Problem 1. Consider a crystal with HCP structure, having anideal c/a ratio. Complete parts (a)-(c) below.
(a) (1.0 pt max) Demonstrate that the ideal c/a ratio equals 26/3.
(b)(0.5 pt max) Find the volumeof one unit cell for a given a value.
(c) (0.5 pt max) Demonstrate thatthe atomic packing factor for this crystal structure is ï°2/6.
Hints: (a) The c/a ratio isconsidered ideal when the distance from some atom to its nearestneighbors within the same hexagonally-packed layer equals thedistance to its nearest neighbors belonging to a differentlayer.
(b) The volume of a prism is theproduct of the area of its base face and the height. Use the c/aratio found in part (a).
(c) Find the relationship betweenthe lattice constant a and the atomic radius R to calculate the APFvalue. Use the unit cell volume found in part (b)
