Combined cluster and atomic displacement expansion for solid solutions andmagnetism
Finite temperature disordered solid solutions and magnetic materials are dicult to study directly using rst principles calculations, due to the large unit cells and many independent samples required. In this work, we develop a combined cluster expansion and atomic displacement expansion, which we t to rst principles energies, forces, and stresses. We then use the expansion to calculate thermodynamic quantities at nearly first principles levels of accuracy. We demonstrate that by treating all the relevant degrees of freedom explicitly, we can achieve improved convergence properties as compared to a simple cluster expansion, and our model naturally includes both configurational and vibrational entropy. In addition, we can treat coupling between structural and chemical or magnetic degrees of freedom. As examples, we use our expansion to calculate properties of Si1-xGex, magnetic MnO, Al with vacancies, and BaxSr1-xTiO3.