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Next: 4.3 Indices of the set of Up: 4. Crystallographic Calculations Using the Reciprocal Previous: 4.1 Scalar product of direct and

4.2 Vector product of two direct lattice vectors

Let us consider two direct lattice vectors:

\begin{displaymath}
\textbf{n}_1 = u_1\textbf{a}+ v_1 \textbf{b} + w_1 \textbf{c...
 ...
\textbf{n}_2 = u_2\textbf{a} + v_2 \textbf{b} + w_2 \textbf{c}\end{displaymath}

Their vector product is equal to:

\begin{displaymath}
\textbf{n}_1 \wedge \textbf{n}_2 = \left\vert\begin{array}
{...
 ...\ u_2 & v_2\end{array} \right\vert \textbf{a} \wedge \textbf{b}\end{displaymath}

Using the definition (2.1) of the basic reciprocal vectors, we may write:

\begin{displaymath}
\textbf{n}_1 \wedge \textbf{n}_2 = V \left\vert\begin{array}...
 ...
{cc}
u_1 & v_1 \\ u_2 & v_2\end{array} \right\vert \textbf{c*}\end{displaymath} (4.1)

This shows that the vector product of two direct lattice vectors is easily expressed in terms of the basic reciprocal vectors.



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