Chapter 16. Local Structure from Total Scattering and Atomic Pair Distribution Function (PDF) Analysis

2008 ◽  
pp. 464-493 ◽  
Author(s):  
Simon Billinge
2018 ◽  
Vol 122 (51) ◽  
pp. 29498-29506 ◽  
Author(s):  
Soham Banerjee ◽  
Chia-Hao Liu ◽  
Jennifer D. Lee ◽  
Anton Kovyakh ◽  
Viktoria Grasmik ◽  
...  

2019 ◽  
Author(s):  
M. Mozammel Hoque ◽  
Sandra Vergara ◽  
Partha P. Das ◽  
Daniel Ugarte ◽  
Ulises Santiago ◽  
...  

Atomic pair distribution function (PDF) analysis has been widely used to investigate nanocrystalline and structurally disordered materials. Experimental PDFs retrieved from electron diffraction (ePDF) in transmission electron microscopy (TEM) represent an attractive alternative to traditional PDF obtained from synchrotron X-ray sources, when employed on minute samples. Nonetheless, the inelastic scattering produced by the large dynamical effects of electron diffraction may obscure the interpretation of ePDF. In the present work, precession electron diffraction (PED-TEM) has been employed to obtain the ePDF of two different sub-monolayer samples ––lipoic acid protected (~ 4.5 nm) and hexanethiolated(~ 4.2 nm, ~ 400-kDa core mass) gold nanoparticles­­––randomly oriented and measured at both liquid-nitrogen and room temperatures, with high dynamic-range detection of a CMOS camera. The electron diffraction data were processed to obtain ePDFs which were subsequently compared with PDF of different ideal structure-models. The results demonstrate that the PED-ePDF data is sensitive to different crystalline structures such as monocrystalline (truncated octahedra) versus multiply-twinned (decahedra, icosahedra) structuresof the face-centered cubic gold lattice. The results indicate that PED reduces the residual from 46% to 29%; in addition, the combination of PED and low temperature further reduced the residual to 23%, which is comparable to X-ray PDF analysis. Furthermore, the inclusion of PED resulted in a better estimation of the coordination number from ePDF. To the best of our knowledge, the precessed electron-beam technique (PED) has not been previously applied to nanoparticles for analysis by the ePDF method.


2006 ◽  
Vol 18 (1) ◽  
pp. 100-106 ◽  
Author(s):  
Gianluca Paglia ◽  
Emil S. Božin ◽  
Damjan Vengust ◽  
Dragan Mihailovic ◽  
Simon J. L. Billinge

2013 ◽  
Vol 46 (2) ◽  
pp. 461-465 ◽  
Author(s):  
Olivier Masson ◽  
Philippe Thomas

The atomic pair distribution function (PDF) as obtained from X-ray or neutron total scattering experiments has proved to be powerful in obtaining valuable structural information for many complex functional materials, be they amorphous or crystalline. In the case of measurements made with X-rays and for samples containing more than one kind of atom, the usefulness of the PDF is, however, somewhat hampered because of the lack of an exact and simple expression relating it to the structure of the materials. Only an approximate relationship exits, which is still in use today. This is particularly detrimental given the wide availability of X-ray sources and the increasing quality of PDFs obtained with laboratory sources. In this paper, the exact and explicit expression of the PDF as obtained from X-ray scattering is derived with respect to partial functions. This expression allows exact and efficient calculation of the PDF from any structure model without using approximate formulae.


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