Step 1: Understand F-centers.
F-centers are crystal defects produced due to the presence of electrons trapped in anion vacancies.
These trapped electrons impart color to the crystal.
Step 2: Formation of F-centers in \(NaCl\).
When \(NaCl\) is heated in sodium vapour:
\[
Na \longrightarrow Na^+ + e^-
\]
The sodium atoms release electrons.
Chloride ions leave their lattice sites creating:
\[
Cl^-
\]
vacancies.
The released electrons occupy these vacant anion sites.
Step 3: Identify the type of defect.
Because extra sodium atoms are effectively introduced into the crystal, there is an excess of metal ions compared to anions.
Thus, the defect produced is:
Metal excess defect
Step 4: Final conclusion.
Hence, F-centers are formed due to
\[
\boxed{\text{Metal excess defect}}
\]