Question

In my professors' lecture notes, there is a passage that reads:

"The unit cell of the BCC lattice likewise consists of two lattice points:

one at R1 = 0a1 + 0a2 + 0a3

the other at R2 = .5a1 + .5a2 + .5a3"

This is confusing. I thought that a bravai lattice was a collection of points that can be 'generated' from a chosen collection of basis vectors, a1, a2 and a3 by superimposing them like so

R = i*a1 + j*a2 + k*a3

Where i, j and k are arbitrary integers. For example, in the simple case of an SC bravai lattice

a1 = a*e_x, a2 = a*e_y and a3 = a*e_z

How come my professor is using non-integer values to locate these points of a BCC bravai lattice?

Answer 1