The Uncertainty in Neutron Diffraction Results Caused by Solving Systems of Linear Equations to Compute the Partial Structural Features

Abstract

Neutron diffraction plays an important role in structural chemistry. In order to reveal the solution structure, the partial radial distribution functions have to be determined by using isotope substitution technique yielding different diffraction pattern while the structural parameters remain unchanged. The extraction of parameters from the series of measurements thus reduces to solving a system of linear equations that is affected by experimental errors. In this article, we give an estimation of the size of this error and also directions on how to minimize this effect by properly selecting the systems to be studied.