Lineshape calculations for two-dimensional powder samples

Abstract

Diffraction studies on two-dimensional adsorbed systems are of great current interest. To obtain large surface areas, which are in particular needed for neutron scattering, one resorts to powder-like substrates. As the expressions derived for the structure factor of a finite two-dimensional (2D) lattice are usually fairly complicated, one runs into difficulties when proper powder averaging is attempted and when final formulae are to be compiled which have to be handy enough to permit fitting the Bragg reflections of the 2D system as a function of all parameters involved. Due to the fact that the 2D structure factor can be expressed with high precision as a linear combination of three elementary functions such as a Gaussian, a Lorentzian and a squared-Lorentzian, we are able to present an algorithm performing the correct powder averaging for both the isotropic case and the one involving preferred orientation. To fit the reflections an easily programmable set of formulae for the three types of cross sections of the Bragg rods is supplied, being valid for unit cells with 1 or 2 atoms. More atoms per cell require an approximation. The impact of a distribution of the size of the 2D crystallites is discussed.