513.001 Molecular and Solid State Physics

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Reciprocal lattice

A hexagonal close packed Bravais lattice has primitive lattice vectors,

a1 = 0.115 x - 0.19918584287042 y nm,
a2 = 0.115 x + 0.19918584287042 y nm,
a3 = 0.18 z nm.

Here x, y, z are the unit vectors in the x, y, and z directions.

What are the primitive lattice vectors of the reciprocal lattice?

b1 = x + y + z 1/m

b2 = x + y + z 1/m

b3 = x + y + z 1/m