Vibrational properties of nanocrystals from the Debye Scattering Equation
Abstract
One hundred years after the original formulation by Petrus J.W. Debije (aka Peter Debye), the Debye Scattering Equation (DSE) is still the most accurate expression to model the diffraction pattern from nanoparticle systems. A major limitation in the original form of the DSE is that it refers to a static domain, so that including thermal disorder usually requires rescaling the equation by a Debye-Waller thermal factor. The last is taken from the traditional diffraction theory developed in Reciprocal Space (RS), which is opposed to the atomistic paradigm of the DSE, usually referred to as Direct Space (DS) approach. Besides being a hybrid of DS and RS expressions, rescaling the DSE by the Debye-Waller factor is an approximation which completely misses the contribution of Temperature Diffuse Scattering (TDS). The present work proposes a solution to include thermal effects coherently with the atomistic approach of the DSE. Here, a deeper insight into the vibrational dynamics of nanostructured materials can be obtained with few changes with respect to the standard formulation of the DSE, providing information on the correlated displacement of vibrating atoms.
- Authors:
-
- Univ. of Trento, Trento (Italy)
- Publication Date:
- Research Org.:
- Argonne National Laboratory (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1241063
- Grant/Contract Number:
- AC02-06CH11357
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Scientific Reports
- Additional Journal Information:
- Journal Volume: 6; Journal Issue: 02; Journal ID: ISSN 2045-2322
- Publisher:
- Nature Publishing Group
- Country of Publication:
- United States
- Language:
- ENGLISH
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; atomistic models; structural properties; structure of solids and liquids
Citation Formats
Scardi, P., and Gelisio, L. Vibrational properties of nanocrystals from the Debye Scattering Equation. United States: N. p., 2016.
Web. doi:10.1038/srep22221.
Scardi, P., & Gelisio, L. Vibrational properties of nanocrystals from the Debye Scattering Equation. United States. https://doi.org/10.1038/srep22221
Scardi, P., and Gelisio, L. Fri .
"Vibrational properties of nanocrystals from the Debye Scattering Equation". United States. https://doi.org/10.1038/srep22221. https://www.osti.gov/servlets/purl/1241063.
@article{osti_1241063,
title = {Vibrational properties of nanocrystals from the Debye Scattering Equation},
author = {Scardi, P. and Gelisio, L.},
abstractNote = {One hundred years after the original formulation by Petrus J.W. Debije (aka Peter Debye), the Debye Scattering Equation (DSE) is still the most accurate expression to model the diffraction pattern from nanoparticle systems. A major limitation in the original form of the DSE is that it refers to a static domain, so that including thermal disorder usually requires rescaling the equation by a Debye-Waller thermal factor. The last is taken from the traditional diffraction theory developed in Reciprocal Space (RS), which is opposed to the atomistic paradigm of the DSE, usually referred to as Direct Space (DS) approach. Besides being a hybrid of DS and RS expressions, rescaling the DSE by the Debye-Waller factor is an approximation which completely misses the contribution of Temperature Diffuse Scattering (TDS). The present work proposes a solution to include thermal effects coherently with the atomistic approach of the DSE. Here, a deeper insight into the vibrational dynamics of nanostructured materials can be obtained with few changes with respect to the standard formulation of the DSE, providing information on the correlated displacement of vibrating atoms.},
doi = {10.1038/srep22221},
journal = {Scientific Reports},
number = 02,
volume = 6,
place = {United States},
year = {Fri Feb 26 00:00:00 EST 2016},
month = {Fri Feb 26 00:00:00 EST 2016}
}
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Works referenced in this record:
Anisotropic atom displacement in Pd nanocubes resolved by molecular dynamics simulations supported by x-ray diffraction imaging
journal, April 2015
- Scardi, P.; Leonardi, A.; Gelisio, L.
- Physical Review B, Vol. 91, Issue 15
Phonons from Powder Diffraction: A Quantitative Model-Independent Evaluation
journal, August 2004
- Goodwin, Andrew; Tucker, Matthew; Dove, Martin
- Physical Review Letters, Vol. 93, Issue 7
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
Limits on phonon information extracted from neutron pair-density functions
journal, August 2003
- Graf, Matthias J.; Jeong, Il-Kyoung; Starr, Daniel L.
- Physical Review B, Vol. 68, Issue 6
Phonons from neutron powder diffraction
journal, September 1999
- Dimitrov, D. A.; Louca, D.; Röder, H.
- Physical Review B, Vol. 60, Issue 9
Grain-size dependence of thermal properties of nanocrystalline elemental selenium studied by x-ray diffraction
journal, December 1997
- Zhao, Y. H.; Lu, K.
- Physical Review B, Vol. 56, Issue 22
Electron Diffraction Studies of Thin Films. II. Anomalous Powder Patterns Produced by Small Crystals
journal, September 1941
- Germer, L. H.; White, Addison H.
- Physical Review, Vol. 60, Issue 6
Zerstreuung von Röntgenstrahlen
journal, January 1915
- Debye, P.
- Annalen der Physik, Vol. 351, Issue 6
Atomistic modeling of lattice relaxation in metallic nanocrystals
journal, March 2013
- Gelisio, L.; Beyerlein, K. R.; Scardi, P.
- Thin Solid Films, Vol. 530
Measuring Correlated Atomic Motion Using X-ray Diffraction
journal, February 1999
- Jeong, Il-Kyoung; Proffen, Thomas; Mohiuddin-Jacobs, Farida
- The Journal of Physical Chemistry A, Vol. 103, Issue 7
Zerstreuung von Röntgenstrahlen
journal, January 1915
- Debye, P.
- Annalen der Physik, Vol. 351, Issue 6
Temperature and polarization dependence of extended x-ray absorption fine-structure spectra
journal, August 1976
- Beni, G.; Platzman, P. M.
- Physical Review B, Vol. 14, Issue 4
Limits on phonon information extracted from neutron pair-density functions
text, January 2002
- Graf, Matthias J.; Jeong, Il-Kyoung; Starr, Daniel L.
- arXiv
Noble-Metal Nanocrystals with Concave Surfaces: Synthesis and Applications
journal, May 2012
- Zhang, Hui; Jin, Mingshang; Xia, Younan
- Angewandte Chemie International Edition, Vol. 51, Issue 31
Extended x-ray absorption fine structure Debye-Waller factors. I. Monatomic crystals
journal, December 1979
- Sevillano, E.; Meuth, H.; Rehr, J. J.
- Physical Review B, Vol. 20, Issue 12
The effects of the size of nanocrystalline materials on their thermodynamic and mechanical properties
journal, September 2014
- Yu, Xiaohua; Zhan, Zhaolin
- Nanoscale Research Letters, Vol. 9, Issue 1
Local Lattice Dynamics in the Mg0.5Al0.5B2 Superconductor
journal, September 2007
- Campi, G.; Proffen, T.; Qiu, X.
- Journal of Superconductivity and Novel Magnetism, Vol. 20, Issue 7-8
Influence of phonons on the pair distribution function deduced from neutron powder diffraction
journal, April 2001
- Reichardt, W.; Pintschovius, L.
- Physical Review B, Vol. 63, Issue 17
Facet-dependent properties of polyhedral nanocrystals
journal, January 2014
- Huang, Michael H.; Rej, Sourav; Hsu, Shih-Chen
- Chemical Communications, Vol. 50, Issue 14
Atomistic modeling of lattice relaxation in metallic nanocrystals
journal, March 2013
- Gelisio, L.; Beyerlein, K. R.; Scardi, P.
- Thin Solid Films, Vol. 530
On the Modeling of the Diffraction Pattern from Metal Nanocrystals
journal, June 2014
- Gelisio, Luca; Scardi, Paolo
- Metallurgical and Materials Transactions A, Vol. 45, Issue 11
Temperature diffuse scattering of nanocrystals
journal, March 2012
- Beyerlein, K. R.; Leoni, M.; Scardi, P.
- Acta Crystallographica Section A Foundations of Crystallography, Vol. 68, Issue 3
Diffraction studies of the thermal properties of nanocrystalline Pd and Cr
journal, November 1992
- Eastman, J. A.; Fitzsimmons, M. R.; Thompson, L. J.
- Nanostructured Materials, Vol. 1, Issue 6
Compilation of temperature factors of cubic elements
journal, May 1988
- Butt, N. M.; Bashir, J.; Willis, B. T. M.
- Acta Crystallographica Section A Foundations of Crystallography, Vol. 44, Issue 3, p. 396-399
Crystallographic control of noble metal nanocrystals
journal, June 2011
- Niu, Wenxin; Xu, Guobao
- Nano Today, Vol. 6, Issue 3
Size effects on Debye temperature, Einstein temperature, and volume thermal expansion coefficient of nanocrystals
journal, July 2006
- Yang, C. C.; Xiao, M. X.; Li, W.
- Solid State Communications, Vol. 139, Issue 4
Decoupling the Geometric Parameters of Shape-Controlled Pd Nanocatalysts
journal, March 2014
- Laskar, Moitree; Skrabalak, Sara E.
- ACS Catalysis, Vol. 4, Issue 4
Lattice dynamics and correlated atomic motion from the atomic pair distribution function
journal, March 2003
- Jeong, I. -K.; Heffner, R. H.; Graf, M. J.
- Physical Review B, Vol. 67, Issue 10
Measuring Correlated Atomic Motion Using X-ray Diffraction
journal, February 1999
- Jeong, Il-Kyoung; Proffen, Thomas; Mohiuddin-Jacobs, Farida
- The Journal of Physical Chemistry A, Vol. 103, Issue 7
Vibrational Properties of Au and Cu Nanocrystals Formed by Ion Implantation
conference, January 2007
- Kluth, P.; Johannessen, B.; Araujo, L. L.
- AIP Conference Proceedings
Works referencing / citing this record:
When Crystals Go Nano - The Role of Advanced X-ray Total Scattering Methods in Nanotechnology: When Crystals Go Nano - The Role of Advanced X-ray Total Scattering Methods in Nanotechnology
journal, August 2018
- Bertolotti, Federica; Moscheni, Daniele; Guagliardi, Antonietta
- European Journal of Inorganic Chemistry, Vol. 2018, Issue 34
When Crystals Go Nano - The Role of Advanced X-ray Total Scattering Methods in Nanotechnology
journal, September 2018
- Bertolotti, Federica; Moscheni, Daniele; Guagliardi, Antonietta
- European Journal of Inorganic Chemistry, Vol. 2018, Issue 34