Dear @Sangram Keshari Mohanty,

To obtain the data values for a Halder-Wagner plot or a Williamson-Hall plot after performing Rietveld refinement in PDXL2 software, follow these steps:

1. Perform Rietveld Refinement:

Complete the Rietveld refinement in PDXL2 using your powder XRD data. Ensure the refinement provides accurate peak profile parameters, as these are essential for strain and crystallite size analysis in the subsequent steps.

2. Extract Peak Broadening Parameters:

After Rietveld refinement, look for peak broadening parameters such as FWHM (Full Width at Half Maximum) or integral breadth of each peak. These values are critical for both Halder-Wagner and Williamson-Hall analyses.

In PDXL2, go to the "Results" section to find refined values for each peak.

3. Identify and Note Reflection Angles (2θ) and Broadening Values:

Record the 2θ values and corresponding peak broadening values for each diffraction peak. PDXL2 typically provides these in the peak list or profile fit results.

4. Calculate Williamson-Hall Plot Data:

For a Williamson-Hall plot:Calculate the strain (ε) and crystallite size (D) using the equation:

βcos⁡θ = kλ/D + 4ϵsin⁡θ

where β is the peak broadening, θ is the Bragg angle, k is a constant (usually 0.9), and λ is the wavelength of the X-ray source.

Plot β cos θ versus 4 sin θ using the extracted data.

5. Calculate Halder-Wagner Plot Data:

For a Halder-Wagner plot:Use the equation:

β²cos⁡²θ/sin⁡θ = k²λ²/D² + ϵ² sin⁡θ

which separates strain and crystallite size contributions more effectively than the Williamson-Hall method.

Calculate values for β²cos⁡²θ/sin⁡θ and sin⁡θ.

6. Export or Record Data:

To export data from PDXL2:Go to File > Export > Data and select the relevant parameters if the software allows.

Alternatively, manually record each 2θ, β, β cos θ, 4 sin θ, or β²cos⁡²θ/sin⁡θ values for plotting.

7. Plotting:

Use software like Excel or Origin to generate the Halder-Wagner or Williamson-Hall plots by inputting the calculated data.

These plots help in assessing the microstrain and crystallite size of materials by analyzing the slope and intercept of the linear fit to the data.