Modelling pair distribution functions (PDFs) of organic compounds: describing both intra- and intermolecular correlation functions in calculated PDFs

2015 ◽  
Vol 48 (1) ◽  
pp. 171-178 ◽  
Author(s):  
Dragica Prill ◽  
Pavol Juhás ◽  
Martin U. Schmidt ◽  
Simon J. L. Billinge
Keyword(s):  
Structural Models ◽  
Simple Approach ◽  
Distribution Functions ◽  
Atomic Motion ◽  
Molecular Systems ◽  
Atomic Pair ◽  
Intermolecular Distances ◽  
Supercell Model ◽  
Pair Distribution Functions ◽  
Modelling Approach

The methods currently used to calculate atomic pair distribution functions (PDFs) from organic structural models do not distinguish between the intramolecular and intermolecular distances. Owing to the stiff bonding between atoms within a molecule, the PDF peaks arising from intramolecular atom–atom distances are much sharper than those of the intermolecular atom–atom distances. This work introduces a simple approach to calculate PDFs of molecular systems without building a supercell model by using two different isotropic displacement parameters to describe atomic motion: one parameter is used for the intramolecular, the other one for intermolecular atom–atom distances. Naphthalene, quinacridone and paracetamol were used as examples. Calculations were done with theDiffPy-CMIcomplex modelling infrastructure. The new modelling approach produced remarkably better fits to the experimental PDFs, confirming the higher accuracy of this method for organic materials.

Atomic pair distribution functions analysis of disordered low-Z materials

2013 ◽  
Vol 15 (22) ◽  
pp. 8544 ◽  
Author(s):  
V. Petkov ◽  
Y. Ren ◽  
S. Kabekkodu ◽  
D. Murphy
Keyword(s):  
Distribution Functions ◽  
Atomic Pair ◽  
Pair Distribution Functions

Algorithm for systematic peak extraction from atomic pair distribution functions

2015 ◽  
Vol 71 (4) ◽  
pp. 392-409 ◽  
Author(s):  
L. Granlund ◽  
S. J. L. Billinge ◽  
P. M. Duxbury
Keyword(s):  
Structural Model ◽  
Information Criterion ◽  
Distribution Functions ◽  
Theory And Practice ◽  
Chi Square ◽  
Information Theoretic ◽  
Atomic Pair ◽  
Structure Solution ◽  
The Impact ◽  
Pair Distribution Functions

The study presents an algorithm, ParSCAPE, for model-independent extraction of peak positions and intensities from atomic pair distribution functions (PDFs). It provides a statistically motivated method for determining parsimony of extracted peak models using the information-theoretic Akaike information criterion (AIC) applied to plausible models generated within an iterative framework of clustering and chi-square fitting. All parameters the algorithm uses are in principle known or estimable from experiment, though careful judgment must be applied when estimating the PDF baseline of nanostructured materials. ParSCAPE has been implemented in the Python programSrMise. Algorithm performance is examined on synchrotron X-ray PDFs of 16 bulk crystals and two nanoparticles using AIC-based multimodeling techniques, and particularly the impact of experimental uncertainties on extracted models. It is quite resistant to misidentification of spurious peaks coming from noise and termination effects, even in the absence of a constraining structural model. Structure solution from automatically extracted peaks using the Liga algorithm is demonstrated for 14 crystals and for C60. Special attention is given to the information content of the PDF, theory and practice of the AIC, as well as the algorithm's limitations.

Atomic ordering in nanosized PtxAu1–x(x= 0, 0.51, 1) by resonant X-ray diffraction and differential atomic pair distribution functions

2012 ◽  
Vol 227 (5) ◽  
pp. 262-267 ◽  
Author(s):  
Valeri Petkov ◽  
Sarvjit Shastri ◽  
Bridgid Wanjala ◽  
Rameshiwori Loukrakpam ◽  
Jin Luo ◽  
...  
Keyword(s):  
Distribution Functions ◽  
X Ray Diffraction ◽  
Atomic Ordering ◽  
X Ray ◽  
Atomic Pair ◽  
Pair Distribution Functions

scholarly journals Algorithm for distance list extraction from pair distribution functions

2019 ◽  
Vol 75 (5) ◽  
pp. 658-668
Author(s):  
Ran Gu ◽  
Soham Banerjee ◽  
Qiang Du ◽  
Simon J. L. Billinge
Keyword(s):  
Optimization Problem ◽  
Equation Model ◽  
Initial Guess ◽  
Distribution Functions ◽  
New Approach ◽  
Gaussian Functions ◽  
Atomic Pair ◽  
Extraction Algorithm ◽  
The Mathematical Model ◽  
Pair Distribution Functions

An algorithm is presented to extract the distance list from atomic pair distribution functions in a highly automated way. The algorithm is constructed via curve fitting based on a Debye scattering equation model. Because of the non-convex nature of the resulting optimization problem, a number of techniques are developed to overcome various computational difficulties. A key ingredient is a new approach to obtain a reasonable initial guess based on the theoretical properties of the mathematical model. Tests on various nanostructured samples show the effectiveness of the initial guess and the accuracy and overall good performance of the extraction algorithm. This approach could be extended to any spectrum that is approximated as a sum of Gaussian functions.

WAXS and PDF-Based Analyses of Chromium Doping in Nanocrystalline Titania (Anatase and Brookite)

2006 ◽  
Vol 915 ◽  
Author(s):  
Hengzhong Zhang ◽  
Benjamin Gilbert ◽  
Bin Chen ◽  
Jillian F. Banfield
Keyword(s):  
Fourier Transforms ◽  
Sol Gel ◽  
Distribution Functions ◽  
Molar Ratio ◽  
Lattice Contraction ◽  
Nanocrystalline Titania ◽  
X Ray Scattering ◽  
Atomic Pair ◽  
Heat Treated ◽  
Pair Distribution Functions

AbstractChromium-doped (0.5-10 % Cr:Ti molar ratio) nanocrystalline titania (5–6 nm) prepared via sol-gel method was examined by synchrotron-based wide angle x-ray scattering (WAXS) for crystal structure determination. Atomic pair-distribution functions (PDF) for both raw and heat-treated samples were obtained by Fourier transforms of the WAXS data. The PDF data were fitted using structural models of nanocrystalline titania that considered phase compositions, lattice parameters, atomic positions and thermal factors. The unit cell of Cr-doped nanocrystalline titania expanded 1-2 % with respect to bulk titania as a consequence of the substitution of Ti by Cr and the generation of oxygen vacancies. We observed a lattice contraction after heat-treatment that may be caused by the redistribution of Cr atoms to nanoparticle surfaces during phase transformation and particle coarsening.

Sign in / Sign up

Export Citation Format

Share Document