BCC lattice - basis and primitive lattice vectors

Physics Q&A
1

Hello,

I’m revisiting the basis and primitive lattice vectors of the BCC lattice. The basis w.r.t. the conventional unit cell should be (0,0,0) and (1/2,1/2,1/2) right?
And the primitive lattice vectors are (a,0,0), (0,a,0) and (a/2, a/2, a/2) right?

In another book I’m reading it says that the primitive lattice vectors should be a/2(-1,1,1), a/2(1,-1,1) and a/2(1,1,-1) so I got confused. But what they do differently is that they don’t choose the primitive lattice vectors with respect to the conventional unit cell right?

Kind regards,
Vincent

2

your lattice vectors are correct. Note that there are infinitely many valid sets of primitive lattice vectors. See also this post Writing the basis - #4 by t.vandersar. Also, the solutions of the warm-up exercises Crystal structure - Open Solid State Notes describe the fcc and bcc lattices