PDF analysis

In addition, many of the ferroelectric solids are mixed ions systems, or alloys, for which local disorder influences the properties. The effect of disorder is most pronounced in the relaxor ferroelectrics, which show glassy ferroelectric behavior with diffuse phase transition [1]. In this chapter we focus on the effect of local disorder on the ferroelectric solids including the relaxor ferroelectrics. As the means of studying the local structure and dynamics we rely mainly on neutron scattering methods coupled with the real-space pair-density function (PDF) analysis. 

It is also possible to prepare crystalline electrides in which a trapped electron acts in effect as the anion. The bnUc of the excess electron density in electrides resides in the X-ray empty cavities and in the intercoimecting chaimels. Stmctures of electri-dides [Li(2,l,l-crypt)]+ e [K(2,2,2-crypt)]+ e , [Rb(2,2,2-crypt)]+ e, [Cs(18-crown-6)2]+ e, [Cs(15-crown-5)2]" e and mixed-sandwich electride [Cs(18-crown-6)(15-crown-5)+e ]6 18-crown-6 are known. Silica-zeolites with pore diameters of vA have been used to prepare silica-based electrides. The potassium species contains weakly bound electron pairs which appear to be delocalized, whereas the cesium species have optical and magnetic properties indicative of electron locahzation in cavities with little interaction between the electrons or between them and the cation. The structural model of the stable cesium electride synthesized by intercalating cesium in zeohte ITQ-4 has been coirfirmed by the atomic pair distribution function (PDF) analysis. The synthetic methods, structures, spectroscopic properties, and magnetic behavior of some electrides have been reviewed. Theoretical study on structural and electronic properties of inorganic electrides has also been addressed recently. ... 

The driving force behind the rapid development of powder diffraction methods over the past 10 years is the increasing need for structural characterization of materials that are only available as powders. Examples are zeolite catalysts, magnets, metal hydrides, ceramics, battery and fuel cell electrodes, piezo- and ferroelectrics, and more recently pharmaceuticals and organic and molecular materials as well as biominerals. The emergence of nanoscience as an interdisciplinary research area will further increase the need for powder diffraction, pair-distribution function (PDF) analysis of powder diffraction pattern allows the refinement of structural models regardless of the crystalline quality of the sample and is therefore a very powerful structural characterization tool for nanomaterials and disordered complex materials. 

Local Structure from Total Scattering and Atomic Pair Distribution Function (PDF) Analysis... 

Although clearly less routine that x-ray diffraction, PDF analysis of conventional polymers has been used, perhaps most notably, in the study of polyolefins [403,404] and polyethylene oxides [405-407]. This PDF approach has also been utilized in structural analysis of PANis [408-413], functionalized polysilanes [356,414], and PPys [290]. An early PDF PANi EB study by Laridjani et al. [410] resolved differences in the local structure of type I and type II samples. Modeling is often used in conjunction... 

In polysilanes, the primary motivation has been to identify the chain conformational sequences and, to a lesser extent, orientation of the side chains. PDF analysis [356] of three atactic poly(methyl- -alklysilanes) in bulk is indicative of a near-planar transoid/ deviant sequencing of the skeletal backbone with relatively low concentrations of either ortho- or gauche-type conformations. Figure 17.24 shows data for atactic poly(methyl-n-propylsilane) and a single-chain model fit. The difference at lower q, <5 A , is due to scattering from interchain correlations. 

Among the techniques that probe the average or long-range structure, powder X-ray diffraction (PXRD) and neutron diffraction (ND) will be briefly discussed. Techniques that provide local, atomistic information that will be mentioned are nuclear magnetic resonance (NMR) spectroscopy. X-ray photoelectron spectroscopy, X-ray absorption spectroscopy, and pair distribution function (PDF) analysis. A brief introduction to the underlying theory of each technique will be provided along with relevant examples to illustrate the type of information that can be... 

Figure 17.2. A. Proposed structure of the Pt2[Ge4Sio] chalcogenide aerogel based on pair distribution function (PDF) analysis of X-ray data. Relevant inter-atomic distances are indicated. B. Different types of Zintl clusters (teal balls = Ge, Sn red balls = S, Se) employed in chalcogel formation with Pt ". Reproduced with permission from Science, 317 490-493 (2007). Copyright 2007, American Association for the Advancement of Science.

Keywords Local atomic bonding, PDF analysis, CMR manganites, Polarons, Ferroelectrics, Superconducting cuprates... 

The arguments above highlight severe compromises made in trying to describe local disorder by simply extending the crystallographic methods. It is much preferred to determine the local structure directly by local probes. In the following we describe the method of pulsed neutron PDF analysis and some of the results obtained by this method that help to understand the properties of electronic ceramics. 

The process of measurement for the PDF analysis is very similar to that for the usual powder diffraction analysis. The main differences from the conventional powder diffraction experiments in obtaining the data are the following ... 

Table 1. Atomic distance and number of neighbors in Ni and SrTi03 determined from the PDF analysis compared to the expected values [8]...

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