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\title{Complete Solid State Physics: Crystal Lattice}
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\section{Crystal Lattice}

A crystal is modeled by translating a basis through a Bravais lattice. The
primitive vectors $\mathbf a_1,\mathbf a_2,\mathbf a_3$ generate lattice
points

$$
\mathbf R=n_1\mathbf a_1+n_2\mathbf a_2+n_3\mathbf a_3,
$$

with integer $n_i$. This is the starting point for using symmetry instead of
tracking every atom separately.

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