One of most general diffraction laws, Debye formula, allows to
calculate X-Ray powder diffraction pattern of any cluster of atoms,
with no additional assumptions about its structure. Nowadays computers
enable a direct ('ab initio') calculations of diffraction profiles for
clusters as large as several hundred in diameter, fairly covering
scale of nanomaterials.
Population of atomic models of SiC, GaN and diamond nanocrystals used
for calculations of the diffraction effects were built to examine the
effects of average grain size, grain size distributions, presence of
stacking faults, shape anisotropies, surface strains, bulk strains or
a combination of above. Genetic Algorithm (GA) survives the fittest
individual model, with compliance to experimental data as a fitness
function.
Here we give some examples of X-Ray-based analysis of nanocrystalline
materials and we will concentrate on sensitivity of the method to some
specific structural properties, in particular to determination of
grain size distribution and presence of stacking faults in individual
crystallites.
In this work we will present the method of performance of 'ab initio'
calculations of the diffraction profiles of nanocrystalline powders
which we developed and we present here as rpnano package being a
software tool for X-Ray characterization of nanostructured materials.
Acknowledgements
This work was supported by the State Committee for Scientific
Research, Grants No. 7/T08A/036/18 and 7/T08A/030/19.

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1. Initial abstract
2. 2nd abstract
3. Real Time Characterisation of nanoMaterials
4. Analysis of density waves in CdSe, SiC, and diamond nanocrystals by application of NanoPDF software package to experimental Pair Distribution Functions.
5. Crystallite size determination from diffraction data: a do-it-yourself tutorial.  
6. Diamond-tungsten carbide nanocomposite
7. Reliable XRD characterization in production or high-throughput laboratory regime
8. GaN substrates with variable surface miscut for laser diode applications
9. Semipolar (2021) UV LEDs and LDs grown by PAMBE
10. High-pressure diffraction study of structural and elastic properties of zircon-type and scheelite-type RVO₄ (R = Nd, Eu)
11. Looking at the real structure of nanocrystals with powder diffraction: the apparent lattice parameter approach
12. Localization of rare-earth dopants in the lattice of nanocrystalline ZrO₂ - EXAFS study
13. Looking beyond limitations of diffraction methods of structural analysis of nanocrystalline materials
14. X-ray and electron microscopy techniques studies on nanocrystalline MgO powder materials prepared by sol-gel method
15. Statystyczna analiza deklarowanych kierunków rozwoju nowoczesnych materiałów w projekcie FOREMAT w powiązaniu z tematami polskich prac doktorskich, habilitacyjnych i grantów KBN
16. Error bars in powder diffraction
17. Synthesis of doped ZnO nanopowders in microwave hydrothermal reactors
18. Characterization of nanopowders
19. Combining microwave and pressure techniques for hydrothermal synthesis of ZnO and ZrO₂ nanopowders doped with a range of metal ions
20. Luminescence properties of zinc oxide nanopowders doped with Al ions obtained by the hydrothermal and vapour condensation methods.
21. Structure of nanocrystalline powders of MgO prepared by sol-gel method
22. Microwave technique applied on the hydrothermal synthesis and sintering of calcia stabilized zirconia nanoparticles
23. Yttrium-Aluminum Garnet Synthesized in the Medium of Supercritical Fluids
24. Growth of GaN layers on silicon and sintered GaN nano-ceramic substrates – TEM investigations
25. Doping of ZnO nanopowders with Mn, Ni and Cr In an ultrasound and microwave driver hydrothermal reaction
26. Localization of rare-earth dopants in the lattice of nanocrystalline ZrO₂ - EXAFS study
27. Characterization of nanocrystalline ZrO₂ doped with Rare-Earth elements synthesized via High Pressure Hydrothermal Method
28. Structure studies on nanocrystalline MgO powders prepared by sol-gel method dried under different conditions
29. Morphology of Al doped Zinc Oxide Obtained using Hydrothermal and Vapour Condensation Methods
30. Growth and properties of ytterbium doped KY(WO₄)₂ nanocomposites
31. Doping of ZnO nanopowders with Mn and Cr in an ultrasound and microwave driven hydrothermal reaction
32. Investigations of phase composition and grain size distribution in Pr doped ZrO2
33. Dyfraktometryczna analiza mikro- i makro-naprężeń w spiekach i kompozytach otrzymanych pod wysokim ciśnieniem i wysoką temperaturą.
34. Badania własności termicznych nanokryształów metodami dyfraktometrycznymi
35. Morphology of Al doped zinc oxide obtained by the vapour condensation method
36. Accuracy of XRD size measurements of nanocrystals
37. Morphology of Al-Doped Zinc Oxide Obtained by the Vapour Condensation Methods
38. Structure of nano-crystals: a key to understanding the unique properties of nano-materials
39. Application of XRD diffraction methods for determination of grain size distribution in nanoparticles
40. Fabrication and micro-structure characterization of Al2O3/Ni-P composites with interpenetrating phases
41. Nanocrystalline SiC compacts obtained by sintering of laser synthesized nanopowders under extreme pressures
42. High-pressure Induced Structural Decomposition of RE-doped YAG Nanoceramics
43. Sintering of nanopowders under high pressure
44. Synthesis and properties of GaAs nano-composites
45. MD simulation of atomic structure of nanocrystals
46. SiC-Zn nanocomposites obtained using high-pressure infiltration technique
47. Sintering temperature effect on structure and properties of Al2O3/Ni-P composites with interpenetrating phases
48. Grain Size and Grain Size Distribution of Nanocrystalline Pr-doped Zirconia Powders Obtained in High Pressure Microwave Reactor
49. Influence of synthesis conditions on the particles size and the morphology of zinc oxide nanopowders
50. Measuring the Grain Size Distribution of Pr-doped Zirconia Nanopowders obtained by Microwave Driven Hydrothermal Synthesis
51. Structural and luminescence properties of yttrium-aluminum garnet (YAG) nanoceramics
52. Fabrication and electrical properties of Eu³⁺:BaTiO₃ nanoceramics for SOFC
53. Analytical expression for Diffraction Line Profile for polydispersive powders
54. FW1/5-4/5M method for determination of the Grain Size Distribution from powder diffraction line profile
55. Dyfrakcyjne badania mikrostruktury polikryształów nanometrowych poddawanych działaniu wysokiego ciśnienia
56. X-ray diffraction studies of thermal properties of bulk- and surface-atoms of nanocrystalline SiC
57. Characterization of nanostructured hydroxyapatite ceramics densified at high-pressure and temperature
58. Powder precursors for nanoceramics: cleaning and compaction
59. Examination of the atomic Pair Distribution Function (PDF) of SiC nanocrystals by in-situ high pressure diffraction
60. Investigation of the microstructure of SiC-Zn nanocomposites by microscopic methods: SEM, AFM and TEM
61. Sythesis of metal-ceramic nanocomposites by high-pressure infiltration
62. X-Ray investigations of the natural and artificial White Etching Layer
63. Zinc oxide nanopowders obtained by the microwave-hydrothermal route
64. Microwave driven hydrothermal synthesis of Pr-doped zirconia nanopowders
65. The influence of temperature and pressure on possibility of obtaining Al₂O₃/Ni-P nanocomposite through hot pressing process.
66. Precise determination of full Grain Size Distribution from diffraction peak profile as a result of kinematical theory of diffraction for polidispersive nanomaterials
67. Generetion and Relaxation of Strain in SiC and GaN under Extreme Pressure
68. Surface Diffraction Effects from Nanopowders under Pressure
69. Influence of high pressure on the polytype structure of nanocrystalline GaN
70. Transformation of fractal microstructure of nanocrystalline SiC and diamond in high pressures - Small Angle Scattering Study
71. Synthesis of Nanocomposites Based on Superhard Ceramic Nanopowders