Question

1. Determine Atomic Packing Factor for HCP when atomic radius is r (show all works for full credits)

2. Determine Atomic Packing Factor for Rhombohedral when atomic radius is r and gamma (angle) is 120 degree (see slide 31, ch 4)

3. Determine Max Linear Densities for BCC and FCC (there are multiple)

4. Determine Max Planar Densities for BCC and FCC (there are multiple)

5. Determine Max Linear Densities on the max Planar Density planes from Q4, then compare them to Max Linear Densities from Q3. Explain.

Answer 1

1. Let a is length of one side hexagonal plane

r is atomic radius

c is height of HCP structure

we can write a = 2r ( according to packing structure)

Atomic packing factor = ((Effective number of atoms) x (volume of one atom)) divided by volume of unit cell

volume of one atom =

Effective number of atoms = z

Hexagonal phase of HCP can be divided into 6 equilateral triangles

Then volume of one unit cell =

contribution of each corner atoms in particular unit cell = th of complete atom

  contribution of each face center atoms in particular unit cell =   th of complete atom

There are 12 corner atoms, 2 face center atoms and 3 stoms within body

  Effective number of atom = 2 + 1 +3 = 6

   =()/3

Atomic packing factor =

= 0.74