Proposal of Analysis Accuracy Improvement Method in Modified Williamson-Hall Method

Abstract

In the dislocation characterization using radiation diffraction, the modified Williamson-Hall (mWH) method gives the parameter α, ϕ and q, in which the information about crystallite size, dislocation density and the character of dislocation are contained respectively. The following mWH equation is applied to determine these parameters in the mWH method.

(ΔK－α)²/K ²＝ϕ²C_h00(1－qΓ )

In the mWH method, the optimal α–value is selected to give the best linear fitting on the above mWH equation. Putting the optimal α-value into the mWH equation, the other parameters ϕ and q are automatically determined in the relation between the left side term and the orientation parameter Γ. The original mWH equation is expressed by the following equation, hence the values of ΔK can be calculated on each {hkl} crystal plane applying the obtained values for parameter α, ϕ and q.

ΔK＝α＋ϕK√C, here C＝C_h00(1－qΓ )

As a result, the Williamson-Hall (WH) plots; K vs. ΔK are constructed by the calculation and they are compared with those obtained by experimentally. After that, the values of full width at half maximum are corrected to minimize the error between experimental and calculated WH plots. This process is termed as the modified Williamson-Hall feed-back (mWHFB) method. It was confirmed that the accuracy of dislocation analysis is greatly improved by applying the mWHFB method in comparison with the conventional mWH method.