Question

Magnesium (Mg) presents at room temperature a compact hexagonal structure (HCP) with parameters reticular a0 = 0.32094 nm and c = 0.52105 nm with an atomic mass of 24.31 g mol-1

Determine: a) The volume of the HCP unit cell; b) The density of Magnesium; c) The Packing Factor for this cell unitary (answers: a) 1.39 x 10-28 m3 ; b)  1740 kg/m3 , c) 0.7471)

Answer 1

The volume of the HCP unit cell for hexagonal structure = 24 r³ (2)^0.5.................................................(1)

and a₀ = 2r and c = 4 (2/3)^0.5 r, so as a₀ & c are given we can calculate r

r = 0.16047

Volume of HCP unit cell = 24*(0.16047)^3 * (2)^0.5= 0.13983nm = 1.39*10^-28 m3

Now volume of theatom can be calculated by assuming the spherical structure of atom as follows:

V_atom = (4 r³) / 3 = 0.0173

density of Mg = atomic weight /V_atom = (24.31/0.0173)=1405

Packing Factor, APF = (Number of particles in unit cell x V_atom )/volume of unit cell

APF = (6 x 0.0173)/0.13983 = 0.7423