Crystallite size and micro-strain analysis
Line profile and peak shape
Line profile analysis or peak shape analysis are used to determine the average crystallite size and lattice strain of nanocrystals from X-ray diffraction (XRD) data. Understanding such microstructural properties leads to control of the material’s physical, mechanical and chemical properties.
Although crystallite size-strain analysis is mostly done on nanocrystals in powder materials, it can also be applied to nanocrystals in thin films.
A polycrystalline material with no lattice strain and crystallites larger than approximately 500 nm show sharp peaks in a powder diffractogram. A broadening of the diffraction peaks can be caused by:
- small crystallite (domain) size, below 500 nm
- lattice strain
- defects in the crystal lattice
Analysis of peak broadening can provide information on the microstructure of the sample and its treatments such as cold rolling, thermal treatment or milling. Methods can range from simple evaluations, such as the Scherrer method which analyzes single diffraction peaks, to more advanced evaluations based on the analysis of the width and shape of multiple diffraction peaks as a function of the diffraction angle.
PANalytical solutions for size-strain analysis
The Empyrean, X'Pert³ Powder, X'Pert³ MRD (XL) diffraction systems deliver data for size-strain analysis when configured for XRD measurements in reflection, transmission or grazing incidence geometry. The CubiX³ system with Bragg-Brentano reflection geometry can also be used for size-strain analysis.
The HighScore Plus and HighScore software packages offer multiple options for profile fitting and size strain-analysis:
- Scherrer calculator (analysis of a single peak width)
- Single line method (analysis of a single peak profile fit)
- Williamson-Hall method (analysis of multiple peak profile fits)
- Size-strain analysis within a Rietveld refinement (analysis of a full pattern fit); HighScore Plus only