Significance of diffraction peak shapes in determining crystallite size distribution: a peak shape analysis procedure for pseudo-Voigt profiles and its application

The width (or breadth) and shape of a diffraction peak are two important characteristics to describe a peak profile. These features are directly associated with the microstructural (size and strain) properties of a material. It is important to separate the contributions of crystallite size and microstrain from the diffraction peak profiles in order to establish their correlation with the physical properties of the sample. While procedures to deconvolve the widths of a diffraction peak profile are extensively documented in the literature, the shape part of the peak profile is usually ignored. In the present work an approach for a quantitative estimation of the peak shape contribution made by crystallite size is discussed to complement the information available via the existing breadth-based methods (BBMs). A relationship between the shape of a diffraction peak profile and the crystallite size distribution for a nanomaterial is presented, which was not hitherto available in the literature. It is shown that the commonly observed difference between crystallite sizes obtained using the Scherrer equation considering two different definitions of peak width, i.e. full width at half-maximum and integral breadth, is also associated with this peak shape parameter. Thus, knowledge of the peak shape has a vital role in microstructural understanding. Therefore, in this work a procedure to isolate the shape part of a diffraction peak profile is described in connection with the existing BBMs used for microstructural analysis. This study further aims to utilize the information on these peak shapes to provide comprehensive details of the effect of crystallite size by considering a log-normal distribution to complement the BBMs. Applications of this approach are shown using several worked examples of practical situations from the literature.