germanium surfaces. This imaging mode allows the quantitative determination of the Young's modulus with nanometer resolution. Heavy-ion irradiation was used to fabricate different self-organized nanostructures on germanium surfaces. Depending on the sample temperature during irradiation, nanoporous sponge-like structures and hexagonally ordered nanodots are obtained. The sponge-like germanium surface is found to exhibit a surprisingly low Young's modulus well below 10 GPa, which furthermore depends on the ion energy. For the nanodot patterns, local variations in the Young's modulus are observed: at moderate sample temperatures, the dot crests have a lower modulus than the dot valley whereas this situation is reversed at high temperatures. These observations are explained by vacancy dynamics in the amorphous germanium matrix during irradiation. Our results furthermore offer the possibility to tune the local elastic properties of nanostructured germanium surfaces by adjusting the ion energy and sample temperature.

Elastic modulus of halloysite nanotubes

This work reports measurements of the elastic modulus of halloysite nanotubes. Nanoscale three-point bending tests were performed on individual nanotubes using an atomic force microscope. Nanotubes exhibit elastic behaviour at small deformations. The stiffness of the tubes, and hence their elastic modulus, was deduced from force curve measurements using an appropriate mechanical model. The boundary conditions were also identified by recording the stiffness profile of a tube along its suspended length. An average elastic modulus of 140 GPa is obtained for a set of tubes with outer diameters ranging between 50 and 160 nm. Moreover, the elastic modulus increases with decreasing outer diameter, with a steep jump below 50 nm. The size dependence of the elastic modulus may be attributed to: (i) surface tension effects for thinner tubes and (ii) a non-negligible contribution of shear deformations to the total deflection for larger tubes.

Fundamental formulations and recent achievements in piezoelectric nano-structures: a review

Piezoelectric nano-structures have been regarded as the next-generation piezoelectric material due to their inherent nano-sized piezoelectricity. This review summarizes the recent theoretical and experimental findings in piezoelectric nano-structures, including piezoelectric nanowires, nanoplates, nanobeams, nanofilms, nanoparticles, and piezoelectric heterogeneous materials containing piezoelectric nano-inhomogeneities. To begin, the types of piezoelectric nano-structured materials and the wide application of piezoelectric nano-structures in recent years are delineated. Next, the theoretical foundations including the definition of surface stress and electric displacement, the surface constitutive relations, the surface equilibrium equations, and nonlocal piezoelectricity, and their applications, are illustrated. Then, the effective mechanical and piezoelectric properties are depicted. Furthermore, the experimental investigations are classified, and some important observations are discussed. Finally, the perspectives and challenges for the future development of piezoelectric nano-structures are pointed out.

Beat phenomena in metal nanowires, and their implications for resonance-based elastic property measurements

The elastic properties of 1D nanostructures such as nanowires are often measured experimentally through actuation of nanowires at their resonance frequency, and then relating the resonance frequency to the elastic stiffness using the elementary beam theory. In the present work, we utilize large scale molecular dynamics simulations to report a novel beat phenomenon in [110] oriented Ag nanowires. The beat phenomenon is found to arise from the asymmetry of the lattice spacing in the orthogonal elementary directions of [110] nanowires, i.e. the [110] and [001] directions, which results in two different principal moments of inertia. Because of this, actuations imposed along any other direction are found to decompose into two orthogonal vibrational components based on the actuation angle relative to these two elementary directions, with this phenomenon being generalizable to <110> FCC nanowires of different materials (Cu, Au, Ni, Pd and Pt). The beat phenomenon is explained using a discrete moment of inertia model based on the hard sphere assumption; the model is utilized to show that surface effects enhance the beat phenomenon, while effects are reduced with increasing nanowire cross-sectional size or aspect ratio. Most importantly, due to the existence of the beat phenomena, we demonstrate that in resonance experiments only a single frequency component is expected to be observed, particularly when the damping ratio is relatively large or very small. Furthermore, for a large range of actuation angles, the lower frequency is more likely to be detected than the higher one, which implies that experimental predictions of the Young's modulus obtained from resonance may in fact be under-predictions. The present study therefore has significant implications for experimental interpretations of the Young's modulus as obtained via resonance testing.

In situ TEM electromechanical testing of nanowires and nanotubes

The emergence of one-dimensional nanostructures as fundamental constituents of advanced materials and next-generation electronic and electromechanical devices has increased the need for their atomic-scale characterization. Given its spatial and temporal resolution, coupled with analytical capabilities, transmission electron microscopy (TEM) has been the technique of choice in performing atomic structure and defect characterization. A number of approaches have been recently developed to combine these capabilities with in-situ mechanical deformation and electrical characterization in the emerging field of in-situ TEM electromechanical testing. This has enabled researchers to establish unambiguous synthesis-structure-property relations for one-dimensional nanostructures. In this article, the development and latest advances of several in-situ TEM techniques to carry out mechanical and electromechanical testing of nanowires and nanotubes are reviewed. Through discussion of specific examples, it is shown how the merging of several microsystems and TEM has led to significant insights into the behavior of nanowires and nanotubes, underscoring the significant role in-situ techniques play in the development of novel nanoscale systems and materials.

Controlled fabrication of photoactive copper oxide-cobalt oxide nanowire heterostructures for efficient phenol photodegradation

Fabrication of oxide nanowire heterostructures with controlled morphology, interface, and phase purity is critical for high-efficiency and low-cost photocatalysis. Here, we have studied the formation of copper oxide-cobalt nanowire heterostructures by sputtering and subsequent air annealing to result in cobalt oxide (Co(3)O(4))-coated CuO nanowires. This approach allowed fabrication of standing nanowire heterostructures with tunable compositions and morphologies. The vertically standing CuO nanowires were synthesized in a thermal growth method. The shell growth kinetics of Co and Co(3)O(4) on CuO nanowires, morphological evolution of the shell, and nanowire self-shadowing effects were found to be strongly dependent on sputtering duration, air-annealing conditions, and alignment of CuO nanowires. Finite element method (FEM) analysis indicated that alignment and stiffness of CuO-Co nanowire heterostructures greatly influenced the nanomechanical aspects such as von Mises equivalent stress distribution and bending of nanowire heterostructures during the Co deposition process. This fundamental knowledge was critical for the morphological control of Co and Co(3)O(4) on CuO nanowires with desired interfaces and a uniform coating. Band gap energies and phenol photodegradation capability of CuO-Co(3)O(4) nanowire heterostructures were studied as a function of Co(3)O(4) morphology. Multiple absorption edges and band gap tailings were observed for these heterostructures, indicating photoactivity from visible to UV range. A polycrystalline Co(3)O(4) shell on CuO nanowires showed the best photodegradation performance (efficiency ~50-90%) in a low-powered UV or visible light illumination with a sacrificial agent (H(2)O(2)). An anomalously high efficiency (~67.5%) observed under visible light without sacrificial agent for CuO nanowires coated with thin (∼5.6 nm) Co(3)O(4) shell and nanoparticles was especially interesting. Such photoactive heterostructures demonstrate unique sacrificial agent-free, robust, and efficient photocatalysts promising for organic decontamination and environmental remediation.

Lattice anharmonicity in defect-free Pd nanowhiskers

We have investigated anharmonic behavior of Pd by applying systematic nanoscale tensile testing to near defect-free nanowhiskers offering a large range of elastic strain. We measured size-dependent deviations from bulk elastic behavior in nanowhiskers with diameters as small as ∼30 nm. In addition to size-dependent variations in Young's modulus in the small strain limit, we measured nonlinear elasticity at strains above ∼1%. Both phenomena are attributed to higher-order elasticity in the bulklike core upon being biased from its equilibrium configuration due to the role of surface stresses in small volumes. Quantification of the size-dependent second- and third-order elastic moduli allows for calculation of intrinsic material nonlinearity parameters, e.g., δ. Comparison of the size-independent values of δ in our nanowhiskers with studies on bulk fcc metals lends further insight into the role of length scales on both elastic and plastic mechanical behavior.

Size-dependent bandgap modulation of ZnO nanowires by tensile strain

We quantified the size-dependent energy bandgap modulation of ZnO nanowires under tensile strain by an in situ measurement system combining a uniaxial tensile setup with a cathodoluminescence spectroscope. The maximal strain and corresponding bandgap variation increased by decreasing the size of the nanowires. The adjustable bandgap for the 100 nm nanowire caused by a strain of 7.3% reached approximately 110 meV, which is nearly double the value of 59 meV for the 760 nm nanowire with a strain of 1.7%. A two-step linear feature involving bandgap reduction caused by straining and a corresponding critical strain was identified in ZnO nanowires with diameters less than 300 nm. The critical strain moved toward the high strain level with shrunken nanowires. The distinct size effect of strained nanowires on the bandgap variation reveals a competition between core-dominated and surface-dominated bandgap modulations. These results could facilitate potential applications involving nanowire-based optoelectronic devices and band-strain engineering.

Strain-gradient effect on energy bands in bent ZnO microwires

The table of contents image illustrates the strain-gradient effect on the optical-electronic properties in a bent ZnO microwire, with a much stronger red-shift on the outer tensile side than a blue-shift on the inner compressive side. The low temperature cathodoluminescence cross-sectional scanning spectra on the strain-neutral middle-plane are highlighted by thicker black lines, which clearly shows a strain-gradient induced red-shift.

The piezotronic effect of zinc oxide nanowires studied by in situ TEM

Piezotronics is a new field integrating piezoelectric effect into nanoelectronics, which has attracted much attention for the fundamental research and potential applications. In this paper, the piezotronic effect of zinc oxide (ZnO) nanowires, including the response of the electrical transport and photoconducting behaviors on the nanowire bending, has been investigated by in situ transmission electron microscopy (TEM), where the crystal structure of ZnO nanowires were simultaneously imaged. Serials of consecutively recorded current-voltage (I-V) curves along with an increase of nanowire bending show the striking effect of bending on their electrical behavior. With increasing the nanowire bending, the photocurrent of ZnO nanowire under ultraviolet illumination (UV) drops dramatically and the photo response time becomes much shorter. In addition, the dynamic nanomechanics of ZnO nanowires were studied inside TEM. These phenomena could be attributed to the piezoelectric effect of ZnO nanowires, and they suggest the potential applications of ZnO nanowires on piezotronic devices.

A review of mechanical and electromechanical properties of piezoelectric nanowires

Piezoelectric nanowires are promising building blocks in nanoelectronic, sensing, actuation and nanogenerator systems. In spite of great progress in synthesis methods, quantitative mechanical and electromechanical characterization of these nanostructures is still limited. In this article, the state-of-the art in experimental and computational studies of mechanical and electromechanical properties of piezoelectric nanowires is reviewed with an emphasis on size effects. The review covers existing characterization and analysis methods and summarizes data reported in the literature. It also provides an assessment of research needs and opportunities. Throughout the discussion, the importance of coupling experimental and computational studies is highlighted. This is crucial for obtaining unambiguous size effects of nanowire properties, which truly reflect the effect of scaling rather than a particular synthesis route. We show that such a combined approach is critical to establish synthesis-structure-property relations that will pave the way for optimal usage of piezoelectric nanowires.

In situ three-dimensional reciprocal-space mapping during mechanical deformation

Mechanical deformation of a SiGe island epitaxically grown on Si(001) was studied by a specially adapted atomic force microscope and nanofocused X-ray diffraction. The deformation was monitored during in situ mechanical loading by recording three-dimensional reciprocal-space maps around a selected Bragg peak. Scanning the energy of the incident beam instead of rocking the sample allowed the safe and reliable measurement of the reciprocal-space maps without removal of the mechanical load. The crystal truncation rods originating from the island side facets rotate to steeper angles with increasing mechanical load. Simulations of the displacement field and the intensity distribution, based on the finite-element method, reveal that the change in orientation of the side facets of about 25° corresponds to an applied pressure of 2-3 GPa on the island top plane.

Measuring true Young's modulus of a cantilevered nanowire: effect of clamping on resonance frequency

The effect of clamping on resonance frequency and thus measured Young's modulus of nanowires (NWs) is systematically investigated via a combined experimental and simulation approach. ZnO NWs are used in this work as an example. The resonance tests are performed in situ inside a scanning electron microscope and the NWs are cantilevered on a tungsten probe by electron-beam-induced deposition (EBID) of hydrocarbon. EBID is repeated several times to deposit more hydrocarbons at the same location. The resonance frequency increases with the increasing clamp size until approaching that under the "fixed" boundary condition. The critical clamp size is identified as a function of NW diameter and NW Young's modulus. This work: 1) exemplifies the importance of considering the effect of clamping in measurements of Young's modulus using the resonance method, and 2) demonstrates that the true Young's modulus can be measured if the critical clamp size is reached. Design guidelines on the critical clamp size are provided. Such design guidelines can be extended to other one-dimensional nanostructures such as carbon nanotubes.

Interferometric detection of extensional modes of GaN nanorods array

Femtosecond pump probe spectroscopy experiments were carried out to observe extensional modes of GaN nanorods. Different orders of extensional modes were generated and observed following the absorption of femtosecond light pulses. This observation confirms that with a diameter on the order of 100 nm, no mechanical change is expected compared to bulk GaN. We propose and demonstrate that the detection of these modes is achieved through the modulation of the Fabry-Pérot cavity formed by the nanorod array. The extensional modes change the nanorods length and thus modify the reflectivity of the rod-array cavity.

Vibration and buckling analysis of a piezoelectric nanoplate considering surface effects and in-plane constraints

This work investigates the surface effects on the vibration and buckling behaviour of a simply supported piezoelectric nanoplate (PNP) by using a modified Kirchhoff plate model. Two kinds of in-plane constraints are defined for the PNP, and the surface effects are accounted in the modified plate theory through the surface piezoelectricity model and the generalized Young–Laplace equations. Simulation results show that the influence of surface effects on the plate resonant frequency depends on the in-plane constraints significantly. For the PNP with different in-plane constraints, the effects of the applied electric potential, the mode number, the plate aspect ratio and the plate thickness on the resonant frequency are examined with consideration of the surface effects. The possible mechanical buckling of the PNP is also studied, and it is found that the surface effects on the critical electric voltage for buckling are sensitive to the plate thickness and aspect ratio. Our results also reveal that there exists a critical transition point at which the combined surface effects on the critical electric voltage may vanish under certain conditions.

Size dependence of dielectric constant in a single pencil-like ZnO nanowire

Scanning conductance microscopy (SCM) is used to measure the dielectric constant of a single pencil-like zinc oxide (ZnO) nanowire with the diameters ranging from 85 to 285 nm. As the diameter decreases, the dielectric constant of ZnO nanowire is found to decrease from 6.4 to 2.7, which is much smaller than that of the bulk ZnO of 8.66. A core-shell composite nanowire model in terms of the surface dielectric weakening effect is proposed to explore the origin of the size dependence of dielectric constant, and the experimental results are well explained.

Timoshenko beam model for buckling of piezoelectric nanowires with surface effects

This paper investigates the buckling behavior of piezoelectric nanowires under distributed transverse loading, within the framework of the Timoshenko beam theory, and in the presence of surface effects. Analytical relations are given for the critical force of axial buckling of nanowires by accounting for the effects of surface elasticity, residual surface tension, and transverse shear deformation. Through an example, it is shown that the critical electric potential of buckling depends on both the surface stresses and piezoelectricity. This study may be helpful in the characterization of the mechanical properties of nanowires and in the calibration of the nanowire-based force sensors.

Elastic modulus of a polymer nanodroplet: theory and experiment

We redevelop a theoretical model that, in conjunction with atomic force microscopy (AFM), can be used as a noninvasive method for determination of the elastic modulus of a polymer nanodroplet residing on a flat, rigid substrate. The model is a continuum theory that combines surface and elasticity theories for prediction of the droplet's elastic modulus, given experimental measurement of its adsorbed height. Utilization of AFM-measured heights for relevant droplets reported in the literature and from our own experiments illustrated the following: the significance of both surface and elasticity effects in determining a polymer droplet's spreading behavior; the extent of a continuum theory's validity as one approaches the nanoscale; and a droplet size effect on the elastic modulus.

Nanoscale elastic modulus of single horizontal ZnO nanorod using nanoindentation experiment

We measure the elastic modulus of a single horizontal ZnO nanorod [NR] grown by a low-temperature hydrothermal chemical process on silicon substrates by performing room-temperature, direct load-controlled nanoindentation measurements. The configuration of the experiment for the single ZnO NR was achieved using a focused ion beam/scanning electron microscope dual-beam instrument. The single ZnO NR was positioned horizontally over a hole on a silicon wafer using a nanomanipulator, and both ends were bonded with platinum, defining a three-point bending configuration. The elastic modulus of the ZnO NR, extracted from the unloading curve using the well-known Oliver-Pharr method, resulted in a value of approximately 800 GPa. Also, we discuss the NR creep mechanism observed under indentation. The mechanical behavior reported in this paper will be a useful reference for the design and applications of future nanodevices.

Subangstrom profile imaging of relaxed ZnO(10 ̅10) surfaces

Relaxation is a most basic structural behavior of free surfaces, however, direct observation of surface relaxation remains challenging in atomic-scale. Herein, single-crystalline nanoislands formed in situ on ZnO nanowires and nanobelts are characterized using aberration-corrected transmission electron microscopy combined with ab initio calculations. For the first time, displacements of both Zn and O atoms in the fresh (10 ̅10) facets are quantified to accuracies of several picometers and the under-surface distributions of contractions and rotations of Zn-O bonds are directly measured, which unambiguously verify the theoretically predicted relaxation of ZnO (10 ̅10) free surfaces. Finally, the surface relaxation is directly correlated with the size effects of electromechanical properties (e.g., elastic modulus and spontaneous polarization) in ZnO nanowires.

A computational and experimental investigation of the mechanical properties of single ZnTe nanowires

One-dimensional nanostructures such as ZnTe, CdTe, Bi(2)Te(3) and others have attracted much attention in recent years for their potential in thermoelectric devices among other applications. A better understanding of their mechanical properties is important for the design of devices. A combined experimental and computational approach has been used here to investigate the size effects on the Young's modulus of ZnTe nanowires (NWs). The mechanical properties of individual ZnTe nanowires in a wide diameter range (50-230 nm) were experimentally measured inside a high resolution transmission electron microscope using an atomic force microscope probe with the ability to record in situ continuous force-displacement curves. The in situ observations showed that ZnTe NWs are flexible nanostructures with the ability to withstand relatively high buckling forces without becoming fractured. The Young's modulus is found to be independent of nanowire diameter in the investigated range, in contrast to reported results for ZnO NWs and carbon nanotubes where the modulus increases with a decrease in diameter. Molecular dynamics simulations performed for nanowires with diameters less than 20 nm show limited size dependence for diameters smaller than 5 nm. The surface atoms present lower Young's modulus according to the simulations and the limited size dependency of the cylindrical ZnTe NWs is attributed to the short range covalent interactions.

Electrical actuation and readout in a nanoelectromechanical resonator based on a laterally suspended zinc oxide nanowire

In this paper, we present experimental results describing enhanced readout of the vibratory response of a doubly clamped zinc oxide (ZnO) nanowire employing a purely electrical actuation and detection scheme. The measured response suggests that the piezoelectric and semiconducting properties of ZnO effectively enhance the motional current for electromechanical transduction. For a doubly clamped ZnO nanowire resonator with radius ~10 nm and length ~1.91 µm, a resonant frequency around 21.4 MHz is observed with a quality factor (Q) of ~358 in vacuum. A comparison with the Q obtained in air (~242) shows that these nano-scale devices may be operated in fluid as viscous damping is less significant at these length scales. Additionally, the suspended nanowire bridges show field effect transistor (FET) characteristics when the underlying silicon substrate is used as a gate electrode or using a lithographically patterned in-plane gate electrode. Moreover, the Young's modulus of ZnO nanowires is extracted from a static bending test performed on a nanowire cantilever using an AFM and the value is compared to that obtained from resonant frequency measurements of electrically addressed clamped–clamped beam nanowire resonators.

Role of five-fold twin boundary on the enhanced mechanical properties of fcc Fe nanowires

The role of 5-fold twin boundary on the structural and mechanical properties of fcc Fe nanowire under tension is explored by classical molecular dynamics. Twin-stabilized fcc nanowire with various diameters (6-24 nm) are examined by tension tests at several temperatures ranging from 0.01 to 1100 K. Significant increase in the Young's modulus of the smaller nanowires is revealed to originate from the central area of quinquefoliolate-like stress-distribution over the 5-fold twin, rather than from the surface tension that is often considered as the main source of such size-effects found in nanostructures. Because of the excess compressive stress caused by crossing twin-boundaries, the atoms in the center behave stiffer than those in bulk and even expand laterally under axial tension, providing locally negative Poisson's ratio. The yield strength of nanowire is also enhanced by the twin boundary that suppresses dislocation nucleation within a fcc twin-domain; therefore, the plasticity of nanowire is initiated by strain-induced fcc→bcc phase transformation that destroys the twin structure. After the yield, the nucleated bcc phase immediately spreads to the entire area, and forms a multigrain structure to realize ductile deformation followed by necking. As temperature elevated close to the critical temperature between bcc and fcc phases, the increased stability of fcc phase competes with the phase transformation under tension, and hence dislocation nucleations in fcc phase are observed exclusively at the highest temperature in our study.

Electron beam irradiation stiffens zinc tin oxide nanowires

We report a remarkable phenomenon that electron beam irradiation (EBI) significantly enhances the Young's modulus of zinc tin oxide (ZTO) nanowires (NWs), up to a 40% increase compared with the pristine NWs. In situ uniaxial buckling tests on individual NWs were conducted using a nanomanipulator inside a scanning electron microscope. We propose that EBI results in substantial atomic bond contraction in ZTO NWs, accounting for the observed mechanically stiffening. This argument is supported by our experimental results that EBI also reduces the electrical conductivity of ZTO NWs.