Pair distribution function and structure factor of spherical particles
Abstract
The availability of neutron spallationsource instruments that provide total scattering powder diffraction has led to an increased application of realspace structure analysis using the pair distribution function. Currently, the analytical treatment of finite size effects within pair distribution refinement procedures is limited. To that end, an envelope function is derived which transforms the pair distribution function of an infinite solid into that of a spherical particle with the same crystal structure. Distributions of particle sizes are then considered, and the associated envelope function is used to predict the particle size distribution of an experimental sample of gold nanoparticles from its pair distribution function alone. Finally, complementing the wealth of existing diffraction analysis, the peak broadening for the structure factor of spherical particles, expressed as a convolution derived from the envelope functions, is calculated exactly for all particle size distributions considered, and peak maxima, offsets, and asymmetries are discussed.
 Authors:
 Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
 (United States)
 Publication Date:
 OSTI Identifier:
 20787950
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. B, Condensed Matter and Materials Physics; Journal Volume: 73; Journal Issue: 9; Other Information: DOI: 10.1103/PhysRevB.73.094107; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ASYMMETRY; CRYSTAL STRUCTURE; DISTRIBUTION; DISTRIBUTION FUNCTIONS; GOLD; NANOSTRUCTURES; NEUTRON DIFFRACTION; NEUTRONS; PARTICLE SIZE; PARTICLES; POWDERS; SOLIDS; SPHERICAL CONFIGURATION; STRUCTURE FACTORS
Citation Formats
Howell, Rafael C., Proffen, Thomas, Conradson, Steven D., Lujan Neutron Scattering Center, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, and Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545. Pair distribution function and structure factor of spherical particles. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVB.73.0.
Howell, Rafael C., Proffen, Thomas, Conradson, Steven D., Lujan Neutron Scattering Center, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, & Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545. Pair distribution function and structure factor of spherical particles. United States. doi:10.1103/PHYSREVB.73.0.
Howell, Rafael C., Proffen, Thomas, Conradson, Steven D., Lujan Neutron Scattering Center, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, and Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545. Wed .
"Pair distribution function and structure factor of spherical particles". United States.
doi:10.1103/PHYSREVB.73.0.
@article{osti_20787950,
title = {Pair distribution function and structure factor of spherical particles},
author = {Howell, Rafael C. and Proffen, Thomas and Conradson, Steven D. and Lujan Neutron Scattering Center, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 and Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545},
abstractNote = {The availability of neutron spallationsource instruments that provide total scattering powder diffraction has led to an increased application of realspace structure analysis using the pair distribution function. Currently, the analytical treatment of finite size effects within pair distribution refinement procedures is limited. To that end, an envelope function is derived which transforms the pair distribution function of an infinite solid into that of a spherical particle with the same crystal structure. Distributions of particle sizes are then considered, and the associated envelope function is used to predict the particle size distribution of an experimental sample of gold nanoparticles from its pair distribution function alone. Finally, complementing the wealth of existing diffraction analysis, the peak broadening for the structure factor of spherical particles, expressed as a convolution derived from the envelope functions, is calculated exactly for all particle size distributions considered, and peak maxima, offsets, and asymmetries are discussed.},
doi = {10.1103/PHYSREVB.73.0},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 9,
volume = 73,
place = {United States},
year = {Wed Mar 01 00:00:00 EST 2006},
month = {Wed Mar 01 00:00:00 EST 2006}
}

We utilized the pair distribution function method to characterize the pressureinduced polyamorphic transition in Ce60Al20Cu20 and Ce55Al45 metallic glass at room temperature. Using synchrotron highenergy xray diffraction we collected scattering information from a large Qspace coverage, which in turn gave a high resolution g(r) that provided accurate local structure information. We observed a sudden change in compressibility and the nearest neighbor distance at 3.50–6.32 GPa for Ce60Al20Cu20 and 2.20–6.89 GPa for Ce55Al45. The origin of the volume collapse seemed to be pressureinduced qualitative changes in bond shortening that corresponded to different coordination spheres. The polyamorphic transitions in these two systemsmore »

Local structure of ion pair interaction in lapatinib amorphous dispersions characterized by synchrotron xray diffraction and pair distribution function analysis
For many years, the idea of analyzing atomatom contacts in amorphous drugpolymer systems has been of major interest, because this method has always had the potential to differentiate between amorphous systems with domains and amorphous systems which are molecular mixtures. In this study, local structure of ionic and noninonic interactions were studied by HighEnergy Xray Diffraction and Pair Distribution Function (PDF) analysis in amorphous solid dispersions of lapatinib in hypromellose phthalate (HPMCP) and hypromellose (HPMCE3). The strategy of extracting lapatinib intermolecular drug interactions from the total PDF xray pattern was successfully applied allowing the detection of distinct nearest neighbor contactsmore » 
Xray determinations of the liquidstructure factor and paircorrelation function of /sup 4/He
Measurements of the intensity of CuX alpha: x rays scattered from liquid /sup 4/He as a function of temperature and pressure are used to determine the liquidstructure factor and paircorrelation function of the fluid. Data are reported for 1.16less than or equal toTless than or equal to3.5 K at the three densities 150.3, 162.5, and 171.0 kg/m/sup 3/. Earlier data of Robkoff and Hallock are reanalyzed and found to be in excellent agreement with our new results. The temperature dependence of the structure factor at fixed density is in good agreement with predictions based on the thermal population of rotonsmore » 
QUANTUM STATISTICS OF INTERACTING PARTICLES THERMODYNAMIC QUANTITIES AND PAIR DISTRIBUTION FUNCTION
An alterrative approach to the quantum statistics of interacting particles is proposed. It consists of calculating the equilibrium thermodynamical quantities of the manybody system via the pair distribution function with the assumption that the particles interact with each other only through pair central forces. The proposed approach has some advantage over the usual treatment via the partition function in that the pair distribution function is easier to deal with than the partition function in certain circumstances particularly when the collective motion description of the system is desirable. This is because only the pair distribution function can be expressed directly inmore »