Ab initio thermodynamics of Ba _cSr _(1-c)TiO ₃ solid solutions

Based on ab initio calculations for a number of the Ba _cSr _(1-c)TiO ₃ (BST) super-lattices, we developed a thermodynamic approach to these solid solutions. In particular, we calculate the BST phase diagram and show that at relatively low temperatures (below 400 K for c=0.5 and 300 K for c=0.1) the spinodal decomposition of the solid solution occurs. As a result, we predict for small Ba concentrations formation of BaTiO ₃ nanoregions in a predominantly SrTiO ₃ matrix and vice versa, which is confirmed by the Raman, polarization, ultrasonic, neutron diffraction, and diffusion experiments.