Is it possible to pack spheres more densely than in cubic close packing and hexagonal close packing structures? Explain.
(coordination number is 12 for both structures)
To determine if it is possible to pack spheres more densely than in cubic close packing (CCP) and hexagonal close packing (HCP) structures, we need to understand the maximum possible coordination number for sphere packing. The coordination number refers to the maximum number of adjacent spheres that can touch a central sphere in a given packing arrangement.
In both CCP and HCP structures, the coordination number is 12, which means that each sphere is in contact with 12 neighboring spheres. This arrangement is already relatively efficient in terms of maximizing packing density.
To ascertain if higher coordination numbers are possible, we need to explore alternative packing arrangements. One such arrangement is called the face-centered cubic (FCC) structure, which has a coordination number of 12, similar to CCP and HCP. FCC is essentially a stacked arrangement of CCP layers in which spheres are added in the voids created between the spheres of adjacent layers.
Another possible arrangement is called the body-centered cubic (BCC) structure, which has a coordination number of 8. In the BCC structure, each sphere is in contact with 8 neighboring spheres. BCC packing has a lower coordination number than CCP and HCP but maintains reasonable packing density.
By exploring various packing arrangements, it becomes evident that packing spheres more densely than CCP and HCP structures, while still maintaining a high coordination number, is indeed unlikely. These arrangements, specifically CCP, HCP, and FCC, are known as the densest sphere packings in three dimensions. They achieve high packing efficiencies due to the optimal use of available space. Therefore, it is generally accepted that these structures are the most efficient ways to pack spheres in three-dimensional space.