College of Materials Science and Technology, Taiyuan University of Technology

【目的】纳米材料杨氏模量与其对应的大块材料的杨氏模量完全不同,并且具有明显的尺度依赖性,然而纳米材料杨氏模量随尺度的变化却是多样且复杂的。一些金属纳米材料杨氏模量随着尺度减小而增大,并高于块体杨氏模量值;而一些半导体纳米材料的杨氏模量却随尺度的减小而降低,且低于块体杨氏模量值。这种相反的变化趋势的原因却并不清楚。【方法】基于纳米热力学理论,以纳米材料结合能为基础,从原子势函数与材料杨氏模量的内在关系出发,引入反映材料原子键本质的参数,详细推导了纳米材料杨氏模量定量解析过程,阐述了金属、非金属等纳米材料杨氏模量值和其随尺度的变化规律;揭示了纳米材料表面模量、内部模量对体系杨氏模量的贡献,并利用材料参数阐明纳米材料杨氏模量与尺度、原子键的物理关系。【结果】所构建的理论解析模型对零维纳米颗粒、一维纳米线和二维纳米薄膜的杨氏模量都进行了成功的预测。

【Purposes】 The Young’s moduli of nanomaterials are completely different from these of their bulk counterparts, and the size effect on Young’s modulus is greatly obvious. Mo- reover, the change trend of Young’s modulus with size is complicate. With size dropping, the Young’s moduli of some metallic nanomaterials increase, while they decrease for some semicon- ductor nanomaterials. However, the reason why size effect on the Young’s modulus of nanoma- terials varies, is still unclear. 【Methods】 In this study, on the basis of the thermodynamic theory and cohesive energy of nanomaterials, a theoretical model for the size-dependent Young’s modu- lus of nanomaterials is deduced. In this model, the inherent relationship between atomic potential and the Young’s modulus is taken into account, and material coefficient that directly reflects the bond nature in a material is introduced. The established model can well explain the change trend of Young’s modulus with size for metallic and nonmetallic materials, and also discover the con- tributions of surface modulus and interior modulus for the Young’s modulus in a nanomaterial. Simultaneously, the physical mechanism of relationship of Young’s modulus with size or atomic bond is explained. 【Conclusions】 The predictions for the Young’s moduli of zero-dimensional nanoparticles, one-dimensional nanowires, and two-dimensional nanofilms are obtained by analy- zing the established theoretical model in this study.

李慧.纳米材料杨氏模量的尺度依赖性[J].太原理工大学学报,2024,55(3):427-436.

LI Hui.The Young’s modulus of nanomaterials:size effect[J].Journal of Taiyuan University of Technology,2024,55(3):427-436.