Cluster expansion Monte Carlo study of indium–aluminum segregation and homogenization in CuInSe2–CuAlSe2 pseudobinary alloys†
The influence of temperature and Al content on the segregation and homogenization behaviour of In–Al atoms in CuIn1−xAlxSe2 (CIAS) pseudobinary alloys is studied using a combination of cluster expansion Monte Carlo simulations and first-principles calculations. Such alloys are promising materials for a number of solar-energy-related applications. We found that the segregation of In–Al atoms in CIAS alloys with different Al contents occurs at relatively low temperatures. The cluster morphology of Al(In) atoms in CIAS alloys at 73 K appears in an ellipsoidal, rod-like or lamellar form, depending on the Al(In) content. The spatial distribution of In–Al atoms becomes homogeneous as the temperature increases. By determining the inhomogeneity degree σ of In–Al distributions in CIAS alloys at a series of temperatures, we found that the variation of σ with temperature (T) for all the considered CIAS alloys are sigmoidal in general and the sharp decrease in σ within a certain temperature range implies the occurrence of inhomogeneous-to-homogeneous phase transition. The inhomogeneity degree σ of CIAS alloys before or after the phase transition (phase segregation) increases as the content of Al(x) and In(1 − x) atoms gets closer. The σ(T) data points obtained by us can be well fitted with the Boltzmann function, which can give several physically meaningful parameters such as the phase transition temperature T0, temperature range of phase transition ΔT and so on. The fitted T0 and ΔT values for CIAS alloys with different Al content were proved to be reliable. The novel method for predicting the T0 and ΔT may be applied to many other binary or pseudobinary material systems with positive formation energy.