Cubic lattice structure

In figure

• The simple cubic structure (abbreviated sc) has an atom located at each corner of the unit cell.

• The bodycentered cubic (bcc) lattice has an additional atom at the center of the cube, and

• The face-centered cubic (fcc) unit cell has atoms at the eight corners and centered on the six faces.

All three structures have different primitive cells, but the same cubic unit cell. We will generally work with unit cells.

• As atoms are packed into the lattice in any of these arrangements, the distances between neighboring atoms will be determined by a balance between the forces that attract them together and other forces that hold them apart.

• For now, we can calculate the maximum fraction of the lattice volume that can be filled with atoms by approximating the atoms as hard spheres.

For example, Figure given below illustrates the packing of spheres in a face-centered cubic cell of side a, such that the nearest neighbors touch. The dimension a for a cubic unit cell is called the lattice constant. For the fee lattice the nearest neighbor distance is one-half the diagonal of a face, or . Therefore, for the atom centered on the face to just touch the atoms at each corner of the face, the radius of the sphere must be one-half the nearest neighbor distance,