Nearest Neighbors in solid state, but with basis

[Adoniram]

Homework Statement

What is the area of the primitive cell for the lattice shown below? The nearest neighbor separation is "a."

Homework Equations

Here's the lattice we were given on our handout, and I have added the lines to indicate the square lattice (in red), the basis (in purple), and lattice points (circled in blue). Another potential basis is in green.

The Attempt at a Solution

Is the "nearest neighbor" any atom in the crystal, or is it only referring to lattice point-related neighbors?

If any atom (not necessarily lattice points) counts as a nearest neighbor, then the primitive cell has area 8a².

If it's only between lattice points, then the area would be a².

Any text I refer to (I've looked at 4) only talk about nearest neighbors in terms of lattices without a basis. (For example, the SC lattice has 6 nearest neighbors, etc). But they never seem to indicate what the case might be when you have a basis...

 

[mfb]

Is the "nearest neighbor" any atom in the crystal, or is it only referring to lattice point-related neighbors?

Lattice-point-related neighbors only. For the overall crystal structure, the inner details of a cell do not matter.