Electrostatic boundary conditions

Periodic structures containing alternating layers of different ferroelectric and non-ferroelectric materials - superlattices (SLs) - have received increased attention. High-quality ferroelectric SLs with nearly atomically sharp interfaces in various perovskite systems have been synthesized and investigated [14, 24—27, 49-56], and also studied theoretically [44, 57-64]. Properties of such structures are not just a simple combination of the properties known for constituent bulk materials, as they are affected by both mechanical (lattice-mismatch-induced strain) and electrostatic boundary conditions at multiple interfaces located within close proximity to each other. Strain engineering is one of the most appealing ways to... 

For the electrostatic boundary condition, in this work we use the Basic Stem (BS) model developed by Behrens and Grier [9] in which the silica surfaces acquire charges in contact with water by the dissociation of silanol groups, SiOH SiO + H, so that the zeta potential (0 on the interface can be expressed as a function of the surface charge density (cr) ... 

To finalize the statement of the problem, we should complete the above equation by suitable boundary conditions. Such boundary conditions correspond to the electrostatic boundary conditions on the PE-FE interface... 

We have made use of the electrostatic boundary condition (14) in order to replace an electrostatic barrier term, e(t/ o — i)/T, with the approximate term 4nl/a )Bjerrum length (about 7 A for water at room temperature). 

Electrostatic boundary conditions applied at the cavity surface (which is thus a real cavity in this sense rather than an arbitrary mathematical one as used in some Lorentz field arguments) then gave the cavity field jS. for field in the surrounding dielectric as = 3 E/ 1), the reaction... 

For high surface potentials and thinner films, we have to specify the electrostatic boundary condition. For constant surface potential, we apply Eq. (4.60). For constant surface charge, Eq. (4.61) is suitable. 

---