Problem 19 - Chemistry: An Atoms-Focused Approach

Question

Explain the difference between cubic closest-packed and hexagonal closest- packed arrangements of identical spheres.

Step-by-Step Solution

Answer

Answer: The main difference between ccp and hcp arrangements lies in their atomic arrangement patterns in consecutive layers. For ccp, it's either ABABAB or ABCABC, while for hcp, it's ABABAB. Both ccp and hcp have the same coordination numbers (12) meaning each sphere is surrounded by 12 neighbors, and they also share the same packing efficiency (74.05%).

Step 1: Understanding cubic closest-packed (ccp) arrangement

To begin, we need to understand the structure of a cubic closest-packed (ccp) arrangement. In ccp, the spheres (atoms, ions, or molecules) are arranged in a repeating sequence of three layers, named ABABAB or ABCABC, where each sphere in the A-layer is surrounded by six spheres in the B-layer, and vice versa. In the ABCABC sequence, a C-layer is added, with each sphere in the C-layer also surrounded by six spheres from the B-layer.

Step 2: Understanding hexagonal closest-packed (hcp) arrangement

In a hexagonal closest-packed (hcp) arrangement, the spheres are orderly arranged in a repeating pattern of two layers, named ABABAB, where spheres in the A-layer are surrounded by six spheres in the B-layer, and vice versa. The difference between the ccp and hcp arrangement becomes apparent when we observe the third layer of the ccp arrangement. In the hcp arrangement, there's no designated C layer, unlike the ccp arrangement.

Step 3: Coordination number of ccp and hcp arrangements

The coordination number is the number of nearest neighbors for a sphere (atom, ion, or molecule) in the structure. In both ccp and hcp arrangements, each sphere has a coordination number of 12. This means that each sphere in ccp or hcp has 12 spheres (neighbors) surrounding it, which are touching it.

Step 4: Packing efficiency of ccp and hcp arrangements

Packing efficiency measures the ratio of the volume occupied by the spheres to the total volume of the unit cell. Both cubic closest-packed (ccp) and hexagonal closest-packed (hcp) structures have the same packing efficiency of 74.05%. This means that 74.05% of the unit cell's volume is occupied by the spheres, while the remaining 25.95% is empty space.

Step 5: Compare ccp and hcp arrangements

Cubic closest-packed (ccp) and hexagonal closest-packed (hcp) arrangements differ in their regular structure and layer sequence, but they have the same coordination numbers (12) and packing efficiencies (74.05%). The main difference between these two arrangements lies in their atomic arrangement patterns in consecutive layers. For ccp, it's either ABABAB or ABCABC, while for hcp, it's ABABAB.