The employment of the Debye function to model line profiles in the powder diffraction pattern from small crystallites is briefly reviewed. It is also demonstrated that for the case of very small spherical particles, it is necessary to average patterns from multiple constructions of the particle to have complete agreement with reciprocal space models. In doing so it is demonstrated that the technique of Debye function analysis is best suited for systems with only a few possible atomic arrangements.

Total Scattering Methods are nowadays widely used for the characterization of defective and nanosized materials. They commonly rely on highly accurate neutron and synchrotron diffraction data collected at dedicated beamlines. Here, we compare the results obtained on conventional laboratory equipment and synchrotron radiation when adopting the Debye Function Analysis method on a simple nanocrystalline material (a synthetic iron oxide with average particle size near to 10 nm). Such comparison, which includes the cubic lattice parameter, the sample stoichiometry and the microstructural (size-distribution) analyses, highlights the limitations, but also some strengthening points, of dealing with conventional powder diffraction data collections on nanocrystalline materials.

A NIST SRM certified to address the issue of crystallite size measurement through a line profile analysis has been under development for several years. In order to prepare the feedstock for the SRM, nano-crystalline zinc oxide was produced from thermal decomposition of zinc oxalate. The thermal processing parameters were chosen to yield particles in two size ranges, one with a distribution centered at approximately 15 nm and another centered at 60 nm. Certification data were collected on a NIST-built diffractometer equipped with a Johansson incident beam monochromator and scintillation detector. Data were analyzed using whole powder pattern modeling to determine microstructural data. The analysis shows domains to be in the form of discs of a fairly small aspect ratio. While both materials exhibit the effects of stacking faults through broadening of specific hkl reflections, their presence in the 60 nm is more difficult to discern. Images of the crystallites obtained with transmission electron microscopy are consistent with the results from the X-ray diffraction analyses.

Two polymorphs of Holmium molybdate, known as β'-phase and γ-phase, were prepared by solid state reaction with different thermal treatments. These polycrystalline samples have been studied for the first time by X-ray thermodiffractometry from room temperature up to 1300 K. We found that the initial β'-phase undergoes a transition to a β-phase and then to a γ-phase. The γ (hydrated)-phase, turns to the γ (dehydrated)-phase and then to the β-phase. Each sequence involves a reversible and an irreversible phase transition for Ho2(MoO4)3. Both polymorphs have remarkable physical properties like nonlinear optics, ferroelectricity and negative thermal expansion. We have calculated the linear expansion coefficients of both phases. We have obtained a positive coefficient for the β'-phase and a negative one for the γ-phase. Moreover, we have made a comparison of the obtained coefficients with previous results for other rare earth molybdates.

The NaYF4:Yb3+,Tb3+ (x Yb: 0.20, x Tb: 0.04) materials were prepared by the co-precipitation method. The as-prepared material was washed with and without water and thereafter annealed at 500 °C. This resulted in materials with moderate (with water) and very high (without water) up-conversion luminescence intensity. The structural details causing the differences in luminescence intensity were investigated at room temperature with X-ray powder diffraction and Rietveld analyses. All materials crystallized in the hexagonal form (P63/m, No. 176, Z: 1.5) with a composition very close to stoichimetric. The local structural details revealed microstrains in the rare earth sublattice that were relaxed for the material with very high up-conversion luminescence intensity thus decreasing energy losses and enhancing up-conversion.

Monte Carlo domain structure simulation and Debye equation calculation of XRD patterns were used to confirm the formation of domain structure and investigate its peculiarities. Correspondence of simulated XRD patterns with synchrotron powder diffraction experiments is achieved on the conditions that beside of 90o rotations of brownmillerite-like domains inside perovskite-like matrix each domain contains areas with perpendicularly oriented tetrahedral chains. Influence of such parameters as stoichiometry, average domain size, orthorhombic distortion degree on the XRD patterns is considered.

The crystal structures of KCaVO4 and RbBaVO4, synthesized at high-pressure/high-temperature and by a conventional solid-state reaction, respectively, were determined using X-ray powder diffraction data. These compounds were found to have the β-K2SO4 structure type (space group Pnma, Z = 4) with parameters a = 7.2628(5) Å, b = 5.7258(4) Å, c = 9.6854(7) Å (KCaVO4), and a = 7.8887(1) Å, b = 5.9589(1) Å, c = 10.3958(2) Å (RbBaVO4). The unit cell volume of KCaVO4, 402.77(5) Å3, is significantly lower than for the low-temperature modification reported previously, 436.2 Å3. The difference can be explained by a pressure-induced phase transition to a more dense state resulting from the rotation of tetrahedra and the exchange of oxygen atoms from the first and second coordination spheres for potassium and calcium atoms.

Polycrystalline compounds in the Zn1-xNdxCr2Se4 system were prepared by solid state reaction using selenides (ZnSe, Cr2Se3) and pure elements (Nd, Se) as starting materials. The structural properties were determined by X-ray diffraction and the chemical composition confirmed by SEM-EDX. The observed symmetry is cubic, space group Fd3m, while the lattice parameter varies from 10.4955(7)Å to 10.4976(7)Å, and is larger than for the pure matrix. The solubility limit for the current synthesis route lies below x = 0.1. The magnetic moments, effective and saturation, increase with increasing amount of Nd ions. The Neel temperature TN and ΘCW drop, respectively, to 17.4K and 81K for x = 0.1, independently indicating that neodymium is incorporated into the spinel lattice and promotes antiferromagnetic coupling between the Cr3+ ions.

The ferroic phase transition in LaEr(MoO4)3 has been analyzed for the first time. It has been confirmed that this compound undergoes a phase transition from a tetragonal system (paraelectric-paraelastic phase), with space group P-421 m [β-Gd2(MoO4)3 averaged phase] to an orthorhombic system (ferroelectric-ferroelastic phase), with space group Pba2 [β'-Gd2(MoO4)3 phase] in a reversible process. This phenomenon, together with the observed demixing at high temperature has been studied using different techniques. LaEr(MoO4)3 samples have been obtained by the conventional solid-state synthesis. The thermal dependence of the crystal structure was studied by powder X-ray and neutron diffraction, following a new refining procedure in which the symmetry modes of atomic displacements from the paraelectric-paraelastic structure were analyzed. Dielectric spectroscopy measurements have confirmed the structural results, showing a very smooth phase transition. Finally, calculations within the framework of Density Functional Theory show a behavior of the lattice parameters similar to that observed in our experiments.

Using high resolution powder neutron diffraction data, we show that there is a distinct anomaly in the structural noncentrosymmetry around the magnetic transition point TN for bulk and nanoscale BiFeO3. It appears that the structural noncentrosymmetry - which gives rise to the ferroelectric polarization - is suppressed anomalously by ~1% (of the average noncentrosymmetry at above the magnetic transition) in the bulk sample and by ~12% in the nanoscale sample as the magnetic transition is approached from higher temperature. This observation shows that the multiferroic coupling improves in the nanoscale sample which is expected to brighten the application prospects of nanoscale BiFeO3 in nanospintronics-based sensor devices.

PACS Nos. 75.70.Cn, 75.75.-c

Ab initio X-ray powder diffraction structural analyses from laboratory data have been widely employed in the characterization of coordination polymers not affording single crystals of suitable quality to undergo conventional structural determinations. This is particularly true for coordination polymers built upon strong ligand-to-metal bonds, as those formed by anionic, nitrogen-based heterocycles - pyrazolates, imidazolates, pyrimidinolates and more complex moieties derived therefrom. More than one hundred species belonging to this class have been structurally characterized in the last three decades, affording key, otherwise inaccessible stereochemical and supramolecolar features. This contribution summarizes our most recent experience in the XRPD structural characterization of pyrazolato-based coordination polymers, devoting a special consideration to the methodologies and tricks which allowed us to juxtapose the structural description of these materials to their physico-chemical and, above all, functional properties.

Neutron diffraction studies of the La0.5Ba0.5CoO2.8 at the different temperatures has been performed. This solid solution crystallizes in the cubic structure (Pm3m space group) and exhibits below TN ~ 250K G-type antifferomagnetic ordering. Applied pressure suppresses magnetic ordering. Anomalous changes of the lattice parameters under pressure have been found.

The X-ray micro-diffraction laboratory technique was applied to study the quantitative changes of austenite content in TRIP steels after deformation and to reveal the phase composition of precipitates in an inner part of a hearth of a blast furnace. The usefulness of this technique was shown by calculating the austenite content after tensile test in three different parts of a small tensile test sample and after a clinching test in two areas of a clinching joint. The calculations showed the decrease in austenite content in deformed parts in comparison to not deformed areas. The presence of various kinds of chlorides, including the iron oxide chloride hydroxide in a sample taken from a graphite refractory lining of blast furnace, was confirmed by micro-diffraction patterns.

Semifluorinated (SF) side chain polymers show phase separation between polymer backbone and SF side chains. Due to strong interaction between SF segments the side chains determine the structure behaviour strongly, often resulting in layered structures in which backbones and layers of SF side chains alternate. The interest in this work was directed to find out the dependence of these structures on concentration of SF side chains. Thin films of random copolymers consisting of methylmethacrylate (MMA) and semifluorinated side chain methacrylate (SFMA) segments and with different fluorine content in the perfluoroalkyl side chains (abbreviated as H10F10 and H2F8) were prepared by spin-coating. Phase separation and structure changes were initiated by external subsequent annealing. Corresponding bulk material served as basic information. Generation of ordered structures and variation of film parameters were observed using different X-ray scattering methods (XRR, GIWAXS, and GISAXS). The phase behaviour in bulk is governed by the SF side chain amount and their specific fluorine content which control the self-organization tendency of SF side chains. Additionally, the confinement in thin films generates an orientation of side chains normally to film surface.

Nanocrystalline anatase powders synthesised by various chemical processes as super/subcritical fluid extraction, sol-gel technique and hydrolysis of titanium alkoxides in hydrogen peroxide were studied by X-ray diffraction (XRD) whole profile modelling method (WPPM) in order to reveal correlations between structural and micro-structural parameters as well as sample treatment conditions. Anisotropy of the diffraction line broadening due to truncated bipyramidal shape of anatase crystals was discussed. The hkl-anisotropy can be very strong but also almost negligible in dependence on relative ratio of the crystallite dimensions. The latter was the case for the studied samples. The size of synthesised anatase nanoparticles was within the range 3–25 nm. The theoretical total surface area of crystallites calculated from XRD was in a good correlation with the surface area measured by the nitrogen physisorption up to the temperature 400–450 °C, when the particles started to agglomerate. At atomic scale a unit cell volume contraction with decreasing crystallite size and a significant deficiency in the Ti-site occupancy was observed. Both effects were attributed to the presence of Ti-vacancies and a linear coefficient between the relative cell volume contraction and the fraction of Ti-vacancies was estimated to (–0.017 ± 0.003).

Atomistic copper nanocrystals were investigated via Molecular Dynamics (MD) under hydrostatic pressure to probe the relationship between applied load and structure deformation. The corresponding X-ray powder diffraction patterns were generated from the atomic coordinates. The analysis followed both the traditional Williamson-Hall approach based on pseudo-Voigt fitting and an alternative, more accurate method able to derive the integral breadths without applying a fitting. The Williamson-Hall results show discrepancies not fully associated with an issue of fitting.

Calcium hydroxyl and fluoroapatite (CaHAp and CaFAp) were prepared in the presence of the 2-carboxyletylphosphonic acid (2-CEPA), by hydrothermal method. The incorporation of phosphonic acid within the apatite structure was confirmed by powder XRD, IR and MAS-NMR spectroscopies and SSA. The X-ray powder analysis showed that the cristallinity was not affected by the presence of organic moieties. IR spectroscopy showed new vibration modes related to phosphonate groups. 31P MAS-NMR spectra exhibit new signals, assigned to the presence of organic phosphorus. Specific surface area (SSA) increases with increasing of phosphonate amount, especially for CaHAp. According to these results, a mechanism is proposed for the formation of two types of ionic interaction (-C-O-Ca) and (Ca-O-Porg).

The present paper is about the estimation of lattice deformation from data collected from manufactures directly on site. The aim here is to give evidence that the concept of the Mean Equivalent Lattice (MEL), when applied to “on site X-Ray Diffraction” is the basis for a reliable qualification of the material rheology to external solicitations. Such method allows for the identification of lattice deformations without resorting to the computation of the residual stress with using the elasticity constants (i.e. tensile, shear and rigidity constants E, μ, ν); these elasticity constants descend from the classical theory of solid mechanics, where the continuum mechanics and the material isotropic model are the fundaments. Any MEL deformation is instead related to the variation of the d-spacing among lattice planes which are connected to the anisotropic atomic arrangement. So the macroscopic scale is constituted by a number of MELs and related boundaries. The recent on site X-ray diffraction technology may offer effective and easy solutions, with a significant impact on reliability of results, simplification, economy and time consuming.

A variable frequency ferroelectric polarisation measurement system has been designed and built at the UK's Diamond Light Source. The electric field induced phase transitions in Pb(Zr1−xTix)O3 (PZT) have been used to test the facility via in-situ measurements of electric polarisation and XRD. Stroboscopic and real time data collection methods on polycrystalline samples were employed as a function of frequency to determine the dynamic ferroelectric response. The system has been shown to deliver XRD patterns of good statistical quality measured over 40 points of a ferroelectric PE loop. The system is now available on station I11 as a user facility at the Diamond Light Source.