In the average structure refinement of molecular materials, split positions are often encountered. As a consequence a molecule on one site can be present in more than one orientation. The typical structure refinement stops there and does not consider diffuse scattering, which allows statements about short range order interactions. Building and refining a short range order model to analyze the diffuse scattering takes the structure refinement to the next level.
A complex molecular crystal will usually consist of several components on several sites within the unit cell. Furthermore, a single site may be occupied by molecules in different orientations e.g. a first molecule in orientations A and B on site 1 and a second molecule in orientations C and D on site 2, see Fig. 1. In such systems short range order is common: On a local scale, the molecules tend to show preferred pair-wise arrangements. Characterizing this local order enables profound statements about molecular interactions .
With the help of molecular form factors  and the theory of diffuse scattering (e.g. Warren ), we developed a method that characterizes correlated chemical short range occupational disorder directly in reciprocal space. The diffuse scattering IDiff can be expressed as a function of the indices h,k,l in reciprocal space:
Where ILaue is the Laue scattering () and ISRO is the short range order scattering:
Here (u,v,w) are vectors in direct space, ns is the number of different sites and ki is the number of possible components on site i. mAi is the concentration of component A on site i, FAi is the molecular form factor of the molecule type A on site i. are the Warren-Cowley short range order parameters, that encode the probability to find an AB pair separated by vector (u,v,w). All parameters, except thecan directly be determined from the average structure refinement.
We apply this formula for the analysis of the diffuse scattering of 9-Bromo-10-Methylanthracene . The model for the short range order can be developed directly in reciprocal space and the formula can be used to perform a least squares regression analysis to fit the short range order parameters quantitatively.
Our method to characterize complex molecular disorder using single crystal diffuse scattering is a powerful tool to understand and model molecular interactions in disordered crystals. As the method treats data directly in reciprocal space and enables least squares fitting of disorder models, calculations can be performed on desktop computers without the excessive use of computation time.Figure 1: