Question

why is a/2 used in the formula a= a/2[i j k) for a lattice vector?

why is a/2 used in the formula a= a/2[i j k) for a lattice vector?

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Answer #1

In the case of for example the primitive unit cell of BCC lattice, we can see that the position of atoms in the lattice are half way from the edges of the lattice. The position of the atom from the origin is half times the distance of the edge from the origin as shown in the figure below.

Thus lattice vectors are

In case of FCC, the configuration of atoms is shown below.

The lattice vectors are

Thus, because of the position of the atom from the origin, factor of 1/2 is coming.

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