> One of the materials is most likely impossible to synthesize

Is this a "actual impossible because it's inherently contradictory", or "we just don't know how to do it yet but give us a year"?

We don't know a way to precisely place atoms in a checkerboard pattern like that, without getting it so hot that the arrangement is destroyed.

It maybe could be possible but beyond the reach of current material science.

"Likely Impossible" as in, we would need a revolutionary discovery in how thermodynamics apply to crystal formation.