Modified Williamson-Hall Plot (MWHP) Method:

After introducing the dislocation contrast factor into WHP formula, the equation turns out to be

where, D_U = crystallite size; ρ=dislocation density; C = C_hkl = dislocation contrast factor; b = Berger vector of dislocation; B = constant; θ_B = Bragg angle in degrees; Δθ_B = FWHM in radians; λ = wavelength of X-rays =1 .54056Å ); q = constant.

Figure 5.05: Analysis of XRD data using MWHP method after including dislocation contrast factor [4].

Figure 5.05 shows the analysis of XRD data using MWHP method after including the dislocation contrast factor. It is clear from the figure that all the data points fall in a straight line without much deviation. Hence, the average crystal size and dislocation density causing strain in the sample can be determined from the slope and intercept of the straight line fit, respectively.

Ref.[4]: T. D. Shen et al, Physical Review B 72 (2005) 014431.