Update 10_xray_solutions.md

src/10_xray_solutions.md

@@ -142,19 +142,32 @@ plt.show()
 ## Exercise 4: Structure factors
 
 1.
-$$
-S(\mathbf{G}) = \sum_j f_j e^{i \mathbf{G} \cdot \mathbf{r_j}} = f(1 + e^{i \pi (h+k+l)})
-$$
+$S(\mathbf{G}) = \sum_j f_j e^{i \mathbf{G} \cdot \mathbf{r_j}} = f(1 + e^{i \pi (h+k+l)})$
+
 2.
+
 Solving for $h$, $k$, and $l$ results in 
 
-$$
+$
 S(\mathbf{G}) = \begin{cases}
     2f, \: \text{if $h+k+l$ is even}\\
     0, \: \text{if $h+k+l$ is odd}.
 \end{cases}
-$$
-Thus if $h+k+l$ is odd, diffraction peaks disappear.
+$
+
+Thus if $h+k+l$ is odd, diffraction peaks dissapear
+
+3.
+
+Let $f_1 \neq f_2$, then
+
+$
+S(\mathbf{G}) = \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}       
+$
+
 
 4.
 Due to bcc systematic absences, the peaks from lowest to largest angle are: