A note on elastic scattering from assemblies of particles

The area-averaged distributions for particle assemblies are important both for interpreting the elastic scattering data and for understanding dynamics. The former is shown by deriving an expression to relate the angular distribution of scattered intensity for particles with uniform scattering density and the Fourier transform of the area fraction. The area fraction also appears to play a role in dynamics as the minima of the structure factors for fluidized suspensions and simple liquids are approximately the same as the zeros of the Fourier transform of the area fraction [Singh & Joseph (1995). Int. J. Multiph. Flow, 21, 1-26; Singh (1996). Phys. Rev. E, 53, 5904-5915]. Since the area-fraction zeros (and also the form-factor zeros for particles with uniform scattering density) are in the wavenumber range for which the structure-factor measurements are needed, a deconvolution procedure is required to recover the structure factor from the scattered intensity distribution. The problem associated with the zeros of the form factor can be avoided by modifying the scattering density distribution in the particles such that the modified form factor is nonzero for the desired wavenumber range.