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note
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Reflections for the (200) lattice plane at 6.21 Å and (400) lattice plane at 3.08 Å are present 90° from the {020} reflections and are also exactly 90° from the [001) zone axis. The orientation of the {020} and {200} reflections with respect to the [001] zone axis indicates that this belt grows in the [010] direction with the width and thickness of the belt oriented in the [100] and [001] directions, respectively.
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In the ED patterns, the (011) and (011) reflections appear to be oriented towards the length of the nanobelt. However, the [011] is not the growth direction because the angle between the [011] zone axis and the (011) lattice plane is 62.8°. ruling out this possibility unless the belt happens to be oriented at an extreme angle of ∼27° with respect to the TEM grid. The closest growth direction is [013] (the (013) and (013) lattice planes are oriented 87.3° and 92.7° from the [011] zone axis). This is consistent with the image and the ED pattern: the {200} planes appear perpendicular to the growth direction, which meets expectations since the [200] direction is oriented at 90° from both the [011] and [013] directions in the mendipite crystal structure. The visible lattice planes running down the length of the nanobelt match the {013} d spacing as well.
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47
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32744459482
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For an introductory review of birefringence and polarization microscopy, see http://www.olympusmicro.com/primer/java/polarizedlight/crystal/index.html.
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