Field sums for extended dipoles in ferroelectric polymers

A previously described method for calculating the Lorentz factor L for orthorhombic polar crystals is modified to allow discussion of dipoles of finite size. In this approach, the field due to a lattice of point charges ±q separated by a distance d is calculated. The Lorentz factor, which relates the field at a lattice site to the macroscopic polarization, is found as a function of the dipole length d, and is seen to vary appreciably with changes in the separation between the charges. Assumption of a value of 1/3 for L can thus lead to significant errors in determining the self-consistent polarization of crystals consisting of polarizable molecules.