Synthesis and characterization of ceria doped zinc ferrite nanopowdered crystallites

In this paper, we have reported the synthesis of fine crystallites of ceria doped zinc ferrite by co-precipitation and an open air heat treatment method. X-ray diffraction (XRD) gave the data for structural analysis. The XRD data were refined by Rietveld refinement using FullProf suite software. The evolution of the crystalline phases has been analyzed. The effect of precursor concentration is reflected in the resulting diffractogram. Structural characterization revealed the cubic structure of zinc ferrite with a space group of FD-3m(227) and the cubic structure of CeO with a space group of fm-3m(225). Structural parameters such as the lattice constant of the direct lattice, the lattice constant of the reciprocating lattice, lattice strain, covalent bond angle, dislocation density, crystallite size and Wyckoff positions were calculated.

History of the reciprocal lattice

History of the development of the reciprocal lattice is reviewed. The reciprocal lattice as an essential tool for the study of diffraction experiments by ordered structures and characterization of their structural properties is widely taught in any text of solid state or chemistry, but usually without discussion of its history. This article aims to give a coherent historical perspective on the reciprocal lattice. First, a basic introduction to the reciprocal lattice concept, its mathematical foundation and physical origin, and its relationship with the direct lattice is provided. Then a detailed chronicle of ideas leading to the concept of the reciprocal lattice is presented, including a review of the contributions of Gibbs, Ewald, and others. The polar lattice concept, the great ancestor of the reciprocal lattice, is presented.

Role of scaffold network in controlling strain and functionalities of nanocomposite films

Strain is a novel approach to manipulating functionalities in correlated complex oxides. However, significant epitaxial strain can only be achieved in ultrathin layers. We show that, under direct lattice matching framework, large and uniform vertical strain up to 2% can be achieved to significantly modify the magnetic anisotropy, magnetism, and magnetotransport properties in heteroepitaxial nanoscaffold films, over a few hundred nanometers in thickness. Comprehensive designing principles of large vertical strain have been proposed. Phase-field simulations not only reveal the strain distribution but also suggest that the ultimate strain is related to the vertical interfacial area and interfacial dislocation density. By changing the nanoscaffold density and dimension, the strain and the magnetic properties can be tuned. The established correlation among the vertical interface—strain—properties in nanoscaffold films can consequently be used to tune other functionalities in a broad range of complex oxide films far beyond critical thickness.

Mechanical cloak design by direct lattice transformation

Spatial coordinate transformations have helped simplifying mathematical issues and solving complex boundary-value problems in physics for decades already. More recently, material-parameter transformations have also become an intuitive and powerful engineering tool for designing inhomogeneous and anisotropic material distributions that perform wanted functions, e.g., invisibility cloaking. A necessary mathematical prerequisite for this approach to work is that the underlying equations are form invariant with respect to general coordinate transformations. Unfortunately, this condition is not fulfilled in elastic–solid mechanics for materials that can be described by ordinary elasticity tensors. Here, we introduce a different and simpler approach. We directly transform the lattice points of a 2D discrete lattice composed of a single constituent material, while keeping the properties of the elements connecting the lattice points the same. After showing that the approach works in various areas, we focus on elastic–solid mechanics. As a demanding example, we cloak a void in an effective elastic material with respect to static uniaxial compression. Corresponding numerical calculations and experiments on polymer structures made by 3D printing are presented. The cloaking quality is quantified by comparing the average relative SD of the strain vectors outside of the cloaked void with respect to the homogeneous reference lattice. Theory and experiment agree and exhibit very good cloaking performance.

Energy-filtered electron diffuse scattering of ferroelectrics PMN and PMN-xPT

PbMb1/3Nb2/3O3 (PMN) and its solid solution (1-x)PbMb1/3Nb2/3O3-(x)PbTiO3 (PMN-xPT) are relaxor ferroelectrics which have attracted attention in the last few decades because of their very interesting dielectric and piezoelectric properties and have since be two of the most extensively studied. All the previous studies emphasized the role of the local structural fluctuations leading to local changes in symmetries [1] due to displacements of ions in the unit-cell. We studied PMN and PMN-xPT by electron diffuse scattering using an in-column energy filter and Imaging-Plates as detector. We found evidences for streaks of intensity along the [110]* direction as previously found in PbZn1/3Nb2/3O3 (PZN) with neutron diffraction [2]. Moreover, weak diffuse scattering sheets can be observed along (111)* reciprocal planes showing the existence of correlations along the [111] directions of the direct lattice. Figure 1 shows a diffraction pattern taken along [02-1] zone axis presenting both diffuse features. This can be related to the displacement of Pb ions along the diagonals of the cube found by simulation [3] but greatly complexify the analysis of the shape of the diffuse intensity. Compared to the neutron, electron diffraction has the advantage of two dimensional recording of diffuse scattering and eventually sensitivity to charge ordering but quantitative analysis is limited due to the complication of multiple scattering and the lack of sufficient energy resolution for the study of inelastic phonon scattering.