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Published byPauline Owen Modified over 5 years ago
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Hexagonal Crystals In the three-axis coordinate system, a problem arises for hexagonal crystals in that some crystallographic equivalent directions will not have the same set (family) of indices. Hence, a four-axis (Miller-Bravais) coordinate system is used.
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HCP Crystallographic Directions
- a3 a1 a2 z Algorithm 1. Vector repositioned (if necessary) to pass through origin. 2. Read off projections in terms of unit cell dimensions a1, a2, a3, or c 3. Adjust to smallest integer values 4. Enclose in square brackets, no commas [uvtw] dashed red lines indicate projections onto a1 and a2 axes a1 a2 a3 -a3 2 a 1 Adapted from Fig. 3.8(a), Callister & Rethwisch 8e. [ 1120 ] ex: ½, ½, -1, =>
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HCP Crystallographic Directions
Hexagonal Crystals 4 parameter Miller-Bravais lattice coordinates are related to the direction indices (i.e., u'v'w') as follows. Fig. 3.8(a), Callister & Rethwisch 8e. - a3 a1 a2 z = ' w t v u ) ( + - 2 3 1 ] uvtw [
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The need for 4-axes = ' w t v u ) ( + - 2 3 1 ] uvtw [ ®
[100] and [110] are equivalent directions. But, they don’t belong to the same family of directions. After converting to 4-axes, you will see that they belong to the same family of directions. = ' w t v u ) ( + - 2 3 1 ] uvtw [
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Conversion of Directional Indices
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Determine the Miller-Bravais directional indices for the direction shown in green.
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3.35 Determine indices for the directions shown in the following hexagonal unit cells:
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Determine the 3-axis indices and then convert them to 4-axis indices, and draw the direction in the diagram.
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