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PHY.K02UF Molecular and Solid State Physics | ||||
$\large \vec{k}=u\vec{b}_1+v\vec{b}_2+w\vec{b}_3\,:\,(u,v,w)$
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The real space and reciprocal space primitive translation vectors are:
$\large \vec{a}_1 = \frac{a}{2}(\hat{x}+\hat{y})-\frac{c}{2}\hat{z}$ $\large \vec{a}_2 = \frac{a}{2}(\hat{x}-\hat{y})+\frac{c}{2}\hat{z}$ $\large \vec{a}_3 = \frac{a}{2}(-\hat{x}+\hat{y})+\frac{c}{2}\hat{z}$,
$\large \vec{b}_1 = \frac{2\pi}{a}(\hat{k_x}+\hat{k_y})$ $\large \vec{b}_2 =\frac{2\pi}{a}\hat{k_x}+\frac{2\pi}{c}\hat{k_z}$ $\large \vec{b}_3 = \frac{2\pi}{a}\hat{k_y}+\frac{2\pi}{c}\hat{k_z}$.