Dislocation characterization by the direct-fitting/modified Williamson–Hall (DF/mWH) method in cold worked ferritic steel

X-ray diffraction is a powerful tool for dislocation characterization, which includes evaluation of dislocation distribution, nature of dislocation, and dislocation density. In the Williamson–Hall (WH) plots, the full width at half maximum (FWHM) is plotted relative to the diffraction angle for each diffraction peak and the method corresponds to the basic approach for dislocation characterization. However, the elastic anisotropy in each crystal plane makes the analysis of WH plots difficult because elastic anisotropy also affects the FWHM of diffraction peaks. In order to correct the effect of elastic anisotropy, Ungár developed a unique methodology by using the contrast factor C, and this is termed as the modified Williamson–Hall (mWH) method. Conversely, researchers developed a new methodology termed as the “direct-fitting (DF) method,” in which the elastic anisotropy is corrected by directly applying the diffraction Young’s modulus ratio (ω). In the DF method, a linear relation is realized in the corrected WH plots, and reliable values are obtained for the parameter α that contains information on the crystallite size. In the present study, the α-value obtained using the DF method was applied to the mWH equation, and dislocation characterization was performed in a low carbon ferritic steel (Fe-0.0056%C) by cold rolling. The results indicated that increasing the extent of cold rolling decreases the screw component of dislocation, and monotonically increases the parameter φ (which contains the information of dislocation density). Additionally, the parameter A (which depends on the dislocation arrangement) was evaluated at approximately 0.50 for cold worked ferrite.