I'd like to know how to calculate the dislocation density for metal with grain size > 1um
Hi Suho,
Calculating dislocation density in a metal with a grain size larger than 1 micron (μm) can be more challenging and is not always straightforward. This is because dislocations interact in a different way than in materials with smaller grain sizes. Dislocation density is often quantified using methods such as X-ray diffraction (XRD) or transmission electron microscopy (TEM).
1. X-ray diffraction can be used to estimate the average dislocation density in a polycrystalline metal. The dislocation density (ρ) can be related to the full-width at half-maximum (FWHM) of the diffraction peaks using the Williamson-Hall equation: ρ = (4 * K) / (λ * β * cos(θ)) Where:
K is a constant related to the dislocation character (typically around 0.94 for pure metals).
λ is the X-ray wavelength.
β is the FWHM of the diffraction peak.
θ is the Bragg angle.
Keep in mind that this equation provides an average dislocation density and doesn't differentiate between grain boundaries and dislocations within grains.
2. Transmission Electron Microscopy (TEM) can provide more detailed information about dislocation arrangements within individual grains and at grain boundaries. This technique involves preparing thin TEM samples and using high-resolution imaging to directly visualize dislocations.
Remember that the above methods mentioned provide approximate estimates and might require careful calibration and validation.
Hope this helps,
Kind regards
Dear Suho Song ,
Hope this articles will help!
Article X-ray line profile analysis of the deformation microstructur...
Article X-ray line profile analysis on the deformation microstructur...
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Dear Suho Song,
a conventional approach to acquiring information on the dislocation density of any material is given by the Wilkens model. This model requires the knowledge of the edge and screw dislocation types present in your case, which are often tabulated or can be simulated. This approach also allows the obtention of fractions between the types of dislocation of the material. However, it is important to have a rough initial estimation of the dislocation density value, in the outer-cutoff radius where the dislocation takes place in the crystal, as well as the burgers value of the given slip system. The Wilkens model falls under the scope of the Whole Powder Pattern Modelling (WPPM) available in the conventional tools of the Total Pattern Analysis Software (TOPAS) or the PM2K software. The advantage of the WPPM relies on the complete disregard for synodal functions for the peak shape fitting and the physical information from the Wilkens model provides some physical restraints for the refinement.
The downside of the XRD techniques for solving this kind of problem is that they often overestimate the quantity of dislocation present. Although, the value retrieved by the Wilkens approach might serve as a scale and be useful when comparing different materials.
I place here below three references that might help in your research work:
https://doi.org/10.1107/S160057671801289X
https://topas.awh.durham.ac.uk/doku.php?id=wppm_macros
https://www.researchgate.net/publication/230824177_PM2K_A_flexible_program_implementing_Whole_Powder_Pattern_Modelling
To employ these techniques, the instrumental resolution function must be carefully modelled by a standard material (e. g. LaB6 or Si), once the effect of any microstructural feature is also present in the peak breadth.
With regards,
Marcelo.
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