We carried out a grazing incidence X-ray diffraction analysis of the Si(1 1 3) 3 x 2 surface using synchrotron radiation. We compared the experimental structure factors obtained from the integrated intensities of the fractional-order reflections with the calculated structure factors of the dimerized structure model of Ranke. By minimizing the R-factor, we determined the position and the size of the pentagon in the 3 x 1 dimerized structure model of Ranke. In addition, we found that a model with randomly distributed interstitial atoms at the center of the pentagon gives a smaller R-factor value. (C) 2004 Elsevier B.V. All rights reserved.