From fb72477f17a0a5045eb867aa5236d2fbe6a0e7d5 Mon Sep 17 00:00:00 2001
From: Anton Akhmerov <anton.akhmerov@gmail.com>
Date: Thu, 18 Mar 2021 22:41:31 +0000
Subject: [PATCH] rewording
---
src/10_xray_solutions.md | 7 +++++--
1 file changed, 5 insertions(+), 2 deletions(-)
diff --git a/src/10_xray_solutions.md b/src/10_xray_solutions.md
index 3415c6eb..c01c48f1 100644
--- a/src/10_xray_solutions.md
+++ b/src/10_xray_solutions.md
@@ -38,11 +38,14 @@ $$
$$
2.
+
+Because the relation between direct and reciprocal lattice is symmetric, so are the expressions for the direct lattice vectors through the reciprocal ones:
+
$$
\mathbf{a}_{i} \epsilon_{ijk} = \frac{2\pi}{V^*} (\mathbf{b}_{j} \times \mathbf{b}_{k})
$$
-whereas $\epsilon_{ijk}$ is the [Levi-Civita tensor](https://en.wikipedia.org/wiki/Levi-Civita_symbol#Three_dimensions)
+where $\epsilon_{ijk}$ is the [Levi-Civita tensor](https://en.wikipedia.org/wiki/Levi-Civita_symbol#Three_dimensions)
3.
One set of the BCC primitive lattice vectors is given by:
@@ -61,7 +64,7 @@ $$
$$
which is forms a reciprocal FCC lattice.
-Using the result in Subquestion 2, the vice versa result is trivial
+The opposite relation follows directly from our previous result.
4.
Because the 1st Brillouin Zone is the Wigner-Seitz cell of the reciprocal lattice, we need to construct the Wigner-Seitz cell of the FCC lattice.
--
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