It is known that the micro-strain in cold worked iron can be evaluated by the classical Williamson-Hall method using the three data of diffraction peaks: {110}, {211} and {220}. It is not clarified that the obtained value gives the true micro-strain or not. In addition, the accuracy of analysis is not so high because the diffraction strength from {220} plane is generally very weak. In this paper, three methods, i.e. classical Williamson-Hall method, Diffraction Young's Modulus Correction method and Direct Fitting method, ware attempted to reconfirm the reasonability of the classical Williamson-Hall method and to estimate accurate values of the parameter α and the micro-strain ε in the Williamson-Hall equation. The results obtained are as follows: 1) Elastic anisotropy in the Williamson-Hall plots is corrected using the parameter ω which relates to the values of diffraction Young's modulus. 2) The optimal values of parameter ω can be determined by the Direct Fitting method, which can be used to determine the timely orientation-dependent diffraction Young's modulus (E * hkl) in cold worked specimens. 3) It was confirmed that the classical Williamson-Hall method can generally give reliable values for the parameter α and the microstrain ε. 4) No large difference is found for the values of micro-strain ε from the three methods. 5) There is a clear linearity between the micro-strain ε and yield stress in cold rolled iron specimens.
Williamson-Hall (WH) plots are characterized by irregular arrangement of data due to the elastic anisotropy in each {hkl} plane. In order to correct the effect of elastic anisotropy, Ungár developed a unique methodology using the contrast factor C, so called the modified Williamson-Hall (mWH) method. When X-ray with the wave length λ was used for diffraction analysis and diffraction angle θ and integral breadth β was obtained in each diffraction peak, the following mWH equation is constructed as functions of the parameter K (= 2sinθ/λ) and ΔK (= βcosθ/λ).
X-ray diffraction is a powerful tool for characterizing the microstructure of steels. However, the strained surface by mechanical grinding could cause some errors in X-ray diffraction analysis. In this work, the strained layer was found to affect peak intensity, peak positions and enlarge the full width at half maximum. A quantitative relation between the depth of damaged layer and particle size of sander papers was established.
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