Question

8 An x-ray diffractometer recorder chart for an element that has either the BCC or the FCC crystal structure showed diffraction peaks at the following 20 angles:40.663°, 47.314°, 69.144°, and 83.448°. (Wavelength of the incoming radiation was 0.15405 nm.) (10 %) (a) Determine the crystal structure of the element. (b) Determine the lattice constant of the element.

Answer 1

Given

2θ angles are

40.663°,47.314°,69.144° and 83.448°

Wavelength= 0.15405 nm

Determining crystal

Let's consider first two angles

2θ = 40.663 and 47.314

θ = 20.3315 and 23.657

Now calculate sin θ

Sin 20.3315 = 0.3474

Sin 23.657 = 0.4013

Now

Sin^{​​​​2}20.3315/sin²23.657 = 0.1207/ 0.1610

= 0.75

So it is FCC

b)

Lattice constant

Here we consider the miller indices ( 1 1 1)

a = λ/2 √(h^{​​​​​​2} + k^{​​​​​​2} + l^{​​​​​​2})/sin²θ

= (0.15405/2)√(1+1+1)/0.1207

= 0.077025 * 4.98548

= 0.384 nm