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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

Published on


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


  • 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

Tags, a resource for nanoscience and nanotechnology, is supported by the National Science Foundation and other funding agencies. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.