Finnish Research and Engineering, Helsinki, Finland
Abstract:
Defects and frequently used defect models of solids are reviewed. Signatures for identifying the disorder from x‐ray and neutron scattering data are given. To give illustrative examples how technologically important defects contribute to x‐ray and neutron scattering numerical method able to treat non‐periodical solids possessing several simultaneous defect types is given for simulating scattering in nanosize disordered clusters. The approach takes particle size, shape, and defects into account and isolates element specific signals. As a case study a statistical approximation model for lead‐zirconate titanate Pb(ZrxTi)O3, 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 is referred to as microstrain. 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 composition is given correctly. The composition at which the rhombohedral and tetragonal cells are equally abundant was . Selected x‐ray and neutron 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° 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.
)O3, 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 is referred to as microstrain. 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 composition is given correctly. The composition at which the rhombohedral and tetragonal cells are equally abundant was 
. Selected x‐ray and neutron 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° 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. 