Answer:
The [111] direction is close packed; the linear packing factor is 1.
Explanation:
Lattice parameter = a₀ = 0.35089nm
Directions 100, 110 and 111
r = <u>3a₀ </u>
4
where r = repeat distance
r = <u>3(0.35089)</u>
4
r = 0.1519nm
For [100]; r = a₀ = 0.35089nm
Linear density = 1/a₀ = 2.85points/nm
linear density = 1/a₀ = 2.85 points/nm
linear packing fraction = (2)(0.1519)(2.85) = 0.866
For [110]; r = 2a₀ = 0.496 nm
linear density = 1/a₀ = 2.015 points/nm
linear packing fraction = (2)(0.1519)(2.015) = 0.612
For [111]: r = 3a₀/2 = 0.3039 nm
linear density= 2/3a₀ = 3.291 points/nm
linear packing fraction = (2)(0.1519)(3.291) = 1
Therefore, from the above, [111] direction is close packed; the linear packing factor is 1.
