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Hexagonal Crystals

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 of indices. Hence, a four-axis ( Miller-Bravais ) coordinate system is used. . Four-axis. Three-axis. z. a 2. -.

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Hexagonal Crystals

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  1. 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 of indices. Hence, a four-axis (Miller-Bravais) coordinate system is used. Four-axis Three-axis

  2. z a2 - a2 a3 -a3 a 2 a1 2 a3 ex: ½, ½, -1, 0 => [1120] a 1 2 dashed red lines indicate projections onto a1 and a2 axes a1 HCP Crystallographic Directions Algorithm 1. Vector repositioned (if necessary) to pass through origin.2. Read off projections in terms of unit cell dimensions a1, a2, a3, or c3. Adjust to smallest integer values4. Enclose in square brackets, no commas [uvtw] Adapted from Fig. 3.8(a), Callister & Rethwisch 8e.

  3. z ® u [ ' v ' w ' ] [ uvtw ] 1 = - u ( 2 u ' v ' ) 3 a3 a2 1 = - v ( 2 v ' u ' ) a1 3 - = - + t ( u v ) = w w ' Fig. 3.8(a), Callister & Rethwisch 8e. HCP Crystallographic Directions • Hexagonal Crystals • 4 parameter Miller-Bravais lattice coordinates are related to the direction indices (i.e., u'v'w') as follows. [010]  [110] 

  4. Conversion of Directional Indices [111] [112‾ 3]

  5. Determine the Miller-Bravais directional indices for the direction shown in green. Directional Indices

  6. 3.35 Determine indices for the directions shown in the following hexagonal unit cells:

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