SAXS and WAXS probe the anisotropy of scattering intensities in reciprocal space. When nanoscale features or crystalline domains are preferentially aligned, their scattering becomes direction-dependent, producing characteristic azimuthal modulations.
From these patterns, SAXS/WAXS enables quantitative extraction of:
- Mean orientation direction, defining how the structural motif (e.g., lamellae, fibrils, crystallites) aligns with respect to a sample reference frame
- Degree of orientation, based on the sharpness or spread of the azimuthal intensity distribution
- Orientation distribution functions, derived using tensor-based models [1] or moment analysis
- Orientation metrics such as Herman’s orientation factor, providing a single-valued descriptor of alignment [2]
These parameters can be computed from specific reflections in WAXS (e.g., crystal lattice planes) or from structural features observed in SAXS (e.g., lamellar stacks, fibrillar scattering).
Figure 1. Azimuthal profile of the q = 0.27 nm-1 Bragg reflection of a high density polyethylene. The mean orientation is found at 39.9° for a rate of 17% oriented scatterers.
[1] D. K. Cinader, W. R. Burghardt, X-ray scattering studies of orientation in channel flows of a lyotropic liquid crystalline polymer, Polymer 40.15, (1999), DOI: 10.1016/S0032-3861(98)00667-3
[2] J.J. Hermans, P.H. Hermans, D. Vermaas, A. Weidinger, Quantitative evaluation of orientation in cellulose fibers from the X-ray fiber diagram, Recl. Trav. Chim. Pays- Bas 65 (1946), DOI: 10.1002/recl.19460650605
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