Items for "Homometric solutions"

Structure determination without Fourier inversion. Part II: The use of intensity ratios and inequalities

Using for a one-dimensional centrosymmetric structure of m equal point scatterers an m-dimensional coordinate parameter space P^m and the (n – 1) independent ratios q(h, k) = [I′(h)/I′(k)]^1/2 = g′(h)/g′(k) of n > 1 structure amplitudes observed on relative scale it is shown that the determination of the structure or possibly homometric structures is equivalent to finding the common intersection(s) of (n – 1) ≥ m independent isosurfaces Q[h, k; q] of dimension (m – 1).
A fast and efficient reduction of the parameter space to the fraction(s) of P^m that contain(s) the solution(s) can already be achieved on the basis of the qualitative inequalities between the observations...

Keywords: Crystal structure analysis, Parameter-space reduction, Intensity inequalities, Homometric solutions