Lattice vector ($\mathbf{R}={\sum }_i{n}_i{\mathbf{a}}_i,n_i\in \mathbb{Z}$)

A direct lattice vector is an integer linear combination of primitive translation vectors ${\mathbf{a}}_i$ of a Bravais lattice. Translating by such a vector preserves the lattice. Its dot product with every reciprocal lattice vector is an integer multiple of $2\pi$ in the angular-wavevector convention.