diff --git a/src/10_xray_solutions.md b/src/10_xray_solutions.md index 3415c6eb5d71af1d23317e99c6954be8cd1268fa..c01c48f1996544a5f9ae4f148f2c01a1bbcd9708 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.