Atomic-scale investigation on the ultra-large bending behaviours of layered sodium titanate nanowires

Liu, Qiong; Zhan, Haifei; Zhu, Hua; Sun, Ziqi; Bell, John; Bo, Arixin; Gu, Yuantong

doi:10.1039/c9nr02082a

Cited by 7 publications

(8 citation statements)

References 41 publications

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“…A colloidal thin film was used to induce the bending deformation directly, protecting NWs from damage and contamination during the NW manipulation and welding involved in the methods mentioned above. 13,14,28 Unlike conventional ZnO NWs, the as-prepared wurtzite ZnO NWs inherit rich axial SFs lying in pyramidal I (π 1 ) planes or prismatic planes introduced during the synthetic process. The ZnO NWs possess considerable flexibility with measured ultralarge bending strains up to 20%.…”

Section: ■ Introductionmentioning

confidence: 99%

Exceptional Deformability of Wurtzite Zinc Oxide Nanowires with Growth Axial Stacking Faults

et al. 2021

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To ensure reliability and facilitate the strain engineering of zinc oxide (ZnO) nanowires (NWs), it is significant to understand their flexibility thoroughly. In this study, singlecrystalline ZnO NWs with rich axial pyramidal I (π 1 ) and prismatic stacking faults (SFs) are synthesized by a metal oxidation method. Bending properties of the as-synthesized ZnO NWs are investigated at the atomic scale using an in situ high-resolution transmission electron microscopy (HRTEM) technique. It is revealed that the SF-rich structures can foster multiple inelastic deformation mechanisms near room temperature, including active axial SFs' migration, deformation twinning and detwinning process in the NWs with growth π 1 SFs, and prevalent nucleation and slip of perfect dislocations with a continuous increased bending strain, leading to tremendous bending strains up to 20% of the NWs. Our results record ultralarge bending deformations and provide insights into the deformation mechanisms of single-crystalline ZnO NWs with rich axial SFs.

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Section: ■ Introductionmentioning

confidence: 99%

Exceptional Deformability of Wurtzite Zinc Oxide Nanowires with Growth Axial Stacking Faults

et al. 2021

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“…In this way the global rigid displacements are eliminated. 5 Based on the three previous hypotheses, the displacement eld is derived as the outcome of the coupled eects generated by both longitudinal and transver-…”

Section: Kinematicsmentioning

confidence: 99%

“…The bending behaviors of nanowire families and other one-dimensional nanomaterials with layered crystalline structures are also investigated at the atomicscale [5] (see also [6] and [7]). In this context, there is a growing interest in the exoelectric eect, since experimental results demonstrate large exoelectric bending [8], [9].…”

Section: Introductionmentioning

confidence: 99%

Nonuniform bending theory of hyperelastic beams in finite elasticity

Lanzoni

Tarantino

2021

International Journal of Non-Linear Mechanics

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This paper deals with the equilibrium problem of slender beams inexed under variable curvature in the framework of fully nonlinear elasticity. For the specic case of uniform exion, the authors have recently proposed a mathematical model. In that analysis, the complete threedimensional kinematics of the beam is taken into account, both deformations and displacements are considered large and a compressible Mooney-Rivlin law is assumed for the stored energy function. In the present paper, the kinematics of the aforementioned model has been reformulated taking into account beams under variable curvature. Subsequently, focusing on the local determination of the curvature, new equilibrium conditions on cross sections are introduced in the mathematical formulation. The governing equations take the form of a coupled system of three equations in integral form, which is solved numerically through an iterative procedure. Thus, for the generic class of hyperelastic and isotropic materials, explicit formulae for the displacement eld, the stretches and stresses in every point of the beam, following both Lagrangian and Eulerian descriptions, are derived. The analysis developed allows to study a very wide class of equilibrium problems for nonlinear beams under dierent restraint conditions and subject to generic external load systems. By way of example, the Euler beam has been considered and the formulae obtained have been specialized for a specic neoprene rubber material, the constitutive constants of which are determined experimentally. The shapes assumed by the beam as the load multiplier increases are shown through some graphs. The distributions of stretches and Cauchy stresses are plotted for the most stressed cross section. Some comparisons were made using a Finite Element code. In addition, the accuracy of the solution obtained is estimated by evaluating a posteriori that the equilibrium equations are locally satised.

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“…The SMA wire is connected to both ends of the beam, so that a small change in the strain of the SMA wire results in a large bending deformation of the beam [19]. There is a growing interest in the flexoelectric effect, since experimental results shown large flexoelectric bending [20], [21], [22] and [23]. In particular, a direct observation of extraordinarily large and reversible bending in dysprosium scandate is reported in [24].…”

Section: Introductionmentioning

confidence: 99%

Bending of nanobeams in finite elasticity

Lanzoni

Tarantino

2021

International Journal of Mechanical Sciences

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Motivated by the need to have a nonlinear beam model usable at the nanoscale, in this paper, the equilibrium problem of inflexed nanobeams in the context of nonlocal finite elasticity is investigated. Therefore, considering both deformations and displacements large the complete threedimensional kinematics of an inflexed nanobeam is derived on the basis of classic assumption that cross sections maintain their planarity (Bernoulli Navier hypothesis). Extending the Eringen theory, a constitutive law in integral form for the nonlocal tensor of Cauchy stresses has been then proposed. Finally, by imposing the equilibrium conditions, the governing equations are obtained. These take the form of a coupled system of three equations in integral form, which is solved numerically. Explicit formulae for displacements, stretches and stresses in every point of the nanobeam are derived. By way of example, a simply supported nanobeam has been considered. The shapes assumed by the inflexed nanobeam, as the internal characteristic length varies, are shown through some graphs. The results obtained have been discussed and compared with those provided by the local theory.

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Atomic-scale investigation on the ultra-large bending behaviours of layered sodium titanate nanowires

Cited by 7 publications

References 41 publications

Exceptional Deformability of Wurtzite Zinc Oxide Nanowires with Growth Axial Stacking Faults

Exceptional Deformability of Wurtzite Zinc Oxide Nanowires with Growth Axial Stacking Faults

Nonuniform bending theory of hyperelastic beams in finite elasticity

Bending of nanobeams in finite elasticity

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