Question

Calculating the packing fraction (The percent space occupied by atom) for a hexagonal unit cell requires a bit more trigonometry than the same calculation for a cubic cell. However, based on your observations, which of the cubic cells would you expect to have the same packing fraction as the hexagonal cell? Explain your reasoning?

Answer 1

hexagonal closed packing and face centred closed packing has same packing fraction.=0.74.

FCC and HCP Structure

The face centered cubic and hexagonal close packed structures both have a packing factor of 0.74, consist of closely packed planes of atoms, and have a coordination number of 12. The difference between the fcc and hcp is the stacking sequence. The hcp layers cycle among the two equivalent shifted positions whereas the fcc layers cycle between three positions. As can be seen in the image, the hcp structure contains only two types of planes with an alternating ABAB arrangement. Notice how the atoms of the third plane are in exactly the same position as the atoms in the first plane. However, the fcc structure contains three types of planes with a ABCABC arrangement. Notice how the atoms in rows A and C are no longer aligned. Remember that cubic lattice structures allow slippage to occur more easily than non-cubic lattices, so hcp metals are not as ductile as the fcc metals.