Ferroelectric materials were considered. Because of high cyclic loading during device lifetimes, fatigue phenomena occur, involving material degradation and a decrease in the electromechanical coupling capability. The causes were assumed to be ionic and electronic charge carriers, which interacted with each other, with microstructural elements in the bulk and with interfaces. Accumulation of defects could primarily led to degradation, or finally to mechanical damage and dissociation reactions. In order to get a better understanding of the defect accumulation processes, the defect accumulation could be described in continuum models, e.g. phase field formulations. The aim here was to obtain the defect parameters used by comparing the results of molecular dynamics simulations with the continuous spatial fields. Transferring data from the atomic to the continuum level was a field of active research. On the atomic level, Coulomb–interaction causes a displacement field incompatible to an elastic solution. In order to circumvent this difficulty, the volume expansion or contraction of a volume around the defect was used to determine defect parameters.

Modelling of Point Defects in Anisotropic Media with an Application to Ferroelectrics. O.Goy, R.Mueller, D.Gross: Computational Materials Science, 2009, 45[3], 812-5