show solution 10

mkdocs.yml

@@ -44,7 +44,7 @@ nav:
     - Tight-binding model: '7_tight_binding_model_solutions.md'
     - Many atoms per unit cell: '8_many_atoms_solutions.md'
     - Crystal structure: '9_crystal_structure_solutions.md'
-    # - X-ray diffraction: '10_xray_solutions.md'
+    - X-ray diffraction: '10_xray_solutions.md'
     # - Nearly free electron model: '11_nearly_free_electron_model_solutions.md'
     # - Band structures in 2D: '12_band_structures_in_higher_dimensions_solutions.md'
     # - Basic principles: '13_semiconductors_solutions.md'

src/10_xray_solutions.md

@@ -77,7 +77,7 @@ Since $\rho=d / V$, we must maximize $d$. To do that, we must minimize $|G|$ (Su
 ## Exercise 3: X-ray scattering in 2D
 
 ### Subquestion 1
-```
+```python
 def reciprocal_lattice(N = 7, lim = 40):
     y = np.repeat(np.linspace(-18.4*(N//2),18.4*(N//2),N),N)
     x = np.tile(np.linspace(-13.4*(N//2),13.4*(N//2),N),N)
@@ -103,7 +103,7 @@ $k = \frac{2 \pi}{\lambda} = 37.9 nm^{-1}$
 
 Note that $|k| = |k'| = k $ since elastic scatering
 
-```
+```python
 reciprocal_lattice()
 # G vector
 plt.arrow(0,0,13.4*2,18.4,color='r',zorder=10,head_width=2,length_includes_head=True)
@@ -144,15 +144,9 @@ $$
 
 ### Subquestion 4
 
-For FCC, the structure factor is the following:
+Due to bcc systematic absences, the peaks from lowest to largest angle are:
+$(110),(200),(211), (220), (310)$
 
+### Subquestion 5
 
-$S_\mathbf{G} = $
-$$
-\begin{cases}
-      4f & \text{if $h,k,l$ are all odd or even}\\
-      0 & \text{if otherwise}
-\end{cases}       
-$$
-
-Since $(110)$ have mixed odd and even indices, no diffraction peak will be observed on FCC. For BCC, however, $(110)$ gives $1+1+0 = 2$ even number, so there will be diffraction.
+$a = 2.9100 \unicode{xC5}$