Multi-armed nanorods and nanobars of semiconductor selenium were simultane- ously synthesized in the light of biomineralization process through bio-membrane bi-templates of rush at room temperature. The multi-armed na...Multi-armed nanorods and nanobars of semiconductor selenium were simultane- ously synthesized in the light of biomineralization process through bio-membrane bi-templates of rush at room temperature. The multi-armed nanorods are 60 nm in diameter and 1.5 μm in length; the nanobars are 150 nm in diameter and 1000—1100 nm in length. The XRD pattern indicates that these nanocrystals were crystallized in the hexagonal structure with lattice constants a = 0.437 nm, c = 0.495 nm. The possible formation mechanism was investigated.展开更多
A naturally discrete nanobar implies that the continuum axiom fails, and the surface-to-volume ratio is very large. The nonlocal theory of elasticity releasing the continuum axiom and the surface theory of elasticity ...A naturally discrete nanobar implies that the continuum axiom fails, and the surface-to-volume ratio is very large. The nonlocal theory of elasticity releasing the continuum axiom and the surface theory of elasticity are therefore employed to model tensile nanobars in this work. As commonly believed in the current practice, the axial nonlocal effect is only taken into account to analyze the mechanical behaviors of nanobars, regardless of the three-dimensional inherent atomistic interactions. In this study,a three-dimensional nonlocal constitutive law is developed to model the true nonlocal effect of nanobars, and based on which,a self-consistent variational bar model is proposed. It has been revealed for the first time how both the cross-sectional nonlocal interactions and the axial nonlocality affect the tensile behaviors of nanobars. It is found that the nonlocal influence predicted by the currently axial nonlocal bar model is grossly underestimated. Both the nonlocal cross-sectional and axial interactions become significant when the length-to-height ratio of nanobars is small. If the length-to-height ratio is relatively large(slender bars), the main nonlocal effect stems, however, from the nonlocal cross-sectional effect, rather than the axial nonlocal effect. This work also shows that it is possible to overcome the ill-posed problem of the pure nonlocal integral elasticity by employing both the pure nonlocal integral elasticity and surface elasticity. A well-posed size-dependent governing equation has been established for modeling nanobars under tension, and closed-form solutions are derived for their displacements. Based on the closed-form solutions, the effective elastic modulus is obtained and will be useful for calibrating the physical quantities in the "discretecontinuum" transition region for a span-scale modeling approach. It is shown that the effective elastic modulus may be softening or hardening, depending on the competition between the surface(modulus-hardening) and nonlocal(modulus-softening) effects.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.20175013&20471042)Nano-Foundation of Shanghai in China(Grant Nos.0259 nm021,0352 nm129).
文摘Multi-armed nanorods and nanobars of semiconductor selenium were simultane- ously synthesized in the light of biomineralization process through bio-membrane bi-templates of rush at room temperature. The multi-armed nanorods are 60 nm in diameter and 1.5 μm in length; the nanobars are 150 nm in diameter and 1000—1100 nm in length. The XRD pattern indicates that these nanocrystals were crystallized in the hexagonal structure with lattice constants a = 0.437 nm, c = 0.495 nm. The possible formation mechanism was investigated.
基金support of the National Natural Science Foundation of China(Grant No.51605172)support of the Fundamental Research Funds for the Central Universities,Zhongnan University of Economics and Law(Grant No.2722020JCG060)the National Natural Science Foundation of China(Grant No.11801570)。
文摘A naturally discrete nanobar implies that the continuum axiom fails, and the surface-to-volume ratio is very large. The nonlocal theory of elasticity releasing the continuum axiom and the surface theory of elasticity are therefore employed to model tensile nanobars in this work. As commonly believed in the current practice, the axial nonlocal effect is only taken into account to analyze the mechanical behaviors of nanobars, regardless of the three-dimensional inherent atomistic interactions. In this study,a three-dimensional nonlocal constitutive law is developed to model the true nonlocal effect of nanobars, and based on which,a self-consistent variational bar model is proposed. It has been revealed for the first time how both the cross-sectional nonlocal interactions and the axial nonlocality affect the tensile behaviors of nanobars. It is found that the nonlocal influence predicted by the currently axial nonlocal bar model is grossly underestimated. Both the nonlocal cross-sectional and axial interactions become significant when the length-to-height ratio of nanobars is small. If the length-to-height ratio is relatively large(slender bars), the main nonlocal effect stems, however, from the nonlocal cross-sectional effect, rather than the axial nonlocal effect. This work also shows that it is possible to overcome the ill-posed problem of the pure nonlocal integral elasticity by employing both the pure nonlocal integral elasticity and surface elasticity. A well-posed size-dependent governing equation has been established for modeling nanobars under tension, and closed-form solutions are derived for their displacements. Based on the closed-form solutions, the effective elastic modulus is obtained and will be useful for calibrating the physical quantities in the "discretecontinuum" transition region for a span-scale modeling approach. It is shown that the effective elastic modulus may be softening or hardening, depending on the competition between the surface(modulus-hardening) and nonlocal(modulus-softening) effects.
