Illinois MATSE 280 Introduction to Engineering Materials, Lecture 3 Part 3: Crystallographic Points, Directions, and Planes

By Duane Douglas Johnson1, Omar N Sobh2

1. Iowa State University (formerly University of Illinois Urbana-Champaign) 2. University of Illinois at Urbana-Champaign

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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

Cite this work

Researchers should cite this work as follows:

  • Duane Douglas Johnson; Omar N Sobh (2008), "Illinois MATSE 280 Introduction to Engineering Materials, Lecture 3 Part 3: Crystallographic Points, Directions, and Planes," https://nanohub.org/resources/5469.

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