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Competitive Heterogeneous Nucleation onto a Microscopic Impurity in a Potts Model

Many metastable systems can nucleate to multiple competing stable or intermediate metastable states. In this work, a Potts model, subject to external fields, is used to study the competitive nucleation of two phases attempting to grow on a microscopic impurity. Monte Carlo simulations are used to calculate the free energy surfaces for the system under different conditions, where the relative stability of the phases is adjusted by changing the interaction parameters, and the nucleation rates obtained using multicomponent transition state theory are compared with the rates measured using the survival probability method. We find that the two methods predict similar nucleation rates when the free energy barrier used in the transition state theory is defined as the work required to form a critical embryo from the metastable phase. An analysis of the free energy surfaces also reveals that the competition between the nucleating phases leads to an effective drying of the impurity which slows down the nucleation rate compared to the single phase case.