Question

Question: By examining Figure 21.17, determine the number of nearest neighbors, second nearest neighbors, and third nearest neighbors of a $\mathit{C}{\mathit{s}}^{\mathbf{+}}$ion in crystalline CsCl. The nearest neighbors of the$\mathit{C}{\mathit{s}}^{\mathbf{+}}$ ion are $\mathit{C}{\mathit{l}}^{\mathbf{-}}$ions, and the second nearest neighbors are $\mathit{C}{\mathit{s}}^{\mathbf{+}}$ions.

Short answer

The number of nearest neighbors, second nearest neighbors, and third nearest neighbors of cesium ion are 8, 6, and 12, respectively.

Step-by-step solution

The number of nearest neighbors, and second nearest neighbors.

The structure of CsCl follows the body-centered unit cell (bcc) pattern.

Here, the central atom is a cesium ion, and the 8 surrounded atoms are chlorine ions.

Therefore, the first coordination number (nearest neighbors) of central $C{s}^{+}$ion is 8 $C{l}^{-}$ions present in the same unit cell.

Later, the second nearest neighbors are 6. These are the 6 $C{s}^{+}$ions present at the 6 nearest neighboring unit cells.

The third nearest neighbors of a cesium ion in crystalline CsCl.

Now, the third nearest neighbor of a cesium ion is 12 $C{l}^{-}$ions present in the eight-unit cells around.