GATE 2020 PH – Question 54
A simple cubic Bravais lattice with parameter a has a monatomic basis at $\mathbf r_1=0$ and $\mathbf r_2=(a/4)(\hat{\mathbf x}+\hat{\mathbf y}+\hat{\mathbf z})$. The scattering-vector change is $\mathbf K=n_1\mathbf G_1+n_2\mathbf G_2+n_3\mathbf G_3$, with primitive reciprocal vectors $\mathbf G_i$. For $(n_1,n_2,n_3)=(3,3,2)$, find the geometrical structure factor.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 2 to 2
Explanation
The geometrical factor is $S=\sum_j e^{i\mathbf K\cdot\mathbf r_j}=1+e^{i\mathbf K\cdot\mathbf r_2}$. For simple cubic reciprocal vectors, $\mathbf K\cdot\mathbf r_2=(2\pi/a)(a/4)(3+3+2)=4\pi$. Thus $S=1+e^{i4\pi}=2$. The atomic scattering amplitude is separate from this geometrical factor.
More Diffraction methods for structure determination questions
All Diffraction methods for structure determination questions →