Magnesium Crystallization in HCP Structure

Lattice Constant of Magnesium
The lattice constant of a crystal is the distance between the lattice points in a unit cell. For magnesium, the lattice constant is given as 0.32 nm.

Hexagonal Close-Packed (HCP) Structure
The HCP structure is one of the crystal structures in which the atoms are arranged in a close-packed manner. In this structure, the atoms are arranged in layers, with each layer having a hexagonal arrangement. The layers are stacked on top of each other, and the atoms in the subsequent layers fit into the depressions of the previous layer.

Nearest Neighbor Distance in Magnesium
In the HCP structure, the nearest neighbor distance can be calculated by considering the arrangement of atoms in the hexagonal layers.

Calculating Nearest Neighbor Distance:
To calculate the nearest neighbor distance, we can consider the hexagonal layer as a regular hexagon. The distance between the center of the hexagon and any of its vertices is equal to the radius of the atom.

Using basic geometry, we can calculate the radius of the atom as follows:

1. In a regular hexagon, the radius (r) is equal to the distance between the center and any of its vertices.
2. The length of each side of the hexagon is equal to the lattice constant (a).
3. The radius (r) can be calculated by dividing the length of one side of the hexagon (a) by 2 times the cosine of 30 degrees.
r = a / (2 * cos(30°))

Substituting the value of the lattice constant (a = 0.32 nm) into the equation:

r = 0.32 nm / (2 * cos(30°))
r = 0.32 nm / (2 * √(3)/2)
r = 0.32 nm / (√(3))
r ≈ 0.185 nm

Therefore, the nearest neighbor distance in magnesium is approximately 0.185 nm.