Volume 227, Issue 5 - Analysis of Complex Materials

A novel approach for studying local spin and atomic dynamics in liquids, glasses and crystalline solids with disorder is discussed. In this approach the dynamic structure factor obtained by inelastic neutron or X-ray scattering is Fourier-transformed to real space into the dynamic atomic pair-density function (DPDF). We discuss the nature of the DPDF and show examples of the results obtained by this method. It is demonstrated that the DPDF primarily represents local dynamics, whereas traveling waves contribute only to broadening the peaks. Thus this method complements the conventional analysis of the dynamic structure factor in terms of dispersion relationship of collective dynamics.

Theory and principles of the three-dimensional pair distribution function analysis of disordered single crystals are introduced. The mathematical framework is presented and the appearance of pair distribution function patterns is discussed on the examples of some basic disorder models. It is further demonstrated how pair distribution function maps are affected by typical experimental problems. Approaches for a better understanding of such effects and strategies for a proper handing of artifacts in diffuse scattering experiments are proposed.

Quantitatively reliable atomic pair distribution functions (PDFs) have been obtained from nanomaterials in a straightforward way from a standard laboratory transmission electron microscope (TEM). The approach looks very promising for making electron derived PDFs (ePDFs) a routine step in the characterization of nanomaterials because of the ubiquity of such TEMs in chemistry and materials laboratories. No special attachments such as energy filters were required on the microscope. The methodology for obtaining the ePDFs is described as well as some opportunities and limitations of the method.

At present synchrotron and neutron sources are the preferred choice for PDF analysis, but there is clearly an increasing need for a PDF solution based on inhouse diffraction equipment. Such a solution, though limited, will benefit areas where quick feedback about the materials properties is important and will allow the routine application of PDF analysis for materials characterization in university laboratories as well as industrial R&D departments. One interesting application is the use of the PDF technique for comparing amorphous pharmaceutical substances [1]. It is worth mentioning that the use of in-house diffraction equipment for PDF analysis has been reported on numerous occasions (see for example [2–4]). This article describes the latest developments of laboratory X-ray equipment for PDF analysis and discusses some results obtained with such equipment. Three examples — C 60 , amorphous MoS3 and crystalline CeO 2 — were chosen to demonstrate different aspects of PDF data collection optimization.

Resonant X-ray diffraction and differential atomic pair distribution functions method is illustrated with results from a study of 4.5(3) nm Pt, Au and Pt 0.51 Au 0.49 particles. By doing experiments at two energies close to the K absorption edge of Pt the atomic correlations relative to Pt and Au atoms in the alloy particles are differentiated. The experimental data show that Pt and Au atoms in all three samples arrange in a face centered cubic type structure while keeping their bond lengths of 2.76 Å and 2.86 Å, respectively, virtually unchanged. This leads to increased local structural distortions in the alloyed Pt 0.51 Au 0.49 particles that may affect their catalitic properties substantially.

Fast, time-resolved pair distribution function (PDF) methods were applied in situ , to probe the mechanism and kinetics of supported gold nanoparticle formation. The PDF provides quantitative details on how the population and structure of different species evolve throughout the reaction. By fitting reaction models to the changes in species concentration, the reaction mechanism can be identified, with measurements at multiple temperatures allowing an estimation of the apparent activation energy. Here, for the formation of Au nanoparticles supported on γ -Al 2 O 3 , we find that the reaction follows a zeroth-order reaction mechanism with an activation energy of ∼73 kJ mol –1 .

Rare Earth doped ceria materials (Ce 1– x RE x O 2– x /2 ) are widely studied for their application in solid oxide fuel cell devices. In this work, RE (Yb, Y, Nd, La)-doped ceria samples at constant ( x = 0.25) doping rate were subjected to a combined synchrotron radiation and neutron powder diffraction study. The dopants were chosen in order to cover a wide range of dopant-ionic radii. The effect of doping on the average structure is investigated using conventional Rietveld analysis, while the Pair Distribution Function technique is used to explore the spatial extent of disorder as well as the local structure. Two models for mapping the local structure, in terms of oxygen relaxation and nano-phase separation, are presented.

A combination of neutron total scattering measäurement and reverse Monte Carlo (RMC) refinement is applied to the study of apical Cu—O bond distortions in the high- T c superconductor YBa 2 Cu 3 O 6.93 . We show that the average structure is not consistent with a split-site model for the corresponding Cu and O positions, but that the local structure nevertheless reveals the existence of two separate apical Cu—O bond lengths. Using G ( r ) data obtained from a variety of Q max values we show that this result is independent of the data treatment methodology. We also find that the resulting ‘short’ and ‘long’ Cu—O bond lengths agree well with the results of previous äEXAFS studies. The existence of bimodal apical Cu—O bond distributions in the context of a single-site average structure model is interpreted in terms of correlated displacements of the Cu and O atoms. We investigate the possibility of clustering of short apical Cu—O bonds within our RMC configurations.

A combination of X-ray and neutron PDF measurements with powder diffraction and EXAFS data was used to determine the structures of a V—Mo—Nb-oxide catalyst and its poorly crystallized precursors that exhibit the strongest catalytic activities. The crystalline material belongs to space group P -4 2 1 m, a = 22.8, c = 4.002, and is build up of pentagonal MeO 7 bipyramids surrounded by edge sharing Me-octahedrons (Me = Mo, V, Nb). In the average structure all MeO 7 units are at the same z -level, while the local structure analysis shows systematic shifts along [001]. Samples synthesized at 300 °C and 400 °C exhibit a nanostructure, whose local structure predates the final crystalline structure. Initial nanoparticles are spherical and grow predominantly along the c -axis. The successful analysis required a reverse analysis that took the crystalline material as starting model for the samples synthesized at lower temperatures.

Mg 2 Co- and MgCo 2 -like local atomic arrangements in mechanically alloyed Mg x Co 100– x were investigated using atomic pair distribution function (PDF) analysis derived from synchrotron X-ray total scattering data. We show that changes in Mg x Co 100– x PDFs with x are well explained by the structural features of Mg 2 Co and MgCo 2 . This strongly supports our two-phase model picture where Mg 2 Co-like phase continuously increases while MgCo 2 decreases with increasing Mg content in Mg x Co 100– x .

Geopolymers are a class of alternative cementitious material, synthesised via alkaline activation of aluminosilicate precursors. The atomistic nature of geopolymer precursors and binders remain largely elusive due to their inherent amorphicity and heterogeneity; nevertheless, pair distribution function analysis is one experimental technique capable of elucidating accurate structural representations of these amorphous materials, when combined with advanced molecular simulation methods. Here, it is shown that, when analysed in isolation, some valuable information can be gained from pair distribution functions of geopolymer precursors and binders. However, when used in conjunction with molecular simulations such as density functional theory and coarse-grained Monte Carlo analysis, there is the potential to generate accurate atomistic representations revealing new information regarding local structural environments. A novel methodology combining real-space refinements and density functional simulations in an iterative manner (DFT-PDF) has been used to generate an accurate structural representation of the geopolymer precursor metakaolin. The structural representation obtained from this technique reveals the existence of III-coordinated aluminium, which exemplifies the power of the DFT-PDF iterative methodology in probing uncommon chemical environments in materials. The potential for density functional theory-based coarse-grained Monte Carlo analysis to elucidate the structure of geopolymer binders and other heterogeneous materials is also discussed.

Using a combination of Rietveld and reverse Monte Carlo (RMC) refinement of neutron total scattering data, we find that the 10 K structure of zinc(II) isonicotinate shows strong evidence of static disorder. This disorder takes the form of transverse displacements of the isonicotinate ligand and results in elongated atomic displacement parameters and dampening of the experimental G ( r ). We analyse the RMC configurations using an approach derived from geometric algebra. Complications regarding the inclusion of hydrogenous guest molecules within the pore structure are discussed. This study highlights the way in which structural flexibility can give rise to multiple low-energy ground states in metal-organic framework materials.