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The sign, $\sigma_{\mathrm{side}}$, of $\xi$ depends on which side of the orientation vector $\left| a \right>$ the scattering vector $\left| Q \right>$
is located. The sign can be found by calculating the (covariant) cross product of $\left| a \right>$ and $\left| Q \right>$ to give an out-of-plane vector
which can be compared with the given scattering plane up vector.
\paragraph*{Special case}
Special case for cubic crystals, $g_{ij}=\delta_{ij}\cdot\left(2\pi/ a \right)^2$:
