Calculate Dislocation from Williamson-Hall Plot

[murphyberger]

I would like to calculate the dislocation from the WH plot. I have HRXRD mesurement results with (004),(111) and (115) for omega and omega-2theta. Please someone guide me how to do?

 

[sfarrel2]

The williamson hall plot is rather simple to do.

Simply plot the FWHM of your rocking curves vs Tan^2(\theta)

Where theta is your bragg angle.




You are also going to have to subtract out some of the information that is burried with in the FWHM. This includes:Instrument broadening,Intrinsic FWHM, Sample Curvature broadening,etc.

 

[oswaler]

To calculate the dislocation from a Williamson-Hall plot, you will need to use the formula:

β^2 = β0^2 + (4επλ)sin^2θ

Where β is the full width at half maximum (FWHM) of the peak, β0 is the instrumental broadening, ε is the strain, λ is the X-ray wavelength, and θ is the Bragg angle.

To begin, you will need to plot your FWHM values for each peak (004, 111, and 115) against the sin^2θ values. This will give you a straight line on a graph, known as the Williamson-Hall plot.

Next, you will need to determine the slope of the line, which corresponds to the strain (ε) in the material. The intercept of the line with the x-axis (sin^2θ = 0) corresponds to the instrumental broadening (β0).

Using the values for ε and β0, you can then calculate the dislocation density (ρ) using the formula:

ρ = (4ε)/b^2

Where b is the Burgers vector, which can be determined from the lattice spacing of the material.

It is important to note that this method assumes a uniform distribution of dislocations throughout the material. If this is not the case, additional corrections may need to be applied to the data.

I hope this helps guide you in calculating the dislocation from your Williamson-Hall plot. If you require further assistance, please consult with a materials science expert or refer to relevant literature on the topic.