Origin of antiphase domain boundaries and their effect on the dielectric constant of $Ba0.5Sr0.5TiO3$ films grown on MgO substrates

Epitaxial $Ba1−xSrxTiO3$ (BST) with $x=0.5$ films were grown on MgO substrates using pulsed-laser deposition. We have observed a high density of antiphase domain boundaries (ADB) in these BST films. We attribute the formation of the ADBs to the different crystal symmetry of the film and the substrate. Adjacent domains have an in plane phase shift of $12[110],$ or $12[11̄0]$ thus creating a phase shift of the in plane lattice planes of $12[010]$ or $12[100]$ across the boundary. We have used first-principles calculations to obtain the effect of the ADBs on the dielectric constant of $SrTiO3$ and found that they lower the effective in plane dielectric constant in the direction normal to the ADB. Upon annealing, the density of ADBs decreases and the dielectric properties improve.