Pair distribution function analysis

Toby B FI and Egami T 1992 Accuracy of pair distribution function analysis applied to crystalline and noncrystalline materials Aota Crystaiiogr.k 48 336-46... 

The importance of the pore size in Prussian blue analogues is supported by differential pair distribution function analysis of X-ray and neutron scattering data of hydrogen- and deuterium-loaded Mn3[Co(CN)6]2 [119]. This shows that no evidence for adsorption interactions with unsaturated metal sites exists and that the hydrogen molecules are disordered about the center of the pores defined by the cubic framework. In conclusion, experimental results indicate that optimum pore dimensions in Prussian blue analogues are predominantly responsible for the heat of adsorption at low loadings rather than the polarizing effect of open metal sites. 

Toby BH, Egami T (1992) Accuracy of Pair Distribution Function-Analysis Applied to Crystalline and Noncrystalline Materials. Acta Crystallogr A48 336-346 Tomilin MG (1997) Interaction of liquid crystals with a solid surface. J Opt Technol 64 452-475 Toraya H, Hibino H, Ohsumi K (1996) A New Powder Diffractometer for Synchrotron Radiation with a Multiple-Detector System. J Synchrot Radiat 3 75-83... 

Pair Distribution Function Analysis Macroscopic Orientational Order... 

Breger J, Dupre N, Chupas P, Lee P, Proffen T, Parise J, Grey C (2005) Short- and long-range order in the positive electrode material, Li(NiMn)(0.5)O-2 a joint X-ray and neutron diffraction, pair distribution function analysis and NMR study. J Am Chem Soc... 

C.E. White, J.L. Provis, A. Llobet, T. Proifen, J.S.J. van Deventer, Evolution of local structure in geopolymer gels an in situ neutron pair distribution function analysis, J. Am. Ceram. Soc. 94 (2011) 3532-3539. 

Key B, Mraerette M, Tatascon JM, Grey CP (2011) Pair distribution function analysis and solid state NMR studies of silicon electrodes fm lithium ion battmies understanding the (de) lithiation mechanisms. J Am Chem Soc 133 503—512... 

Fig. 19 Neutron pair distribution function analysis of (a) bulk BaTiOs and (b) 5 nm BaTiOs nanoparticles. Clear differences are noted in the profile of both samples. The bulk sample is well described by the tetragonal P mm model above 4 nm, while the split peak for the Ti-O distance at 2 nm is better fit to a rhombohedral Kim model (see inset). For the 5 nm sample, the sample is well described by the P mm tetragonal model. From (b) it is also possible to see the contributions made by the benzyl alcohol capping group. 2010 American Chemical Society. 

V. Petkov, S. J. L. Billinge, J. Heising, and M. G. Kanatzidis, "Application of Atomic Pair Distribution Function Analysis to Materials with Intrinsic Disorder. Three-Dimensional Structure of Exfoliated-Restacked WSj Not Just a Random Turbostratic Assembly of Layers," y. Am. Chem. Soc., 122 [47], 11571-76 (2000). 

L. Bell, P. Sarin, R. P. Haggerty, P. E. Driemeyer, P. J. Chupas, and W. M. Kriven, "X-ray Pair Distribution Function Analysis of a Metakaolin-Based, KAISi206 5.5H20 Inorganic Polymer (Geopolymer)," / Mater. Chem., 18 [48], 5974-81 (2()08). 

H. Toby, and T. Egami, "Accuracy of Pair Distribution Function-Analysis Applied to Crystalline and Noncrystalline Materials," Acta Crystallogr. A., 48,336-46 (1992). 

C.D. Martin, S.M. Antao, P.J. Chupas, P.L. Lee, S.D. Shastri, J.B. Parise, Quantitative high-pressure pair distribution function analysis of nanocrystalline gold. Appl. Phys. Lett. 86(6), 061910 (2005)... 

Although this relationship looks similar to Eq. (3.257) for irreversible transfer, the Stern-Volmer constant of the latter (ko = k,) is different from Kf, which accounts for the reversibility of ionization during the geminate stage. The difference between Kg = R (0) and its irreversible analog K from (3.372) is worthy of special investigation based on the analysis of pair distribution functions obeying Eqs. (3.359). 

Analysis of the radial pair distribution function for the electron centroid and solvent center-of-mass computed at different densities reveals some very interesting features. At high densities, the essentially localized electron is surrounded by the solvent resembling the solvation of a classical anion such as Cr or Br. At low densities, however, the electron is sufficiently extended (delocalized) such that its wavefunction tunnels through several neighboring water or ammonia molecules (Figure 16-9). 

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. 

At this point it should also be mentioned that approaches not based upon the pair distribution function have sometimes been used in computer simulations to try to extract structural information. Geometrical constructions, such as Voronoi polyhedra [13,14], while formally elegant, can be difficult to implement and provide only qualitative rather than detailed information. Analysis based upon the examination of instantaneous configurations, another... 

In this section we will examine how spatial distribution function analysis can be used to bring new insights and a better understanding of the local structure in pure liquid systems. Implications to other properties, either determined by or related to the pair distribution function, will be discussed. 

Modern theory of associative fluids is based on the combination of the activity and density expansions for the description of the equilibrium properties. The activity expansions are used to describe the clusterization effects caused by the strongly attractive part of the interparticle interactions. The density expansions are used to treat the contributions of the conventional nonassociative part of interactions. The diagram analysis of these expansions for pair distribution functions leads to the so-called multidensity integral equation approach in the theory of associative fluids. The AMSA theory represents the two-density version of the traditional MSA theory [4, 5] and will be used here for the treatment of ion association in the ionic fluids. 

In addition to the repulsive part of the potential given by Eq. (4), a short-range attraction between the macroions may also be present. This attraction is due to the van der Waals forces [17,18], and can be modelled in different ways. The OCF model can be solved for the macroion-macroion pair-distribution function and thermodynamic properties using various statistical-mechanical theories. One of the most popular is the mean spherical approximation (MSA) [40], The OCF model can be applied to the analysis of small-angle scattering data, where the results are obtained in terms of the macroion-macroion structure factor [35], The same approach can also be applied to thermodynamic properties Kalyuzhnyi and coworkers [41] analyzed Donnan pressure measurements for various globular proteins using a modification of this model which permits the protein molecules to form dimers (see Sec. 7). 

Crystal structures can be determined exactly by means of x-ray diffraction and the periodicity of the lattice introduces some simplicity into the mathematical analysis. There is no such simplicity for amorphous materials. Only a statistical description is possible. In particular, a one-dimensional correlation function is often presented in the form of a radial distribution function, which is a pair-distribution function averaged over all atomic pairs. It is compatible with a large number of possible structures. The challenge is to separate out one of these realistic and compatible structures from the even greater number of random networks that are poor representations of the structure. 

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

The accuracy of the analysis presented in this paper is determined by the validity of two key approximations (1) the description of the energy transfer dynamics by the first order cumulant expansion method, (2) the use of a Gaussian chromophore pair distribution function. Although originally developed for, and successfully applied to, the problem of energy transfer in disordered infinite volume systems, the cumulant method can be modified to provide a highly accurate description of energy transfer in finite volume systems such as polymer coils (2 ). ... 

The thermal conductivity coefficient has been derived from Browniah motion theory by Irving and Kirkwood33 in terms of the equilibrium singlet and pair distribution functions °/a) and °/Thermal conduction under a macroscopic temperature difference involves a gradient in the mean square molecular velocity rather than in the mean molecular velocity. The steady-state radial distribution function then remains spherically symmetric except for a small correction arising from the number density variation with the temperature. As the analysis introduces no new assumptions and is somewhat lengthy, it will not be reproduced here. The resulting equation for the thermal conductivity coefficient x is... 

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