Ab initio based study on atomic ordering in {(Ba, Sr)}TiO$_3$

\ We combine density functional theory and molecular dynamics simulations to investigate the impact of Sr concentration and atomic ordering on the structural and ferroelectric properties of (Ba, Sr)TiO$_3$. On one hand, the macroscopic structural properties are rather insensitive to atomic ordering. On the other hand, the Curie temperature and polarization differ by $9$\% and $17$\% for different symmetries of the Sr distribution, respectively. Local ordering of Sr induces preferential polarization directions and influences the relative stability of the three ferroelectric phases.