another attempt

src/10_xray_solutions.md

@@ -141,19 +141,13 @@ plt.show()
 
 ## Exercise 4: Structure factors
 
-1.
-$S(\mathbf{G}) = \sum_j f_j e^{i \mathbf{G} \cdot \mathbf{r_j}} = f(1 + e^{i \pi (h+k+l)})$
-
-2.
-
-Solving for $h$, $k$, and $l$ results in 
-
+1,2
 $$
-S(\mathbf{G}) = 
+S(\mathbf{G}) = \sum_j f_j e^{i \mathbf{G} \cdot \mathbf{r_j}} = f(1 + e^{i \pi (h+k+l)}) =
 \begin{cases}
-        2f, \: \mathrm{if\: h+k+l\: is \:even}\\
-        0,  \: \mathrm{if\: h+k+l\: is \:odd}.
-\end{cases}
+      2f & \text{if $h+k+l$ is even}\\
+      0 & \text{if $h+k+l$ is odd}
+\end{cases}       
 $$
 
 Thus if $h+k+l$ is odd, diffraction peaks dissapear
@@ -165,10 +159,9 @@ Let $f_1 \neq f_2$, then
 $$
 S(\mathbf{G}) = 
 \begin{cases}
-        f_1+f_2, \: \mathrm{if\: h+k+l\: is \:even}\\
-        f_1-f_2,  \: \mathrm{if\: h+k+l\: is \:odd}.
-\end{cases}
-$$
+      f_1+f_2 & \text{if $h+k+l$ is even}\\
+      f_1-f_2 & \text{if $h+k+l$ is odd}
+\end{cases}   
 
 4.
 Due to bcc systematic absences, the peaks from lowest to largest angle are: