Size-dependent Young’s modulus and surface stress-induced bending of nanofilms

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SCIENTIA SINICA Physica, Mechanica & Astronomica
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SCIENTIA SINICA Physica, Mechanica & Astronomica, Volume 45, Issue 8: 086801(2015) https://doi.org/10.1360/SSPMA2015-00074

Size-dependent Young’s modulus and surface stress-induced bending of nanofilms

JianGang LI1, NaRiSu BAI2,*, GuoHong YUN1,2,*
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  • ReceivedFeb 15, 2015
  • AcceptedMar 31, 2015
  • PublishedJul 2, 2015
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Abstract

考虑纳米薄膜表面弹性及其作用厚度得到了纳米薄膜尺度依赖的杨氏模量的表达式. 通过考虑表面层厚度, 引入了表面效应的二级和三级修正, 这有助于对纳米薄膜弹性性质进行更深入的研究. 针对纳米薄膜上、下两个表面上表面应力不平衡的情况, 由能量极小原理得到了表面应力导致的单层纳米薄膜的弯曲公式. 通过将本文弹性(及弯曲)理论同前人工作进行比较, 研究了表面层厚度对薄膜弹性性质影响的规律, 揭示了本文理论与前人理论的内在联系.


Funded by

内蒙古自治区高校青年科技英才计划资助项目(NJYT-12-B07)

国家自然科学基金(11072104)


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  • Click to view Download high-quality image

    图1

    (网络版彩图)考虑表面层厚度ts及表面杨氏模量Ys的纳米薄膜示意图. 图中表面附近透明绿色背景部分为有一定厚度ts的表面层. 坐标参考面选择为薄膜几何中间面

  • Click to view Download high-quality image

    图2

    (网络版彩图)Si纳米薄膜的杨氏模量Yf随薄膜厚度t的变化曲线, 实验细节可参阅文献[18]

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    图3

    (a) 不考虑表面层厚度ts时, 不同的表面弹性系数S对杨氏模量Yf的影响; (b) 当表面弹性系数S取一定值时, 不同的表面层厚度ts对杨氏模量Yf的影响

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    图4

    (网络版彩图)Si纳米薄膜由上、下表面应力不平衡所导致的弯曲曲率随纳米薄膜厚度的变化曲线. 作为比较, 经典Stoney公式即S ′=0 的曲线亦在图中画出. (a) 考虑表面层厚度ts时Si纳米薄膜的弯曲曲率; (b) 不考虑表面层厚度时不同表面弹性S′ 对Si纳米薄膜弯曲曲率的影响

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    图5

    当表面弹性S′取一定值时, 考虑表面层厚度ts, core-surface模型与经典Stoney公式曲率之间的对比. (a) 表面弹性系数为-188 N/m; (b) 表面弹性系数为-238 N/m; (c) 表面弹性系数为-470 N/m; (d) 表面弹性系数为-595 N/m

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    图6

    纳米薄膜弯曲理论与分子动力学模拟Si纳米管半径R的对应比较. (a) 纵坐标采用自然坐标; (b) 纵坐标采用对数坐标. 分子动力学模拟纳米薄膜弯曲半径的详细内容可参阅文献[7].

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