Answer to Question #167979 in Material Science Engineering for ashish

Question

6) A cubic crystal with a=5.60Å is set initially with the incident beam travelling along the [100] direction. The crystal is then rotated clockwise about [001] through an angle ω until the (460) reflection is first produced with Cu Kα radiation. Calculate the Bragg angle θ for the (460) reflection and determine the angle ω

Answer 1

2d sin $\theta$ = n $\lambda$ (Braggs Law)

a = d (h² + k² + l²)^1/2

5.60 A = d (4² + 6² + 0²)^1/2

d = 0.78 A

2 x 0.78 x 10^-10 m x sin $\theta$ = 154.18 x 10^-12 m

sin $\theta$ = 0.9883

$\theta$ = 81°