onsider CaCl2 with bcc unit cell, what fraction of octahedralholes are occupied by Ca2+ if Cl- occupy lattice points

To determine the fraction of octahedral holes occupied by Ca2+ in a CaCl2 crystal with a bcc (body-centered cubic) unit cell, we need to consider the arrangement of the Cl- ions on the lattice points.

In a bcc unit cell, there are 2 lattice points. Each lattice point is associated with one Cl- ion. Therefore, there are a total of 2 Cl- ions in the unit cell.

Now, let's consider the arrangement of the Cl- ions. In a bcc unit cell, the Cl- ions are located at the corners of the unit cell. Each corner is shared by 8 unit cells, so each Cl- ion contributes 1/8 to the unit cell it is located in.

Since there are 2 Cl- ions in the unit cell, the total contribution of Cl- ions to the unit cell is 2 * (1/8) = 1/4.

Now, let's consider the octahedral holes in the unit cell. In a bcc unit cell, there is 1 octahedral hole located at the center of the unit cell. This octahedral hole can be occupied by a Ca2+ ion.

Therefore, the fraction of octahedral holes occupied by Ca2+ ions is 1/4.

In conclusion, in a CaCl2 crystal with a bcc unit cell, 1/4 of the octahedral holes are occupied by Ca2+ ions.