Symmetry, Structure, and Tensor Properties of Materials

Schematic of molecular crystal structure.
Crystal structure of the cuprate compound Bi2Sr2CaCu2O8+δ or Bi2212, showing the copper (purple)–oxygen (black) layer responsible for superconductivity. (Image courtesy of Lawrence Berkeley Laboratory.)


MIT Course Number


As Taught In

Fall 2005



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Course Features

Course Description

This course covers the derivation of symmetry theory; lattices, point groups, space groups, and their properties; use of symmetry in tensor representation of crystal properties, including anisotropy and representation surfaces; and applications to piezoelectricity and elasticity.