Atomic Positions:
0 0 0 and \(1 \over 2\) \(1 \over 2\) 0, \(1 \over 2\) 0 \(1 \over 2\), 0 \(1 \over 2\) \(1 \over 2\)
Atoms touch along body diagonal:
Coordination \(= \color{maroon}{12}\)
Atoms per unit cell:
\(n = N_i + {N_f \over 2} + {N_c \over 8} = 0 + 3 + 1 = 4 \)
Lattice parameter:
\(a = \color{red}{{2\sqrt{2} r_{\mathrm{FCC}}}}\)
Atomic packing factor:
\(\mathrm{APF} = {n V_{\mathrm{atom}} \over V_{\mathrm{u.c.}}} = \color{red}{0.74} \)
Calculate density:
\(\rho = {\color{green}{n} \color{maroon}{A} \over \color{darkcyan}{V_{\mathrm{u.c.}}} \color{purple}{N_{\mathrm{A}}}}\)