6. The shape of the Wigner–Seitz unit cell of a hexagonal lattice (in 3-D) is:
(a) Hexagonal
(b) Rhombic dodecahedral
(c) Cubic
(d) Truncated octahedral
7. Show that every edge (side) of the polyhedron (square or hexagon) bounding
the Wigner–Seitz unit cell of the body-centered cubic lattice is x times the
length of the conventional unit cell, where x is:
(a)
ffiffi ffi
2
p
1
(b)
ffiffi ffi
2
p
2
(c)
ffiffi ffi
2
p
3
(d)
ffiffi ffi
2
p
4
8. Show that the ratio of the lengths of the diagonals of each parallelogram face of
the Wigner–Seitz unit cell for fcc lattice is:
(a)
ffiffi ffi
2
p : 1
(b)
ffiffi ffi
2
p : 2
(c)
ffiffi ffi
2
p : 3
(d)
ffiffi ffi
2
p : 4
9. The primitive translation vectors of a three-dimensional lattice are a = 2 ^ i + ^ j, b =
2 ^ j and c = ^ k. The primitive reciprocal lattice vector a* is:
(a) p ^ i
(b) 2p ^ i
(c) 3p ^ i
(d) 4p ^ i
10. The primitive translation vectors of a three-dimensional lattice are a = 2 ^ i + j, b =
2 ^ j and c = ^ k. The primitive reciprocal lattice vector b* is:
(a) p/2(- ^ i -2 ^ j)
(b) p/2(- ^ i + 2 ^ j)
(c) p/2( ^ i + 2 ^ j)
(d) p/2( ^ i -2 ^ j)
88
2 Unit Cell Construction