4.1 Scalar product of direct and reciprocal lattice vectors

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Let us consider a direct lattice vector

$\begin{displaymath} u\textbf{a} + v\textbf{b} + w\textbf{c}\end{displaymath}$

and a reciprocal lattice vector

$\begin{displaymath} h\textbf{a*} + k\textbf{b*} + l\textbf{c*}\end{displaymath}$

Using (2.3), their scalar product is equal to:

hu + kv + lw