Q1(d). Cubic and tetragonal Bravais lattices

Answer in brief

Cubic: three lattices P, I, F with minimum symmetry four 3-fold axes; tetragonal: two lattices P, I with minimum symmetry one 4-fold axis along c.

Key points

• Cubic, a = b = c, α = β = γ = 90°: primitive P (Z = 1), body-centred I (Z = 2), face-centred F (Z = 4).
• Cubic minimum symmetry: four 3-fold axes along the body diagonals (class 23).
• Tetragonal, a = b ≠ c, α = β = γ = 90°: primitive P (Z = 1) and body-centred I (Z = 2).
• Tetragonal minimum symmetry: one 4-fold axis parallel to c.
• Tetragonal C reduces to a smaller tetragonal P, tetragonal F to tetragonal I; a base-centred cubic lattice loses the 3-fold axes.