# HCP vs. CCP vs BCC

Hexagonal Closet Packaging vs. Cubic Closet Packaging (face-centered) vs. Body-centered

a) Which of the three types of packaging has the least efficient arrangement of atoms? Justify the answer.

b) How do the two more efficient forms of packing compare regarding volume?

c) What is the relationship between coordination number, packing, and density (as mass/volume).

d) State the coordination number of each type of packing, i.e., what is the number of neighbours touching each atom in an infinite array of space lattices?

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#### Solution Preview

In a crystal the atoms are arranged in a regular repeating pattern. The smallest repeating unit is called the unit cell. The entire structure can be reconstructed the unit cell. The unit cell is characterized by three lengths and three angles. The quantities a and b are the lengths of the sides of the base of the cell and g is the angle between these two sides. The angles a and b describe the angles between the base and the vertical sides of the unit cell and c is the height of the unit cell.

To form a three-dimensional closest packed structure, the hexagonal closest packed planes must be stacked such that atoms in successive planes nestle in the triangular spaces in the overlying plane. Note that there are six of these spaces surrounding each atom in the hexagonal ...

#### Solution Summary

Hexagonal Closet Packaging vs. Cubic Closet Packaging (face-centered) vs. Body-centered in terms of efficiency. Calculation of coordination number and density for each.