I'm confused with the lattice structure of $\rm CsCl$. It should be categorized as simple cubic, but I wonder why it is not body-centered-cubic (BCC)? Is that because there are two types of atoms, each of them form the same cubic structure, so we say it's simple cubic with a two-atom basis? Can I say that it's a superposition of two simple cubic lattices?


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Lattice and crystal structure are 2 different things; the lattice is an infinite periodic, repeating array of points not atoms! The crystal structure is obtained by the convolution of the lattice with a basis (i.e. an atom or a group of atoms).

In CsCl the lattice type is primitive because the atom at the centre of the unit cell is not the same as the one at the corners. So your basis is constituted of Cs at corners (coincident with the position of the primitive lattice points) and Cl at the center of the cube.

PS: it is equivalent to describe the structure with Cl at corners and Cs at the center of the cube because the Wyckoff sites of Cs and Cl in this structure have the same symmetries.


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