This material has been donated by expert crystallographers and educations to help others teach the wonders of crystallography. Although it is hosted by the CCDC to help provide our community with resources to teach crystallography it has not been peer reviewed or checked and should be used at your own risk and discretion.

By downloading any of the files below you are agreeing to cite both the author and the institution given in brackets when you use any of these resources.


Online Courses

  • Direct and reciprocal lattices - Chapter 4 of the Crystallography website from CSIC's Department of Crystallography and Structural Biology (from Prof. Martin Martinez-Ripoll)
    • The content of this website is available in English and in Spanish (at this link)
    • Citation: If you intend to use this resource in a classroom setting, you must agree to cite the resource following the instructions within the website homepage.
    • Topics: Reciprocal lattice, Direct lattice, Miller indices, Symmetry

Practice Problems

  • Practice examples by Mike Zdilla (Mike Zdilla, Temple University) 
    • Relevant Sections: Reciprocal Lattice worksheet, Reciprocal Lattice, Ewald Sphere, Structure Factors