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If $\ce{NaCl}$ crystallizes in an fcc lattice, its coordination number should be 12. Then why do we say that $\ce{NaCl}$ has a coordination number of 6? Also, if $\ce{CsCl}$ crystallizes in a simple cubic lattice, why is it's coordination number 8 and not 6, as for other simple cubic lattices?

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NaCl

NaCl is not monoatomic. When discussing coordination number of cations in ionic compounds, the number refers to the anions the cations is surrounded by (or bonded to, or touching).

NaCl structure

The blue Na+ cations are bonded to six other Cl- anions: top, bottom, left, right, forward, backwards (in this image). They are not bonded and do not touch the other Na+ cations in the diagonals.

CsCl

CsCl is not a "simple" simple cubic. Each of the different ions, Cs+ and Cl- by themselves are simple cubic, but they are interpenetrating to form something that looks like a body centered cubic:

CsCl structure

A mono atomic simple cubic will have coordination number of six, but this is an ionic compound. Thus, each cation or anion that sits in the center of the cube is bonded to the eight anions or cations (respectively) that sit in the vertices of the cube.

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  • $\begingroup$ @ron I just read this on goo.gl/o28dWh: "Caesium Chloride is a type of unit cell that is commonly mistakened as Body-Centered Cubic. This misconception is easy to make, since there is a center atom in the unit cell, but CsCl is really a Non-closed packed structure type. . . . CsCl crystallize in a primitive cubic lattice which means the cubic unit cell has nodes only at its corners. The structure of CsCl can be seen as two interpenetrating cubes, one of Cs+ and one of Cl-. The ions are not touching one another. Touching would cause repulsion between the anion and cation. $\endgroup$ – Leponzo Dec 8 '14 at 20:01
  • $\begingroup$ But how is there "repulsion between the anion and cation"? Only like charges repel. $\endgroup$ – Leponzo Dec 8 '14 at 20:07
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    $\begingroup$ I edited to clarify the body-centered-simple-cubic issue. I'm not sure what they mean about the repulsion. $\endgroup$ – Gimelist Dec 8 '14 at 20:47
  • $\begingroup$ "Each of the different ions, Cs⁺ and Cl⁻ by themselves are simple cubic . . ." According to Wikipedia, the crystal structure of chlorine is orthorhombic, while that of caesium is bcc. So, how do they combine to form a simple cubic structure for CsCl? $\endgroup$ – Leponzo Dec 9 '14 at 7:38
  • $\begingroup$ You are confusing the structures of the mono atomic substances with the structures they assume in a compound. These things are not the same. $\endgroup$ – Gimelist Dec 9 '14 at 8:00

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