For the hexagonal close-packed crystal: (12 points) a. How many atoms are associated with the unit cell? b. What is the coordination number? c. What is the atomic packing factor?

Answer :

(a) Total number of atoms in the cell = 6

(b) The coordination number of HCP is, 12

(c) The atomic packing factor is, 74.0 %

Explanation :

Hexagonal close-packed structure (HCP) :

Crystal structure : The manner in which the atoms or ions are spatially arranged.

(a) The HCP unit cell consist of three primitive unit cells in a hexagonal prism. That means, 3 atoms are in the middle layer and 12 atoms are at top and bottom layers and 2 face atoms.

So, the total number of atoms in the cell = 3 + (1/2)×2 + (1/6)×6 × 2 = 6

(b) Coordination number : It is defined as any constituent particle in a crystal is the number of its nearest neighbours.

The coordination number of HCP is, 12

(c) Packing fraction or factor : It is defined as the percentage of the total space filled by the particles.

since the atomic number is the number of protons in the nucleus, as we move to the left on the periodic table, the electrostatic pull between the nucleus and the valence electron shell decreases. as we move down a group (vertical column), the valence shell energy level gets further and further from the nucleus.