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Theoretical Study of Atomic Relaxation in 90° Domain Walls of Ferroelectric Perovskite Films

In this work we study the extent of atomic relaxation in the 90° domains of a ferroelectric film assumed to be in the tetragonal phase, epitaxially grown on a cubic substrate. The problem is solved within the framework of a Frenkel-Kontorova-type model, that is, a discrete chain of atoms harmonically coupled and subjected to the periodical action of an on-site substrate potential. The equilibrium atomic displacements as a function of the model parameters, including film and substrate lattice constants, have been analytically calculated by solving the Euler-Lagrange equations and minimizing total energy. We have applied the model for calculating atomic displacements in PbTiO3 and BaTiO3 thin films constrained to typical substrates. Predictions are made concerning the optimal substrate period ensuring the coherent matching between atoms in the ferroelectric layer and substrate atoms.