• Length:
    5 Weeks
  • Effort:
    8–10 hours per week
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  • Course Type:
    Instructor-led on a course schedule


About this course

Skip About this course
Structure determines so much about a material:  its properties, its potential applications, and its performance within those applications.  This course is the second in a three-part series from MIT’s Department of Materials Science and Engineering that explores the structure of a wide variety of materials with current-day engineering applications.  Taken together, these three courses provide similar content to MIT’s sophomore-level materials structure curriculum.

Part 2 provides an introduction to the study of crystallography.  We begin by looking at crystals and their symmetries in two dimensions.  Then, we expand into three dimensions, exploring the underlying crystalline structures that underpin most of the materials that surround us.  Finally, we look at how tensors can be used to represent the properties of three-dimensional materials, and we show how these change as a function of the crystalline symmetry.

If you would like to explore the structure of materials further, we encourage you to enroll in Part 1 and Part 3 of the course.

Crystal structure image by User: Materialscientist on Wikimedia.
Photo of quartz by User: JJ Harrison on Wikimedia. (CC BY-SA) 2.5

What you'll learn

Skip What you'll learn
  • How to describe symmetry in both two and three dimensions
  • How tensors can be used to represent the properties of materials in three dimensions
  • How the symmetry of a material influences the materials properties
Part 1: Symmetry in 2D Crystals
  • Translation, mirror, glide and rotation symmetry
Part 2: Point groups in 2D
  • Allowed rotational symmetries in crystals
  • The 10 2D point groups
  • An introduction to crystallographic notation
Part 3: Plane groups in 2D
  • The five 2D lattice types
  • The 17 plane groups in 2D
Part 4: Symmetry in 3D Crystals
  • Inversion, Roto-Inversion, and Roto-reflection
  • Screw symmetry
Part 5: 3D Space Point groups
  • Space point groups
  • Stereographic projection
Part 6: 3D Space Groups
  • Crystal lattices
  • Space groups
Part 7: An Introduction to Tensors
  • Symmetry constraints on materials properties
  • Coordinate transformation

Meet your instructors

Silvija Gradečak
Massachusetts Institute of Technology

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