  Defects and defect models of solids are reviewed. A numerical method able to
treat non-periodical solids possessing several simultaneous defect types is
given for simulating scattering in nanosize clusters. The approach takes
particle size, shape, and defects into account and isolates element specific
signals. Examples illustrating how laboratory scale facilities can be used to
extract crucial information about defects are given. As a case study a
statistical approximation model for lead-zirconate-titanate (PZT) is
introduced. PZT is a material possessing several defect types, including
substitutional, displacement and surface defects. Spatial composition variation
is taken into account by introducing a model in which the edge lengths of each
cell depend on the distribution of Zr and Ti ions in the cluster. Spatially
varying edge lengths and angles are referred to as microstrain. The Pb, Zr and
Ti cation positions were adjusted by bond-valence sum (BVS) model to fullfil
nominal valence requirement. The model is applied to compute the scattering
from ellipsoid shaped PZT clusters and to simulate the structural changes as a
function of average composition. Two-phase co-existence range, the so called
morphotropic phase boundary (MPB) composition is given correctly. To make a
comparison with commonly used x-ray and neutron diffraction data selected Bragg
reflection intensities and line shapes were simulated. Examples of the effect
of size and shape of the scattering clusters on diffraction patterns are given
and the particle dimensions, computed through Scherrer equation, are compared
with the exact cluster dimensions. Scattering from two types of 180 degree
domains in spherical particles, one type assigned to Ti-rich PZT and the second
to the MPB and Zr rich PZT, is computed. We show how the method can be used for
modelling polarization reversal.
