Size-dependent Mechanical Properties Research Articles

Size Dependent Mechanical Properties of Graphene Nanoribbons: Molecular Dynamics Simulation

Strain engineering is an effective method to tune the band gap and electronic transport properties of graphene nanoribbons (GNRs). However, strain/stress field may promote the system deviating from the equilibrium state, and the mechanical stability will become one of the key issues for reliable services of relevant devices. In this paper, the size-dependent mechanical properties of GNRs under tensile loading were studied by Molecular Dynamics (MD) simulations. The results indicate that the yield stress of both zigzag and armchair GNRs decreases with the ribbon length changing from 240 Å to 30 Å. However, the ductility of armchair GNRs was significantly improved. Radial Distribution Function (RDF) was employed to analyze the evolution of atomic configurations. It showed that lattice shearing is the main mechanism for the ductility of armchair GNRs.

SYNTHESIS OF NOVEL NANOSTRUCTURED LANTHANUM COBALT FERRITE MIXED METAL OXIDES BY SOL–GEL

Properties of nanoscale materials are very interesting and these are either comparable to or superior to those of bulk. These materials are interesting due to their exciting size dependent optical, electronic, magnetic, thermal, mechanical and chemical properties. Different mole ratios of nanostructured mixed metal oxides of LaCo x Fe 1-x O 3-δ (x = 0 to 1) were prepared by the sol–gel method by varying the mole ratios of iron and cobalt substrates. The compounds were sintered for 700°C in the tubular furnace for 8 h. The purity of the compounds was analyzed by TG-DTA. The compounds were characterized by X-ray diffraction (XRD), Fourier transform infrared (FT-IR) and scanning electron microscopy (SEM) studies were employed to study the structural phases, vibrational frequencies, surface morphology of the highest humidity sensing compounds.

Size dependent mechanical properties of electrospun polymer fibers from a composite structure

The elastic modulus of individual electrospun polyvinyl-alcohol (PVA) fibers was measured using atomic force microscopy (AFM) based bending tests. Results indicated an increase in the elastic modulus as the fiber diameter decreased. Consideration of electrospun fibers as a composite structure consisting of a shell region of aligned polymer chains surrounding a bulk-like isotropic core was analytically modeled and showed good agreement with the experimental data. Phase contrast AFM imaging of focused ion beam (FIB) prepared PVA fiber cross-sections provided a method of observing the shell–core structure directly and supported the model proposed. These findings indicate the potential for considerable polymer chain alignment for the production of high performance fibers using electrospinning methods.

Size dependent mechanical properties of single crystalline nickel nanowires

Using a simple micromechanical device, in situ tensile testing of single crystalline nickel (Ni) nanowires (NWs) with different diameters (100 to 300 nm) and crystalline orientations was performed inside a scanning electron microscope. With the aid of a quantitative nanoindenter and corresponding theoretical analysis, the load applied to the sample and the sample displacement were ascertained from nanoindenter load versus displacement curves so as to obtain engineering stress-strain curves. Limited plasticity and brittle-like fracture modes were evident in the Ni NWs investigated, and the breaking strength values were found to be much higher than that of the bulk material. More important, the critical resolved shear stress was found to increase as the NW diameter decreased, showing strong size dependence. The quantitative experimental results from this work could offer important insights into the origin of the size dependent mechanical behaviors of metals at the nano-scale.

Analytical study on size-dependent static pull-in voltage of microcantilevers using the modified couple stress theory

In this paper an analytical solution for size-dependent response of cantilever micro-beams is presented. Using the modified couple stress theory, the small scale effects are accounted for. Employing the Modified Variational Iteration Method, efficient and accurate analytical expressions for the deflection of the micro-beam are presented. Very good agreement is observed between the present work results and available experimental data. This study may be helpful to characterize the size-dependent mechanical properties of MEMS. Consequently, the proposed analytical solution can be used as an efficient tool for studying the effects of the material or geometrical parameters on small scale devices consisting of micro-beams for their design and optimization which requires a large number of simulations.

A variable constraint tube model for size effects of polymer nano-structures

We develop a molecular-based hyperelastic model to simulate the size dependent mechanical properties of polymer nano-structures. We assume that polymer chains are confined to a different “tube” size in a boundary layer than that in the core, which alters the free energy and produces the size effect. Simulations also explore anisotropic orientations of polymer chains and surface tension. The axial modulus of nanofibers is studied in detail, although the model is applicable to other systems like thin films and nano-biological systems.

Size-dependent non-linear mechanical properties of graphene nanoribbons

An atomistic, spring-based, non-linear finite element method is implemented in order to predict the non-linear mechanical behavior of graphene nanoribbons. According this method, appropriate non-linear springs are utilized to simulate each interatomic interaction. Their force–displacement curve follows the relation between the first differentiation of the potential energy of the corresponding interaction-bond deformation. The potential which corresponds to the bond angle variation is simulated by a torsional spring, while the bond stretching is simulated by a uniaxial compression/extension spring. The linear approximation, commonly made in the literature for the bond angle bending interaction, is not followed here and thus the overall non-linear response of the specific interaction is accurately introduced into the model. Following the proposed formulation, the tensile uniaxial stress–strain behavior for various graphene nanoribbons, of zigzag as well as armchair orientation, arise. The results demonstrate that the linear and non-linear mechanical properties are strongly dependent on the structure as well as on the size of the graphene strip tested.

Molecular dynamics study on diamond nanowires mechanical properties: Strain rate, temperature and size dependent effects

Using molecular dynamics simulations, strain rate, temperature and size dependent mechanical properties of < 001 > orientation diamond nanowires are investigated. It is found that, for the same cross-sectional areas, strain rates have almost no effect on yield strength and Young's modulus, provided strain rates are within the range from 0.001 to 0.025 ps − 1 . Our calculated results have also indicated that, at the temperature ranging from 100 to 500 K, diamond nanowires' yield strength, Young's modulus, fracture strength and fracture strain are all decreasing with increasing temperature. Furthermore, at the temperature of 300 K, yield strength, Young's modulus, fracture strength and fracture strain increase dramatically with increasing cross sectional area. Finally, orientation dependent diamond nanowires mechanical properties are studied.

Finite element model of ionic nanowires with size-dependent mechanical properties determined by ab initio calculations

A finite element procedure for modeling crystalline nanostructures such as nanowires is proposed. The size effects exhibited by nanoobjects are captured by taking into account a surface energy, following the classical Gurtin–Murdoch surface elasticity theory. An appropriate variational form and a finite element approach are provided to model and solve relevant problems numerically. We describe a simplified technique based on projection operators for constructing the surface elements. The methodology is completed with a computational procedure based on ab initio calculations to extract elastic coefficients of general anisotropic surfaces. The FEM continuum model is validated by comparisons with complete ab initio models of nanowires with different diameters where size-dependent mechanical properties are observed. The FEM continuum model can then be used to model similar nanostructures in ranges of sizes or geometries where analytical or atomistic model is limited. The validated model is applied to the analysis of size effects in the bending of an AlN nanowire.

Surface effects in various bending-based test methods for measuring the elastic property ofnanowires

The size-dependent elastic property of nanowires induced by the surface effect isinvestigated by using the core–shell model. The overall effective elastic moduli ofnanowires with regular polygonal cross-sections are unified into a simple and explicitrelation. It is found that the effect of surface elasticity on the elastic moduli can bewell characterized by two dimensionless material and geometric parameters withclear physical meaning. Finite element simulations demonstrate that the derivedtheoretical relation is applicable for all the vibration, bending, and buckling testmethods for measuring the mechanical properties of nanowires. The analyticalresult is also validated by comparing it with relevant experimental measurements.This study is helpful not only for interpreting various phenomena associatedwith size-dependent mechanical properties of nanowires but also for developingand evaluating test techniques for material characterization at the nanoscale.

Higher-order harmonic resonances and mechanical properties of individual cadmium sulphide nanowires measured by in situ transmission electron microscopy

The higher-order harmonic resonances, including second and third harmonic modes, were induced by applying alternative current signals inside a high-resolution transmission electron microscope (HRTEM), which have been used to study the mechanical properties of individual cadmium sulphide (CdS) nanowires. Young's moduli (E) and mechanical quality factors (Q) of individual CdS nanowires with diameters in the range of 50-350 nm were measured with the assistance of the mechanical resonances. The results indicate that the smooth nanowires have larger E and Q in comparison with the rough nanowires, and for the rough nanowires, E and Q increase with increasing diameters. The morphology- and size-dependent mechanical properties of CdS nanowires are directly correlated with their structure, as imaged by in situ TEM.

Size-dependent mechanical properties of PVA nanofibers reduced via air plasmatreatment

Organic nanowires/fibers have great potential in applications such as organicelectronics and soft electronic techniques. Therefore investigation of their mechanicalperformance is of importance. The Young’s modulus of poly(vinyl alcohol) (PVA)nanofibers was analyzed by scanning probe microscopy (SPM) methods. Air plasmatreatment was used to reduce the nanofibers to different sizes. Size-dependentmechanical properties of PVA nanofibers were studied and revealed that theYoung’s modulus increased dramatically when the scales became very small (<80 nm).

Field-Induced Microwave Absorption in Ni Ferrite Nanoparticles

Ferrite nanoparticles are in the last years a matter of strong interest due to the fact that nanoscale materials possess size-dependent optical, electronic, magnetic, thermal, mechanical, and chemical properties that are comparable to or superior to those of bulk material counterparts, as well as its potential applications in sensors or microwave devices. Nickel ferrites, which are well-known technological materials in various electronic devices, were prepared in the form of nanoparticles by a modified sol-gel technique employing coconut oil, and then annealed at different temperatures in the 400 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> C-1200 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> C range. This route of preparation has been revealed to be one efficient and cheap technique to obain high-quality nickel ferrite nanosized powder. Sample particle sizes obtained with X-ray diffraction data and Scherrer's formula lie in 13-138 nm, with increased size with annealing temperature. Magnetic field-induced microwave absorption in nanoscale ferrites is a recent an active area of research, in order to characterize and explore potential novel applications. In the present work, microwave magnetoabsorption data of the annealed nickel ferrite nanoparticles are presented. These data have been obtained with a system developped in our laboratory, based on a network analyzer that operates in the frequency range 0-8.5 GHz. We can observe a resonance peak with applied fields of up to 400 mT. The results are interpreted on the basis of ferromagnetic resonance theory.

Three-Dimensional Modeling for Thin Plate-Like Structures Including Surface Effects by Using State Space Method

A three-dimensional (3-D) approach based on the state space method is proposed to study size-dependent mechanical properties of ultra-thin plate-like elastic structures considering surface effects. The structure is modeled as a laminate composed of a bulk bounded with upper and bottom surface layers, which are allowed to have different material properties from the bulk layer. State equations, including the surface properties of the structure, can be established on the basis of 3-D fundamental elasticity to analyze the size-dependent static characteristics of the thin plate-like structure. Compared with two-dimensional plate theories based size-dependent models for thin film structures in literature, the present 3-D approach is exact, which can provide benchmark results to assess the accuracy of 2-D plate theories and various numerical approaches. To show the feasibility of the proposed approach, a 3-D analytical solution for a simply supported plate-like thin structure including surface layers is derived. An algorithm is proposed for the calculation of the state equations obtained to ensure that the numerical results can reveal the surface effects clearly even for extremely thin surface layers. Numerical examples are carried out to exhibit the surface effects and some discussions are provided based on the results obtained.

Molecular Dynamics Simulation of ZnO Nanowires: Size Effects, Defects, and Super Ductility

Molecular dynamics simulations of ZnO nanowires under tensile loading were performed and compared with simulations of TiO(2) wires to present size-dependent mechanical properties and super ductility of metal oxide wires. It is shown that while large surface-to-volume ratio is responsible for their size effects, ZnO and TiO(2) wires displayed opposite trends. Although the stiffness of both wires converged monotonically to their bulk stiffness values as diameter increases, bulk stiffness represented the upper bound for ZnO nanowires as opposed to the lower bound for TiO(2) wires. ZnO nanowires relaxed to either completely amorphous or completely crystalline states depending on wire thickness, whereas a thin amorphous shell is always present in TiO(2) nanowires. It was also found that when crystalline ZnO nanowires are stretched, necking initiated at localized amorphous regions to eventually form single-atom chains which can sustain strains above 100%. Such large elongations are not observed in TiO(2) nanowires. Using the analogy of a clothesline, an explanation is offered for the necessary conditions leading to super ductility.

Thickness and grain size dependent mechanical properties of Cu films studied by nanoindentation tests

The hardness and the elastic modulus of Cu films with thickness (t) and grain size (d) have been investigated by nanoindentation tests. The d and the indentation depth increase linearly with the increase in t. The hardness rises with the decrease in t, whereas the elastic modulus is independent of t and it is about 20% less than conventional coarse-grained Cu. The enhanced hardness is attributed to the smaller d and the indentation depth. The analysis of load–displacement curves indicates that the scope of the critical shear stress for different thick Cu films ranges from 3.2 to 4.1 GPa, which is similar to the theoretical shear stress of single crystalline Cu. The present results are explained by the dislocation mediated mechanism even if d reaches about 16.4 nm for the Cu film with t = 180 nm.

A geometrically nonlinear finite element model of nanomaterials with consideration of surface effects

In conventional continuum mechanics, the surface energy is usually small and negligible. But at nano-length scale, it becomes a significant part of the total elastic energy due to the high specific surface area of nanomaterials. A geometrically nonlinear finite element (FE) model of nanomaterials with considering surface effects is developed in this paper. The aim is to extend the conventional finite element method (FEM) to analyze the size-dependent mechanical properties of nanomaterials. A numerical example, analysis of InAs quantum dot (QD) on GaAs (0 0 1) substrate, is given in this paper to verify the validity of the method and demonstrate surface effects on the stress fields of QDs.

The influence of surface effects on size-dependent mechanical properties of silicon nanobeams at finite temperature

Silicon is one of the most remarkable materials for applications in mechanical sensors. A semi-continuum atomistic lattice model is proposed here for the size-dependent mechanical analysis of a silicon nanobeam, with the influence of surface effects and temperature taken into consideration. Based on the quasiharmonic approximation, the strain energy of the silicon nanobeam with several relaxed layers at a finite temperature is obtained by using the anharmonic Keating model. The semi-continuum model predicts that the size effects of Young's modulus for simple tension depend on both the relaxation coefficient and the temperature, and the size effects of the effective elastic modulus of the bending silicon nanobeam depend on the temperature and the competition between the relaxation coefficient and the surface tension, while the influences of surface effects and temperature on the effective bending stiffness are too small to be considered. This model also shows that the temperature coefficients of Young's modulus and the effective elastic modulus are negative and nonlinear.

Size-Dependent Mechanical Properties of Polymer-nanowires Fabricated by Two-photon Lithography

AbstractTwo-photon lithography allows us to fabricate arbitrary three-dimensional structures with micro/nano-spatial resolution. The intrinsic three-dimensional spatial resolution of two-photon lithography is a promising tool for developing a variety of novel photonic and mechanical nano-devices. In addition, two-photon lithography makes it possible to study the properties of polymers of micro/nano-meter dimension [1-4]. In this presentation, we show the evidence that the elasticity and the transition temperature of polymers start to show size-dependent characteristics when the size of the polymer decreases down to a few hundreds of nanometers. We fabricated free-standing polymer nano-wires in the shape of coil spring by two-photon lithography, and measured the elasticity of the nano-wires by applying a mechanical tension onto the springs through laser trapping technique under temperature control. From the stretching length of the spring generated by a certain optical force, the spring constant of the spring and the shear modulus of polymer were calculated from simple Hook’s law. The material we used is a compound of methyl-methacrylate, dipentaerythritol hexaacrylate, benzil, and 2-benzyl-2-(dimethylamino)-4’-morpholino-butyrophenone. We scanned a light spot of a Ti:Sapphire laser at 780 nm with a pulse width of 80 fs focused by a 1.4 NA microscope objective to shape the polymer nano-wires suspended by a thick pillar. We observed that the elasticity of the polymer, which is usually an invariable coefficient, changes according to the thickness of the polymer wire. Furthermore, we changed the temperature of the entire polymer structures from -20 to 40 °C with measuring the elasticity of the springs. We observed phase transition of polymer wires with a rapid change of the share modulus, which also shows a size-dependent behavior. Recently, the similar experimental results, i.e. the drop of the glass transition temperature, were also reported in thin polymer nano-films. Our result is a clear evidence of such a nano size-effect of mechanical properties in polymers confirmed from free-standing polymer nanostructures. [1]S. Nakanishi, H. Yoshikawa, S. Shoji, Z. Sekkat, and S. Kawata, J. Phys. Chem. B 112, 3586-3589 (2008). [2] S. Nakanishi, S. Shoji, S. Kawata, and H.-B. Sun, Appl. Phys. Lett. 91, 063112 (2007). [3]H. Ishitobi, S. Shoji, T. Hiramatsu, H.-B. Sun, Z. Sekkat, and S. Kawata, Opt. Express 16, 14106-14114 (2008). [4]S. Kawata, H.-B. Sun, T. Tanaka, and K. Takada, Nature, 412, 697 (2001).

Influence of microstructure on the mechanical properties and the forming behaviour of very thin metal foils

The demand for accurate process design of microforming processes is increasing steadily due to ongoing miniaturisation. Occurring size effects, however, prevent the transfer of existing know-how of standard sheet forming processes with conventional dimensions like blanking, bending and deep drawing on microforming processes. These size effects are either generally valid for all microforming processes, as the influence of the share of surface grains are process-specific, like the influence of large strain gradients as they appear, e.g. in bending processes. A decisive parameter for the occurrence of size effects is the ratio of material mean grain size to foil thickness. For a simulation-based description of microforming processes, the implementation of size-dependent material behaviour in finite element (FE) simulation is essential. Hence, a reliable determination of size-dependent mechanical properties as input data for FE simulation is needed to provide a broad fundamental database for a future theoretical description of microforming processes. In the present paper, the influence of the material microstructure on the mechanical properties of metal foils with thicknesses ranging from 25 to 500 μm is discussed based on tensile tests, bulge tests and fundamental bending experiments. Challenges resulting from the small thickness of the metal foils are pointed out, and future demands regarding determination of material characteristics of thin metal foils are presented.