Aluminium sheet of thickness 1mm is deformed with various process to compare the dislocation density.
You can go through these previous discussions:
https://www.researchgate.net/post/How_can_i_calculate_dislocations_density_from_the_XRD_patterns2
https://www.researchgate.net/post/How_to_determine_the_dislocation_density_by_XRD_and_subsequent_analysis
Dear Simson Daniel,
Both original and modified "Williamson-Hall (W-H) analyses" are conducted to attain the internal strain/dislocation density information from the broadening of diffraction peaks.
Here, the original W-H method, the breadth of diffraction peaks was interpreted to be from the combined effect of internal strain and grain size:
βcosθ = Cεsinθ + Kλ/D
where,
β = breadth of a specific reflection peak,
θ = diffraction angle,
ε = internal strain,
λ = wavelength of the photon,
D = average grain size,
C and K are adjustable constants.
Comparing this to the standard equation for a straight line.
y = mx + c
where,
m = slope &
c = intercept.
The slope of the plot βCosθ vs Sinθ yields (Cε) strain & the intercept gives Kλ/D.
In addition, you can use "Cauchy-Gaussian" equation for measuring crystallite size and strain.
Also, for use williamson hall plot of xrd to calculate dislocation density of deformed sheet metal following research articles and link is given.
Kindly go through the same for better understanding.
01. Article X-Ray Line Broadening from Filed Aluminum and Wolfram
02. Article The Effect of Dislocation Contrast on X-ray Line Broadening:...
03. http://prism.mit.edu/xray/oldsite/5a%20Estimating%20Crystallite%20Size%20Using%20XRD.pdf
04. https://www.researchgate.net/post/Which_method_is_better_for_calculating_the_dislocation_density_by_XRD#view=5b7072afe29f82345c1d7cce
I hope I have answered your question.
With Best Wishes,
Samir G. Pandya
You can also refer this paper for Al-alloys
Article Characterization of Microstructure, Mechanical Properties an...
Simson D The dislocation density is a measure of the number of dislocations in a unit volume of a crystalline material i.e. the length of dislocation lines per unit volume of the crystal (m/m3) Edge dislocation Screw dislocation Dislocations distort a crystal lattice, causing elastic stress around the dislocation line, & hence strain energy. For ultimate strength, dislocations are to be eliminated.
In this video, I have discussed the nature of dislocation density and how to calculate the dislocation density from XRD using origin. In the case you want to further ask about it, please do comment on the specific video, I'll respond to it shortly. I have provided the practice as well as calculations files here. Thanks
https://youtu.be/WyvwytYYSK8
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