Accuracy Limits of Pair Distribution Function Analysis in Structural Characterization of Nanocrystalline Powders by X-ray Diffraction
Abstract
We report the minimum errors of structural parameters, namely lattice parameter, crystallite size, and atomic displacement parameters, expected from Pair Distribution Function (PDF) analysis of nanocrystalline gold powders for the first time by a self-consistent computational methodology. Although PDF analysis has been increasingly used to characterize nanocrystalline powders by X-rays, the current literature includes no established error bounds to be expected from the resulting structural parameters. For accurate interpretation of X-ray diffraction data, these error bounds must be determined, and the obtained structural parameters must be cleared from them. Our novel methodology includes: 1) simulation of ideal powder diffraction experiments with the use of the Debye scattering equation, 2) pair distribution function analysis of the diffraction data with the Diffpy-CMI analysis software, and 3) determination of the errors from PDF analysis of the simulated diffraction data by comparing them with real-space analysis of spherical gold nanocrystals that are 30 nm size and smaller. Our results show that except for the lattice parameters and even with an ideal crystalline powder sample and ideal diffraction data, the extracted structural parameters from PDF analysis diverge from their true values for the studied nanopowder. These deviations are dependent on the average size of the nanocrystals and the energy of the X-rays selected for the diffraction experiments, where lower X-ray energies and small-sized nanocrystalline powders lead to greater errors.
Keywords
pair distribution function analysis powder diffraction X-rays nanocrystalline powders Debye scattering equation.
Supporting Institution
Tübitak
Project Number
BİDEB 2232 International Fellowship of Outstanding Researchers Program (Project no:118C268)
Thanks
Dr. İlknur Eruçar Dr. Shangmin Xiong
References
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Abstract
Project Number
BİDEB 2232 International Fellowship of Outstanding Researchers Program (Project no:118C268)
References
- 1. Prasad N, Karthikeyan B. Tunable bandgap and blue emission of ZnS nanoparticles induced by controlled S vacancies. Journal of Applied Physics. 2019 Feb 28;125(8):085702.
- 2. Tran N, Zhao W, Carlson F, Davidson JH, Stein A. Metal Nanoparticle–Carbon Matrix Composites with Tunable Melting Temperature as Phase-Change Materials for Thermal Energy Storage. ACS Appl Nano Mater. 2018 Apr 27;1(4):1894–903.
- 3. Ingham B. X-ray scattering characterisation of nanoparticles. Crystallography Reviews. 2015 Oct 2;21(4):229–303.
- 4. Kang S-JL, Park J-H, Ko S-Y, Lee H-Y. Solid-State Conversion of Single Crystals: The Principle and the State-of-the-Art. Green DJ, editor. J Am Ceram Soc. 2015 Feb;98(2):347–60.
- 5. Neder RB, Proffen T. Exact and fast calculation of the X-ray pair distribution function. J Appl Crystallogr. 2020 Jun 1;53(3):710–21.
- 6. Rietveld HM. A profile refinement method for nuclear and magnetic structures. J Appl Crystallogr. 1969 Jun 2;2(2):65–71.
- 7. Juhás P, Farrow CL, Yang X, Knox KR, Billinge SJL. Complex modeling: a strategy and software program for combining multiple information sources to solve ill posed structure and nanostructure inverse problems. Acta Crystallogr A Found Adv. 2015 Nov 1;71(6):562–8.
- 8. Petkov V, Bedford N, Knecht MR, Weir MG, Crooks RM, Tang W, et al. Periodicity and Atomic Ordering in Nanosized Particles of Crystals. J Phys Chem C. 2008 Jun 1;112(24):8907–11.
- 9. Popa NC, Balzar D. Size-broadening anisotropy in whole powder pattern fitting. Application to zinc oxide and interpretation of the apparent crystallites in terms of physical models. J Appl Crystallogr. 2008 Jun 1;41(3):615–27.
- 10. Bugaev AL, Guda AA, Lomachenko KA, Shapovalov VV, Lazzarini A, Vitillo JG, et al. Core–Shell Structure of Palladium Hydride Nanoparticles Revealed by Combined X-ray Absorption Spectroscopy and X-ray Diffraction. J Phys Chem C. 2017 Aug 24;121(33):18202–13.
- 11. Xiong S, Öztürk H, Lee S-Y, Mooney PM, Noyan IC. The nanodiffraction problem. J Appl Crystallogr. 2018 Aug 1;51(4):1102–15.
- 12. Toby BH, Egami T. Accuracy of pair distribution function analysis applied to crystalline and non-crystalline materials. Acta Crystallogr A Found Crystallogr. 1992 May 1;48(3):336–46.
- 13. Farrow CL, Billinge SJL. Relationship between the atomic pair distribution function and small-angle scattering: implications for modeling of nanoparticles. Acta Crystallogr A Found Crystallogr. 2009 May 1;65(3):232–9.
- 14. Plimpton S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. Journal of Computational Physics. 1995 Mar;117(1):1–19.
- 15. Sheng HW, Kramer MJ, Cadien A, Fujita T, Chen MW. Highly optimized embedded-atom-method potentials for fourteen fcc metals. Phys Rev B. 2011 Apr 20;83(13):134118.
- 16. Öztürk H, Yan H, Hill JP, Noyan IC. Sampling statistics of diffraction from nanoparticle powder aggregates. J Appl Crystallogr. 2014 Jun 1;47(3):1016–25.
- 17. Debye P. Zerstreuung von Röntgenstrahlen. Ann Phys. 1915;351(6):809–23.
- 18. Warren BE. X-ray diffraction. Dover ed. New York: Dover Publications; 1990. 381 p. ISBN: 978-0-486-66317-3.
- 19. Juhás P, Davis T, Farrow CL, Billinge SJL. PDFgetX3 : a rapid and highly automatable program for processing powder diffraction data into total scattering pair distribution functions. J Appl Crystallogr. 2013 Apr 1;46(2):560–6.
- 20. Trueblood KN, Bürgi HB, Burzlaff H, Dunitz JD, Gramaccioli CM, Schulz HH, et al. Atomic Dispacement Parameter Nomenclature. Report of a Subcommittee on Atomic Displacement Parameter Nomenclature. Acta Crystallogr A Found Crystallogr. 1996 Sep 1;52(5):770–81.
- 21. Dippel A-C, Roelsgaard M, Boettger U, Schneller T, Gutowski O, Ruett U. Local atomic structure of thin and ultrathin films via rapid high-energy X-ray total scattering at grazing incidence. IUCrJ. 2019 Mar 1;6(2):290–8.
- 22. Gilbert B. Finite size effects on the real-space pair distribution function of nanoparticles. J Appl Crystallogr. 2008 Jun 1;41(3):554–62.
- 23. Guinier A. X-Ray Diffraction: In Crystals, Imperfect Crystals, and Amorphous Bodies. Dover Publications, Mineola, NY, USA; 2013. ISBN: 978-0-486-68011-8.
- 24. Huang WJ, Sun R, Tao J, Menard LD, Nuzzo RG, Zuo JM. Coordination-dependent surface atomic contraction in nanocrystals revealed by coherent diffraction. Nature Mater. 2008 Apr;7(4):308–13.
- 25. Xiong S, Lee S-Y, Noyan IC. Average and local strain fields in nanocrystals. J Appl Crystallogr. 2019 Apr 1;52(2):262–73.
- 26. Li group. Least-Square Atomic Strain [Internet]. 2005.
- 27. Stukowski A, Markmann J, Weissmüller J, Albe K. Atomistic origin of microstrain broadening in diffraction data of nanocrystalline solids. Acta Materialia. 2009 Mar;57(5):1648–54. ISBN: 978-0-486-68011-8.
Details
| Primary Language | English |
|---|---|
| Journal Section | Articles |
| Authors | |
| Project Number | BİDEB 2232 International Fellowship of Outstanding Researchers Program (Project no:118C268) |
| Publication Date | May 31, 2022 |
| Submission Date | October 13, 2021 |
| Acceptance Date | March 13, 2022 |
| Published in Issue | Year 2022 Volume: 9 Issue: 2 |
