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The local deposition temperature is ∼400-500°C, which is high enough to prevent physical adsorption of molecules on the surface during the growth. Thus, the ionic charges on the surface are likely uncompensated and are electrostatically effective for producing the helical structure.
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0347392025
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The calculation was made based on following approximations: [1] the thickness of the nanobelt is much smaller than the radius of the nanoring (t ≪: R); [2] the width (W) of the nanobelt is significantly larger than its thickness, so that the edge effect is small. However, it is the difference between the electrostatic energy before and after rolling into a cylinder that matters to the final result; if the edge effect before and after rolling is preserved, the edge effect, if any, is almost canceled out in the final equation. [3] The surface charges are due to the unique crystallographic structure of ZnO, and they are bound to the atoms, thus, the surface charge density is preserved after rolling into a cylinder. Therefore, the total charge on the inner surface of the cylinder is Q = 2π(R - t/2)Wσo. The change in electrostatic energy is (Formula Presented) (for t ≪ R) where β = t/2R.
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32
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0347392026
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note
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Because the thickness of the nanobelt is very small and the ring radius is large, the radial stress across the nanobelt is negligible because the two sides are free surfaces without external force. The strain along the z-direction (the axis of the cylinder) is also zero because there is no twisting. The only strain is along the φ-direction. The elastic energy is the volume integration of the φ-direction strain energy. The bending modulus used for the calculation was based on the experimentally measured value for ZnO nanobelts with inclusion of geometrical factor.
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0346131097
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In-situ heating of the helical nanostructure has been carried out in TEM under vacuum of 10-8 Torr. Heating the specimen to 400°C generated a high concentration of oxygen vacancies based our previous study in ref. 19, but no visible change in the shape of the helical nanostructure was found, suggesting that the role played by point defects in the formation of helical structure is undetectable.
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41
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0346761744
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note
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Thanks the support from NSF and NASA URETI. Thanks to Profs. Min Zhou and Ashok Saxena for discussion.
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