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Cesium chloride has a cubic structure with eight $Cs$ atoms at each corner of each cube and one $Cl$ in the middle of the cube. It is stated in my solid state book that this crystal cannot be described by a BCC lattice due to the fact that the atoms are not equivalent whereas they should be by definition of a lattice.

But I have some trouble understanding this. I thought that a lattice is just a mathematical handiness of describing the real physical crystal. A lattice consists of points (whereas the atoms are not points) and is independent on the crystal. Why can’t we just put points on the atoms and describe the crystal completely this way? Why do the atoms need to be equivalent such that we can use a certain lattice ?

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  • $\begingroup$ You need a lattice (each lattice point looks the same) and a basis, the thing you put on the lattice point. Since a caesium atom is not a chlorine atom, they are not the same. $\endgroup$ – Jon Custer Jan 24 at 1:31
  • $\begingroup$ @JonCuster That comment looks suspiciously like an answer... ;) $\endgroup$ – PM 2Ring Jan 24 at 6:17
  • $\begingroup$ FWIW, there are diagrams of the alkali metal halide crystals on Wikipedia. With the lighter metals they are FCC, but with the larger Cs ion they're BCC (except for the fluoride). $\endgroup$ – PM 2Ring Jan 24 at 9:24
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In my experience, the best way of looking at a crystalline structure is as a Bravais lattice of 3D translations of a physical unit (the basis) which contains the information about the positions of the atoms.

In the case of some structures like CsCl, it may happen that if one would disregard the chemical species of the atoms, it could be possible to describe the crystalline structure as a different (more symmetric) Bravais lattice. However this could be done only at the price of ignoring the physical origin of translation symmetry: the fact that the crystalline environment seen before and after any Bravais lattice translation must be the same. If you start close to a Cs and you end up close to a Cl something has visibly changed.

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