Abstract
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 [Di-1, Di] of the full range of distances, a polynomial in the two variables (r - Di-1)1/2 and (Di - r)1/2 such that its expansions around r = Di-1 and r = Di simultaneously coincide with the left and right expansions of γ''(r) around Di-1 and Di up to the terms O(r - Di-1)K/2 and O(Di - 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.
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Schedule a callMore From: Acta crystallographica. Section A, Foundations and advances
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