What is the most probable unit cubic cell for the Xray diffr

What is the most probable unit cubic cell for the X-ray diffraction pattern below? B. If atomic radius of the above crystal system is 0.1241 nm. Calculate the lattice parameter, a, then interplanar spacing d_111?

Solution

Answer:

A) Using Selection Rules for Cubic Crystals,

d_hkl = (a / (h² + k² + l²)^1/2); where \'a\' is the lattice spacing; h,k,l are Miller indices of the Bragg plane;

One of the Allowed Reflection is, h + k + l = even. In this problem, (110), (200), (211) all are even. Additionally, those are second, fourth, and sixth order reflection respectively.

So, based on the allowed reflections, the given x ray pattern is most probable is Body Centre Cubic (BCC).

B) For BCC crystal,

Given the data from the problem is,

R = 0.1241 nm; then we have substitute the above formula (1),

then a = 0.286596674 nm;

the d₁₁₁ = (0.286596674 x 10^-9 ) / 3^1/2 = 0.1654667 nm .