@@ -563,7 +563,7 @@ We are nearly there, but we are left with finding out the relation between $\phi
...
@@ -563,7 +563,7 @@ We are nearly there, but we are left with finding out the relation between $\phi
Recall the concept of Miller planes.
Recall the concept of Miller planes.
These are sets of planes identified by their Miller indices $(h,k,l)$ which intersect the lattice vectors at $\mathbf{a}_1 / h$, $\mathbf{a}_2 / k$ and $\mathbf{a}_3 / l$.
These are sets of planes identified by their Miller indices $(h,k,l)$ which intersect the lattice vectors at $\mathbf{a}_1 / h$, $\mathbf{a}_2 / k$ and $\mathbf{a}_3 / l$.
It turns out that Miller planes are normal to the reciprocal lattice vector $\mathbf{G} = h \mathbf{b}_1 + k \mathbf{b}_2 + l \mathbf{b}_3$ and the distance between subsequent Miller planes is $d_{hkl} = 2 \pi/\lvert \mathbf{G} \rvert$ (you will derive this in [today's exercise](https://solidstate.quantumtinkerer.tudelft.nl/10_xray/#exercise-2-miller-planes-and-reciprocal-lattice-vectors)).
It turns out that Miller planes are normal to the reciprocal lattice vector $\mathbf{G} = h \mathbf{b}_1 + k \mathbf{b}_2 + l \mathbf{b}_3$ and the distance between subsequent Miller planes is $d_{hkl} = 2 \pi/\lvert \mathbf{G} \rvert$ (you will derive this in [today's exercise](10_xray.md#exercise-2-miller-planes-and-reciprocal-lattice-vectors)).
Substituting the expression for $\lvert \mathbf{G} \rvert$ into the expression for the distance between Miller planes we get:
Substituting the expression for $\lvert \mathbf{G} \rvert$ into the expression for the distance between Miller planes we get:
