An analytical expression for the diffraction line profile for polydispersive powders (particularly, nanopowders) with Gamma Grain Size Distribution is derived. The expression consists of elementary functions only and can readily replace standard functions (like Gaussian, Lorentzian or Pearson) for diffraction peak fitting purposes. This allows for direct Grain Size Distribution determination using standard fitting software.

X-ray diffraction is a well established experimental method sensitive to both (i) crystal structure, (ii) size and shape of the crystallites. The latter property of diffraction is especially appreciated in case of nanocrystals, when small size of the objects makes diffraction techniques a feasible tool for crystallite size determination. Theory of powder diffraction describesa diffraction pattern as a set of diffraction peaks (located in reciprocal space according to Bragg law, with intensities defined by the structure factor) convoluted with some line profile (defined by crystal shape and size). An analytical formula for the line profile for spherical crystallites of same size (monodispersive powder) was given by Wilson 1. Later, similar formulas were given for other crystallites shapes 2,3,4. In the present paper formula for line profile for polydispersive powder consisting of spherical grains with the Gamma Grain Size Distribution (GSD) is presented.

Applied Crystallography, Proceedings of the XIX Conference, World Scientific, pp.43-50

1. FULLTEXT: Analytical expression for Diffraction Line Profile for polydispersive powders, PDF document, version 1.3, 0.4MB

• Legal notice:
  

  Copyright (c) Pielaszek Research, all rights reserved.
  The above materials, including auxiliary resources, are subject to Publisher's copyright and the Author(s) intellectual rights. Without limiting Author(s) rights under respective Copyright Transfer Agreement, no part of the above documents may be reproduced without the express written permission of Pielaszek Research, the Publisher. Express permission from the Author(s) is required to use the above materials for academic purposes, such as lectures or scientific presentations.
  In every case, proper references including Author(s) name(s) and URL of this webpage: https://science24.com/paper/1296 must be provided.

1. Initial abstract
2. 2nd abstract
3. Real Time Characterisation of nanoMaterials
4. Reliable XRD characterization in production or high-throughput laboratory regime
5. Localization of rare-earth dopants in the lattice of nanocrystalline ZrO₂ - EXAFS study
6. X-ray and electron microscopy techniques studies on nanocrystalline MgO powder materials prepared by sol-gel method
7. Statystyczna analiza deklarowanych kierunków rozwoju nowoczesnych materiałów w projekcie FOREMAT w powiązaniu z tematami polskich prac doktorskich, habilitacyjnych i grantów KBN
8. Error bars in powder diffraction
9. Characterization of nanopowders
10. Structure of nanocrystalline powders of MgO prepared by sol-gel method
11. Microwave technique applied on the hydrothermal synthesis and sintering of calcia stabilized zirconia nanoparticles
12. Localization of rare-earth dopants in the lattice of nanocrystalline ZrO₂ - EXAFS study
13. Characterization of nanocrystalline ZrO₂ doped with Rare-Earth elements synthesized via High Pressure Hydrothermal Method
14. Structure studies on nanocrystalline MgO powders prepared by sol-gel method dried under different conditions
15. Morphology of Al doped Zinc Oxide Obtained using Hydrothermal and Vapour Condensation Methods
16. Investigations of phase composition and grain size distribution in Pr doped ZrO2
17. Morphology of Al doped zinc oxide obtained by the vapour condensation method
18. Accuracy of XRD size measurements of nanocrystals
19. Morphology of Al-Doped Zinc Oxide Obtained by the Vapour Condensation Methods
20. Application of XRD diffraction methods for determination of grain size distribution in nanoparticles
21. Grain Size and Grain Size Distribution of Nanocrystalline Pr-doped Zirconia Powders Obtained in High Pressure Microwave Reactor
22. Measuring the Grain Size Distribution of Pr-doped Zirconia Nanopowders obtained by Microwave Driven Hydrothermal Synthesis
23. FW1/5-4/5M method for determination of the Grain Size Distribution from powder diffraction line profile
24. Dyfrakcyjne badania mikrostruktury polikryształów nanometrowych poddawanych działaniu wysokiego ciśnienia
25. Precise determination of full Grain Size Distribution from diffraction peak profile as a result of kinematical theory of diffraction for polidispersive nanomaterials
26. X-Ray Characterization of Nanostructured Materials
27. Generetion and Relaxation of Strain in SiC and GaN under Extreme Pressure
28. Influence of high pressure on the polytype structure of nanocrystalline GaN
29. Transformation of fractal microstructure of nanocrystalline SiC and diamond in high pressures - Small Angle Scattering Study