Semigrand canonical Monte Carlo simulation with the Gibbs-Duhem integration technique: Formulation for alloy phase diagrams and attempt on In_xGa_1-xN/GaN

We give formulation for the Gibbs-Duhem integration (GDI) method in the semigrand canonical (SGC) ensemble in which the total number of particles N is fixed with the chemical potential differences between species Δμ_i (≡μ_i - μ₁; i = 2, 3, ...) specified. For a binary system in the isobaric SGC ensemble, the equation to be integrated in the T-Δμ plane is d(Δμ^eq)/dT = -Δh/TΔx, where Δμ^eq gives Δμ at equilibrium between phases I and II at temperature T, Δh represents enthalpy difference h^II - h^I, and Δx represents the composition differences x^II - x^I. Attempting application of SGC Monte Carlo simulation with the GDI technique to a pseudobinary semiconductor alloy, In_xGa_{1 - x}N, is presented, the preliminary result of which reflects the asymmetric nature of an excess energy curve calculated on the basis of an empirical interatomic potential used in the present Monte Carlo simulation.