ID Correlation Function Analysis

1D Structural Entities. In materials science, stmctural entities which can satisfactorily be represented by layer stacks are ubiquitous. In the field of polymers they have been known for a long time [156]. Similar is the microfibrillar [157] structure. Compared to the microflbrils, the layer stacks are distinguished by the large lateral extension of their constituting domains. Both entities share the property that their two-phase structure is predominantly described by a ID density function, Ap (rj), which is varying along the principal axis, rs, of the structural entity. 

1D Intensity. As already mentioned (cf. p. 126 and Fig. 8.12), the isotropic scattering of a layer-stack structure is easily desmeared from the random orientation of its entities by Lorentz correction (Eq. 8.44). For materials with microfibrillar structure this is more difficult. Fortunately microfibrils are, in general, found in highly oriented fiber materials where they are oriented in fiber direction. In this case the one-dimensional intensity in fiber direction, 

Warning. For isotropic materials the ID projection / j and the Lorentz correction yield different ID intensities. Both are related by 

Model functions for the ID intensity have early been developed [128,158] and fitted to scattering data. The classical model-free structure visualization goes back to 

VONK [159,160] and describes the structure by the ID correlation function yi (rs) in physical space. 

---