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Presents a polydisperse analysis of absolute small-angle intensities scattered by activated carbons. Description of the analyzed samples and absolute intensities; Assumptions and description of the model; Calculation of the corresponding specific surfaces and densities of the samples.

Deals with a study which analyzed small-angle x-ray intensities scattered by natural coals, assuming that coals behave as polydisperse distributions of cubic particles. Comparison between fractality and polydispersity; Evaluation of the particle form factors; Discussion of the dependence of particle form factors on the interlayer spacing.

A rather detailed report is presented on the present status of the algebraic approach to the phase problem in the case of an ideal crystal in order to make clear that some points must still be proven for it to apply to neutron scattering. To make this extension, the most important results that were previously obtained in the case of X-ray scattering are derived again by a different procedure. By so doing, the three-dimensional case is treated explicitly, the polynomial equations in a single variable whose roots determine the positions of the scattering centres are explicitly reported and the procedure is shown to generalize to neutron scattering, overcoming the difficulty related to the non-positivity of the scattering density. In this way, it is fully proven that the atomicity assumption removes the phase ambiguity in the sense that the full diffraction pattern of an ideal crystal can uniquely be reconstructed from a suitable finite portion of it in both X-ray and neutron scattering. The procedures able to isolate these portions that contain the pattern's full information are also given. [ABSTRACT FROM AUTHOR]

Investigates the autocorrelation function of a finite particle with the shape of a right cylinder by the autocorrelation function of the particle right section. Proof of the first part of the statement and the second part of the statement; Solution to integral relation.

Reports on the determination of the thickness of a film deposited on a porous sample by comparing the tail behavior of the relevant small-angle scattering intensity with that predicted on the basis of some theoretical models of the film structure. Analysis of the small-angle scattering intensities of a set of samples obtained by coating, via an evaporative technique.

Presents a simple derivation of the leading asymptotic term of small-angle scattering intensities relevant to anisotropic particulate samples. Anisotropic Porod law; Scattering intensities collected by two-dimensional detector.

Shows that the Porod coefficient is proportional to the sum of the reciprocal Gaussian curvatures at all the points of the interface where the normals are either parallel or antiparallel to the direction of the considered scattering vector. Generalization of the results to particles with non-convex surfaces; Three kinds of q-tangency points.

Reports that the integral expressions of the derivatives of the small-angle scattering correlation function are obtained in terms of the parametric equations of the interphase surfaces. Integral expression for each derivative; Limiting values of the derivatives of the correlation function.

An algebraic approximation, of order K, of a polyhedron correlation function (CF) can be obtained from γ''(r), its chord-length distribution (CLD), considering first, within the subinterval [D i-1 , D i ] of the full range of distances, a polynomial in the two variables (r - D i-1 ) 1/2 and (D i - r) 1/2 such that its expansions around r = D i-1 and r = D i simultaneously coincide with the left and right expansions of γ''(r) around D i-1 and D i up to the terms O(r - D i-1 ) K/2 and O(D i - r) K/2 , respectively. Then, for each i, one integrates twice the polynomial and determines the integration constants matching the resulting integrals at the common end-points. The 3D Fourier transform of the resulting algebraic CF approximation correctly reproduces, at large q's, the asymptotic behaviour of the exact form factor up to the term O[q -(K/2+4) ]. For illustration, the procedure is applied to the cube, the tetrahedron and the octahedron.

The chord-length distribution function [γ''(r)] of any bounded polyhedron has a closed analytic expression which changes in the different subdomains of the r range. In each of these, the γ''(r) expression only involves, as transcendental contributions, inverse trigonometric functions of argument equal to R[r, Δ 1 ], Δ 1 being the square root of a second-degree r polynomial and R[x, y] a rational function. As r approaches δ, one of the two end points of an r subdomain, the derivative of γ''(r) can only show singularities of the forms |r - δ| -n and |r - δ| -m+1/2 , with n and m appropriate positive integers. Finally, the explicit analytic expressions of the primitives are also reported.

The form of a particle, which is homogeneous, finite, strictly convex, smooth and centrosymmetric, can uniquely be determined if the leading asymptotic term of its form factor is known along each direction of reciprocal space. If the central symmetry is lacking, all the admissible particle forms are among the solutions of a partial differential equation with given boundary conditions. The possible practical relevance of this result is discussed.

The equations to be solved in order to determine the best discrete-valued approximation to a given electron or scattering-length density function are worked out. A simple illustration is reported.