In a hexagonal close-packed (HCP) material, let a represent theinteratomic spacing within a close-packed layer (plane), and let crepresent the lattice parameter normal (perpendicular) to theselayers. There are two close-packed layers stacked along c in theconventional unit cell, as described in Lecture 3. (i) Find anexpression for a in terms of the atomic radius R. (ii) Now imaginethe same close-packed layers, made from the same atoms as before(i.e. R does not change), but now stacked to form a cubic closepacked (CCP) material. There are three close-packed layers stackedalong the body diagonal of the conventional face centered cubic(FCC) unit cell of CCP material. Find an expression that relatesthe atomic radius R to the close-packed layer spacing in this unitcell. (Hint: both R and the close-packed layer spacing can bewritten in terms of the length of any edge of the FCC unit cell.)(iii) Use your answer from (ii) to obtain an expression thatrelates c to R in the HCP structure. (iv) Use your answers from (i)and (iii) to show that c/a ~ 1.633 in perfect HCP materials. (v)Many HCP materials do not have this ideal value of c/a. What is thepractical significance / consequence of departures from the idealc/a value?
