Separation of Coherently Diffracting Domain Size and Micro Strain by X-Ray Line Profile Analysis

Abstract

It has been shown by Warren and Averbach that the coherently diffracting domain size and the micro strain contributions to the broadening of the line profile can be separated by application of Fourier series method. However, this method requires at least two orders of the same reflection which are not necessarily obtained in many cases. Garrod and Auld, Krishnan et al. have suggested, and carried out, to separate the domain size and the micro strain by application of the approximation method which can be analysed from a single reflection only.In the present study, the value of the domain size and the micro strain obtained from a single reflection only were compared with those obtained by the Warren and Averbach method, by using (111), (222), (200) and (400) reflections of electrodeposited nickel. Moreover, the results obtained by Fourier series method were compared with those obtained by the half-value breadth method.The results obtained are summarized as follows.(1) The domain size on (111), (20) reflections, determined from the intercept of -lnAL/L vs. L where e>>L, agree with those obtained by Warren and Averbach method within the experimental errors, but it is found not to be possible to determine the domain size on (222), (400) reflections.(2) It is found to be possible to determine the domain size on the first and the second order reflection from-(dALdL)L→0=1/ e, where L→0, ADL, l0≅1 and the results approximate comparatively to those obtained by Warren and Averbach method within the experimental errors.(3) It is found that the mean value of the r.m.s. strain calculated by equations and approximate comparatively to those obtained by Warren and Averbach method except for the large L values of (111), (200) reflections.(4) Comparing the domain size and the micro strain obtained by the half-value breadth method and Warren and Averbach method, the half-value breadth method gives the larger value for the domain size and also shows a little larger value for the micro strain, when the r.m.s. strain obtained by Warren and Averbach method are considered over the average domain size.