The effect of the shape function on small-angle scattering analysis by the maximum-entropy method

Abstract

Analysis of small‐angle scattering data to obtain a particle‐size distribution is dependent upon the shape function used to model the scattering. From a maximum‐entropy analysis of small‐angle scattering data, the effect of shape‐function selection on the obtained size distribution is demonstrated using three different shape functions to describe the same scattering data from each of two alloys. The alloys have been revealed by electron microscopy to contain a distribution of randomly oriented and mainly noninteracting irregular ellipsoidal precipitates. A comparison is made between the different forms of the shape function. The effect of an incident‐wavelength distribution is also shown. The importance of testing appropriate shape functions and validating these against other microstructural studies is discussed.

Small-angle neutron scattering investigation on pore growth in nickel-aluminide during SHS: Effect of heat removal

“…However, in all practical situation, as there are various modulations on the surfaces of the ellipsoidal pores, the pores can be viewed as globules and the form factor can be well approximated as [24]:…”

“…where χ(β) is a function of only β [24]. D(R) represents the pore size distribution and for a lognormal distribution:…”

SANS investigation on pore growth in self propagating high-temperature-synthesized nickel aluminide: the effect of heat removal

“…The extracted single scattering profile (SSP) for each specimen have been analyzed with respect to a polydisperse globular particle model [6].…”

Multimodal Particle-Size Distribution or Fractal Surface of Acrylic Acid Copolymer Nanoparticles: A Small-Angle X-ray Scattering Study using Direct Fourier and Indirect Maximum-Entropy Methods

“…In small-angle scattering, the maximum-entropy method has previously been used for estimation of distance distribution functions (Hansen & Pedersen, 1991;MOiler & Hansen, 1994) and size distributions (e.g. Potton, Daniell & Rainford, 1988;Morrison, Corcoran & Lewis, 1992;Jemian & Allen, 1994).…”