Local monodisperse approximation

When interparticle correlations are involved, the calculation of the intensity function becomes more complex since it involves essentially all interactions between particle 1 with size Xi and particle 2 with size X2, particle 3 with size Xs, and so on. Fortunately, these systems can be approximated by the local monodisperse approximation (LMA), which assumes that particles are surrounded only by other particles of the same size [44]. Following this approximation, the corresponding scattering intensity can be described as... 

For a polydisperse system that contains inter-particle (inhomogeneity) interferences, Eq. (6.34) cannot be used by simple multiplication by the structured factor, as in Eq. (6.33). Although this has been used for significantly narrow distributions [37, 38, 59], there are better ways to properly account for structure in a polydisperse system. One such method, for relatively narrow size distributions, is by using the so-called local monodisperse approximation [60]. This approximation ignores the interference between different sized inhomogeneities and assumes that only like-sized inhomogeneities interact. 

On the other hand, the scattering intensity of the scatterers with a crystal lattice in a thin film, fi, can be expressed as the product of the stmcture factor S(q) and form factor P(q) of the particles under a local monodisperse approximation ... 

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