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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:
\begin{equation} \large \vec{a}_1=\frac{a}{2}(\hat{x}+\hat{z}),\quad \vec{a}_2=\frac{a}{2}(\hat{x}+\hat{y}),\quad\vec{a}_3=\frac{a}{2}(\hat{y}+\hat{z}),\\ \large \vec{b}_1=\frac{2\pi}{a}(\hat{k}_x-\hat{k}_y+\hat{k}_z),\quad \vec{b}_2=\frac{2\pi}{a}(\hat{k}_x+\hat{k}_y-\hat{k}_z),\quad\vec{b}_3=\frac{2\pi}{a}(-\hat{k}_x+\hat{k}_y+\hat{k}_z). \end{equation}The first Brillouin zone of an fcc lattice has the same shape (a truncated octahedron) as the Wigner-Seitz cell of a bcc lattice. Some crystals with an fcc Bravais lattice are Al, Cu, C (diamond), Si, Ge, Ni, Ag, Pt, Au, Pb, NaCl.