Broadening Microstructure Analysis Program(BMAP): an isotropic and anisotropic crystallite size and strain calculator

Abstract

BMAPcalculator is a simplified software tool to obtain microstructure characteristics and to investigate their isotropic and anisotropic nature using some common broadening methods. The Scherrer and Stokes–Wilson methods as well as the Williamson–Hall plot (microstructure isotropy) and modified Williamson–Hall models (strain anisotropy) are implemented in the calculations. TheBMAPinput data are the X-ray diffraction peak parameters (the full width at half-maximum or integral breadth and peak position) of a measured line profile and of a reference one. The components of the measured line profile or corrected broadening are based on several approximations (Cauchy, Gauss or Voigt). The linear least-squares fit is used to calculate the size–strain values, and the correlation coefficient for accepting the results. The calculator is applied to an X-ray diffraction experiment of NiO nanoparticles prepared by a sol–gel method for testing. The results ofBMAPcalculator and theMAUDprogram, combined with an anisotropic Popa rules approach, are compared. The uniform stress model based on the Cauchy approximation is the most suitable one in cubic nanostructure nickel oxide, with an average crystallite size of 24 nm and anisotropic strains of 1.54 × 10−3, 0.61 × 10−3, 1.77 × 10−3and 1.49 × 10−3using the {111}, {200}, {220} and {311} reflections, respectively. Generally, for non-Rietveld users, it is useful to collect different methods into one program to depict the anisotropic nature of materials.