Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: A numerical method for deriving shape functions of nanoparticles for pair distribution function refinements

Abstract

We report that in the structural refinement of nanoparticles, discrete atomistic modeling can be used for small nanocrystals (< 15 nm), but becomes computationally unfeasible at larger sizes, where instead unit-cell-based small-box modeling is usually employed. However, the effect of the nanocrystal's shape is often ignored or accounted for with a spherical model regardless of the actual shape due to the complexities of solving and implementing accurate shape effects. Recent advancements have provided a way to determine the shape function directly from a pair distribution function calculated from a discrete atomistic model of any given shape, including both regular polyhedra (e.g. cubes, spheres, octahedra) and anisotropic shapes (e.g. rods, discs, ellipsoids) [Olds et al. (2015). J. Appl. Cryst. 48, 1651–1659], although this approach is still limited to small size regimes due to computational demands. In order to accurately account for the effects of nanoparticle size and shape in small-box refinements, a numerical or analytical description is needed. This article presents a methodology to derive numerical approximations of nanoparticle shape functions by fitting to a training set of known shape functions; the numerical approximations can then be employed on larger sizes yielding a more accurate and physically meaningful refined nanoparticle size.more » Lastly, the method is demonstrated on a series of simulated and real data sets, and a table of pre-calculated shape function expressions for a selection of common shapes is provided.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]
+ Show Author Affiliations
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Neutron Scattering Division
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1474606
Grant/Contract Number:  
AC05-00OR22725; AC02-06CH11357
Resource Type:
Accepted Manuscript
Journal Name:
Acta Crystallographica. Section A, Foundations and Advances (Online)
Additional Journal Information:
Journal Name: Acta Crystallographica. Section A, Foundations and Advances (Online); Journal Volume: 74; Journal Issue: 4; Journal ID: ISSN 2053-2733
Publisher:
International Union of Crystallography
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; nanoparticles; shape function; pair distribution function; total scattering

Citation Formats

Usher, Tedi-Marie, Olds, Daniel P., Liu, Jue, and Page, Katharine L. A numerical method for deriving shape functions of nanoparticles for pair distribution function refinements. United States: N. p., 2018. Web. doi:10.1107/S2053273318004977.
Copy to clipboard
Usher, Tedi-Marie, Olds, Daniel P., Liu, Jue, & Page, Katharine L. A numerical method for deriving shape functions of nanoparticles for pair distribution function refinements. United States. https://doi.org/10.1107/S2053273318004977
Copy to clipboard
Usher, Tedi-Marie, Olds, Daniel P., Liu, Jue, and Page, Katharine L. Wed . "A numerical method for deriving shape functions of nanoparticles for pair distribution function refinements". United States. https://doi.org/10.1107/S2053273318004977. https://www.osti.gov/servlets/purl/1474606.
Copy to clipboard
@article{osti_1474606,
title = {A numerical method for deriving shape functions of nanoparticles for pair distribution function refinements},
author = {Usher, Tedi-Marie and Olds, Daniel P. and Liu, Jue and Page, Katharine L.},
abstractNote = {We report that in the structural refinement of nanoparticles, discrete atomistic modeling can be used for small nanocrystals (< 15 nm), but becomes computationally unfeasible at larger sizes, where instead unit-cell-based small-box modeling is usually employed. However, the effect of the nanocrystal's shape is often ignored or accounted for with a spherical model regardless of the actual shape due to the complexities of solving and implementing accurate shape effects. Recent advancements have provided a way to determine the shape function directly from a pair distribution function calculated from a discrete atomistic model of any given shape, including both regular polyhedra (e.g. cubes, spheres, octahedra) and anisotropic shapes (e.g. rods, discs, ellipsoids) [Olds et al. (2015). J. Appl. Cryst. 48, 1651–1659], although this approach is still limited to small size regimes due to computational demands. In order to accurately account for the effects of nanoparticle size and shape in small-box refinements, a numerical or analytical description is needed. This article presents a methodology to derive numerical approximations of nanoparticle shape functions by fitting to a training set of known shape functions; the numerical approximations can then be employed on larger sizes yielding a more accurate and physically meaningful refined nanoparticle size. Lastly, the method is demonstrated on a series of simulated and real data sets, and a table of pre-calculated shape function expressions for a selection of common shapes is provided.},
doi = {10.1107/S2053273318004977},
journal = {Acta Crystallographica. Section A, Foundations and Advances (Online)},
number = 4,
volume = 74,
place = {United States},
year = {2018},
month = {6}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1107/S2053273318004977
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal

Figures / Tables:

Figure 1 Figure 1: Schematic describing the steps in Section 2.1 to generate a numerical approximation for the shape function of a given shape. Starting at the left, Step 1. is construction of a training set of nanocrystal models; shown here are three representative cubes. The colors of the cubes in Stepmore » 1 correspond to the line colors in Steps 2 and 3. Step 2. is calculation of PDFs from the finite nanocrystal models. Step 3. is extraction of the shape functions from the PDFs using DShaper and conversion of the shape functions to $γ$($r$) . Step 4. is fitting $γ$($r$) with a numerical approximation. The result in Step 4. is shown for a set of nine nanocube $γ$($r$) (black dots) fit with the two-Gaussian $γ$$num$($r$) (color lines). The difference curves are shown offset below and demonstrate good agreement between $γ$($r$) and $γ$$num$($r$) )« less
All figures and tables (12 total)
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Multiple Wurtzite Twinning in CdTe Nanocrystals Induced by Methylphosphonic Acid
journal, January 2006

  • Carbone, Luigi; Kudera, Stefan; Carlino, Elvio
  • Journal of the American Chemical Society, Vol. 128, Issue 3
  • DOI: 10.1021/ja054893c

Electrochemical Photolysis of Water at a Semiconductor Electrode
journal, July 1972

  • Fujishima, Akira; Honda, Kenichi
  • Nature, Vol. 238, Issue 5358, p. 37-38
  • DOI: 10.1038/238037a0

Efficient algorithms for calculating small-angle scattering from large model structures
journal, May 2014

The Problem with Determining Atomic Structure at the Nanoscale
journal, April 2007

Combined fitting of small- and wide-angle X-ray total scattering data from nanoparticles: benefits and issues
journal, March 2014

  • Gagin, Anton; Allen, Andrew J.; Levin, Igor
  • Journal of Applied Crystallography, Vol. 47, Issue 2
  • DOI: 10.1107/S1600576714001046

Highly Crystalline Multimetallic Nanoframes with Three-Dimensional Electrocatalytic Surfaces
journal, February 2014

For high-pressure experiments using total scattering spectrometer NOVA at J-PARC
journal, March 2010

Molecular arrangement in water: random but not quite
journal, March 2012

Solvothermal synthesis and controlled self-assembly of monodisperse titanium-based perovskite colloidal nanocrystals
journal, January 2015

  • Caruntu, Daniela; Rostamzadeh, Taha; Costanzo, Tommaso
  • Nanoscale, Vol. 7, Issue 30
  • DOI: 10.1039/C5NR00737B

Fast synthesis and refinement of the atomic pair distribution function
journal, May 2015

Three-dimensional controlled growth of monodisperse sub-50 nm heterogeneous nanocrystals
journal, January 2016

  • Liu, Deming; Xu, Xiaoxue; Du, Yi
  • Nature Communications, Vol. 7, Issue 1
  • DOI: 10.1038/ncomms10254

DISCUS : a program for diffuse scattering and defect-structure simulation
journal, April 1997

Complex modeling: a strategy and software program for combining multiple information sources to solve ill posed structure and nanostructure inverse problems
journal, September 2015

  • Juhás, Pavol; Farrow, Christopher L.; Yang, Xiaohao
  • Acta Crystallographica Section A Foundations and Advances, Vol. 71, Issue 6, p. 562-568
  • DOI: 10.1107/S2053273315014473

Single Crystal Manganese Oxide Multipods by Oriented Attachment
journal, November 2005

  • Zitoun, David; Pinna, Nicola; Frolet, Nathalie
  • Journal of the American Chemical Society, Vol. 127, Issue 43
  • DOI: 10.1021/ja0555926

GEM — General materials diffractometer at ISIS
journal, December 1997

Size, Shape, and Internal Atomic Ordering of Nanocrystals by Atomic Pair Distribution Functions: A Comparative Study of γ-Fe 2 O 3 Nanosized Spheres and Tetrapods
journal, October 2009

  • Petkov, Valeri; Cozzoli, P. Davide; Buonsanti, Raffaella
  • Journal of the American Chemical Society, Vol. 131, Issue 40
  • DOI: 10.1021/ja9067589

On the True Photoreactivity Order of {001}, {010}, and {101} Facets of Anatase TiO2 Crystals
journal, January 2011

  • Pan, Jian; Liu, Gang; Lu, Gao Qing Max
  • Angewandte Chemie International Edition, Vol. 50, Issue 9
  • DOI: 10.1002/anie.201006057

Anatase TiO2 single crystals with a large percentage of reactive facets
journal, May 2008

  • Yang, Hua Gui; Sun, Cheng Hua; Qiao, Shi Zhang
  • Nature, Vol. 453, Issue 7195
  • DOI: 10.1038/nature06964

Real-space calculation of powder diffraction patterns on graphics processing units
journal, April 2010

  • Gelisio, Luca; Azanza Ricardo, Cristy Leonor; Leoni, Matteo
  • Journal of Applied Crystallography, Vol. 43, Issue 3
  • DOI: 10.1107/S0021889810005133

Complexity at mesoscopic lengthscale
journal, August 2015

Nanoscale Ni/Mn Ordering in the High Voltage Spinel Cathode LiNi 0.5 Mn 1.5 O 4
journal, September 2016

Insights into the Local Structure of Tb-Doped KY 3 F 10 Nanoparticles from Synchrotron X-ray Diffraction
journal, August 2017

  • Ichikawa, Rodrigo U.; Linhares, Horacio M. S. M. D.; Peral, Inma
  • ACS Omega, Vol. 2, Issue 8
  • DOI: 10.1021/acsomega.7b00668

Resolving the Structure of Ti 3 C 2 T x MXenes through Multilevel Structural Modeling of the Atomic Pair Distribution Function
journal, December 2015

Precise implications for real-space pair distribution function modeling of effects intrinsic to modern time-of-flight neutron diffractometers
journal, June 2018

  • Olds, Daniel; Saunders, Claire N.; Peters, Megan
  • Acta Crystallographica Section A Foundations and Advances, Vol. 74, Issue 4
  • DOI: 10.1107/S2053273318003224

Structural coherence and ferroelectricity decay in submicron- and nano-sized perovskites
journal, August 2008

Building a high resolution total scattering powder diffractometer - upgrade of NPD at MLNSC
journal, December 2002

  • Proffen, T.; Egami, T.; Billinge, S. J. L.
  • Applied Physics A: Materials Science & Processing, Vol. 74, Issue 0
  • DOI: 10.1007/s003390201929

Building and refining complete nanoparticle structures with total scattering data
journal, February 2011

  • Page, Katharine; Hood, Taylor C.; Proffen, Thomas
  • Journal of Applied Crystallography, Vol. 44, Issue 2
  • DOI: 10.1107/S0021889811001968

Structure and energetics of stoichiometric TiO 2 anatase surfaces
journal, March 2001

Relationship between the atomic pair distribution function and small-angle scattering: implications for modeling of nanoparticles
journal, April 2009

  • Farrow, Christopher L.; Billinge, Simon J. L.
  • Acta Crystallographica Section A Foundations of Crystallography, Vol. 65, Issue 3, p. 232-239
  • DOI: 10.1107/S0108767309009714

The Polaris powder diffractometer at ISIS
journal, June 1992

Pair distribution function and structure factor of spherical particles
journal, March 2006

DShaper : an approach for handling missing low- Q data in pair distribution function analysis of nanostructured systems
journal, October 2015

  • Olds, Daniel; Wang, Hsiu-Wen; Page, Katharine
  • Journal of Applied Crystallography, Vol. 48, Issue 6
  • DOI: 10.1107/S1600576715016581

Ferroelectric order in individual nanometre-scale crystals
journal, July 2012

  • Polking, Mark J.; Han, Myung-Geun; Yourdkhani, Amin
  • Nature Materials, Vol. 11, Issue 8
  • DOI: 10.1038/nmat3371

Titanium Dioxide Nanomaterials:  Synthesis, Properties, Modifications, and Applications
journal, July 2007

  • Chen, Xiaobo; Mao, Samuel S.
  • Chemical Reviews, Vol. 107, Issue 7
  • DOI: 10.1021/cr0500535

Percolating bulk heterostructures from neutron reflectometry and small-angle scattering data
journal, December 2012

The Morphology of TiO 2 (B) Nanoparticles
journal, October 2015

  • Hua, Xiao; Liu, Zheng; Bruce, Peter G.
  • Journal of the American Chemical Society, Vol. 137, Issue 42
  • DOI: 10.1021/jacs.5b08434

Anisotropic phase segregation and migration of Pt in nanocrystals en route to nanoframe catalysts
journal, August 2016

  • Niu, Zhiqiang; Becknell, Nigel; Yu, Yi
  • Nature Materials, Vol. 15, Issue 11
  • DOI: 10.1038/nmat4724

Manganese(II) Oxide Nanohexapods:  Insight into Controlling the Form of Nanocrystals
journal, April 2006

  • Ould-Ely, Teyeb; Prieto-Centurion, Dario; Kumar, A.
  • Chemistry of Materials, Vol. 18, Issue 7
  • DOI: 10.1021/cm052492q

Reactivity of Anatase TiO 2 Nanoparticles:  The Role of the Minority (001) Surface
journal, October 2005

  • Gong, Xue-Qing; Selloni, Annabella
  • The Journal of Physical Chemistry B, Vol. 109, Issue 42
  • DOI: 10.1021/jp055311g

The Nanoscale Ordered MAterials Diffractometer NOMAD at the Spallation Neutron Source SNS
journal, September 2012

  • Neuefeind, Jörg; Feygenson, Mikhail; Carruth, John
  • Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 287
  • DOI: 10.1016/j.nimb.2012.05.037

Ferroelectric Barium Titanate Nanocubes as Capacitive Building Blocks for Energy Storage Applications
journal, October 2014

  • Parizi, Saman Salemizadeh; Mellinger, Axel; Caruntu, Gabriel
  • ACS Applied Materials & Interfaces, Vol. 6, Issue 20
  • DOI: 10.1021/am502547h

Reciprocal-space instrumental effects on the real-space neutron atomic pair distribution function
journal, January 2004

  • Qiu, Xiangyun; Božin, Emil S.; Juhas, Pavol
  • Journal of Applied Crystallography, Vol. 37, Issue 1
  • DOI: 10.1107/S0021889803026670

Structure and Stability of SnO 2 Nanocrystals and Surface-Bound Water Species
journal, April 2013

  • Wang, Hsiu-Wen; Wesolowski, David J.; Proffen, Thomas E.
  • Journal of the American Chemical Society, Vol. 135, Issue 18
  • DOI: 10.1021/ja312030e

PDFfit2 and PDFgui: computer programs for studying nanostructure in crystals
journal, July 2007

Monopod, Bipod, Tripod, and Tetrapod Gold Nanocrystals
journal, December 2003

  • Chen, Sihai; Wang, Zhong Lin; Ballato, John
  • Journal of the American Chemical Society, Vol. 125, Issue 52, p. 16186-16187
  • DOI: 10.1021/ja038927x

Uncovering the intrinsic geometry from the atomic pair distribution function of nanomaterials
journal, July 2009

Local and average structures of BaTiO3-Bi(Zn1/2Ti1/2)O3
journal, November 2016

  • Usher, Tedi-Marie; Iamsasri, Thanakorn; Forrester, Jennifer S.
  • Journal of Applied Physics, Vol. 120, Issue 18
  • DOI: 10.1063/1.4967222

Effects of Bragg peak profiles and nanoparticle sizes on the real-space pair distribution function
journal, January 2005

  • Jeong, Il-Kyoung; Graf, M. J.; Heffner, R. H.
  • Journal of Applied Crystallography, Vol. 38, Issue 1
  • DOI: 10.1107/S0021889804025841

Nanoparticulate TiO2(B): An Anode for Lithium-Ion Batteries
journal, January 2012

  • Ren, Yu; Liu, Zheng; Pourpoint, Frédérique
  • Angewandte Chemie International Edition, Vol. 51, Issue 9
  • DOI: 10.1002/anie.201108300

Colloidal Synthesis and Characterization of Tetrapod-Shaped Magnetic Nanocrystals
journal, September 2006

  • Cozzoli, P. Davide; Snoeck, Etienne; Garcia, Miguel Angel
  • Nano Letters, Vol. 6, Issue 9
  • DOI: 10.1021/nl061112c

Finite size effects on the real-space pair distribution function of nanoparticles
journal, May 2008

Total scattering atomic pair distribution function: new methodology for nanostructure determination
journal, May 2016

Ferroelectric properties of composites containing BaTiO 3 nanoparticles of various sizes
journal, January 2014

Structure determination of molecular nanocomposites by combining pair distribution function analysis and solid-state NMR
journal, January 2015

  • Bendeif, E. -E.; Gansmuller, A.; Hsieh, K. -Y.
  • RSC Advances, Vol. 5, Issue 12
  • DOI: 10.1039/C4RA11470A

Unit-cell scale mapping of ferroelectricity and tetragonality in epitaxial ultrathin ferroelectric films
journal, December 2006

  • Jia, Chun-Lin; Nagarajan, Valanoor; He, Jia-Qing
  • Nature Materials, Vol. 6, Issue 1
  • DOI: 10.1038/nmat1808

Crystal Structure and the Paraelectric-to-Ferroelectric Phase Transition of Nanoscale BaTiO 3
journal, June 2008

  • Smith, Millicent B.; Page, Katharine; Siegrist, Theo
  • Journal of the American Chemical Society, Vol. 130, Issue 22
  • DOI: 10.1021/ja0758436

Probing Local Dipoles and Ligand Structure in BaTiO 3 Nanoparticles
journal, August 2010

  • Page, Katharine; Proffen, Thomas; Niederberger, Markus
  • Chemistry of Materials, Vol. 22, Issue 15
  • DOI: 10.1021/cm100440p

Nonaqueous Synthesis of TiO 2 Nanocrystals Using TiF 4 to Engineer Morphology, Oxygen Vacancy Concentration, and Photocatalytic Activity
journal, April 2012

  • Gordon, Thomas R.; Cargnello, Matteo; Paik, Taejong
  • Journal of the American Chemical Society, Vol. 134, Issue 15
  • DOI: 10.1021/ja300823a

The interpretation of real-space information from small-angle scattering experiments
journal, April 1979

Characteristics of Barium Titanate Nanocube Ordered Assembly Thin Films Fabricated by Dip-Coating Method
journal, September 2013

  • Mimura, Ken-ichi; Kato, Kazumi
  • Japanese Journal of Applied Physics, Vol. 52, Issue 9S1
  • DOI: 10.7567/JJAP.52.09KC06

Nanoparticulate TiO2(B): An Anode for Lithium-Ion Batteries
journal, January 2012

  • Ren, Yu; Liu, Zheng; Pourpoint, Frédérique
  • Angewandte Chemie, Vol. 124, Issue 9
  • DOI: 10.1002/ange.201108300

Titanium Dioxide Nanomaterials: Synthesis, Properties, Modifications, and Applications
journal, October 2007

On the True Photoreactivity Order of {001}, {010}, and {101} Facets of Anatase TiO2 Crystals
journal, January 2011

Structure determination of molecular nanocomposites by combining pair distribution function analysis and solid-state NMR
journal, August 2015

  • Schaniel, Dominik; Bendeif, El-Eulmi; Gansmuller, Axel
  • Acta Crystallographica Section A Foundations and Advances, Vol. 71, Issue a1
  • DOI: 10.1107/s2053273315094292

Single Crystal Manganese Oxide Multipods by Oriented Attachment.
journal, January 2006

Pair distribution function and structure factor of spherical particles
text, January 2005

    Sort by:
    [ × clear filter / sort ]

    Works referencing / citing this record:

    Reverse Monte Carlo modeling for low-dimensional systems
    journal, August 2019

    • Zhang, Yuanpeng; McDonnell, Marshall; Liu, Wei
    • Journal of Applied Crystallography, Vol. 52, Issue 5
    • DOI: 10.1107/s160057671901080x

    A simple correction for the parallax effect in X-ray pair distribution function measurements
    journal, September 2019

    • Marlton, Frederick; Ivashko, Oleh; Zimmerman, Martin v.
    • Journal of Applied Crystallography, Vol. 52, Issue 5
    • DOI: 10.1107/s1600576719011580

    A simple correction for the parallax effect in X-ray pair distribution function measurements
    text, January 2019

    • Marlton, Frederick; Ivashko, Oleh; Von Zimmermann, Martin
    • Deutsches Elektronen-Synchrotron, DESY, Hamburg
    • DOI: 10.3204/pubdb-2019-03307
      Sort by:
      [ × clear filter / sort ]

      Figures / Tables found in this record:

      Figure 1 (p. 6)figure
      Table 1 (p. 7)table
      Figure 2 (p. 8)figure
      Figure 3 (p. 12)figure
      Figure 4 (p. 13)figure
      Figure 5 (p. 15)figure
      Figure 6 (p. 16)figure
      Figure 7 (p. 18)figure
      Figure S1 (p. 22)figure
      Figure S2 (p. 23)figure
      Figure S3 (p. 24)figure
      Figure S4 (p. 24)figure
        [ × clear filter / sort ]
        Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

        Similar Records in DOE PAGES and OSTI.GOV collections: