  The vacancy concentration at finite temperatures is studied for a series of
(CoCrFeMn)$_{1-x_\mathrm{Ni}}$Ni$_{x_\mathrm{Ni}}$ alloys by grand-canonical
Monte-Carlo (MC) simulations. The vacancy formation energies are calculated
from a classical interatomic potential and exhibit a distribution due to the
different chemical environments of the vacated sites. In dilute alloys, this
distribution features multiple discrete peaks, while concentrated alloys
exhibit an unimodal distribution as there are many different chemical
environments of similar vacancy formation energy. MC simulations using a
numerically efficient bond-counting model confirm that the vacancy
concentration even in concentrated alloys may be calculated by the established
Maxwell-Boltzmann equation weighted by the given distribution of formation
energies. We calculate the variation of vacancy concentration as function of Ni
content in the (CoCrFeMn)$_{x_\mathrm{Ni}}$Ni$_{1-x_\mathrm{Ni}}$ and prove the
excellent agreement of the thermodynamic model and the results from the
grand-canonical Monte-Carlo simulations.
