  Nucleation phenomena are ubiquitous in nature and the presence of impurities
in every real and experimental system is unavoidable. Yet numerical studies of
nucleation are nearly always conducted for entirely pure systems. We have
studied the behaviour of the droplet free energy in two dimensional Ising model
in the presence of randomly positioned static and dynamic impurities. We have
shown that both the free energy barrier height and critical nucleus size
monotonically decreases with increasing the impurity density for the static
case. We have compared the nucleation rates obtained from Classical Nucleation
Theory and the Forward Flux Sampling method for different densities of the
static impurities. The results show good agreement. In the case of dynamic
impurities, we observe preferential occupancy the impurities at the boundary
positions of the nucleus when the temperature is low. This further boosts
enhancement of the nucleation rate due to lowering of the effective interfacial
free energy.
