氧化锌纳米线力学性能的实验和理论纳米力学研究
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摘要
力学性能是材料最基本的物理性能之一，对纳米材料力学性能及其尺寸效应的研究不仅有助于揭示小尺度下结构－性能的内在关联，也对微纳机电器件的发展具有指导意义，而定量化的表征和测量技术是认识尺寸效应规律的前提。本文完善了扫描电子显微镜（SEM）中的原位单轴拉伸方法，保证了纳米线轴向的良好对中和应力－应变曲线的准确测量。以轴向为[0001]的，高质量的氧化锌（ZnO）单晶纳米线为研究对象，获得了拉伸模量、断裂强度、断裂应变等性能参数的可靠的实验结果。在此基础上，建立了弹性模量和强度性能尺寸效应的理论模型。
对于一系列直径为18～204nm的ZnO纳米线测量的拉伸模量表现随直径减小而增大的尺寸效应。直径小于120nm左右时，拉伸模量的增大趋势起初弱于本研究组此前测量的弯曲模量；当直径继续减小到30nm以下时，拉伸模量很快增大并与弯曲模量趋近。基于包含自由表面和应变梯度项的能量方法，本文求解了纳米线径向的弛豫应变函数，并首次阐明了“芯－壳”复合结构模型中的表面层厚度的物理意义。弛豫应变函数的形态随纳米线直径的变化很好地解释了实验中加载方式对尺寸效应行为的影响。
虽然表面弛豫是弹性模量的尺寸效应最基础的机制，弛豫表面的原子结构的直接观察目前仍有相当的挑战性。本文结合球差校正的高分辨透射电子显微术和基于密度泛函理论的模拟，首次直接观察并在亚埃尺度测量了ZnO{1010}表面的弛豫应变特征及其在表面以下的分布，从而证实了有关ZnO表面原子结构的普遍预测，并支持了上述弛豫应变函数的模型。本文还在ZnO{1010}表面首次观察到了一种重构现象，展现了表面丰富的结构行为。
对于一系列直径为18～114nm的ZnO单晶纳米线，原位SEM实验测量的断裂强度和断裂应变表现显著的分散性，同时，强度的下限随直径减小而显著增加，改进形式的指数标度律很好描述了这一尺寸效应。基于原位阴极荧光光谱实验和单轴拉伸过程的分子动力学模拟，本文证实ZnO纳米线中存在的原子空位（点缺陷）的数量与直径有关，并且点缺陷的数量和空间构型都会影响强度性能。从而本文最终提出，Griffith的经典断裂力学仍然适用于单晶纳米线，而“关键缺陷”尺寸的核心概念对应于点缺陷的有效数量。这个简单的模型可能成为理解纳米尺度的强度性能的基础。
Mechanical properties are amongst the most basic properties in materials, andinvestigations on the size effects of mechanical properties in nano-sized specimens notonly manifest the intrinsic structure-property relationships, but also play essential rolesin the progress of micro-and nano-electromechanical devices.
In this dissertation, methodologies for in situ uniaxial tensile testing in scanningelectron microscope (SEM) are completed. Axial alignment of nanowires (NWs) aremaintained throughout testing, and stress-strain curves are accurately measured, basedon which the tensile moduli, fracture strengths, and fracture strains in [0001]-orientedsingle-crystalline zinc oxide (ZnO) NWs are quantitatively determined, and theoreticalmodels are developed for their diameter (D) dependences.
Measured in ZnO NWs with D ranging from18to204nm, the tensile moduliincrease as D decreases; meanwhile, behaviors of size effect are affected by the loadingmode. Tensile moduli are lower than the previously measured bending moduli, andincrease slower than the latter with decreasing D. However, they get close rapidly to thebending moduli as D decreasing below about30nm. Based on an energy minimizationapproach including the surface-related and strain-gradient terms, the radial-distributedrelaxation function in nanowires are analytically derived, the diameter dependence ofwhich well explains our experimental findings. Moreover, physical meaning of the shellthickness in the widely-interested core-shell model is clarified for the first time.
Although surface relaxation works as the basic mechanism for elasticity size effect,direct observation of the atomic structures in relaxed surfaces remains challenging. Inthis dissertation, the characteristic quantities of ZnO{1010} surface relaxation, as wellas their in-depth distributions, are directly measured with a sub-angstrom resolution,based on combining aberration-corrected transmission electron microscopy with abinitio calculations, the well-predicted surface structure in ZnO is thus verified. Thisstudy also supports the conception of relaxation function. Moreover, a novel mechanismfor surface reconstruction in ZnO{1010} is revealed for the first time.
Diameter dependence of fracture strengths and fracture strains in single-crystallineZnO NWs with D ranging from18to114nm is experimentally revealed by in situ SEM.The strength properties are remarkably scattered, with their lower-bound following a modified power-form scaling law. Based on in situ cathodoluminescence measurementsand molecular dynamics simulations of the uniaxial tensile stress-strain curves, theattendance of point defects are confirmed, the diameter-dependent quantities of which,as well as their stochastic spatial configurations, dominate the NW strengths. Therefore,the Griffith’s classic fracture mechanics still works well in single-crystalline NWs, aslong as the critical defect sizes are attributed to the effective quantities of point defects.Our studies provide a simple, but basic, understanding for the size effect of strengths insingle crystalline NWs.
对于一系列直径为18～204nm的ZnO纳米线测量的拉伸模量表现随直径减小而增大的尺寸效应。直径小于120nm左右时，拉伸模量的增大趋势起初弱于本研究组此前测量的弯曲模量；当直径继续减小到30nm以下时，拉伸模量很快增大并与弯曲模量趋近。基于包含自由表面和应变梯度项的能量方法，本文求解了纳米线径向的弛豫应变函数，并首次阐明了“芯－壳”复合结构模型中的表面层厚度的物理意义。弛豫应变函数的形态随纳米线直径的变化很好地解释了实验中加载方式对尺寸效应行为的影响。
虽然表面弛豫是弹性模量的尺寸效应最基础的机制，弛豫表面的原子结构的直接观察目前仍有相当的挑战性。本文结合球差校正的高分辨透射电子显微术和基于密度泛函理论的模拟，首次直接观察并在亚埃尺度测量了ZnO{1010}表面的弛豫应变特征及其在表面以下的分布，从而证实了有关ZnO表面原子结构的普遍预测，并支持了上述弛豫应变函数的模型。本文还在ZnO{1010}表面首次观察到了一种重构现象，展现了表面丰富的结构行为。
对于一系列直径为18～114nm的ZnO单晶纳米线，原位SEM实验测量的断裂强度和断裂应变表现显著的分散性，同时，强度的下限随直径减小而显著增加，改进形式的指数标度律很好描述了这一尺寸效应。基于原位阴极荧光光谱实验和单轴拉伸过程的分子动力学模拟，本文证实ZnO纳米线中存在的原子空位（点缺陷）的数量与直径有关，并且点缺陷的数量和空间构型都会影响强度性能。从而本文最终提出，Griffith的经典断裂力学仍然适用于单晶纳米线，而“关键缺陷”尺寸的核心概念对应于点缺陷的有效数量。这个简单的模型可能成为理解纳米尺度的强度性能的基础。
Mechanical properties are amongst the most basic properties in materials, andinvestigations on the size effects of mechanical properties in nano-sized specimens notonly manifest the intrinsic structure-property relationships, but also play essential rolesin the progress of micro-and nano-electromechanical devices.
In this dissertation, methodologies for in situ uniaxial tensile testing in scanningelectron microscope (SEM) are completed. Axial alignment of nanowires (NWs) aremaintained throughout testing, and stress-strain curves are accurately measured, basedon which the tensile moduli, fracture strengths, and fracture strains in [0001]-orientedsingle-crystalline zinc oxide (ZnO) NWs are quantitatively determined, and theoreticalmodels are developed for their diameter (D) dependences.
Measured in ZnO NWs with D ranging from18to204nm, the tensile moduliincrease as D decreases; meanwhile, behaviors of size effect are affected by the loadingmode. Tensile moduli are lower than the previously measured bending moduli, andincrease slower than the latter with decreasing D. However, they get close rapidly to thebending moduli as D decreasing below about30nm. Based on an energy minimizationapproach including the surface-related and strain-gradient terms, the radial-distributedrelaxation function in nanowires are analytically derived, the diameter dependence ofwhich well explains our experimental findings. Moreover, physical meaning of the shellthickness in the widely-interested core-shell model is clarified for the first time.
Although surface relaxation works as the basic mechanism for elasticity size effect,direct observation of the atomic structures in relaxed surfaces remains challenging. Inthis dissertation, the characteristic quantities of ZnO{1010} surface relaxation, as wellas their in-depth distributions, are directly measured with a sub-angstrom resolution,based on combining aberration-corrected transmission electron microscopy with abinitio calculations, the well-predicted surface structure in ZnO is thus verified. Thisstudy also supports the conception of relaxation function. Moreover, a novel mechanismfor surface reconstruction in ZnO{1010} is revealed for the first time.
Diameter dependence of fracture strengths and fracture strains in single-crystallineZnO NWs with D ranging from18to114nm is experimentally revealed by in situ SEM.The strength properties are remarkably scattered, with their lower-bound following a modified power-form scaling law. Based on in situ cathodoluminescence measurementsand molecular dynamics simulations of the uniaxial tensile stress-strain curves, theattendance of point defects are confirmed, the diameter-dependent quantities of which,as well as their stochastic spatial configurations, dominate the NW strengths. Therefore,the Griffith’s classic fracture mechanics still works well in single-crystalline NWs, aslong as the critical defect sizes are attributed to the effective quantities of point defects.Our studies provide a simple, but basic, understanding for the size effect of strengths insingle crystalline NWs.
引文
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