Question

(c) Hexagonal close-packing (hcp) is an important close-packed structure. The first layer of spheres (of radius r) is placed at the A sites, as shown. The second layer is placed at the B sites, each touching three spheres in the A layer. The third layer repeats the A layer, and so on. A A A A А B A A A А A A B B B B OOOOOO B i. Find primitive lattice vectors of the hcp lattice and determine the basis. Hints: • Only one of the A and B are lattice sites. • To obtain the out-of-plane primitive lattice vector, it is helpful to calculate the vertical dis- tance between the centre of a B atom and the centre of the neighbouring A atoms. ii. Hence calculate the volume of the unit cell and the packing fraction. Compare to the packing fractions of the cubic lattices.

Can you explain which one of A and are the lattice sites and why please? and since there's only A and B does that mean there are only two primitive lattice vectors or three? (A bit confused here) Many thanks