Profile Function of Bragg Reflections in Powder Diffraction

The profile function of the Bragg reflection is composed of the contributions of the apparent size and shape of the crystallites, of the strain and of the instrument function. The contribution of the strain is obtained from the displacement distribution of the unit cells. The apparent shape and size of the crystallites and the anisotropy of the strain are presented in terms of spherical harmonics, which are adapted to the symmetry. The apparent crystallite shape and size and strain of Mo (body-centred cubic) and PbBr₂ (orthorhombic) are determined from powder diffraction pattern measurements. The calculated line profiles agree closely with the measurements and only a few spherical harmonic terms are needed.