From c85154e4fff457aad46c84f3b21c8f09a04d6e1e Mon Sep 17 00:00:00 2001
From: Bowy La Riviere <b.m.lariviere@student.tudelft.nl>
Date: Fri, 19 Mar 2021 09:18:06 +0000
Subject: [PATCH] Update 10_xray_solutions.md

---
 src/10_xray_solutions.md | 25 +++++++++++++++++++------
 1 file changed, 19 insertions(+), 6 deletions(-)

diff --git a/src/10_xray_solutions.md b/src/10_xray_solutions.md
index b4f36497..8d9d9b92 100644
--- a/src/10_xray_solutions.md
+++ b/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:
-- 
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