On multiple small-angle scattering

An analytical approach has been taken for analyzing the multiple scattering effects in small angle scattering (SAS) from both monodisperse and polydisperse systems. Two limiting regions, viz the Guinier region and the Porod region have been studied. A modified form of Guinier law has been deduced for the scattered intensity distribution in the region of small wave vector transfer, q. In the regionq(=|q|)→∞, it is shown that the effect of multiple scattering does not alter the Porod (q ⁻⁴) law. In the case of polydisperse systems, a correlation has been established between the size distribution of the inhomogeneities and the experimentally extractable parameters. The validity of the formalism has been examined by reinterpretation of the multiple SANS data (Hardman-Rhyne and Berk 1985) on polydisperse Al₂O₃ samples. This formalism is useful in characterizing the inhomogeneities from SAS measurements, particularly when thick samples are used.