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#### Abstract

Crystallographic Points, Directions, and Planes

**Issues to Address...**

How to define points, directions, planes, as well as

linear, planar, and volume densities

- Define basic terms and give examples of each:
- Points (atomic positions)
- Vectors (defines a particular direction - plane normal)
- Miller Indices (defines a particular plane)
- relation to diffraction
- 3-index for cubic and 4-index notation for HCP

**Content**

- Points, Directions, and Planes in Terms of Unit Cell Vectors
- POINT Coordinates
- Crystallographic Directions
- Symmetry Equivalent Directions
- Families and Symmetry: Cubic Symmetry
- Designating Lattice Planes
- Crystallographic Planes in FCC: (100), (110), and (111)
- Comparing Different Crystallographic Planes
- Directions in HCP Crystals and 4-index notation
- Miller Indices for HCP Planes
- Basal Plane in HCP
- Another Plane in HCP
- SUMMARY

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