Reliability of the Simplified Integral-Breadth Methods in Diffraction Line-Broadening Analysis

A comparison between different simplified integral-breadth methods, often used in the Rietveld-refinement programs to calculate coherent domain size and lattice strain, is carried out. It is shown that systematic differences exist for both domain size and strain, when they simultaneously broaden diffraction lines. Among different approximations, the values of domain size exceptionally scatter and sometimes are completely false (negative or not real). A comparison to the alternative Fourier method shows that all the simplified integral-breadth methods overestimate domain size, but especially the Cauchy-Cauchy approximation. The root-mean-square strain and the upper limit of strain are related in the general case of the Voigt strain-broadened line profile. It is shown that they should not differ much as the profile changes between the Gauss and Cauchy extremes. The pure-Gauss size-broadened profile is incompatible with the definitions of surface-weighted domain size and column-length distribution function.