1. .. . is a reciprocal lattice vector of the reciprocal lattice. 2. Another helpful ingredient in the proof is the " reciprocal lattice vectors ". 3. These reciprocal lattice vectors of the FCC represent the basis vectors of a BCC real lattice. 4. E are energies, k and q are wave vectors and G denotes a reciprocal lattice vector . 5. An arbitrary vector, G, defines the reciprocal lattice vector between the ends of any two k vectors. 6. For face-centered cubic and body-centered cubic lattices, the primitive lattice vectors are not orthogonal. 7. Consider what happens when the lattice vectors are varied, resulting in a change in the reciprocal lattice vectors. 8. Consider what happens when the lattice vectors are varied, resulting in a change in the reciprocal lattice vectors . 9. The dispersion relations show conics of the free-electron energy dispersion parabolas for all possible reciprocal lattice vectors . 10. Physically, the reciprocal lattice vectors act as additional chunks of momentum which the lattice can impart to the phonon. 
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