The Sodium Chloride Structure
from page 80 of Ashcroft / Mermin textbook
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A lattices with a basis is also necessary, however, in describing crystal structures in which the atoms and ions are located at only at the points of Bravis lattice, but in which the crystal structure nevertheless lacks the full translational symmetry of Bravis lattice because more than one kind of atoms or ions is present.
For example,
sodium chloride (NaCl) consists of equal numbers of sodium and chlorine ions placed at alternate points of a simple cubic lattice, in such a way that each ion has six of the other kind of ions as its nearest neighbours.
最近傍の原子はもう片方の原子になっている
This structure can be described as a face-centered cubic lattice with a basis consisting of a sodium ion at 0 and a chlorine ion at the center of the conventional cubic cell, $ \frac{a}{2}(\hat{x}+\hat{y}+\hat{z})
https://gyazo.com/e1fd3d23d6e72ebe99df98aad9d042da
each color of point forms FCC