Question

Diffraction from an unknown cubic metal is observed to occur at the following values of θ when using CuKα radiation. Determine the crystal structure to find the lattice constant.
20.1⁰, 29.2⁰, 36.6⁰, 43.5⁰, 50.2⁰, 57.4⁰, 65.5⁰

a) What is the crystal structure?
SC, BCC or FCC

b)Express the value of the lattice constant in m

Answer 1

a. BCC

Answer 2

i think b only ask for the expression, not the actual value????...beside, in order to get the actual value of lattice constant, we need the radius...is the radius given or can it be determined???...

i tried expressing the lattice constant for the BCC as 4r/sqrt3 but can't get the correct format.

Answer 3

The value of the radius is not given

Answer 4

For CuKα-radiation λ=1.541•10⁻¹⁰ m.
From equation
sin²θ₁/(h²+k²+l²)₁=sin²θ₂/(h²+k²+l²)₂=…. const,
sin²θ₁/1= sin²θ₂/2= sin²θ₃/3=… sin²θ ₇/7.
For the given data
0.118/1 = 0.238/2=0.3555/3=0.4738/4=0.59/5=
=0.7097/6=0.828/7=0.118 =>
The crystal structure is simple cubic –SC.
sin²θ/(h²+k²+l²)=const=λ²/4a²
a= sqrt{λ²(h²+k²+l²)/2sin²θ }= >
a= sqrt{λ²(1²+0²+0²)₁/2sin²θ₁}=
= sqrt{(1.541•10⁻¹⁰)²(1²+0²+0²)/2sin²20.1⁰}=3.17•10⁻¹⁰m.

Answer 5

3.17*10^-10