fix equations with \begin{cases} not rendering

src/10_xray_solutions.md

@@ -119,9 +119,9 @@ plt.show()
 ## Exercise 4: Structure factors
 
 ### Subquestion 1
-
+$S_\mathbf{G} = \sum_j f_j e^{i \mathbf{G} \cdot \mathbf{r_j}} = f(1 + e^{i \pi (h+k+l)}) =$
 $$
-S_\mathbf{G} = \sum_j f_j e^{i \mathbf{G} \cdot \mathbf{r_j}} = f(1 + e^{i \pi (h+k+l)}) = \begin{cases}
+\begin{cases}
       2f & \text{if $h+k+l$ is even}\\
       0 & \text{if $h+k+l$ is odd}
 \end{cases}       
@@ -134,9 +134,9 @@ where we used sum over the basis of BCC in $j$.
 See when $S_G$ is zero
 
 ### Subquestion 3
-
+$S_\mathbf{G} =$
 $$
-S_\mathbf{G} = \begin{cases}
+\begin{cases}
       f_1 + f_2 & \text{if $h+k+l$ is even}\\
       f_1 - f_2 & \text{if $h+k+l$ is odd}
 \end{cases}       
@@ -146,8 +146,9 @@ $$
 
 For FCC, the structure factor is the following:
 
+
+$S_\mathbf{G} = $
 $$
-S_\mathbf{G} = 
 \begin{cases}
       4f & \text{if $h,k,l$ are all odd or even}\\
       0 & \text{if otherwise}