Old Errors and New Corrections in X-Ray Line Profile Analysis

In recent years there has been an increasing awareness of the errors involved in X-Ray line profile analysis which is used to calculate coherently diffracting particle size, local strains and stacking fault probabilities in materials. Here a modified version of a Least Squares Analysis (L.S.A.) of the Fourier coefficients is presented. This method gives a possibility of making new corrections in a more natural and accurate way to the errors in the line profile analysis.The first error involves the fact that experimentally one accumulates data as a function of θ - the Bragg angle, whereas the Fourier analysis is made in terms of equidistant steps in sin θ, In the L.S.A. the data does not have to be given in equidistant steps of sin θ in order to be analyzed, so that this type of error does not exist at all.In the L.S.A. there is also no need for the explicit separation of the Kαl component from the total doublet line profile. This type of analysis is taken here one step further and it is shown that one can calculate the Fourier coefficients of each one of two merging lines. Each of these lines may be doublets in themselves and the two series of Fourier coefficients are calculated around the centers of gravity of their Kαl components respectively.The existence of an extra background which usually affects the Fourier coefficients when calculated by the Fourier transform method does not affect the L.S.A. except for a normalization factor. Here it is shown that this gives the possibility of calculating the strains without errors associated with the extra background.