Atomic pair distribution function

Molecular dynamics permits one to determine rapidly varying atom-pair distribution functions In order to do that, one counts the number of... 

Fig. 1.2. Schematic diagram of the atom pair distribution functions for a crystalline and amorphous solid and a gas, scaled to the average separation of nearest neighbor atoms, showing the different degree of structural order.

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. ... 

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

Total scattering data can be analyzed by fitting models directly in reciprocal-space [i.e., the S Q) function is fit]. However, an alternative and intuitive approaeh is to Fourier transform the data to real-spaee to obtain the atomic pair distribution function (PDF), which is then fit in real-space. The reduced pair distribution function, G r), is related to S Q) through a sine Fourier transform aeeording to ... 

Similarly, the Fourier transform of the scattered intensity in the form of S Q), yields the reduced atomic pair distribution function, G(r), defined by Equation (1). This is strictly correct when the sample is made of a single element. We will discuss later an approximate extension, which works excellently in practice, to the more interesting case of multiple elements. 

PDFgui atomic pair distribution function, Th. Proffen and S. J. L. 

Figure 4.5 From the result of a molecular dynamics simulation, the x-ray scattering intensity was calculated, and from it (r), given in the broken curve, was derived, by using exactly the same procedure as was used to treat experimental x-ray scattering intensities. The solid curve is the C-C atom pair distribution function calculated directly from the simulation result. (From Mondello et al.13)...

Narten AH, Thiessen WE, Blum L (1982) Atom pair distribution functions of liquid water at 25°C from neutron diffraction. Science 217 1033-1034... 

Another approach that is gaining acceptance in the catalysis world is the use of total scattering formalisms and, particularly, the analysis of the nanoscale structural order from the atomic pair distribution function (PDF). Although this approach has a long history, the advent of synchrotron and novel detectors has provided a powerful tool to analyse nanoscale. The PDF method can yield precise short and long range structural and size information provided that special care is applied to the measurement and handling of data. The atomic PDF, G(g), is defined as ... 

Proffen T, Billinge SJL (1999) PDFFIT, a program for full profile structural refinement of the atomic pair distribution function. J Appl Crystallogr 32 572-575... 

PDF Atomic pair distribution function obtained from the analysis of the Bragg and diffuse... 

A coherent introduction to the formalism required to do this is given, and the basic concepts and technical terms are briefly explained. Paying attention to recent developments in materials research, we treat aperiodic, disordered, and amorphous materials as well. Consequently, besides the conventional three-dimensional (3-D) descriptions, the higher-dimensional crystallographic approach is outlined, and so is the atomic pair distribution function used to describe... 

Fig. 1.3-15 Radial atomic pair distribution function G(r) of an amorphous material. Its shape can be deduced from diffuse scattering...

Non-Bragg diffraction intensities I(Q) and therefore a normalized structure function S(Q) can be obtained, for example, from an X-ray or neutron powder diffrac-togram. The sine Fourier transform of S(Q) yields a normalized radial atomic pair distribution function G r) ... 

Dykhne T, Taylor R, Florence A, BiUinge SL (2011) Data requirements for the reliable use of atomic pair distribution functions in amorphous pharmaceutical fingerprinting. Pharm Res 28 1041-1048... 

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