Direct determination of the structure of barium stearate multilayers by x-ray diffraction

Diffraction of X-rays is recorded from barium stearate multilayer systems with from 2 to 60 double layers or unit cells. The generalized Patterson function P'(x) is calculated by an integral Fourier transform of observed intensity data from a specimen containing only two unit cells. The Patterson function P(0)(x) of a single unit cell is determined from P'(x) and the electron density distribution of a bimolecular leaflet is obtained by a deconvolution procedure of P(0)(x) after Hosemann and Bagchi. The electron density distribution is also calculated independently by a conventional Fourier synthesis with an experimentally established set of phases. The results of the two methods are consistent and fit a physical model of the bimolecular leaflet. A direct analysis, therefore, can be performed if diffraction is observed from multilayer systems with a small number of unit cells.