Small-Angle X-Ray-Scattering Investigation of Submicroscopic Porosity with Fractal Properties

Abstract

A method is developed for analyzing the outer part of the small-angle x-ray or neutron

Combined SANS and SAXS study of the action of ultrasound on the structure of amorphous zirconia gels

“…Bale and Schmidt [57] proposed a more exact criterion for a certain characteristic size of inhomogeneities: q min R  3.5.…”

“…Bale and Schmidt [57] have also shown that for porous materials in which the interfaces are surface fractals with a fractal dimension 2 ≤ D s < 3, the scattering intensity depends on the momentum transfer in a power law form:…”

Small-angle x-ray-scattering study of phase separation and crystallization in the bulk amorphousMg62Cu25Liu1, Johnson2, Schneider3 et al. 1999Phys. Rev. B

“…20 The fractal nature of the system can be delineated from the power-law exponents derived from the scattering data. [21][22][23] If I(Q) varies as Q Ϫp in a Q region, where QR g ӷ1, then pϽ3 denotes that the scattering system may be a mass fractal 22,23 and 3ϽpϽ4 corresponds to a surface fractal. 21 The fractal dimension of the surface, D s , is D s ϭ6Ϫp.…”

“…[21][22][23] If I(Q) varies as Q Ϫp in a Q region, where QR g ӷ1, then pϽ3 denotes that the scattering system may be a mass fractal 22,23 and 3ϽpϽ4 corresponds to a surface fractal. 21 The fractal dimension of the surface, D s , is D s ϭ6Ϫp. 21 The extent of deviation of p from 4 can be used as a qualitative measure of the surface roughness.…”

“…21 The fractal dimension of the surface, D s , is D s ϭ6Ϫp. 21 The extent of deviation of p from 4 can be used as a qualitative measure of the surface roughness. The prefactor I(0)ϭNV 2 (⌬ ) 2 , 24 where N is the number of particles per unit volume, V is the volume of the particle, and ⌬ is the difference in the electron density between the particles and the matrix.…”