Simple Cubic, fcc and bcc

There are three cubic structures that general chemistry students are taught.  They are called simple cubic, face-centred cubic, and body-centred cubic.  They vary in how the atoms/spheres are arranged inside of it.

Simple Cubic

  • Each layer is stacked on the previous layer perfectly.
  • There are 8 eighths (one in each corner) for a total of ONE atom in the unit cell

Body-Centred Cubic

  • Each layer is offset from the layer before.  Arrangements duplicate themselves every other layer.
  • There are 8 eights (one in each corner) and one full atom in the centre for a total of TWO atoms in the unit cell

Face-Centred Cubic

  • Each layer is offset from the layer before.  Arrangements duplicate themselves every third layer.
  • There are 8 eighths (one in each corner), and 6 halves (one on each face of the cube) for a total of FOUR atoms in the unit cell.

The following formulas show how the sphere (atom) radius, r, is related to the unit cell edge length, a

images from http://spaceflight.esa.int/impress/text/education/Glossary/Glossary_B.html