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Everywhere I see on the internet, it says BCC, but my professor still says "it is cubic lattice, no matter which book/website might tell you otherwise".

The argument was that for deciding which lattice it is, we only see the atoms/ions which make up the lattice, in this case Br, and they're only present at the corners of the cube, which seems correct. I haven't seen this being said anywhere else, and every site says CsBr is BCC, considering the Cs at body center while deciding the structure.

I do understand its just a cube with Br at corners and Cs in the middle, but I want to know what the correct terminology here.

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    $\begingroup$ It is cubic lattice, and calling it BCC is an abuse of language. In the real BCC lattice the cube's center is equivalent to its corner. $\endgroup$ Nov 10, 2023 at 10:52
  • $\begingroup$ en.wikipedia.org/wiki/… $\endgroup$
    – DotCounter
    Nov 10, 2023 at 18:19

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Lattice and crystal structure are two different objects. A lattice exists in the geometrical space and is formed by lattice points characterized by having the same geometrical properties; on these bases are defined the Bravais lattices. Crystal structures are obtained by the convolution of a lattice with a motif (one or more atoms with a mutual geometrical relationship); a structure exists in real space and is formed by atoms. Don't confuse atoms with lattice points.

CsBr crystallizes in the Pm-3m space group; "P" means that the underlying lattice is primitive, not body-centered. The motif in this case is given by two atoms, Cs and Br. Cs atoms are located at the vertexes of the cube, the same positions as the P lattice, whereas Br is at the center (but you can also describe the structure in the opposite way, with Cs at the center and Br at the vertexes). The important thing is that atoms at the center and those at vertexes are chemically different; for this reason, the lattice is P and not I (=bcc). If all atoms were Cs, you would have a bcc structure.

Cubic P and cubic I (=bcc) are both cubic lattices, but with different symmetry operations.

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