Calculate the maximum packing fraction of the unit cell volume that can be filled by hard spheres in the Hexagonal structure
Relevant eq: Volume of spheres is number of lattice points multiplied with the maximum volume of one sphere.
The Attempt at a Solution
I know maxium is obtained when c = a i.e when height of the cell is as high as one of the sides in the hexagon. Hence, maximum sphere radius is a/2 (I have shown geometrically that the spheres can touch eachother).
Now I am to determine the number of lattice points in this structure, I know that one primitive cell contains totally one lattice point, and a unit cell of a hexagonal structure can be made up by exactly three primitve cells, so the number of lattice points is 3. Is that the correct way to do this?
The rest I can figure out by my self, just are unsure how to determine the number of lattice points.