Domain statistics and ferroelectric transients

The statistical problem involved in calculating the ferroelectric polarization and switching current resulting from an arbitrary number and distribution of domains is examined. A general scheme for calculating the polarization based upon the successive evaluation of overlap integrals is proposed and illustrated in detail for a random distribution. Calculation of the polarization and current for different numbers of randomly distributed domains are reported and compared with the prediction of Avrami's relation as well as with relevant experimental results. A brief discussion of Avrami's original statistical derivation is contained in an appendix and a more elegant derivation presented.