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GATE 2021 PH – Question 13

Solid State Physics · Diffraction methods for structure determination · 1 mark · Multiple choice

A one-dimensional diatomic lattice consists of alternating atoms P and Q as shown. The separation between adjacent Q atoms is $a$, and P lies midway between them. For diffraction satisfying $a\cos\theta=n\lambda$, which statement about the intensity is correct? Assume atomic form factors and instrument resolution do not depend on $\theta$.

Diagram for GATE 2021 PH question 13
  1. Even-order reflections have lower intensity than odd-order reflections.
  2. Odd-order reflections have lower intensity than even-order reflections.
  3. Odd-order reflections have zero intensity.
  4. Even-order reflections have zero intensity.

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Correct answer: (B) Odd-order reflections have lower intensity than even-order reflections.

Explanation

The two atoms in a unit cell have a relative phase $n\pi$ at the stated diffraction condition. The structure factor is $F_n=f_Q+f_Pe^{in\pi}=f_Q+(-1)^nf_P$. Hence even orders have intensity proportional to $(f_Q+f_P)^2$, whereas odd orders have $(f_Q-f_P)^2$. Odd orders are weaker, but need not vanish because P and Q have different scattering factors.

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