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calculate the reciprocal lattice of the BCC structure

calculate the reciprocal lattice of the BCC structure
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Answer #1

The conventional unit cell for the bcc lattice has two lattice points per cell - one at (0, 0, 0) and one at (1/2, 1/2, 1/2).

To calculate the reciprocal lattice, we instead use the primitive unit cell, which has basis vectors a1 = (1/2, 1/2, -1/2), a2 = (1/2, 1/2, 1/2) and a3 = (1/2, -1/2, 1/2) when referred to the conventional cell.

The reciprocal lattice vectors can then be calculated:

b1=a2×a3/a1⋅a2×a3=(1,0,1)

b2=a3×a1/a1⋅a2×a3=(0,1,1)

b3=a1×a2/a1⋅a2×a3=(1,1,0)

You should be able to recognise these as (scaled versions of) the primitive lattice vectors of a face-centred cubic (fcc) lattice, which is the reciprocal of a bcc lattice.

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