Manifestation of the statistical nature of a medium in multiple small-angle scattering

It has been emphasized in the recent past that the beam-broadening feature of multiple scattering can be used to investigate large inhomogeneities which are otherwise inaccessible by means of small-angle scattering due to the inherent resolution constraint. However, the treatment of data on multiple small-angle scattering from a polydisperse sample needs more critical evaluation. As multiple small-angle scattering deals with large inhomogeneities, the scattering mean free path L may not be appreciably large in comparison to the linear dimension R of the inhomogeneities for many systems. When L >> R , the scattering medium can be treated in a mean-field way and such a medium has been termed an `effective medium'. But when the condition L >> R does not hold, the statistical nature of the medium is manifested. The manifestation is a modulation of the multiple-scattering profile compared with that from an effective medium. In the present paper, we report for the first time an experimental demonstration of the manifestation of the statistical nature of the medium in an experiment based on multiple small-angle neutron scattering on sintered alumina with varying sample thickness. The effect of the statistical nature of the medium has been observed for L / R >1000.