Which type of close packed structure has the least unfilled space?

The face-centered cubic (FCC) structure, also known as cubic close packed, features a close packing arrangement where atoms are located at each of the corners and the centers of each face of the cube. This arrangement allows for a highly efficient packing of atoms, resulting in a coordination number of 12.

In FCC, the spatial efficiency is maximized due to the optimal arrangement of spheres, leading to a packing efficiency of approximately 74%. This means that only about 26% of the volume is unfilled space, which is the least when compared to other close-packed structures. Both hexagonal close packed (HCP) and cubic close packed arrangements exhibit similar packing efficiencies, but they are strictly geometrically different in arrangement; however, they effectively have the same packing density.

On the other hand, other structures like body-centered cubic (BCC) have a lower packing efficiency of about 68% due to its different arrangement, which results in more unfilled space. Therefore, when evaluating the various types of close-packed structures, the face-centered cubic configuration demonstrates that it has the least unfilled space due to its optimal arrangement and coordination.