Tracking morphotropic phase boundary through total scattering technique

Morphotropic phase boundary (MPB) is an important theme in the research of ferroelectric materials since materials often exhibit enhanced physical properties at MPB. Although an established understanding of creating MPB behaviour relies on invoking instability of average crystal structure or a low-symmetry monoclinic phase in the system driven by composition [1], the actual mechanism is far more complex and heavily dependent on the local ordering of cations as evidences found in recent diffuse scattering studies [2] on both lead-based and lead-free systems. We have studied an important and popular ferroelectric system xBiScO3-(1-x) PbTiO3 (BS-PT), which was first reported in 2001 with MPB characteristics [3], through total scattering technique to understand its structural evolution as a function composition in the vicinity of the MPB. Total scattering technique which is essentially the analysis of the pair distribution function (PDF) of a system, provides crucial structural information at the microscopic level which are not easily available from conventional structural analysis like Rietveld refinement. Both x-ray and neutron powder diffraction experiments were carried out on six different compositions of BS-PT in the range 0.30 < x < 0.40 and neutron PDFs were analysed through RMC simulations to extract the behaviour of individual cations. It was observed that locally there was no abrupt change in any of the cation-cation correlations to assign the MPB unambiguously, however a trend was noticed in the sigmas of individual cationic displacements where the reported MPB composition show a minimum.

Magic Sized Clusters in ZnO Nanoparticle Formation - an in-situ PDF study

Semiconductor nanoparticles (NP) such as zinc oxide (ZnO) are commonly produced in sol-gel processes. The final NP powders are well characterized with respect to their crystallinity, which fundamentally governs their physical and chemical properties. Nevertheless, the nucleation process and the evolution of crystallinity of the nucleating NPs is not yet understood [1]. With the advent of the Rapid Acquisition Pair Distribution Function (PDF) method, time-resolved PDF studies have become possible, and the distinction between molecular clusters and nanoparticles in 1 M aqueous solutions of metal oxide NPs [2] has been demonstrated. However, nucleation in dilute sol-gel processes in more complex organic solutions remains untackled [1]. Our experiments are, to our knowledge, the first in-situ PDF studies in organic solvents. We used a 30 mM ethanolic solution of zinc acetate dihydrate. Several hours after the addition of the organic base tetramethylammonium hydroxide, monodisperse ZnO powders can be obtained. However, directly upon the base addition primary tetrahedral precursors Zn4OAc6 form. Approx. 1 hour later, they evolve into stable magic sized clusters (MSC) of 1.3 nm diameter and wurtzitic structure. Though known to exist for II-VI semiconductor NP such as CdSe [3], MSCs have not been demonstrated for ZnO before. With ongoing reaction time, the final spherical NPs of 2.5 nm diameter evolve at the expense of the MSCs and exist for several hours without undergoing further growth. SAXS studies confirm the PDF data. Fig. 1 shows the experimental PDFs and their fits. The fits are multiphase models of the precursor, the MSC and NP. The solvent shows intermolecular ordering effects whose contribution to the PDF was modelled by a low-frequency wave function. The MSC and NP sketches show a view along the crystallographic c-axis. Based upon these state-of-the art in-situ PDF studies, we suggest a nucleation model based on the existence of magic-sized clusters.

Preferred Orientation, PDF and Debye Equation

The effect of preferred orientation is currently neglected in the Debye Equation and PDF calculations. This is to a large extend justified, especially for the PDF, as the scattering by large sample volumes is detected by an area detector. The integration of powder rings reduces the effects of preferred orientation. As more laboratory PDF measurements become available that use linear position sensitive detectors or single counter detectors, preferred orientation needs to be reconsidered. A Rietveld calculation treats preferred orientation by multiplying the Bragg intensity by a factor that depends on the angle between the reciprocal space vector and the preferred orientation axis. The powder intensity I(Q) is thus multiplied by a complex function that depends at each Q on the degree of preferred orientation, the lattice parameters, reflection multiplicity etc. The effect on the PDF is therefore the convolution by the Fourier transform of this complex function. The Debye equation is derived from a spherical average of the scattering intensity of a finite object. Thus completely random orientation of the powder grains is implicitly assumed. Both, the Debye algorithm and the PDF algorithm calculate the powder pattern, respectively the PDF from a histogram of interatomic distances, which correspond to a spherical average of all interatomic distance vectors. This histogram does not allow for a Rietveld preferred orientation correction. The effects of preferred orientation on the PDF will be presented on the basis of simulated diffraction pattern. An algorithm to describe the changes in the PDF and the inverse sine Fourier transform as a convenient tool to calculate the powder diffraction pattern will be introduced. This is a good alternative to the Debye equation and allows to take preferred orientation into account both for the PDF and the calculated powder.