Phase equilibrium of a CuInSe2–CuInS2 pseudobinary system studied by combined first-principles calculations and cluster expansion Monte Carlo simulations

We report the phase diagram of a CuInSe2–CuInS2 pseudobinary system calculated by a combination of first-principles calculations based on density functional theory, cluster expansion, and Monte Carlo simulations. All formation energies of CuIn(Se1−xSx)2 (CISS) alloys are positive, indicating that CISS alloy is a miscibility gap system and has a tendency to phase separation. The phase diagram computed with conventional cluster expansion shows a miscibility gap with consolute temperature TC=170 K. The contribution of lattice vibrations lowers TC to 130 K. The miscibility gaps for the CuInSe2–CuInS2 system are predicted to be asymmetric. The effect of lattice vibrations on the miscibility gap is found to be large, and the size mismatch mechanism can be used to explain the large vibrational effect in the CuInSe2–CuInS2 system.