GATE MT 2020 Q10. X –ray diffraction pattern from an elemental metal with a FCC crystal structure shows the first peak at a Bragg angle 24.65 degrees. The lattice parameter of this metal is ___nm. Given, wavelength of the X-ray used is 0.1543 nm.

According to Bragg’s law,

Since, reflection is coming from 1^st peak of FCC. Hence plane will be (111).

by putting, λ (wavelength of Xray) = 0.154 nm, Ɵ (bragg’s angle) = 24.5˚

We will get  =>  a = 0.32 nm

Some of you might be thinking why (111) plane correspond to the 1st peak which gives refelction for FCC.

So, For a specific crystal which plane will give refelction and observed in the output of XRD result is guided by some criteria. Those criterias are established by sturcture factor calculation.

• Criteria for FCC is – only those plane will give reflection which have unmixed (hkl) values.  (Unmixed – all h,k,l should be either odd or even)
• Eg – (111), (200), (220), (311) and so on
• That’s why you have h^2+k^+l^ values in ratio of – 3:4:8:11 . . . . .