耦合作用下线材结构力电性能分析
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摘要
在纳米器件、纳机电系统以及热核聚变实验反应堆超导磁体系统等中,涉及大量线材结构力学性能尺度效应、力电耦合作用问题,其直接关系到实际装置的性能指标和可靠运行。为此,本文针对金属纳米线材力学性能,金属纳米线材、zn0纳米线材应用中的电场效应,以及复合超导线材临界电流密度的应变效应开展了理论研究工作。
首先,从原子结合能出发,对有广泛用途的fcc金属纳米线材,建立了基于原子间相互作用规律并便于实际应用的表征其弹性的杨氏模量解析模型。通过考察表面原子弛豫导致的原子键强度的变化,得到了与fcc金属纳米线材杨氏模量尺寸效应相关的尺度函数,给出了估算fcc金属纳米线材杨氏模量的简单公式,该式表明了表面原子弛豫导致的键强化在金属纳米线材杨氏模量尺寸效应中的主导作用,理论模型与实验结果定性吻合；与基于连续介质的建模方法相比,本文分析简化了描述低维材料力学性能尺寸效应所需的材料参数个数。
其次,结合经典的分子动力学模拟和连续介质电动力学,定量给出了外加侧向电场对金属纳米线材力学性质的影响,模拟结果表明：表面电场负压的存在会导致纳米线材杨氏模量的减小和泊松比的增大。同时,这种电场效应随着表面电势的增大而增大、随着纳米线材直径及其与基面距离的增大而减小。
再次,在连续介质力学框架内,通过求解表面应力作用下基底上纳米线材的自平衡应变场,澄清了已有文献关于表面应力对于微纳米梁结构等效刚度的影响机理认识的不足之处,讨论了不同变形模式下纳米线材的力学行为,着重分析了采用机械共振方法测量低维材料力学性能参数时,静电力作用下纳米线材的动力响应行为,给出了表面应力,残余应变,电场对于纳米线材振动频率的影响关系,在此基础上实现了对已有实验中ZnO纳米线材杨氏模量尺寸效应的定量以及定性差异的统一解释。
最后,从应变对Nb3Sn超导材料费米面上态密度的影响出发,给出了描述临界电流密度三维应变效应的标度关系,该标度关系在退化情形下可以很好地描述一维超导线材和二维超导带材临界性能应变作用规律的实验结果；并且本文给出的理论模型在退化情形下与已有的一维经验关系具有形式上的一致性。以拉伸模式下Nb3Sn超导线材临界电流密度的测量为例,初步讨论了线材中超导丝区域应变分布的结构效应。
总之,通过本文的工作,进一步理解了纳米线材杨氏模量的尺寸效应,以及纳米线材力学性能测量中的力电效应,为相关纳米器件的研制以及纳米测量技术完善奠定了一定的基础；同时,对超导线材临界电流密度应变效应的认识,为其在实际工程中的应用提供了一定的理论指导。
Wire structures have wide application prospects in varied fields, including nanodevices, nanoelectromechanical systems (NEMS), and thermonuclear experimental reactor magnet system. The size dependent mechanical properties, and electro-mechanical coupling effects of which are involved in the applications due to gaining relevance in the operation performance criteria and controlling functionality of the actual device. Therefore, theoretical studies on the mechanical properties of metal nanowires, the electric field effects in the metal nanowire/ZnO nanowire based NEMS, and the strain effects in the critical current density of composite superconducting wires are carried on in this thesis.
Firstly, from the viewpoint of the atom binding energy, a Young's modulus model is proposed for the widely used fee metal nanowires, which allows for an analytical study on the elastic behavior from the perspective of atomic interactions and easy application in engineering practice. By examining the bond-strength enhancing arising from the spontaneous bond relaxation, a scale function is obtained and a simple formula characterizing the Young's modulus of the fee metal nanowires is given, which indicate the key role the bond-strength enhancing plays in the size-dependent elastic properties. There is good qualitative agreement between theoretical predictions and experimental observations. The number of material parameters needed for the low dimensional material Young's modulus modeling in this paper is reduced by comparing with the continuum modeling approach.
Secondly, elastic properties of metal nanowires in a transverse electric field are investigated using molecular dynamics simulations and classical electrostatics theory. The negative pressure on the surfaces stemmed from the transverse electric field modifies the Young's modulus and Poisson's ratio of nanowires significantly. The simulation results reveal the decrease in Young's modulus and the increase in Poisson's ratio as a result of the negative pressure. With the increase of the applied voltage and decreasing the distance between the nanowire and the ground plane, the electromechanical coupling effect on elastic properties of nanowires becomes more remarkable.
Thirdly, within the framework of continuum mechanics, the self-equilibrium strain field of nanowire-structure on substrate under the surface stress is derived. An inadequate understanding of the physics responsible for the observed stiffness change of micro/nano cantilevers originating from surface stress in the previous literatures is demonstrated. The mechanical behavior of nanowire under different loading modes is studied; the elastic modulus measurement systems of nanowires using an electric-field-induced resonance flexure method are carefully analyzed. The resonance frequency dependence on the surface stress, the residual strain, as well as the electric field is obtained. On the basis of the analysis, the agreement of the theoretical predictions and experimental observations of different trends of the Young's modulus of ZnO nanowires varying with the diameter is achieved, a unified explanation is made.
Finally, a scaling law for the three-dimensional strain dependence of the critical current of Nb3Sn conductors is established, which considers the strain effects on the electron density of state at the Fermi level. The scaling law, in the degenerate form, describes well experimental data, such as critical properties measurements of one-dimensional superconducting wires and two-dimensional superconducting tapes under applied strain. And there is consistency in the form between the degenerate formula and the one-dimensional empirical relation for the variation of critical current density with the axial strain. Taking the critical current measurements of Nb3Sn wires under tensile loading mode as example, a preliminary study is conducted to investigate the structure effects on the strain field distribution in the superconducting filaments.
In conclusion, through this paper, we can get further understanding of the size dependent Young's modulus of nanowire and the electromechanical effects in the nanowire-based systems. It lays the foundation for the realization of NEMS systems and the improvement of the nanomechanical test systems. At the same time, studying the effects of strain on the critical current density of Nb3Sn composite wires would provide theoretical guidance to engineering application of superconductors.
首先,从原子结合能出发,对有广泛用途的fcc金属纳米线材,建立了基于原子间相互作用规律并便于实际应用的表征其弹性的杨氏模量解析模型。通过考察表面原子弛豫导致的原子键强度的变化,得到了与fcc金属纳米线材杨氏模量尺寸效应相关的尺度函数,给出了估算fcc金属纳米线材杨氏模量的简单公式,该式表明了表面原子弛豫导致的键强化在金属纳米线材杨氏模量尺寸效应中的主导作用,理论模型与实验结果定性吻合；与基于连续介质的建模方法相比,本文分析简化了描述低维材料力学性能尺寸效应所需的材料参数个数。
其次,结合经典的分子动力学模拟和连续介质电动力学,定量给出了外加侧向电场对金属纳米线材力学性质的影响,模拟结果表明：表面电场负压的存在会导致纳米线材杨氏模量的减小和泊松比的增大。同时,这种电场效应随着表面电势的增大而增大、随着纳米线材直径及其与基面距离的增大而减小。
再次,在连续介质力学框架内,通过求解表面应力作用下基底上纳米线材的自平衡应变场,澄清了已有文献关于表面应力对于微纳米梁结构等效刚度的影响机理认识的不足之处,讨论了不同变形模式下纳米线材的力学行为,着重分析了采用机械共振方法测量低维材料力学性能参数时,静电力作用下纳米线材的动力响应行为,给出了表面应力,残余应变,电场对于纳米线材振动频率的影响关系,在此基础上实现了对已有实验中ZnO纳米线材杨氏模量尺寸效应的定量以及定性差异的统一解释。
最后,从应变对Nb3Sn超导材料费米面上态密度的影响出发,给出了描述临界电流密度三维应变效应的标度关系,该标度关系在退化情形下可以很好地描述一维超导线材和二维超导带材临界性能应变作用规律的实验结果；并且本文给出的理论模型在退化情形下与已有的一维经验关系具有形式上的一致性。以拉伸模式下Nb3Sn超导线材临界电流密度的测量为例,初步讨论了线材中超导丝区域应变分布的结构效应。
总之,通过本文的工作,进一步理解了纳米线材杨氏模量的尺寸效应,以及纳米线材力学性能测量中的力电效应,为相关纳米器件的研制以及纳米测量技术完善奠定了一定的基础；同时,对超导线材临界电流密度应变效应的认识,为其在实际工程中的应用提供了一定的理论指导。
Wire structures have wide application prospects in varied fields, including nanodevices, nanoelectromechanical systems (NEMS), and thermonuclear experimental reactor magnet system. The size dependent mechanical properties, and electro-mechanical coupling effects of which are involved in the applications due to gaining relevance in the operation performance criteria and controlling functionality of the actual device. Therefore, theoretical studies on the mechanical properties of metal nanowires, the electric field effects in the metal nanowire/ZnO nanowire based NEMS, and the strain effects in the critical current density of composite superconducting wires are carried on in this thesis.
Firstly, from the viewpoint of the atom binding energy, a Young's modulus model is proposed for the widely used fee metal nanowires, which allows for an analytical study on the elastic behavior from the perspective of atomic interactions and easy application in engineering practice. By examining the bond-strength enhancing arising from the spontaneous bond relaxation, a scale function is obtained and a simple formula characterizing the Young's modulus of the fee metal nanowires is given, which indicate the key role the bond-strength enhancing plays in the size-dependent elastic properties. There is good qualitative agreement between theoretical predictions and experimental observations. The number of material parameters needed for the low dimensional material Young's modulus modeling in this paper is reduced by comparing with the continuum modeling approach.
Secondly, elastic properties of metal nanowires in a transverse electric field are investigated using molecular dynamics simulations and classical electrostatics theory. The negative pressure on the surfaces stemmed from the transverse electric field modifies the Young's modulus and Poisson's ratio of nanowires significantly. The simulation results reveal the decrease in Young's modulus and the increase in Poisson's ratio as a result of the negative pressure. With the increase of the applied voltage and decreasing the distance between the nanowire and the ground plane, the electromechanical coupling effect on elastic properties of nanowires becomes more remarkable.
Thirdly, within the framework of continuum mechanics, the self-equilibrium strain field of nanowire-structure on substrate under the surface stress is derived. An inadequate understanding of the physics responsible for the observed stiffness change of micro/nano cantilevers originating from surface stress in the previous literatures is demonstrated. The mechanical behavior of nanowire under different loading modes is studied; the elastic modulus measurement systems of nanowires using an electric-field-induced resonance flexure method are carefully analyzed. The resonance frequency dependence on the surface stress, the residual strain, as well as the electric field is obtained. On the basis of the analysis, the agreement of the theoretical predictions and experimental observations of different trends of the Young's modulus of ZnO nanowires varying with the diameter is achieved, a unified explanation is made.
Finally, a scaling law for the three-dimensional strain dependence of the critical current of Nb3Sn conductors is established, which considers the strain effects on the electron density of state at the Fermi level. The scaling law, in the degenerate form, describes well experimental data, such as critical properties measurements of one-dimensional superconducting wires and two-dimensional superconducting tapes under applied strain. And there is consistency in the form between the degenerate formula and the one-dimensional empirical relation for the variation of critical current density with the axial strain. Taking the critical current measurements of Nb3Sn wires under tensile loading mode as example, a preliminary study is conducted to investigate the structure effects on the strain field distribution in the superconducting filaments.
In conclusion, through this paper, we can get further understanding of the size dependent Young's modulus of nanowire and the electromechanical effects in the nanowire-based systems. It lays the foundation for the realization of NEMS systems and the improvement of the nanomechanical test systems. At the same time, studying the effects of strain on the critical current density of Nb3Sn composite wires would provide theoretical guidance to engineering application of superconductors.
引文
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