Question

Hexagonal Close-Packed Structure

 a) The conventional HCP unit cell shown to the right is not a Bravais lattice, but it can be defined as a simple hexagonal lattice with a two-atom basis. Draw the simple hexagonal unit cell on this structure and label the fundamental lattice translation vectors as a1,a2, and a3.

 b) Calculate the direction of each lattice translation vector in cartesian coordinates using the cartesian coordinate system shown on the diagram.

 c) In terms of lattice constants a and c, calculate the volumes for both the simple hexagonal and conventional HCP unit cells.

 d) Calculate the number of atoms contained within the simple and the conventional unit cells. Compare the volume ratio between simple and conventional unit cells with the number of atoms in each. In general, do you expect the atoms per volume to depend on your choice of unit cell? Why or why not? 

e) Given an axial ratio of c/a 1.63, calculate the atomic packing factor.

Answer 1