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In Fig. 3 the calculated Young’s moduli of SiNWs are plotted as a function of wire diameter. Similar to previous theoretical findings [20,21], the Young’s modulus generally increases as the wire mean diameter increases. It can be inferred that the Young’s modulus of nanowires would approach the bulk value at certain critical size, and afterwards it would not change much. Our calculations clearly show that nanowires of different directions have distinctly different Young’s moduli. In the size range studied, the wires along [110] direction have the highest value, while [100] wires correspond to the lowest value. The values for [111] and [112] wires are intermediate in size. Previously, Lee et al. [11] studied the Young’s modulus of Si [100] nanowires in detail and they also found that the Young’s modulus increases slowly with wire size. The Young’s modulus for micrometer-sized Si samples along the [100] direction was found to be 140 GPa [22]. For the [110] direction, the measured Young’s modulus of micrometer-sized Si wires was 142–169 GPa [23]. For thinner samples, the Young’s modulus was estimated to be 169 GPa [24]. These previous results showed that the Young’s modulus is hardly influenced by the size reduction from millimeter to micrometer length scale [25]. |
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synht: 金币+15, 翻译EPI+1, ★★★很有帮助, 谢谢! 2012-05-06 16:18:46
synht: 金币+15, 翻译EPI+1, ★★★很有帮助, 谢谢! 2012-05-06 16:18:46
| 图3绘出了SiNW的杨氏模量随线的直径的变化曲线。和之前的理论发现类似[20,21],杨氏模量一般随着线的平均直径的增加而增加。可知,纳米线的直径达到某个临界尺寸时,其杨氏模量逐渐趋于其本体值,之后不会发生大幅变化。我们的计算清楚的显示了,纳米线在不同的方向有着截然不同的杨氏模量。在本研究的尺寸范围内,沿着[110]方向的线具有最高的模量,而[100]方向的模量最低。[111]和[112]方向的模量居中。之前,Lee等[11]详细研究了Si[100]纳米线的杨氏模量,他们也发现杨氏模量随着线尺寸的增加而缓慢增大。微米级的Si样品的杨氏模量在[100]方向下是140GPa[22]。在[110]方向下,测得的杨氏模量为142-169GPa[23]。对于更薄的样品,预测其杨氏模量为169GPa[24]。这些结果显示了杨氏模量几乎不随着尺寸的减小(从毫米级到微米级)而改变。 |
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