Consult a periodic table to find the atomic radius (r) of the atoms in the cubic unit cell. For example, the atomic radius (r) of polonium is 0.167 nm, r = 0.137 nm for tungsten, and r = 0.144 nm for gold.
Study the arrangement of atoms in the cubic crystal unit cell. Use the arrangement to identify the space lattice of the crystal system. The cubic space lattice may be simple cubic (SC), face centered cubic (FCC) or body centered cubic (BCC). Simple cubic unit cells have atoms at the corners of the cube. Face centered cubic cells have extra atoms in the center of each of the cube faces. Body centered cubic cells are similar to simple cubic cells, but contain one extra atom at the center of the cube. For example, polonium crystallizes in a SC structure, tungsten is BCC, and gold is FCC.
Calculate the lattice parameter (a) based on the space lattice of the cubic unit cell. For a SC space lattice, the lattice parameter a = [2 x r]. For example, the lattice parameter for polonium is: a = [2 x r] = [2 x (0.167 nm)] = 0.334 nm. For a FCC space lattice, the lattice parameter a = [4 x r / (2)^1/2]. For example, gold has a lattice parameter a = [4 x r / (2)^1/2] = [4 x (0.144 nm) / (2)^1/2] = 0.407 nm. For a BCC space lattice, the lattice parameter a = [4 x r / (3)^1/2]. For example, tungsten's lattice parameter a = [4 x r / (3)^1/2] = a = [4 x (0.137 nm) / (3)^1/2] = 0.316 nm.