Domain patterns in (111) oriented tetragonal ferroelectric films

The possible domain patterns are developed for (111) oriented epitaxial tet ragonal ferroelectric (FT) films. The domain patterns in the film form as t he result of phase transition from the paraelectric to ferroelectric state to minimize the elastic energy of the system at the expense of creating of domain boundaries and developing non-uniform elastic fields near the film/s ubstrate interface. Six possible domain variants may form, half of which ar e related by the inversion of the polarization vector. The possible domain walls arising between pairs of variants can be derived from the conditions of the mechanical and charge compatibility. These walls are {101} boundarie s (pseudocubic indexing) and can either be inclined or normal to film/subst rate interface. The domain patterns with inclined boundaries have a flat fr ee film surface and possess non-zero net polarization in the direction norm al to the film surface, i.e., they correspond to the poled film state. The domain patterns with normal boundaries lead to 'puckering' of the film surf ace, simultaneously they are related to the unpoled state of ferroelectric films. The coherency defect technique is developed for domain pattern energetics f or (111) oriented F-T films. The coherency defects include (i) a cross-grid of edge dislocations with unbalanced densities (which lead to in-plane bia xial strain field), (ii) Somigliana screw dislocations (which produce alter nating sense of shear in neighboring domains), and (iii) wedge disclination s (which are related to out-of-plane rotations in neighboring domains). Ana lytical calculations of the pattern energy are performed for single embedde d domain and multidomain patterns. These calculations are based on the use of screened configurations for representative coherency elements: disclinat ion and Somigliana screw dislocation dipoles and quadrupoles. It is predict ed that there is no critical thickness for domain pattern formation in (111 ) oriented epitaxial tetragonal ferroelectric films. Tiling of different do main patterns in complex mesoscopic structures is also discussed and suppor ted by experimental observations.