In a hexagonal HCP meterial... In a hexagonal close-packed (HCP) material, let a

Question

In a hexagonal HCP meterial...

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

Explanation / Answer

solution a)

so, a = 2R

hence R = a/2

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