  We consider a tight binding model for localised crystalline defects with
electrons in the canonical ensemble (finite electronic temperature) and nuclei
positions relaxed according to the Born--Oppenheimer approximation. We prove
that the limit model as the computational domain size grows to infinity is
formulated in the grand-canonical ensemble for the electrons. The Fermi-level
for the limit model is fixed at a homogeneous crystal level, independent of the
defect or electron number in the sequence of finite-domain approximations. We
quantify the rates of convergence for the nuclei configuration and for the
Fermi-level.
