HW 3: Structure of Crystalline Solids

Question 1

Convert [1 0 0] direction into the four-index Miller-Bravais scheme for hexagonal unit cells

Answer 1

[ 2 -1 -10 ]

U=1, V=0, W=0

From eq. *plug them *

u= 1/3(2U-V) = 2/3
v=1/3(2V-U) = -1/3
t= -(u+v) = -1/3
w= W = 0

neccessary to multiply by 3 to reduce to lowest set of integers

Question 2

Convert [1 1 1] direction into the four-index Miller-Bravais scheme for hexagonal unit cells

Answer 2

[ 1 1 -2 3]

U=1, V=1, W=1

From eq. *plug them *

u= 1/3(2U-V) = 1/3
v=1/3(2V-U) = 1/3
t= -(u+v) = -2/3
w= W = 1

neccessary to multiply by 3 to reduce to lowest set of integers representing as [uvtw]

Question 3

Chromium has a BCC crystal structure, an atomic radius of 0.1249 nm, and an atmo