513.001 Molecular and Solid State Physics

Length of the largest wave vector

Find the length of the largest wave vector in the first Brillouin zone measured from k = 0 that is parallel to a cube edge [100], parallel to a cube body diagonal [111], and parallel to a cubic face diagonal [110] for

a) a simple cubic lattice.

b) an fcc lattice.

Hint: For a face centered cubic lattice, you should start with the primitive lattice vectors in real space and construct the primitive lattice vectors in reciprocal space. Frome the lattice vectors in reciprocal space you can determine the first Brillouin zone.